WEBVTT Kind: captions Language: en 00:00:00.000 --> 00:00:04.350 align:start position:0% foreign 00:00:04.350 --> 00:00:04.360 align:start position:0% 00:00:04.360 --> 00:00:13.910 align:start position:0% [Music] 00:00:13.910 --> 00:00:13.920 align:start position:0% 00:00:13.920 --> 00:00:15.950 align:start position:0% I<00:00:14.880> think<00:00:14.940> I'm<00:00:15.120> going<00:00:15.240> to<00:00:15.299> steal<00:00:15.540> proof<00:00:15.839> of 00:00:15.950 --> 00:00:15.960 align:start position:0% I think I'm going to steal proof of 00:00:15.960 --> 00:00:17.930 align:start position:0% I think I'm going to steal proof of optimality<00:00:16.500> in<00:00:16.800> this<00:00:16.920> talk<00:00:17.100> from<00:00:17.340> Felix's 00:00:17.930 --> 00:00:17.940 align:start position:0% optimality in this talk from Felix's 00:00:17.940 --> 00:00:19.970 align:start position:0% optimality in this talk from Felix's talk<00:00:18.119> because<00:00:18.420> I<00:00:18.660> really<00:00:18.779> loved<00:00:19.140> that<00:00:19.320> but 00:00:19.970 --> 00:00:19.980 align:start position:0% talk because I really loved that but 00:00:19.980 --> 00:00:21.830 align:start position:0% talk because I really loved that but today<00:00:20.400> we<00:00:20.640> are<00:00:20.760> not<00:00:20.880> going<00:00:21.060> to<00:00:21.180> talk<00:00:21.240> about<00:00:21.420> D5 00:00:21.830 --> 00:00:21.840 align:start position:0% today we are not going to talk about D5 00:00:21.840 --> 00:00:22.609 align:start position:0% today we are not going to talk about D5 we're<00:00:22.140> going<00:00:22.320> to<00:00:22.380> talk<00:00:22.500> about 00:00:22.609 --> 00:00:22.619 align:start position:0% we're going to talk about 00:00:22.619 --> 00:00:25.189 align:start position:0% we're going to talk about multi-dimensional<00:00:23.520> fee<00:00:23.820> markets<00:00:24.300> or<00:00:24.840> kind<00:00:25.140> of 00:00:25.189 --> 00:00:25.199 align:start position:0% multi-dimensional fee markets or kind of 00:00:25.199 --> 00:00:27.109 align:start position:0% multi-dimensional fee markets or kind of the<00:00:25.320> fancy<00:00:25.680> term<00:00:25.859> is<00:00:26.160> how<00:00:26.400> to<00:00:26.519> do<00:00:26.640> Dynamic 00:00:27.109 --> 00:00:27.119 align:start position:0% the fancy term is how to do Dynamic 00:00:27.119 --> 00:00:29.689 align:start position:0% the fancy term is how to do Dynamic pricing<00:00:27.480> for<00:00:27.720> non-fungible<00:00:28.320> resources<00:00:28.920> and 00:00:29.689 --> 00:00:29.699 align:start position:0% pricing for non-fungible resources and 00:00:29.699 --> 00:00:31.550 align:start position:0% pricing for non-fungible resources and this<00:00:29.820> is<00:00:29.939> Joint<00:00:30.240> work<00:00:30.420> with<00:00:30.660> Alex<00:00:30.840> Evans<00:00:31.260> True 00:00:31.550 --> 00:00:31.560 align:start position:0% this is Joint work with Alex Evans True 00:00:31.560 --> 00:00:33.889 align:start position:0% this is Joint work with Alex Evans True and<00:00:31.800> chitra<00:00:32.099> and<00:00:32.279> guillermaranjaris<00:00:33.239> all 00:00:33.889 --> 00:00:33.899 align:start position:0% and chitra and guillermaranjaris all 00:00:33.899 --> 00:00:35.209 align:start position:0% and chitra and guillermaranjaris all right<00:00:34.020> so<00:00:34.320> the<00:00:34.500> first<00:00:34.620> thing<00:00:34.739> I<00:00:34.920> hope<00:00:35.040> to 00:00:35.209 --> 00:00:35.219 align:start position:0% right so the first thing I hope to 00:00:35.219 --> 00:00:37.430 align:start position:0% right so the first thing I hope to convince<00:00:35.520> you<00:00:35.640> of<00:00:35.820> is<00:00:36.360> that<00:00:36.600> fee<00:00:37.020> markets<00:00:37.320> with 00:00:37.430 --> 00:00:37.440 align:start position:0% convince you of is that fee markets with 00:00:37.440 --> 00:00:39.410 align:start position:0% convince you of is that fee markets with the<00:00:37.559> joint<00:00:37.800> unit<00:00:37.980> of<00:00:38.219> account<00:00:38.340> like<00:00:38.760> gas<00:00:39.059> are 00:00:39.410 --> 00:00:39.420 align:start position:0% the joint unit of account like gas are 00:00:39.420 --> 00:00:41.810 align:start position:0% the joint unit of account like gas are actually<00:00:39.719> pretty<00:00:39.960> inefficient<00:00:41.040> and<00:00:41.640> what 00:00:41.810 --> 00:00:41.820 align:start position:0% actually pretty inefficient and what 00:00:41.820 --> 00:00:43.310 align:start position:0% actually pretty inefficient and what we're<00:00:41.940> going<00:00:42.120> to<00:00:42.239> slowly<00:00:42.480> work<00:00:42.780> towards<00:00:43.140> in 00:00:43.310 --> 00:00:43.320 align:start position:0% we're going to slowly work towards in 00:00:43.320 --> 00:00:45.470 align:start position:0% we're going to slowly work towards in this<00:00:43.500> talk<00:00:43.680> is<00:00:44.280> a<00:00:44.460> framework<00:00:44.760> to<00:00:45.059> optimally 00:00:45.470 --> 00:00:45.480 align:start position:0% this talk is a framework to optimally 00:00:45.480 --> 00:00:48.229 align:start position:0% this talk is a framework to optimally set<00:00:45.719> multi-dimensional<00:00:46.620> fees<00:00:47.040> so<00:00:47.640> first<00:00:48.059> part 00:00:48.229 --> 00:00:48.239 align:start position:0% set multi-dimensional fees so first part 00:00:48.239 --> 00:00:50.150 align:start position:0% set multi-dimensional fees so first part of<00:00:48.360> this<00:00:48.480> is<00:00:48.719> like<00:00:48.899> why<00:00:49.140> are<00:00:49.320> transactions<00:00:49.920> so 00:00:50.150 --> 00:00:50.160 align:start position:0% of this is like why are transactions so 00:00:50.160 --> 00:00:52.549 align:start position:0% of this is like why are transactions so expensive<00:00:50.579> why<00:00:51.180> is<00:00:51.360> having<00:00:51.539> one<00:00:51.899> market<00:00:52.079> not 00:00:52.549 --> 00:00:52.559 align:start position:0% expensive why is having one market not 00:00:52.559 --> 00:00:53.869 align:start position:0% expensive why is having one market not necessarily<00:00:53.039> something<00:00:53.280> that<00:00:53.520> you<00:00:53.640> want<00:00:53.760> to 00:00:53.869 --> 00:00:53.879 align:start position:0% necessarily something that you want to 00:00:53.879 --> 00:00:54.529 align:start position:0% necessarily something that you want to do 00:00:54.529 --> 00:00:54.539 align:start position:0% do 00:00:54.539 --> 00:00:57.049 align:start position:0% do and<00:00:55.079> first<00:00:55.260> a<00:00:55.500> little<00:00:55.680> bit<00:00:55.800> of<00:00:55.920> an<00:00:56.039> aside 00:00:57.049 --> 00:00:57.059 align:start position:0% and first a little bit of an aside 00:00:57.059 --> 00:00:58.430 align:start position:0% and first a little bit of an aside um one<00:00:57.360> of<00:00:57.420> the<00:00:57.539> things<00:00:57.600> that<00:00:57.780> we<00:00:57.960> actually<00:00:58.140> do 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and<00:01:11.700> the<00:01:11.939> resources<00:01:12.360> that<00:01:12.659> that<00:01:12.780> op 00:01:12.950 --> 00:01:12.960 align:start position:0% price and the resources that that op 00:01:12.960 --> 00:01:15.350 align:start position:0% price and the resources that that op code<00:01:13.200> consumes<00:01:13.860> you<00:01:14.400> can<00:01:14.460> get<00:01:14.700> something<00:01:15.000> that 00:01:15.350 --> 00:01:15.360 align:start position:0% code consumes you can get something that 00:01:15.360 --> 00:01:17.030 align:start position:0% code consumes you can get something that takes<00:01:15.540> down<00:01:15.780> a<00:01:15.960> network<00:01:16.140> so<00:01:16.439> these<00:01:16.740> have<00:01:16.860> been 00:01:17.030 --> 00:01:17.040 align:start position:0% takes down a network so these have been 00:01:17.040 --> 00:01:19.490 align:start position:0% takes down a network so these have been termed<00:01:17.460> resource<00:01:18.060> exhaustion<00:01:18.600> exhaustion 00:01:19.490 --> 00:01:19.500 align:start position:0% termed resource exhaustion exhaustion 00:01:19.500 --> 00:01:21.830 align:start position:0% termed resource exhaustion exhaustion attacks<00:01:19.979> in<00:01:20.100> the<00:01:20.220> literature<00:01:20.580> and<00:01:21.420> there<00:01:21.540> is<00:01:21.720> a 00:01:21.830 --> 00:01:21.840 align:start position:0% attacks in the literature and there is a 00:01:21.840 --> 00:01:24.289 align:start position:0% attacks in the literature and there is a famous<00:01:21.960> one<00:01:22.259> back<00:01:22.740> in<00:01:22.920> 2016<00:01:23.580> that<00:01:23.939> took<00:01:24.180> down 00:01:24.289 --> 00:01:24.299 align:start position:0% famous one back in 2016 that took down 00:01:24.299 --> 00:01:26.149 align:start position:0% famous one back in 2016 that took down the<00:01:24.479> ethereum<00:01:24.900> network<00:01:25.140> or<00:01:25.680> essentially<00:01:26.040> made 00:01:26.149 --> 00:01:26.159 align:start position:0% the ethereum network or essentially made 00:01:26.159 --> 00:01:28.370 align:start position:0% the ethereum network or essentially made it<00:01:26.340> unusable<00:01:26.880> did<00:01:27.540> not<00:01:27.720> take<00:01:27.900> it<00:01:28.020> down<00:01:28.140> but 00:01:28.370 --> 00:01:28.380 align:start position:0% it unusable did not take it down but 00:01:28.380 --> 00:01:30.230 align:start position:0% it unusable did not take it down but made<00:01:28.560> it<00:01:28.740> very<00:01:28.920> hard<00:01:29.159> to<00:01:29.340> use<00:01:29.520> for<00:01:29.820> quite<00:01:30.000> some 00:01:30.230 --> 00:01:30.240 align:start position:0% made it very hard to use for quite some 00:01:30.240 --> 00:01:32.270 align:start position:0% made it very hard to use for quite some time<00:01:30.479> and<00:01:31.020> this<00:01:31.140> was<00:01:31.259> essentially<00:01:31.619> due<00:01:31.920> to<00:01:32.040> a 00:01:32.270 --> 00:01:32.280 align:start position:0% time and this was essentially due to a 00:01:32.280 --> 00:01:34.310 align:start position:0% time and this was essentially due to a disk<00:01:32.520> read<00:01:32.640> mispricing<00:01:33.360> and<00:01:33.840> of<00:01:33.960> course<00:01:34.080> this 00:01:34.310 --> 00:01:34.320 align:start position:0% disk read mispricing and of course this 00:01:34.320 --> 00:01:37.370 align:start position:0% disk read mispricing and of course this was<00:01:34.500> patched<00:01:34.920> in<00:01:35.100> a<00:01:35.280> subsequent<00:01:35.579> EIP<00:01:36.079> but<00:01:37.079> if 00:01:37.370 --> 00:01:37.380 align:start position:0% was patched in a subsequent EIP but if 00:01:37.380 --> 00:01:39.170 align:start position:0% was patched in a subsequent EIP but if we<00:01:37.500> had<00:01:37.619> a<00:01:37.799> multi-dimensional<00:01:38.520> rather<00:01:38.880> than<00:01:39.000> a 00:01:39.170 --> 00:01:39.180 align:start position:0% we had a multi-dimensional rather than a 00:01:39.180 --> 00:01:40.850 align:start position:0% we had a multi-dimensional rather than a single<00:01:39.420> dimensional<00:01:39.840> Market<00:01:40.020> we<00:01:40.619> might<00:01:40.740> have 00:01:40.850 --> 00:01:40.860 align:start position:0% single dimensional Market we might have 00:01:40.860 --> 00:01:43.249 align:start position:0% single dimensional Market we might have been<00:01:41.040> able<00:01:41.220> to<00:01:41.340> adjust<00:01:41.640> prices<00:01:42.119> such<00:01:42.900> that 00:01:43.249 --> 00:01:43.259 align:start position:0% been able to adjust prices such that 00:01:43.259 --> 00:01:45.710 align:start position:0% been able to adjust prices such that there<00:01:43.979> was<00:01:44.159> no<00:01:44.400> need<00:01:44.640> to<00:01:44.880> actually<00:01:45.060> reprice 00:01:45.710 --> 00:01:45.720 align:start position:0% there was no need to actually reprice 00:01:45.720 --> 00:01:48.710 align:start position:0% there was no need to actually reprice the<00:01:45.900> op<00:01:46.020> codes<00:01:46.320> after<00:01:46.740> the<00:01:47.040> fact<00:01:47.220> however<00:01:48.180> what 00:01:48.710 --> 00:01:48.720 align:start position:0% the op codes after the fact however what 00:01:48.720 --> 00:01:49.910 align:start position:0% the op codes after the fact however what we're<00:01:48.900> going<00:01:49.020> to<00:01:49.140> concentrate<00:01:49.560> a<00:01:49.680> little<00:01:49.799> bit 00:01:49.910 --> 00:01:49.920 align:start position:0% we're going to concentrate a little bit 00:01:49.920 --> 00:01:52.969 align:start position:0% we're going to concentrate a little bit more<00:01:50.040> on<00:01:50.280> today<00:01:50.520> is<00:01:51.540> um<00:01:51.540> throughput<00:01:52.079> is<00:01:52.740> why 00:01:52.969 --> 00:01:52.979 align:start position:0% more on today is um throughput is why 00:01:52.979 --> 00:01:55.490 align:start position:0% more on today is um throughput is why having<00:01:53.460> a<00:01:53.880> single<00:01:54.240> dimension<00:01:54.479> Market<00:01:55.079> is 00:01:55.490 --> 00:01:55.500 align:start position:0% having a single dimension Market is 00:01:55.500 --> 00:01:56.929 align:start position:0% having a single dimension Market is actually<00:01:55.680> bad<00:01:56.040> from<00:01:56.399> kind<00:01:56.579> of<00:01:56.640> the<00:01:56.759> network 00:01:56.929 --> 00:01:56.939 align:start position:0% actually bad from kind of the network 00:01:56.939 --> 00:01:59.389 align:start position:0% actually bad from kind of the network designer's<00:01:57.659> perspective<00:01:58.079> and<00:01:58.680> so<00:01:58.799> this<00:01:58.979> is<00:01:59.100> a 00:01:59.389 --> 00:01:59.399 align:start position:0% designer's perspective and so this is a 00:01:59.399 --> 00:02:01.429 align:start position:0% designer's perspective and so this is a very<00:01:59.520> very<00:01:59.700> stylized<00:02:00.299> example<00:02:00.720> that<00:02:01.020> is<00:02:01.200> not 00:02:01.429 --> 00:02:01.439 align:start position:0% very very stylized example that is not 00:02:01.439 --> 00:02:03.350 align:start position:0% very very stylized example that is not at<00:02:01.560> all<00:02:01.740> like<00:02:02.040> close<00:02:02.399> to<00:02:02.640> in<00:02:02.759> practice<00:02:02.939> but<00:02:03.299> I 00:02:03.350 --> 00:02:03.360 align:start position:0% at all like close to in practice but I 00:02:03.360 --> 00:02:05.090 align:start position:0% at all like close to in practice but I hope<00:02:03.479> it<00:02:03.600> illustrates<00:02:04.020> the<00:02:04.259> idea<00:02:04.560> let's 00:02:05.090 --> 00:02:05.100 align:start position:0% hope it illustrates the idea let's 00:02:05.100 --> 00:02:06.469 align:start position:0% hope it illustrates the idea let's assume<00:02:05.520> that<00:02:05.640> we<00:02:05.759> have<00:02:05.880> a<00:02:05.939> bunch<00:02:06.119> of<00:02:06.240> users 00:02:06.469 --> 00:02:06.479 align:start position:0% assume that we have a bunch of users 00:02:06.479 --> 00:02:08.510 align:start position:0% assume that we have a bunch of users that<00:02:06.659> are<00:02:06.780> submitting<00:02:07.140> transactions<00:02:07.860> some 00:02:08.510 --> 00:02:08.520 align:start position:0% that are submitting transactions some 00:02:08.520 --> 00:02:10.850 align:start position:0% that are submitting transactions some only<00:02:08.819> consume<00:02:09.360> CPU<00:02:09.899> some<00:02:10.140> only<00:02:10.440> consume 00:02:10.850 --> 00:02:10.860 align:start position:0% only consume CPU some only consume 00:02:10.860 --> 00:02:13.430 align:start position:0% only consume CPU some only consume bandwidth<00:02:11.400> the<00:02:11.819> CPU<00:02:12.239> ones<00:02:12.599> have<00:02:12.840> some<00:02:13.080> utility 00:02:13.430 --> 00:02:13.440 align:start position:0% bandwidth the CPU ones have some utility 00:02:13.440 --> 00:02:14.990 align:start position:0% bandwidth the CPU ones have some utility of<00:02:13.680> four<00:02:13.860> so<00:02:14.160> that's<00:02:14.340> kind<00:02:14.520> of<00:02:14.580> how<00:02:14.819> much 00:02:14.990 --> 00:02:15.000 align:start position:0% of four so that's kind of how much 00:02:15.000 --> 00:02:16.610 align:start position:0% of four so that's kind of how much utility<00:02:15.420> they<00:02:15.720> give<00:02:15.900> to<00:02:16.020> the<00:02:16.140> user<00:02:16.379> that 00:02:16.610 --> 00:02:16.620 align:start position:0% utility they give to the user that 00:02:16.620 --> 00:02:18.350 align:start position:0% utility they give to the user that submits<00:02:17.040> it<00:02:17.099> and<00:02:17.520> the<00:02:17.640> bandwidth<00:02:18.060> ones<00:02:18.239> have 00:02:18.350 --> 00:02:18.360 align:start position:0% submits it and the bandwidth ones have 00:02:18.360 --> 00:02:21.050 align:start position:0% submits it and the bandwidth ones have utility<00:02:18.720> of<00:02:19.020> two<00:02:19.200> and<00:02:20.160> let's<00:02:20.280> imagine<00:02:20.520> we<00:02:20.940> have 00:02:21.050 --> 00:02:21.060 align:start position:0% utility of two and let's imagine we have 00:02:21.060 --> 00:02:22.010 align:start position:0% utility of two and let's imagine we have a<00:02:21.180> block 00:02:22.010 --> 00:02:22.020 align:start position:0% a block 00:02:22.020 --> 00:02:24.110 align:start position:0% a block each<00:02:22.560> of<00:02:22.680> these<00:02:22.800> transactions<00:02:23.280> cost<00:02:23.520> one<00:02:23.879> gas 00:02:24.110 --> 00:02:24.120 align:start position:0% each of these transactions cost one gas 00:02:24.120 --> 00:02:27.050 align:start position:0% each of these transactions cost one gas the<00:02:24.599> gas<00:02:24.780> price<00:02:25.020> is<00:02:25.260> three<00:02:25.560> and<00:02:26.280> the<00:02:26.580> block<00:02:26.700> can 00:02:27.050 --> 00:02:27.060 align:start position:0% the gas price is three and the block can 00:02:27.060 --> 00:02:28.910 align:start position:0% the gas price is three and the block can fit<00:02:27.239> four<00:02:27.540> CPU<00:02:28.020> transactions<00:02:28.620> and<00:02:28.800> four 00:02:28.910 --> 00:02:28.920 align:start position:0% fit four CPU transactions and four 00:02:28.920 --> 00:02:31.610 align:start position:0% fit four CPU transactions and four bandwidth<00:02:29.520> transactions<00:02:30.180> well<00:02:30.900> in<00:02:31.260> a<00:02:31.440> single 00:02:31.610 --> 00:02:31.620 align:start position:0% bandwidth transactions well in a single 00:02:31.620 --> 00:02:33.470 align:start position:0% bandwidth transactions well in a single dimensional<00:02:31.980> Market<00:02:32.160> what<00:02:32.459> happens<00:02:32.640> we<00:02:33.300> fill 00:02:33.470 --> 00:02:33.480 align:start position:0% dimensional Market what happens we fill 00:02:33.480 --> 00:02:35.510 align:start position:0% dimensional Market what happens we fill this<00:02:33.660> up<00:02:33.780> with<00:02:34.020> CPU<00:02:34.379> transactions<00:02:35.099> but 00:02:35.510 --> 00:02:35.520 align:start position:0% this up with CPU transactions but 00:02:35.520 --> 00:02:36.710 align:start position:0% this up with CPU transactions but actually<00:02:35.700> we<00:02:35.879> have<00:02:36.060> a<00:02:36.120> lot<00:02:36.239> of<00:02:36.300> block<00:02:36.480> space 00:02:36.710 --> 00:02:36.720 align:start position:0% actually we have a lot of block space 00:02:36.720 --> 00:02:39.110 align:start position:0% actually we have a lot of block space that's<00:02:37.020> not<00:02:37.379> used<00:02:37.739> because<00:02:38.280> these<00:02:38.640> bandwidth 00:02:39.110 --> 00:02:39.120 align:start position:0% that's not used because these bandwidth 00:02:39.120 --> 00:02:40.910 align:start position:0% that's not used because these bandwidth transactions<00:02:39.720> aren't<00:02:40.020> high<00:02:40.260> enough<00:02:40.379> utility 00:02:40.910 --> 00:02:40.920 align:start position:0% transactions aren't high enough utility 00:02:40.920 --> 00:02:43.009 align:start position:0% transactions aren't high enough utility and<00:02:41.580> something<00:02:41.819> like<00:02:42.060> this<00:02:42.239> can<00:02:42.420> happen<00:02:42.660> say 00:02:43.009 --> 00:02:43.019 align:start position:0% and something like this can happen say 00:02:43.019 --> 00:02:44.990 align:start position:0% and something like this can happen say with<00:02:43.319> like<00:02:43.440> an<00:02:43.620> nft<00:02:43.860> mint 00:02:44.990 --> 00:02:45.000 align:start position:0% with like an nft mint 00:02:45.000 --> 00:02:47.270 align:start position:0% with like an nft mint however<00:02:45.660> if<00:02:45.900> we<00:02:46.019> have<00:02:46.140> a<00:02:46.260> 2d<00:02:46.500> market<00:02:46.739> and<00:02:47.099> say 00:02:47.270 --> 00:02:47.280 align:start position:0% however if we have a 2d market and say 00:02:47.280 --> 00:02:49.910 align:start position:0% however if we have a 2d market and say CPU<00:02:47.879> has<00:02:48.239> that<00:02:48.480> cost<00:02:48.720> of<00:02:48.959> three<00:02:49.140> but<00:02:49.379> bandwidth 00:02:49.910 --> 00:02:49.920 align:start position:0% CPU has that cost of three but bandwidth 00:02:49.920 --> 00:02:52.009 align:start position:0% CPU has that cost of three but bandwidth has<00:02:50.040> a<00:02:50.220> cost<00:02:50.340> of<00:02:50.519> one<00:02:50.760> we<00:02:51.420> would<00:02:51.540> actually<00:02:51.720> end 00:02:52.009 --> 00:02:52.019 align:start position:0% has a cost of one we would actually end 00:02:52.019 --> 00:02:53.930 align:start position:0% has a cost of one we would actually end up<00:02:52.140> filling<00:02:52.560> up<00:02:52.680> all<00:02:52.920> the<00:02:53.040> CPU<00:02:53.400> transactions 00:02:53.930 --> 00:02:53.940 align:start position:0% up filling up all the CPU transactions 00:02:53.940 --> 00:02:55.729 align:start position:0% up filling up all the CPU transactions in<00:02:54.120> this<00:02:54.239> block<00:02:54.420> and<00:02:55.019> filling<00:02:55.379> up<00:02:55.440> all<00:02:55.620> the 00:02:55.729 --> 00:02:55.739 align:start position:0% in this block and filling up all the 00:02:55.739 --> 00:02:57.949 align:start position:0% in this block and filling up all the bandwidth<00:02:56.220> transactions<00:02:56.700> as<00:02:56.879> well<00:02:57.060> like<00:02:57.780> I 00:02:57.949 --> 00:02:57.959 align:start position:0% bandwidth transactions as well like I 00:02:57.959 --> 00:02:59.990 align:start position:0% bandwidth transactions as well like I said<00:02:58.019> this<00:02:58.379> is<00:02:58.440> a<00:02:58.620> very<00:02:58.739> stylized<00:02:59.280> example<00:02:59.700> but 00:02:59.990 --> 00:03:00.000 align:start position:0% said this is a very stylized example but 00:03:00.000 --> 00:03:01.729 align:start position:0% said this is a very stylized example but it<00:03:00.120> does<00:03:00.300> illustrate<00:03:00.780> when<00:03:01.019> you<00:03:01.200> price<00:03:01.440> things 00:03:01.729 --> 00:03:01.739 align:start position:0% it does illustrate when you price things 00:03:01.739 --> 00:03:04.369 align:start position:0% it does illustrate when you price things separately<00:03:02.280> or<00:03:03.000> in<00:03:03.120> other<00:03:03.300> words<00:03:03.480> if 00:03:04.369 --> 00:03:04.379 align:start position:0% separately or in other words if 00:03:04.379 --> 00:03:06.890 align:start position:0% separately or in other words if resources<00:03:04.920> are<00:03:05.099> orthogonal<00:03:05.700> they<00:03:06.599> should<00:03:06.720> be 00:03:06.890 --> 00:03:06.900 align:start position:0% resources are orthogonal they should be 00:03:06.900 --> 00:03:09.170 align:start position:0% resources are orthogonal they should be priced<00:03:07.200> separately<00:03:07.560> however<00:03:08.400> that<00:03:08.879> of<00:03:09.060> course 00:03:09.170 --> 00:03:09.180 align:start position:0% priced separately however that of course 00:03:09.180 --> 00:03:11.990 align:start position:0% priced separately however that of course uh<00:03:10.140> needs<00:03:10.620> we<00:03:10.980> need<00:03:11.099> a<00:03:11.280> mechanism<00:03:11.580> for<00:03:11.819> Price 00:03:11.990 --> 00:03:12.000 align:start position:0% uh needs we need a mechanism for Price 00:03:12.000 --> 00:03:14.330 align:start position:0% uh needs we need a mechanism for Price Discovery<00:03:12.540> to<00:03:12.780> do<00:03:12.900> this<00:03:13.080> so<00:03:13.560> how<00:03:13.680> do<00:03:13.860> we<00:03:13.980> decide 00:03:14.330 --> 00:03:14.340 align:start position:0% Discovery to do this so how do we decide 00:03:14.340 --> 00:03:17.030 align:start position:0% Discovery to do this so how do we decide that<00:03:14.640> you<00:03:14.819> know<00:03:14.879> CPU<00:03:15.659> is<00:03:15.900> three<00:03:16.200> and<00:03:16.500> bandwidth 00:03:17.030 --> 00:03:17.040 align:start position:0% that you know CPU is three and bandwidth 00:03:17.040 --> 00:03:19.190 align:start position:0% that you know CPU is three and bandwidth is<00:03:17.159> one<00:03:17.340> or<00:03:17.580> what<00:03:17.819> are<00:03:17.940> those<00:03:18.120> prices<00:03:18.420> uh<00:03:18.959> what 00:03:19.190 --> 00:03:19.200 align:start position:0% is one or what are those prices uh what 00:03:19.200 --> 00:03:20.750 align:start position:0% is one or what are those prices uh what do<00:03:19.319> those<00:03:19.440> prices<00:03:19.620> even<00:03:19.920> mean<00:03:20.099> how<00:03:20.400> do<00:03:20.519> we<00:03:20.580> get 00:03:20.750 --> 00:03:20.760 align:start position:0% do those prices even mean how do we get 00:03:20.760 --> 00:03:23.030 align:start position:0% do those prices even mean how do we get to<00:03:20.879> those<00:03:21.060> prices<00:03:21.379> and<00:03:22.379> I'm<00:03:22.560> going<00:03:22.739> to<00:03:22.800> do<00:03:22.920> a 00:03:23.030 --> 00:03:23.040 align:start position:0% to those prices and I'm going to do a 00:03:23.040 --> 00:03:25.250 align:start position:0% to those prices and I'm going to do a little<00:03:23.099> bit<00:03:23.280> of<00:03:23.459> an<00:03:23.640> aside<00:03:23.940> in<00:03:24.300> that<00:03:24.599> uh<00:03:25.019> I've 00:03:25.250 --> 00:03:25.260 align:start position:0% little bit of an aside in that uh I've 00:03:25.260 --> 00:03:27.050 align:start position:0% little bit of an aside in that uh I've been<00:03:25.440> throwing<00:03:25.800> around<00:03:25.980> this<00:03:26.280> term<00:03:26.459> resource 00:03:27.050 --> 00:03:27.060 align:start position:0% been throwing around this term resource 00:03:27.060 --> 00:03:28.610 align:start position:0% been throwing around this term resource a<00:03:27.239> lot<00:03:27.360> and<00:03:27.900> there's<00:03:28.080> a<00:03:28.200> question<00:03:28.319> of<00:03:28.500> like 00:03:28.610 --> 00:03:28.620 align:start position:0% a lot and there's a question of like 00:03:28.620 --> 00:03:31.009 align:start position:0% a lot and there's a question of like what<00:03:28.860> exactly<00:03:29.280> do<00:03:29.459> I<00:03:29.640> mean<00:03:29.760> by<00:03:29.940> that<00:03:30.180> the 00:03:31.009 --> 00:03:31.019 align:start position:0% what exactly do I mean by that the 00:03:31.019 --> 00:03:32.149 align:start position:0% what exactly do I mean by that the working<00:03:31.080> definition<00:03:31.379> we're<00:03:31.800> going<00:03:31.980> to<00:03:32.040> use 00:03:32.149 --> 00:03:32.159 align:start position:0% working definition we're going to use 00:03:32.159 --> 00:03:33.710 align:start position:0% working definition we're going to use for<00:03:32.340> this<00:03:32.459> talk<00:03:32.700> is<00:03:33.000> anything<00:03:33.239> that<00:03:33.480> can<00:03:33.599> be 00:03:33.710 --> 00:03:33.720 align:start position:0% for this talk is anything that can be 00:03:33.720 --> 00:03:35.869 align:start position:0% for this talk is anything that can be metered<00:03:34.200> so<00:03:34.620> a<00:03:34.739> resource<00:03:35.099> is<00:03:35.220> anything<00:03:35.459> that<00:03:35.760> I 00:03:35.869 --> 00:03:35.879 align:start position:0% metered so a resource is anything that I 00:03:35.879 --> 00:03:38.570 align:start position:0% metered so a resource is anything that I can<00:03:36.000> say<00:03:36.180> how<00:03:36.540> much<00:03:36.780> of<00:03:37.200> uh<00:03:37.620> this<00:03:38.040> thing<00:03:38.220> a 00:03:38.570 --> 00:03:38.580 align:start position:0% can say how much of uh this thing a 00:03:38.580 --> 00:03:41.570 align:start position:0% can say how much of uh this thing a transaction<00:03:38.940> uses<00:03:39.540> so<00:03:40.440> for<00:03:40.680> example 00:03:41.570 --> 00:03:41.580 align:start position:0% transaction uses so for example 00:03:41.580 --> 00:03:43.970 align:start position:0% transaction uses so for example um<00:03:41.640> one<00:03:41.879> thing<00:03:42.000> right<00:03:42.120> now<00:03:42.299> roll<00:03:42.720> up<00:03:42.900> data 00:03:43.970 --> 00:03:43.980 align:start position:0% um one thing right now roll up data 00:03:43.980 --> 00:03:45.949 align:start position:0% um one thing right now roll up data however<00:03:44.580> we<00:03:44.819> could<00:03:44.879> also<00:03:45.120> talk<00:03:45.360> about<00:03:45.540> like 00:03:45.949 --> 00:03:45.959 align:start position:0% however we could also talk about like 00:03:45.959 --> 00:03:47.869 align:start position:0% however we could also talk about like kind<00:03:46.200> of<00:03:46.319> big<00:03:46.500> resources<00:03:46.980> like<00:03:47.400> compute 00:03:47.869 --> 00:03:47.879 align:start position:0% kind of big resources like compute 00:03:47.879 --> 00:03:50.330 align:start position:0% kind of big resources like compute memory<00:03:48.239> and<00:03:48.480> storage<00:03:48.720> we<00:03:49.620> could<00:03:49.739> go<00:03:49.920> down<00:03:50.159> to 00:03:50.330 --> 00:03:50.340 align:start position:0% memory and storage we could go down to 00:03:50.340 --> 00:03:51.949 align:start position:0% memory and storage we could go down to the<00:03:50.459> op<00:03:50.580> code<00:03:50.760> level<00:03:51.060> and<00:03:51.420> think<00:03:51.540> of<00:03:51.720> each 00:03:51.949 --> 00:03:51.959 align:start position:0% the op code level and think of each 00:03:51.959 --> 00:03:54.410 align:start position:0% the op code level and think of each individual<00:03:52.379> opcode<00:03:52.860> as<00:03:53.040> a<00:03:53.159> resource<00:03:53.519> however 00:03:54.410 --> 00:03:54.420 align:start position:0% individual opcode as a resource however 00:03:54.420 --> 00:03:56.390 align:start position:0% individual opcode as a resource however we<00:03:54.659> could<00:03:54.780> also<00:03:55.019> say<00:03:55.260> you<00:03:55.620> know<00:03:55.680> sequences<00:03:56.159> of 00:03:56.390 --> 00:03:56.400 align:start position:0% we could also say you know sequences of 00:03:56.400 --> 00:03:58.130 align:start position:0% we could also say you know sequences of op<00:03:56.519> codes<00:03:56.700> are<00:03:56.940> resources<00:03:57.420> for<00:03:57.720> instance<00:03:57.900> if 00:03:58.130 --> 00:03:58.140 align:start position:0% op codes are resources for instance if 00:03:58.140 --> 00:03:59.750 align:start position:0% op codes are resources for instance if you're<00:03:58.260> calling<00:03:58.560> like<00:03:58.680> a<00:03:58.920> hot<00:03:59.040> storage<00:03:59.340> slot 00:03:59.750 --> 00:03:59.760 align:start position:0% you're calling like a hot storage slot 00:03:59.760 --> 00:04:01.670 align:start position:0% you're calling like a hot storage slot versus<00:03:59.940> a<00:04:00.180> cold<00:04:00.360> storage<00:04:00.599> slot<00:04:01.019> that's<00:04:01.440> going 00:04:01.670 --> 00:04:01.680 align:start position:0% versus a cold storage slot that's going 00:04:01.680 --> 00:04:03.470 align:start position:0% versus a cold storage slot that's going to<00:04:01.799> be<00:04:02.459> um<00:04:02.459> cheaper 00:04:03.470 --> 00:04:03.480 align:start position:0% to be um cheaper 00:04:03.480 --> 00:04:05.869 align:start position:0% to be um cheaper so<00:04:03.900> maybe<00:04:04.140> if<00:04:04.440> we<00:04:04.620> have<00:04:04.860> several<00:04:05.280> storage<00:04:05.519> op 00:04:05.869 --> 00:04:05.879 align:start position:0% so maybe if we have several storage op 00:04:05.879 --> 00:04:07.070 align:start position:0% so maybe if we have several storage op codes 00:04:07.070 --> 00:04:07.080 align:start position:0% codes 00:04:07.080 --> 00:04:08.869 align:start position:0% codes um<00:04:07.140> all<00:04:07.500> in<00:04:07.739> a<00:04:07.920> row<00:04:08.040> that's<00:04:08.400> actually<00:04:08.580> a 00:04:08.869 --> 00:04:08.879 align:start position:0% um all in a row that's actually a 00:04:08.879 --> 00:04:10.130 align:start position:0% um all in a row that's actually a different<00:04:08.940> resource<00:04:09.420> than<00:04:09.599> calling<00:04:09.959> these 00:04:10.130 --> 00:04:10.140 align:start position:0% different resource than calling these 00:04:10.140 --> 00:04:12.710 align:start position:0% different resource than calling these one<00:04:10.260> by<00:04:10.439> one<00:04:10.700> furthermore<00:04:11.700> if<00:04:12.180> we're<00:04:12.360> running 00:04:12.710 --> 00:04:12.720 align:start position:0% one by one furthermore if we're running 00:04:12.720 --> 00:04:15.530 align:start position:0% one by one furthermore if we're running uh<00:04:13.439> full<00:04:13.799> nodes<00:04:14.159> on<00:04:14.580> multi-core<00:04:15.120> machines 00:04:15.530 --> 00:04:15.540 align:start position:0% uh full nodes on multi-core machines 00:04:15.540 --> 00:04:17.990 align:start position:0% uh full nodes on multi-core machines maybe<00:04:15.959> compute<00:04:16.560> on<00:04:16.739> like<00:04:16.919> node<00:04:17.340> or<00:04:17.579> on<00:04:17.820> core 00:04:17.990 --> 00:04:18.000 align:start position:0% maybe compute on like node or on core 00:04:18.000 --> 00:04:19.729 align:start position:0% maybe compute on like node or on core one<00:04:18.299> is<00:04:18.540> a<00:04:18.660> different<00:04:18.780> resource<00:04:19.139> than<00:04:19.260> compute 00:04:19.729 --> 00:04:19.739 align:start position:0% one is a different resource than compute 00:04:19.739 --> 00:04:22.430 align:start position:0% one is a different resource than compute on<00:04:19.859> core<00:04:20.100> 2.<00:04:20.940> and<00:04:21.540> and<00:04:21.720> so<00:04:21.900> on<00:04:22.019> you<00:04:22.199> can<00:04:22.320> imagine 00:04:22.430 --> 00:04:22.440 align:start position:0% on core 2. and and so on you can imagine 00:04:22.440 --> 00:04:23.870 align:start position:0% on core 2. and and so on you can imagine this<00:04:22.860> is<00:04:22.919> a<00:04:23.100> very<00:04:23.220> general<00:04:23.460> construction 00:04:23.870 --> 00:04:23.880 align:start position:0% this is a very general construction 00:04:23.880 --> 00:04:26.330 align:start position:0% this is a very general construction resources<00:04:24.780> can<00:04:24.960> be<00:04:25.139> very<00:04:25.380> dependent<00:04:25.979> on<00:04:26.160> each 00:04:26.330 --> 00:04:26.340 align:start position:0% resources can be very dependent on each 00:04:26.340 --> 00:04:27.110 align:start position:0% resources can be very dependent on each other 00:04:27.110 --> 00:04:27.120 align:start position:0% other 00:04:27.120 --> 00:04:29.210 align:start position:0% other um<00:04:27.180> and<00:04:27.720> so<00:04:27.900> as<00:04:28.199> long<00:04:28.320> as<00:04:28.440> they<00:04:28.620> can<00:04:28.740> be<00:04:28.800> metered 00:04:29.210 --> 00:04:29.220 align:start position:0% um and so as long as they can be metered 00:04:29.220 --> 00:04:31.310 align:start position:0% um and so as long as they can be metered or<00:04:29.400> we<00:04:29.520> can<00:04:29.639> say<00:04:29.759> how<00:04:30.060> much<00:04:30.180> of<00:04:30.360> a<00:04:30.479> trend<00:04:30.780> of<00:04:31.199> a 00:04:31.310 --> 00:04:31.320 align:start position:0% or we can say how much of a trend of a 00:04:31.320 --> 00:04:33.830 align:start position:0% or we can say how much of a trend of a resource<00:04:31.620> a<00:04:31.800> transaction<00:04:32.160> uses<00:04:32.639> uh<00:04:33.360> that<00:04:33.600> fits 00:04:33.830 --> 00:04:33.840 align:start position:0% resource a transaction uses uh that fits 00:04:33.840 --> 00:04:35.330 align:start position:0% resource a transaction uses uh that fits into<00:04:33.960> our<00:04:34.199> framework 00:04:35.330 --> 00:04:35.340 align:start position:0% into our framework 00:04:35.340 --> 00:04:37.189 align:start position:0% into our framework so<00:04:35.699> to<00:04:35.880> formalize<00:04:36.360> this<00:04:36.540> and<00:04:36.720> this<00:04:36.900> is<00:04:36.960> kind<00:04:37.139> of 00:04:37.189 --> 00:04:37.199 align:start position:0% so to formalize this and this is kind of 00:04:37.199 --> 00:04:38.810 align:start position:0% so to formalize this and this is kind of where<00:04:37.320> we<00:04:37.500> get<00:04:37.680> a<00:04:37.919> little<00:04:38.040> bit<00:04:38.160> into<00:04:38.340> the<00:04:38.639> math 00:04:38.810 --> 00:04:38.820 align:start position:0% where we get a little bit into the math 00:04:38.820 --> 00:04:40.930 align:start position:0% where we get a little bit into the math we're<00:04:39.540> going<00:04:39.660> to<00:04:39.720> say<00:04:39.840> a<00:04:40.020> transaction<00:04:40.380> J 00:04:40.930 --> 00:04:40.940 align:start position:0% we're going to say a transaction J 00:04:40.940 --> 00:04:43.490 align:start position:0% we're going to say a transaction J consumes<00:04:41.940> some<00:04:42.180> Vector<00:04:42.540> of<00:04:42.660> resources<00:04:43.139> and 00:04:43.490 --> 00:04:43.500 align:start position:0% consumes some Vector of resources and 00:04:43.500 --> 00:04:45.650 align:start position:0% consumes some Vector of resources and there's<00:04:43.740> so<00:04:43.919> M<00:04:44.100> resources<00:04:44.699> and<00:04:45.180> this<00:04:45.300> Vector 00:04:45.650 --> 00:04:45.660 align:start position:0% there's so M resources and this Vector 00:04:45.660 --> 00:04:48.170 align:start position:0% there's so M resources and this Vector is<00:04:45.780> AJ<00:04:46.199> so<00:04:46.740> essentially<00:04:47.160> the<00:04:47.340> ith<00:04:47.639> element<00:04:47.820> of 00:04:48.170 --> 00:04:48.180 align:start position:0% is AJ so essentially the ith element of 00:04:48.180 --> 00:04:50.210 align:start position:0% is AJ so essentially the ith element of that<00:04:48.300> Vector<00:04:48.720> is<00:04:49.139> going<00:04:49.259> to<00:04:49.380> be<00:04:49.500> the<00:04:49.680> amount<00:04:50.100> of 00:04:50.210 --> 00:04:50.220 align:start position:0% that Vector is going to be the amount of 00:04:50.220 --> 00:04:52.189 align:start position:0% that Vector is going to be the amount of resource<00:04:50.639> I<00:04:50.880> consumed<00:04:51.479> by<00:04:51.600> this<00:04:51.780> transaction 00:04:52.189 --> 00:04:52.199 align:start position:0% resource I consumed by this transaction 00:04:52.199 --> 00:04:54.710 align:start position:0% resource I consumed by this transaction J<00:04:52.620> and<00:04:53.280> now<00:04:53.400> that<00:04:53.639> we're<00:04:53.940> uh<00:04:54.180> starting<00:04:54.479> to 00:04:54.710 --> 00:04:54.720 align:start position:0% J and now that we're uh starting to 00:04:54.720 --> 00:04:56.749 align:start position:0% J and now that we're uh starting to build<00:04:54.840> blocks<00:04:55.440> we're<00:04:55.740> going<00:04:55.979> to<00:04:56.100> denote<00:04:56.580> this 00:04:56.749 --> 00:04:56.759 align:start position:0% build blocks we're going to denote this 00:04:56.759 --> 00:04:59.270 align:start position:0% build blocks we're going to denote this Vector<00:04:57.120> X<00:04:57.360> that<00:04:58.320> essentially<00:04:58.620> is<00:04:58.740> the<00:04:58.919> zero 00:04:59.270 --> 00:04:59.280 align:start position:0% Vector X that essentially is the zero 00:04:59.280 --> 00:05:02.689 align:start position:0% Vector X that essentially is the zero one<00:04:59.460> vector<00:04:59.880> and<00:05:00.479> we<00:05:00.600> have<00:05:00.720> n<00:05:00.960> transactions<00:05:01.800> XJ 00:05:02.689 --> 00:05:02.699 align:start position:0% one vector and we have n transactions XJ 00:05:02.699 --> 00:05:04.670 align:start position:0% one vector and we have n transactions XJ is<00:05:03.120> going<00:05:03.300> to<00:05:03.419> be<00:05:03.540> one<00:05:03.720> if<00:05:04.139> that<00:05:04.259> transaction 00:05:04.670 --> 00:05:04.680 align:start position:0% is going to be one if that transaction 00:05:04.680 --> 00:05:06.350 align:start position:0% is going to be one if that transaction is<00:05:04.979> included<00:05:05.280> in<00:05:05.400> a<00:05:05.520> block<00:05:05.639> and<00:05:06.000> zero 00:05:06.350 --> 00:05:06.360 align:start position:0% is included in a block and zero 00:05:06.360 --> 00:05:08.570 align:start position:0% is included in a block and zero otherwise<00:05:06.780> so<00:05:07.620> this<00:05:07.800> allows<00:05:08.160> us<00:05:08.220> to<00:05:08.460> very 00:05:08.570 --> 00:05:08.580 align:start position:0% otherwise so this allows us to very 00:05:08.580 --> 00:05:10.370 align:start position:0% otherwise so this allows us to very easily<00:05:08.940> write<00:05:09.240> kind<00:05:09.600> of<00:05:09.660> the<00:05:09.780> quantity<00:05:10.259> of 00:05:10.370 --> 00:05:10.380 align:start position:0% easily write kind of the quantity of 00:05:10.380 --> 00:05:12.350 align:start position:0% easily write kind of the quantity of resources<00:05:10.860> that's<00:05:11.160> consumed<00:05:11.639> by<00:05:11.880> a<00:05:12.060> given 00:05:12.350 --> 00:05:12.360 align:start position:0% resources that's consumed by a given 00:05:12.360 --> 00:05:13.909 align:start position:0% resources that's consumed by a given block<00:05:12.479> and<00:05:12.840> we're<00:05:12.960> going<00:05:13.080> to<00:05:13.199> denote<00:05:13.380> that<00:05:13.620> Y 00:05:13.909 --> 00:05:13.919 align:start position:0% block and we're going to denote that Y 00:05:13.919 --> 00:05:17.870 align:start position:0% block and we're going to denote that Y and<00:05:14.639> all<00:05:14.759> this<00:05:14.880> is<00:05:15.060> is<00:05:15.300> summing<00:05:15.720> up<00:05:16.040> the<00:05:17.040> vector 00:05:17.870 --> 00:05:17.880 align:start position:0% and all this is is summing up the vector 00:05:17.880 --> 00:05:19.790 align:start position:0% and all this is is summing up the vector of<00:05:18.419> resources<00:05:18.900> that's<00:05:19.139> consumed<00:05:19.560> by<00:05:19.620> a 00:05:19.790 --> 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in the sum if it's 00:05:26.460 --> 00:05:27.890 align:start position:0% going to include this in the sum if it's one<00:05:26.699> then<00:05:27.000> it's<00:05:27.120> going<00:05:27.300> to<00:05:27.360> be<00:05:27.419> included<00:05:27.780> in 00:05:27.890 --> 00:05:27.900 align:start position:0% one then it's going to be included in 00:05:27.900 --> 00:05:29.749 align:start position:0% one then it's going to be included in the<00:05:28.020> sum<00:05:28.199> and<00:05:28.680> this<00:05:28.860> can<00:05:28.979> be<00:05:29.160> uh<00:05:29.340> written<00:05:29.639> in 00:05:29.749 --> 00:05:29.759 align:start position:0% the sum and this can be uh written in 00:05:29.759 --> 00:05:31.430 align:start position:0% the sum and this can be uh written in kind<00:05:30.000> of<00:05:30.060> this<00:05:30.240> very<00:05:30.539> convenient<00:05:31.020> Matrix 00:05:31.430 --> 00:05:31.440 align:start position:0% kind of this very convenient Matrix 00:05:31.440 --> 00:05:33.650 align:start position:0% kind of this very convenient Matrix Vector<00:05:31.800> notation<00:05:32.160> as<00:05:32.520> well<00:05:32.699> where<00:05:33.419> The 00:05:33.650 --> 00:05:33.660 align:start position:0% Vector notation as well where The 00:05:33.660 --> 00:05:35.749 align:start position:0% Vector notation as well where The Columns<00:05:34.020> of<00:05:34.199> a<00:05:34.380> are<00:05:34.740> going<00:05:34.919> to<00:05:35.100> be<00:05:35.340> the 00:05:35.749 --> 00:05:35.759 align:start position:0% Columns of a are going to be the 00:05:35.759 --> 00:05:37.550 align:start position:0% Columns of a are going to be the transaction<00:05:36.479> vector<00:05:36.840> or<00:05:37.020> the<00:05:37.199> resource 00:05:37.550 --> 00:05:37.560 align:start position:0% transaction vector or the resource 00:05:37.560 --> 00:05:39.290 align:start position:0% transaction vector or the resource vectors<00:05:37.860> for<00:05:38.100> each<00:05:38.220> transaction 00:05:39.290 --> 00:05:39.300 align:start position:0% vectors for each transaction 00:05:39.300 --> 00:05:41.150 align:start position:0% vectors for each transaction all<00:05:39.720> right<00:05:39.840> so<00:05:40.259> now<00:05:40.380> that<00:05:40.560> we<00:05:40.740> kind<00:05:40.800> of<00:05:40.919> have<00:05:41.039> a 00:05:41.150 --> 00:05:41.160 align:start position:0% all right so now that we kind of have a 00:05:41.160 --> 00:05:43.490 align:start position:0% all right so now that we kind of have a notion<00:05:41.460> of<00:05:41.580> a<00:05:41.699> resource<00:05:42.180> and<00:05:43.139> what<00:05:43.380> each 00:05:43.490 --> 00:05:43.500 align:start position:0% notion of a resource and what each 00:05:43.500 --> 00:05:45.710 align:start position:0% notion of a resource and what each resource<00:05:44.039> is<00:05:44.100> we<00:05:44.820> can<00:05:45.000> talk<00:05:45.300> about<00:05:45.419> things 00:05:45.710 --> 00:05:45.720 align:start position:0% resource is we can talk about things 00:05:45.720 --> 00:05:47.689 align:start position:0% resource is we can talk about things about<00:05:46.020> constraining<00:05:46.560> resources<00:05:47.039> targets<00:05:47.580> for 00:05:47.689 --> 00:05:47.699 align:start position:0% about constraining resources targets for 00:05:47.699 --> 00:05:49.670 align:start position:0% about constraining resources targets for resources<00:05:48.180> and<00:05:48.600> charging<00:05:49.320> for<00:05:49.500> each 00:05:49.670 --> 00:05:49.680 align:start position:0% resources and charging for each 00:05:49.680 --> 00:05:51.890 align:start position:0% resources and charging for each individual<00:05:50.100> resource<00:05:50.580> so<00:05:51.300> we're<00:05:51.600> going<00:05:51.780> to 00:05:51.890 --> 00:05:51.900 align:start position:0% individual resource so we're going to 00:05:51.900 --> 00:05:53.810 align:start position:0% individual resource so we're going to first<00:05:52.020> Define<00:05:52.139> a<00:05:52.380> resource<00:05:52.740> Target<00:05:52.919> and 00:05:53.810 --> 00:05:53.820 align:start position:0% first Define a resource Target and 00:05:53.820 --> 00:05:56.029 align:start position:0% first Define a resource Target and that's<00:05:54.000> going<00:05:54.180> to<00:05:54.240> be<00:05:54.300> this<00:05:54.479> B<00:05:54.660> Star<00:05:54.960> and<00:05:55.919> then 00:05:56.029 --> 00:05:56.039 align:start position:0% that's going to be this B Star and then 00:05:56.039 --> 00:05:57.770 align:start position:0% that's going to be this B Star and then the<00:05:56.280> deviation<00:05:56.639> of<00:05:56.880> the<00:05:57.000> target<00:05:57.120> based<00:05:57.660> on 00:05:57.770 --> 00:05:57.780 align:start position:0% the deviation of the target based on 00:05:57.780 --> 00:06:00.469 align:start position:0% the deviation of the target based on what<00:05:58.020> I<00:05:58.259> uh<00:05:58.800> introduced<00:05:59.460> earlier<00:05:59.759> is<00:05:59.940> just<00:06:00.180> ax 00:06:00.469 --> 00:06:00.479 align:start position:0% what I uh introduced earlier is just ax 00:06:00.479 --> 00:06:03.469 align:start position:0% what I uh introduced earlier is just ax minus<00:06:00.840> B<00:06:01.020> remember<00:06:01.259> ax<00:06:01.800> is<00:06:02.039> the<00:06:02.340> quantity<00:06:02.759> of 00:06:03.469 --> 00:06:03.479 align:start position:0% minus B remember ax is the quantity of 00:06:03.479 --> 00:06:05.090 align:start position:0% minus B remember ax is the quantity of um or<00:06:03.780> the<00:06:03.900> resource<00:06:04.199> utilization<00:06:04.680> of<00:06:04.919> a 00:06:05.090 --> 00:06:05.100 align:start position:0% um or the resource utilization of a 00:06:05.100 --> 00:06:06.350 align:start position:0% um or the resource utilization of a particular<00:06:05.400> block 00:06:06.350 --> 00:06:06.360 align:start position:0% particular block 00:06:06.360 --> 00:06:09.110 align:start position:0% particular block and<00:06:06.900> in<00:06:07.080> ethereum<00:06:07.560> this<00:06:08.340> is<00:06:08.460> one-dimensional 00:06:09.110 --> 00:06:09.120 align:start position:0% and in ethereum this is one-dimensional 00:06:09.120 --> 00:06:11.090 align:start position:0% and in ethereum this is one-dimensional so<00:06:09.479> this<00:06:09.660> is<00:06:09.780> going<00:06:09.900> to<00:06:09.960> be<00:06:10.080> a<00:06:10.199> scalar<00:06:10.560> and<00:06:10.919> B 00:06:11.090 --> 00:06:11.100 align:start position:0% so this is going to be a scalar and B 00:06:11.100 --> 00:06:14.450 align:start position:0% so this is going to be a scalar and B Star<00:06:11.340> is<00:06:11.580> just<00:06:11.699> 15<00:06:11.940> million<00:06:12.419> gas<00:06:12.740> we<00:06:13.740> also<00:06:14.100> want 00:06:14.450 --> 00:06:14.460 align:start position:0% Star is just 15 million gas we also want 00:06:14.460 --> 00:06:16.610 align:start position:0% Star is just 15 million gas we also want sometimes<00:06:14.940> a<00:06:15.120> resource<00:06:15.479> limit<00:06:15.600> that<00:06:16.020> says<00:06:16.259> how 00:06:16.610 --> 00:06:16.620 align:start position:0% sometimes a resource limit that says how 00:06:16.620 --> 00:06:19.490 align:start position:0% sometimes a resource limit that says how much<00:06:16.919> or<00:06:17.699> after<00:06:17.940> a<00:06:18.240> certain<00:06:18.479> point<00:06:18.720> a<00:06:19.080> block<00:06:19.259> is 00:06:19.490 --> 00:06:19.500 align:start position:0% much or after a certain point a block is 00:06:19.500 --> 00:06:22.309 align:start position:0% much or after a certain point a block is invalid<00:06:19.979> and<00:06:20.340> then<00:06:20.520> we<00:06:21.060> can<00:06:21.180> have<00:06:21.479> uh 00:06:22.309 --> 00:06:22.319 align:start position:0% invalid and then we can have uh 00:06:22.319 --> 00:06:25.129 align:start position:0% invalid and then we can have uh transactions<00:06:23.160> satisfy<00:06:23.759> something<00:06:24.720> like<00:06:24.960> this 00:06:25.129 --> 00:06:25.139 align:start position:0% transactions satisfy something like this 00:06:25.139 --> 00:06:27.110 align:start position:0% transactions satisfy something like this where<00:06:25.380> ax<00:06:25.800> has<00:06:26.100> to<00:06:26.220> be<00:06:26.340> less<00:06:26.520> than<00:06:26.639> or<00:06:26.819> equal<00:06:26.940> to 00:06:27.110 --> 00:06:27.120 align:start position:0% where ax has to be less than or equal to 00:06:27.120 --> 00:06:28.189 align:start position:0% where ax has to be less than or equal to B 00:06:28.189 --> 00:06:28.199 align:start position:0% B 00:06:28.199 --> 00:06:30.290 align:start position:0% B um<00:06:28.259> in<00:06:28.440> ethereum<00:06:28.860> this<00:06:29.039> is<00:06:29.100> 30<00:06:29.280> million<00:06:29.639> gas<00:06:29.880> so 00:06:30.290 --> 00:06:30.300 align:start position:0% um in ethereum this is 30 million gas so 00:06:30.300 --> 00:06:31.490 align:start position:0% um in ethereum this is 30 million gas so again<00:06:30.419> in<00:06:30.660> ethereum<00:06:31.020> this<00:06:31.259> is<00:06:31.380> all 00:06:31.490 --> 00:06:31.500 align:start position:0% again in ethereum this is all 00:06:31.500 --> 00:06:33.409 align:start position:0% again in ethereum this is all one-dimensional<00:06:32.160> however<00:06:32.759> we're<00:06:33.000> extending 00:06:33.409 --> 00:06:33.419 align:start position:0% one-dimensional however we're extending 00:06:33.419 --> 00:06:35.689 align:start position:0% one-dimensional however we're extending this<00:06:33.539> to<00:06:33.780> a<00:06:33.900> multi-dimensional<00:06:34.560> case<00:06:34.800> finally 00:06:35.689 --> 00:06:35.699 align:start position:0% this to a multi-dimensional case finally 00:06:35.699 --> 00:06:38.570 align:start position:0% this to a multi-dimensional case finally this<00:06:36.060> allows<00:06:36.479> us<00:06:36.720> to<00:06:37.319> talk<00:06:37.560> about<00:06:37.800> prices<00:06:38.160> for 00:06:38.570 --> 00:06:38.580 align:start position:0% this allows us to talk about prices for 00:06:38.580 --> 00:06:40.129 align:start position:0% this allows us to talk about prices for each<00:06:38.759> resource<00:06:39.240> so<00:06:39.720> we're<00:06:39.840> going<00:06:39.960> to<00:06:40.020> have 00:06:40.129 --> 00:06:40.139 align:start position:0% each resource so we're going to have 00:06:40.139 --> 00:06:42.409 align:start position:0% each resource so we're going to have some<00:06:40.319> Vector<00:06:40.680> P<00:06:40.919> this<00:06:41.759> is<00:06:41.880> going<00:06:42.000> to<00:06:42.060> be<00:06:42.120> an<00:06:42.240> M 00:06:42.409 --> 00:06:42.419 align:start position:0% some Vector P this is going to be an M 00:06:42.419 --> 00:06:45.469 align:start position:0% some Vector P this is going to be an M vector<00:06:42.900> and<00:06:43.680> Pi<00:06:44.160> is<00:06:44.520> essentially<00:06:44.819> going<00:06:45.120> to<00:06:45.300> be 00:06:45.469 --> 00:06:45.479 align:start position:0% vector and Pi is essentially going to be 00:06:45.479 --> 00:06:48.950 align:start position:0% vector and Pi is essentially going to be the<00:06:45.900> resource<00:06:46.380> price<00:06:46.680> of<00:06:47.400> uh<00:06:48.060> or<00:06:48.300> the<00:06:48.600> price<00:06:48.780> of 00:06:48.950 --> 00:06:48.960 align:start position:0% the resource price of uh or the price of 00:06:48.960 --> 00:06:51.110 align:start position:0% the resource price of uh or the price of resource<00:06:49.380> I<00:06:49.500> so<00:06:50.039> that<00:06:50.220> allows<00:06:50.580> us<00:06:50.699> to<00:06:51.000> very 00:06:51.110 --> 00:06:51.120 align:start position:0% resource I so that allows us to very 00:06:51.120 --> 00:06:53.450 align:start position:0% resource I so that allows us to very easily<00:06:51.479> write<00:06:51.720> how<00:06:52.500> much<00:06:52.680> a<00:06:53.039> transaction 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00:07:00.720 align:start position:0% is split up into the sum here one thing 00:07:00.720 --> 00:07:02.870 align:start position:0% is split up into the sum here one thing here<00:07:00.960> is<00:07:01.080> when<00:07:01.319> I<00:07:01.440> talk<00:07:01.560> about<00:07:01.740> prices<00:07:02.039> this<00:07:02.759> is 00:07:02.870 --> 00:07:02.880 align:start position:0% here is when I talk about prices this is 00:07:02.880 --> 00:07:04.430 align:start position:0% here is when I talk about prices this is going<00:07:03.000> to<00:07:03.120> be<00:07:03.180> the<00:07:03.419> amount<00:07:03.660> burned<00:07:04.139> by<00:07:04.319> the 00:07:04.430 --> 00:07:04.440 align:start position:0% going to be the amount burned by the 00:07:04.440 --> 00:07:05.870 align:start position:0% going to be the amount burned by the network<00:07:04.560> or<00:07:04.919> essentially<00:07:05.280> the<00:07:05.460> price<00:07:05.639> that 00:07:05.870 --> 00:07:05.880 align:start position:0% network or essentially the price that 00:07:05.880 --> 00:07:08.570 align:start position:0% network or essentially the price that the<00:07:06.120> network<00:07:06.560> charges<00:07:07.560> for<00:07:07.800> a<00:07:07.919> given<00:07:08.160> resource 00:07:08.570 --> 00:07:08.580 align:start position:0% the network charges for a given resource 00:07:08.580 --> 00:07:11.749 align:start position:0% the network charges for a given resource so<00:07:08.940> think<00:07:09.180> like<00:07:09.419> EIP<00:07:09.780> 1559<00:07:10.740> it's<00:07:11.340> not<00:07:11.580> actually 00:07:11.749 --> 00:07:11.759 align:start position:0% so think like EIP 1559 it's not actually 00:07:11.759 --> 00:07:14.150 align:start position:0% so think like EIP 1559 it's not actually going<00:07:12.000> to<00:07:12.180> be<00:07:12.300> the<00:07:12.600> price<00:07:12.720> that<00:07:13.080> uh<00:07:13.319> users<00:07:13.800> pay 00:07:14.150 --> 00:07:14.160 align:start position:0% going to be the price that uh users pay 00:07:14.160 --> 00:07:16.129 align:start position:0% going to be the price that uh users pay say<00:07:14.460> validators<00:07:15.060> for<00:07:15.360> inclusion<00:07:15.900> in<00:07:16.020> the 00:07:16.129 --> 00:07:16.139 align:start position:0% say validators for inclusion in the 00:07:16.139 --> 00:07:18.230 align:start position:0% say validators for inclusion in the block<00:07:16.259> so<00:07:16.500> nothing<00:07:16.680> about<00:07:16.919> tips<00:07:17.340> here<00:07:17.580> this<00:07:18.120> is 00:07:18.230 --> 00:07:18.240 align:start position:0% block so nothing about tips here this is 00:07:18.240 --> 00:07:19.490 align:start position:0% block so nothing about tips here this is just<00:07:18.360> going<00:07:18.479> to<00:07:18.600> be<00:07:18.720> purely<00:07:19.020> the<00:07:19.259> amount 00:07:19.490 --> 00:07:19.500 align:start position:0% just going to be purely the amount 00:07:19.500 --> 00:07:22.730 align:start position:0% just going to be purely the amount that's<00:07:19.680> burned<00:07:20.160> all<00:07:20.880> right<00:07:21.060> so<00:07:21.479> we<00:07:21.900> set<00:07:22.440> up<00:07:22.620> all 00:07:22.730 --> 00:07:22.740 align:start position:0% that's burned all right so we set up all 00:07:22.740 --> 00:07:24.350 align:start position:0% that's burned all right so we set up all the<00:07:22.919> math<00:07:23.099> which<00:07:23.340> is<00:07:23.460> great<00:07:23.699> but<00:07:24.000> we<00:07:24.240> still 00:07:24.350 --> 00:07:24.360 align:start position:0% the math which is great but we still 00:07:24.360 --> 00:07:26.210 align:start position:0% the math which is great but we still have<00:07:24.599> to<00:07:24.720> go<00:07:24.900> back<00:07:25.139> and<00:07:25.380> say<00:07:25.560> well<00:07:25.740> how<00:07:25.979> do<00:07:26.099> we 00:07:26.210 --> 00:07:26.220 align:start position:0% have to go back and say well how do we 00:07:26.220 --> 00:07:27.529 align:start position:0% have to go back and say well how do we actually<00:07:26.400> determine<00:07:26.880> how<00:07:27.120> to<00:07:27.240> charge<00:07:27.360> for 00:07:27.529 --> 00:07:27.539 align:start position:0% actually determine how to charge for 00:07:27.539 --> 00:07:30.230 align:start position:0% actually determine how to charge for each<00:07:27.840> source<00:07:28.740> now<00:07:29.280> there's<00:07:29.460> a<00:07:29.639> number<00:07:29.759> of<00:07:29.940> very 00:07:30.230 --> 00:07:30.240 align:start position:0% each source now there's a number of very 00:07:30.240 --> 00:07:33.110 align:start position:0% each source now there's a number of very reasonable<00:07:30.660> things<00:07:30.900> that<00:07:31.139> we<00:07:31.259> want<00:07:31.639> if<00:07:32.639> the 00:07:33.110 --> 00:07:33.120 align:start position:0% reasonable things that we want if the 00:07:33.120 --> 00:07:35.150 align:start position:0% reasonable things that we want if the utilization<00:07:33.660> that<00:07:33.960> we<00:07:34.080> have<00:07:34.259> is<00:07:34.560> equal<00:07:34.740> to<00:07:34.979> our 00:07:35.150 --> 00:07:35.160 align:start position:0% utilization that we have is equal to our 00:07:35.160 --> 00:07:36.770 align:start position:0% utilization that we have is equal to our Target<00:07:35.280> utilization<00:07:35.940> we<00:07:36.360> probably<00:07:36.479> don't 00:07:36.770 --> 00:07:36.780 align:start position:0% Target utilization we probably don't 00:07:36.780 --> 00:07:38.930 align:start position:0% Target utilization we probably don't want<00:07:37.139> a<00:07:37.380> price<00:07:37.500> to<00:07:37.800> update<00:07:38.039> that<00:07:38.400> seems<00:07:38.759> to<00:07:38.819> be 00:07:38.930 --> 00:07:38.940 align:start position:0% want a price to update that seems to be 00:07:38.940 --> 00:07:40.730 align:start position:0% want a price to update that seems to be kind<00:07:39.120> of<00:07:39.240> like<00:07:39.360> a<00:07:39.539> good<00:07:39.660> price 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align:start position:0% that resource to increase because if we want<00:07:45.960> to<00:07:46.139> make<00:07:46.319> it<00:07:46.500> more<00:07:46.620> expensive<00:07:46.979> so<00:07:47.220> people 00:07:47.390 --> 00:07:47.400 align:start position:0% want to make it more expensive so people 00:07:47.400 --> 00:07:49.670 align:start position:0% want to make it more expensive so people decrease<00:07:47.699> their<00:07:48.120> usage<00:07:48.479> and<00:07:49.139> if<00:07:49.259> we're<00:07:49.440> under 00:07:49.670 --> 00:07:49.680 align:start position:0% decrease their usage and if we're under 00:07:49.680 --> 00:07:51.589 align:start position:0% decrease their usage and if we're under kind<00:07:50.039> of<00:07:50.160> vice<00:07:50.460> versa 00:07:51.589 --> 00:07:51.599 align:start position:0% kind of vice versa 00:07:51.599 --> 00:07:53.510 align:start position:0% kind of vice versa so<00:07:52.020> a<00:07:52.199> number<00:07:52.319> of<00:07:52.500> things<00:07:52.680> have<00:07:52.860> been<00:07:53.039> proposed 00:07:53.510 --> 00:07:53.520 align:start position:0% so a number of things have been proposed 00:07:53.520 --> 00:07:55.610 align:start position:0% so a number of things have been proposed kind<00:07:53.759> of<00:07:53.880> to<00:07:54.000> this<00:07:54.180> end<00:07:54.360> one<00:07:54.900> proposal<00:07:55.319> from 00:07:55.610 --> 00:07:55.620 align:start position:0% kind of to this end one proposal from 00:07:55.620 --> 00:07:57.110 align:start position:0% kind of to this end one proposal from the<00:07:55.680> ethereum<00:07:56.099> research<00:07:56.400> forums<00:07:56.759> back<00:07:57.000> in 00:07:57.110 --> 00:07:57.120 align:start position:0% the ethereum research forums back in 00:07:57.120 --> 00:07:59.830 align:start position:0% the ethereum research forums back in January<00:07:57.539> was<00:07:58.080> this<00:07:58.380> price<00:07:58.620> update<00:07:59.099> rule<00:07:59.460> here 00:07:59.830 --> 00:07:59.840 align:start position:0% January was this price update rule here 00:07:59.840 --> 00:08:02.150 align:start position:0% January was this price update rule here you<00:08:00.840> can<00:08:00.900> kind<00:08:01.020> of<00:08:01.139> go<00:08:01.319> through<00:08:01.500> and<00:08:01.740> basically 00:08:02.150 --> 00:08:02.160 align:start position:0% you can kind of go through and basically 00:08:02.160 --> 00:08:04.189 align:start position:0% you can kind of go through and basically see<00:08:02.699> that<00:08:02.940> it<00:08:03.120> does<00:08:03.240> satisfy<00:08:03.840> these 00:08:04.189 --> 00:08:04.199 align:start position:0% see that it does satisfy these 00:08:04.199 --> 00:08:06.230 align:start position:0% see that it does satisfy these properties<00:08:04.560> that<00:08:04.800> we<00:08:04.979> want<00:08:05.160> however<00:08:05.940> I<00:08:06.120> could 00:08:06.230 --> 00:08:06.240 align:start position:0% properties that we want however I could 00:08:06.240 --> 00:08:07.969 align:start position:0% properties that we want however I could write<00:08:06.360> down<00:08:06.539> a<00:08:06.780> bunch<00:08:06.900> of<00:08:07.020> other<00:08:07.199> price<00:08:07.500> update 00:08:07.969 --> 00:08:07.979 align:start position:0% write down a bunch of other price update 00:08:07.979 --> 00:08:10.070 align:start position:0% write down a bunch of other price update rules<00:08:08.340> that<00:08:08.639> also<00:08:08.880> satisfy<00:08:09.360> these<00:08:09.720> properties 00:08:10.070 --> 00:08:10.080 align:start position:0% rules that also satisfy these properties 00:08:10.080 --> 00:08:12.650 align:start position:0% rules that also satisfy these properties so<00:08:10.919> this<00:08:11.099> kind<00:08:11.340> of<00:08:11.400> begs<00:08:11.699> the<00:08:11.819> question<00:08:12.060> is 00:08:12.650 --> 00:08:12.660 align:start position:0% so this kind of begs the question is 00:08:12.660 --> 00:08:14.390 align:start position:0% so this kind of begs the question is this<00:08:12.780> a<00:08:12.960> good<00:08:13.080> update<00:08:13.319> rule<00:08:13.680> or<00:08:13.860> like<00:08:13.979> what<00:08:14.280> is 00:08:14.390 --> 00:08:14.400 align:start position:0% this a good update rule or like what is 00:08:14.400 --> 00:08:16.070 align:start position:0% this a good update rule or like what is this<00:08:14.520> update<00:08:14.819> rule<00:08:15.180> actually<00:08:15.360> doing<00:08:15.720> are 00:08:16.070 --> 00:08:16.080 align:start position:0% this update rule actually doing are 00:08:16.080 --> 00:08:17.570 align:start position:0% this update rule actually doing are there<00:08:16.259> other<00:08:16.440> update<00:08:16.800> rules<00:08:17.099> that<00:08:17.280> are<00:08:17.400> better 00:08:17.570 --> 00:08:17.580 align:start position:0% there other update rules that are better 00:08:17.580 --> 00:08:20.029 align:start position:0% there other update rules that are better or<00:08:17.880> have<00:08:18.120> different<00:08:18.419> Behavior<00:08:19.080> how<00:08:19.680> do<00:08:19.740> we<00:08:19.860> go 00:08:20.029 --> 00:08:20.039 align:start position:0% or have different Behavior how do we go 00:08:20.039 --> 00:08:21.550 align:start position:0% or have different Behavior how do we go about<00:08:20.160> analyzing<00:08:20.819> this 00:08:21.550 --> 00:08:21.560 align:start position:0% about analyzing this 00:08:21.560 --> 00:08:24.290 align:start position:0% about analyzing this and<00:08:22.560> kind<00:08:23.099> of<00:08:23.160> the<00:08:23.280> punch<00:08:23.520> line<00:08:23.699> of<00:08:23.940> this<00:08:24.120> talk 00:08:24.290 --> 00:08:24.300 align:start position:0% and kind of the punch line of this talk 00:08:24.300 --> 00:08:26.930 align:start position:0% and kind of the punch line of this talk is<00:08:24.900> that<00:08:25.620> um<00:08:25.620> one<00:08:25.919> the<00:08:26.160> all<00:08:26.460> these<00:08:26.639> update 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you<00:08:33.779> can<00:08:33.899> think<00:08:34.020> of<00:08:34.140> is<00:08:34.380> how<00:08:34.680> the 00:08:34.790 --> 00:08:34.800 align:start position:0% which you can think of is how the 00:08:34.800 --> 00:08:36.589 align:start position:0% which you can think of is how the network<00:08:35.039> designer<00:08:35.640> wants<00:08:36.060> the<00:08:36.180> network<00:08:36.300> to 00:08:36.589 --> 00:08:36.599 align:start position:0% network designer wants the network to 00:08:36.599 --> 00:08:39.050 align:start position:0% network designer wants the network to perform<00:08:36.779> of<00:08:37.320> that<00:08:37.440> optimization<00:08:37.979> problem<00:08:38.279> is 00:08:39.050 --> 00:08:39.060 align:start position:0% perform of that optimization problem is 00:08:39.060 --> 00:08:40.610 align:start position:0% perform of that optimization problem is going<00:08:39.180> to<00:08:39.360> then<00:08:39.479> give<00:08:39.719> you<00:08:39.899> a<00:08:40.140> price<00:08:40.200> update 00:08:40.610 --> 00:08:40.620 align:start position:0% going to then give you a price update 00:08:40.620 --> 00:08:43.730 align:start position:0% going to then give you a price update rule<00:08:41.339> so<00:08:41.760> this<00:08:41.940> means<00:08:42.779> essentially<00:08:43.380> what<00:08:43.560> I 00:08:43.730 --> 00:08:43.740 align:start position:0% rule so this means essentially what I 00:08:43.740 --> 00:08:46.430 align:start position:0% rule so this means essentially what I kind<00:08:43.800> of<00:08:43.919> want<00:08:44.039> to<00:08:44.159> convey<00:08:44.580> is<00:08:45.180> the<00:08:45.720> a<00:08:46.080> good<00:08:46.260> way 00:08:46.430 --> 00:08:46.440 align:start position:0% kind of want to convey is the a good way 00:08:46.440 --> 00:08:48.710 align:start position:0% kind of want to convey is the a good way to<00:08:46.620> think<00:08:46.740> about<00:08:46.920> price<00:08:47.220> update<00:08:47.640> rules<00:08:48.000> is<00:08:48.540> not 00:08:48.710 --> 00:08:48.720 align:start position:0% to think about price update rules is not 00:08:48.720 --> 00:08:50.329 align:start position:0% to think about price update rules is not like<00:08:48.899> oh<00:08:49.080> how<00:08:49.320> do<00:08:49.440> I<00:08:49.560> design<00:08:49.680> the<00:08:49.980> best<00:08:50.100> price 00:08:50.329 --> 00:08:50.339 align:start position:0% like oh how do I design the best price 00:08:50.339 --> 00:08:53.150 align:start position:0% like oh how do I design the best price update<00:08:50.760> rule<00:08:51.060> it's<00:08:51.779> what<00:08:52.140> do<00:08:52.320> I<00:08:52.500> actually<00:08:52.740> want 00:08:53.150 --> 00:08:53.160 align:start position:0% update rule it's what do I actually want 00:08:53.160 --> 00:08:55.130 align:start position:0% update rule it's what do I actually want the<00:08:53.399> network<00:08:53.580> Behavior<00:08:54.180> to<00:08:54.360> be<00:08:54.480> so<00:08:54.839> kind<00:08:55.019> of 00:08:55.130 --> 00:08:55.140 align:start position:0% the network Behavior to be so kind of 00:08:55.140 --> 00:08:57.470 align:start position:0% the network Behavior to be so kind of what<00:08:55.320> is<00:08:55.440> my<00:08:55.620> objective<00:08:56.100> and<00:08:56.820> then<00:08:56.940> from<00:08:57.240> there 00:08:57.470 --> 00:08:57.480 align:start position:0% what is my objective and then from there 00:08:57.480 --> 00:09:00.170 align:start position:0% what is my objective and then from there we'll<00:08:57.899> show<00:08:58.140> how<00:08:58.680> to<00:08:58.920> get<00:08:59.760> to<00:08:59.940> the<00:09:00.060> price 00:09:00.170 --> 00:09:00.180 align:start position:0% we'll show how to get to the price 00:09:00.180 --> 00:09:02.930 align:start position:0% we'll show how to get to the price update<00:09:00.600> rule<00:09:01.260> so<00:09:01.740> this<00:09:01.920> brings<00:09:02.160> us<00:09:02.339> to<00:09:02.580> what<00:09:02.820> we 00:09:02.930 --> 00:09:02.940 align:start position:0% update rule so this brings us to what we 00:09:02.940 --> 00:09:04.970 align:start position:0% update rule so this brings us to what we call<00:09:03.120> the<00:09:03.300> resource<00:09:03.660> allocation<00:09:04.080> problem 00:09:04.970 --> 00:09:04.980 align:start position:0% call the resource allocation problem 00:09:04.980 --> 00:09:06.829 align:start position:0% call the resource allocation problem and<00:09:05.519> the<00:09:05.640> setting<00:09:05.880> for<00:09:06.000> now<00:09:06.240> is<00:09:06.480> we're<00:09:06.660> going 00:09:06.829 --> 00:09:06.839 align:start position:0% and the setting for now is we're going 00:09:06.839 --> 00:09:08.389 align:start position:0% and the setting for now is we're going to<00:09:06.959> pretend<00:09:07.380> the<00:09:07.560> network<00:09:07.740> designer<00:09:08.279> is 00:09:08.389 --> 00:09:08.399 align:start position:0% to pretend the network designer is 00:09:08.399 --> 00:09:10.430 align:start position:0% to pretend the network designer is omniscient<00:09:08.940> and<00:09:09.360> gets<00:09:09.660> to<00:09:09.720> choose<00:09:10.019> all<00:09:10.320> the 00:09:10.430 --> 00:09:10.440 align:start position:0% omniscient and gets to choose all the 00:09:10.440 --> 00:09:12.470 align:start position:0% omniscient and gets to choose all the transactions<00:09:11.040> in<00:09:11.220> each<00:09:11.339> block<00:09:11.580> I<00:09:12.120> know<00:09:12.240> this 00:09:12.470 --> 00:09:12.480 align:start position:0% transactions in each block I know this 00:09:12.480 --> 00:09:14.269 align:start position:0% transactions in each block I know this is<00:09:12.660> entirely<00:09:13.080> unrealistic<00:09:13.740> or<00:09:14.040> not<00:09:14.160> even 00:09:14.269 --> 00:09:14.279 align:start position:0% is entirely unrealistic or not even 00:09:14.279 --> 00:09:16.130 align:start position:0% is entirely unrealistic or not even unrealistic<00:09:14.880> it's<00:09:15.060> just<00:09:15.300> absolutely<00:09:15.660> false 00:09:16.130 --> 00:09:16.140 align:start position:0% unrealistic it's just absolutely false 00:09:16.140 --> 00:09:18.350 align:start position:0% unrealistic it's just absolutely false however<00:09:16.920> this<00:09:17.160> is<00:09:17.279> going<00:09:17.459> to<00:09:17.580> allow<00:09:17.820> us<00:09:17.940> to 00:09:18.350 --> 00:09:18.360 align:start position:0% however this is going to allow us to 00:09:18.360 --> 00:09:20.090 align:start position:0% however this is going to allow us to build<00:09:18.540> up<00:09:18.779> a<00:09:19.080> very<00:09:19.200> useful<00:09:19.500> mathematical 00:09:20.090 --> 00:09:20.100 align:start position:0% build up a very useful mathematical 00:09:20.100 --> 00:09:22.190 align:start position:0% build up a very useful mathematical problem<00:09:20.399> that's<00:09:21.120> going<00:09:21.360> to<00:09:21.480> get<00:09:21.660> us<00:09:21.839> to<00:09:22.080> the 00:09:22.190 --> 00:09:22.200 align:start position:0% problem that's going to get us to the 00:09:22.200 --> 00:09:24.110 align:start position:0% problem that's going to get us to the price<00:09:22.380> update<00:09:22.800> rule 00:09:24.110 --> 00:09:24.120 align:start position:0% price update rule 00:09:24.120 --> 00:09:25.910 align:start position:0% price update rule so<00:09:24.480> there's<00:09:24.600> a<00:09:24.779> few<00:09:24.839> things<00:09:25.019> that<00:09:25.260> we<00:09:25.380> need<00:09:25.560> for 00:09:25.910 --> 00:09:25.920 align:start position:0% so there's a few things that we need for 00:09:25.920 --> 00:09:27.590 align:start position:0% so there's a few things that we need for this<00:09:26.100> problem<00:09:26.279> first<00:09:26.640> we<00:09:26.880> want<00:09:27.000> a<00:09:27.300> loss 00:09:27.590 --> 00:09:27.600 align:start position:0% this problem first we want a loss 00:09:27.600 --> 00:09:29.030 align:start position:0% this problem first we want a loss function<00:09:27.899> that's<00:09:28.260> defined<00:09:28.620> by<00:09:28.740> the<00:09:28.920> network 00:09:29.030 --> 00:09:29.040 align:start position:0% function that's defined by the network 00:09:29.040 --> 00:09:31.250 align:start position:0% function that's defined by the network designer<00:09:29.700> and<00:09:30.480> this<00:09:30.720> loss<00:09:31.019> function 00:09:31.250 --> 00:09:31.260 align:start position:0% designer and this loss function 00:09:31.260 --> 00:09:32.329 align:start position:0% designer and this loss function essentially<00:09:31.680> is<00:09:31.800> going<00:09:31.980> to<00:09:32.040> be<00:09:32.100> the 00:09:32.329 --> 00:09:32.339 align:start position:0% essentially is going to be the 00:09:32.339 --> 00:09:34.009 align:start position:0% essentially is going to be the unhappiness<00:09:32.880> with<00:09:33.180> the<00:09:33.360> current<00:09:33.480> resource 00:09:34.009 --> 00:09:34.019 align:start position:0% unhappiness with the current resource 00:09:34.019 --> 00:09:35.389 align:start position:0% unhappiness with the current resource utilization 00:09:35.389 --> 00:09:35.399 align:start position:0% utilization 00:09:35.399 --> 00:09:37.670 align:start position:0% utilization so<00:09:35.820> there's<00:09:36.000> a<00:09:36.240> few<00:09:36.360> very<00:09:36.720> reasonable<00:09:37.200> or 00:09:37.670 --> 00:09:37.680 align:start position:0% so there's a few very reasonable or 00:09:37.680 --> 00:09:39.650 align:start position:0% so there's a few very reasonable or potentially<00:09:38.459> kind<00:09:38.700> of<00:09:38.760> silly<00:09:39.060> loss<00:09:39.360> functions 00:09:39.650 --> 00:09:39.660 align:start position:0% potentially kind of silly loss functions 00:09:39.660 --> 00:09:41.750 align:start position:0% potentially kind of silly loss functions that<00:09:39.839> we<00:09:39.959> could<00:09:40.080> choose<00:09:40.380> one<00:09:41.100> is<00:09:41.279> this<00:09:41.459> so<00:09:41.640> the 00:09:41.750 --> 00:09:41.760 align:start position:0% that we could choose one is this so the 00:09:41.760 --> 00:09:44.210 align:start position:0% that we could choose one is this so the loss<00:09:42.060> function<00:09:42.300> of<00:09:42.480> Y<00:09:42.720> remember<00:09:43.140> Y<00:09:43.680> is<00:09:43.920> going 00:09:44.210 --> 00:09:44.220 align:start position:0% loss function of Y remember Y is going 00:09:44.220 --> 00:09:46.190 align:start position:0% loss function of Y remember Y is going to<00:09:44.339> be<00:09:44.580> the<00:09:45.120> resource<00:09:45.480> utilization<00:09:45.899> of<00:09:46.080> a 00:09:46.190 --> 00:09:46.200 align:start position:0% to be the resource utilization of a 00:09:46.200 --> 00:09:48.769 align:start position:0% to be the resource utilization of a given<00:09:46.500> block<00:09:46.680> maybe<00:09:47.580> it's<00:09:47.940> zero<00:09:48.360> if<00:09:48.660> we're 00:09:48.769 --> 00:09:48.779 align:start position:0% given block maybe it's zero if we're 00:09:48.779 --> 00:09:50.389 align:start position:0% given block maybe it's zero if we're exactly<00:09:49.200> at<00:09:49.320> our<00:09:49.440> Target<00:09:49.620> and<00:09:50.040> it's<00:09:50.220> Infinity 00:09:50.389 --> 00:09:50.399 align:start position:0% exactly at our Target and it's Infinity 00:09:50.399 --> 00:09:51.829 align:start position:0% exactly at our Target and it's Infinity otherwise 00:09:51.829 --> 00:09:51.839 align:start position:0% otherwise 00:09:51.839 --> 00:09:53.509 align:start position:0% otherwise another<00:09:52.320> thing<00:09:52.560> we<00:09:52.680> could<00:09:52.800> do<00:09:52.920> is<00:09:53.160> we<00:09:53.399> could 00:09:53.509 --> 00:09:53.519 align:start position:0% another thing we could do is we could 00:09:53.519 --> 00:09:55.250 align:start position:0% another thing we could do is we could say<00:09:53.700> that<00:09:54.060> actually<00:09:54.300> we<00:09:54.660> don't<00:09:54.779> care<00:09:54.959> if<00:09:55.140> we're 00:09:55.250 --> 00:09:55.260 align:start position:0% say that actually we don't care if we're 00:09:55.260 --> 00:09:56.930 align:start position:0% say that actually we don't care if we're under<00:09:55.500> the<00:09:55.740> target<00:09:55.860> we<00:09:56.339> only<00:09:56.459> care<00:09:56.640> if<00:09:56.760> we're 00:09:56.930 --> 00:09:56.940 align:start position:0% under the target we only care if we're 00:09:56.940 --> 00:09:59.030 align:start position:0% under the target we only care if we're over<00:09:57.120> the<00:09:57.300> target<00:09:57.480> so<00:09:58.019> we<00:09:58.200> can<00:09:58.320> say<00:09:58.560> okay<00:09:58.740> the 00:09:59.030 --> 00:09:59.040 align:start position:0% over the target so we can say okay the 00:09:59.040 --> 00:10:00.350 align:start position:0% over the target so we can say okay the loss<00:09:59.279> is<00:09:59.399> zero<00:09:59.700> if<00:09:59.760> we're<00:09:59.880> under<00:10:00.000> the<00:10:00.180> Target 00:10:00.350 --> 00:10:00.360 align:start position:0% loss is zero if we're under the Target 00:10:00.360 --> 00:10:02.810 align:start position:0% loss is zero if we're under the Target and<00:10:00.959> it's<00:10:01.080> Infinity<00:10:01.320> otherwise 00:10:02.810 --> 00:10:02.820 align:start position:0% and it's Infinity otherwise 00:10:02.820 --> 00:10:04.670 align:start position:0% and it's Infinity otherwise again<00:10:03.360> these<00:10:03.839> might<00:10:04.019> not<00:10:04.200> be<00:10:04.380> what<00:10:04.560> you 00:10:04.670 --> 00:10:04.680 align:start position:0% again these might not be what you 00:10:04.680 --> 00:10:05.509 align:start position:0% again these might not be what you actually<00:10:04.800> want<00:10:04.980> to<00:10:05.100> do<00:10:05.160> in<00:10:05.339> practice 00:10:05.509 --> 00:10:05.519 align:start position:0% actually want to do in practice 00:10:05.519 --> 00:10:07.430 align:start position:0% actually want to do in practice potentially<00:10:06.300> you<00:10:06.660> want<00:10:06.779> to<00:10:06.899> have<00:10:07.140> something 00:10:07.430 --> 00:10:07.440 align:start position:0% potentially you want to have something 00:10:07.440 --> 00:10:08.990 align:start position:0% potentially you want to have something where<00:10:07.860> if<00:10:08.100> you're<00:10:08.220> a<00:10:08.399> little<00:10:08.459> bit<00:10:08.640> off<00:10:08.760> the 00:10:08.990 --> 00:10:09.000 align:start position:0% where if you're a little bit off the 00:10:09.000 --> 00:10:11.509 align:start position:0% where if you're a little bit off the target<00:10:09.380> you're<00:10:10.380> not<00:10:10.620> that<00:10:10.740> unhappy<00:10:11.220> and<00:10:11.339> then 00:10:11.509 --> 00:10:11.519 align:start position:0% target you're not that unhappy and then 00:10:11.519 --> 00:10:13.610 align:start position:0% target you're not that unhappy and then it<00:10:11.700> grows<00:10:11.940> say<00:10:12.120> quadratically<00:10:12.779> as<00:10:13.080> you<00:10:13.320> as 00:10:13.610 --> 00:10:13.620 align:start position:0% it grows say quadratically as you as 00:10:13.620 --> 00:10:15.829 align:start position:0% it grows say quadratically as you as your<00:10:13.800> deviation<00:10:14.220> increases<00:10:14.820> but<00:10:15.480> the<00:10:15.660> whole 00:10:15.829 --> 00:10:15.839 align:start position:0% your deviation increases but the whole 00:10:15.839 --> 00:10:17.930 align:start position:0% your deviation increases but the whole point<00:10:16.080> is<00:10:16.260> we<00:10:16.560> only<00:10:16.680> need<00:10:17.160> something<00:10:17.640> that 00:10:17.930 --> 00:10:17.940 align:start position:0% point is we only need something that 00:10:17.940 --> 00:10:19.970 align:start position:0% point is we only need something that tells<00:10:18.240> us<00:10:18.360> kind<00:10:18.779> of<00:10:18.839> the<00:10:19.080> unhappiness<00:10:19.680> with 00:10:19.970 --> 00:10:19.980 align:start position:0% tells us kind of the unhappiness with 00:10:19.980 --> 00:10:22.430 align:start position:0% tells us kind of the unhappiness with the<00:10:20.160> current<00:10:20.279> resource<00:10:20.700> utilization<00:10:21.240> then<00:10:22.200> we 00:10:22.430 --> 00:10:22.440 align:start position:0% the current resource utilization then we 00:10:22.440 --> 00:10:24.290 align:start position:0% the current resource utilization then we need<00:10:22.560> some<00:10:22.800> way<00:10:22.980> to<00:10:23.160> say<00:10:23.339> what<00:10:23.640> is<00:10:23.760> the<00:10:23.940> set<00:10:24.120> of 00:10:24.290 --> 00:10:24.300 align:start position:0% need some way to say what is the set of 00:10:24.300 --> 00:10:26.630 align:start position:0% need some way to say what is the set of allowable<00:10:24.720> transactions<00:10:25.620> and<00:10:26.100> in<00:10:26.220> this<00:10:26.399> we're 00:10:26.630 --> 00:10:26.640 align:start position:0% allowable transactions and in this we're 00:10:26.640 --> 00:10:29.150 align:start position:0% allowable transactions and in this we're going<00:10:26.820> to<00:10:26.940> encode<00:10:27.480> all<00:10:27.839> constraints<00:10:28.380> in<00:10:29.040> the 00:10:29.150 --> 00:10:29.160 align:start position:0% going to encode all constraints in the 00:10:29.160 --> 00:10:31.850 align:start position:0% going to encode all constraints in the set<00:10:29.339> s<00:10:29.640> so<00:10:30.240> this<00:10:30.420> is<00:10:30.540> going<00:10:30.660> to<00:10:30.839> be<00:10:31.019> this<00:10:31.500> binary 00:10:31.850 --> 00:10:31.860 align:start position:0% set s so this is going to be this binary 00:10:31.860 --> 00:10:34.310 align:start position:0% set s so this is going to be this binary set<00:10:32.300> that<00:10:33.300> encodes<00:10:33.660> things<00:10:33.899> like<00:10:34.080> Network 00:10:34.310 --> 00:10:34.320 align:start position:0% set that encodes things like Network 00:10:34.320 --> 00:10:36.230 align:start position:0% set that encodes things like Network constraints<00:10:34.860> so<00:10:35.100> like<00:10:35.279> earlier<00:10:35.580> a<00:10:35.880> block<00:10:36.060> in 00:10:36.230 --> 00:10:36.240 align:start position:0% constraints so like earlier a block in 00:10:36.240 --> 00:10:37.850 align:start position:0% constraints so like earlier a block in ethereum<00:10:36.660> is<00:10:36.779> invalid<00:10:37.200> if<00:10:37.320> it's<00:10:37.440> over<00:10:37.620> 30 00:10:37.850 --> 00:10:37.860 align:start position:0% ethereum is invalid if it's over 30 00:10:37.860 --> 00:10:40.190 align:start position:0% ethereum is invalid if it's over 30 million<00:10:38.399> gas<00:10:38.640> however<00:10:39.480> there's<00:10:39.779> a<00:10:39.959> lot<00:10:40.019> of 00:10:40.190 --> 00:10:40.200 align:start position:0% million gas however there's a lot of 00:10:40.200 --> 00:10:42.949 align:start position:0% million gas however there's a lot of complex<00:10:40.940> interactions<00:10:41.940> among<00:10:42.300> transactions 00:10:42.949 --> 00:10:42.959 align:start position:0% complex interactions among transactions 00:10:42.959 --> 00:10:45.230 align:start position:0% complex interactions among transactions as<00:10:43.140> well<00:10:43.320> so<00:10:43.860> for<00:10:44.100> instance<00:10:44.339> if<00:10:44.820> a<00:10:45.060> lot<00:10:45.120> of 00:10:45.230 --> 00:10:45.240 align:start position:0% as well so for instance if a lot of 00:10:45.240 --> 00:10:46.790 align:start position:0% as well so for instance if a lot of Searchers<00:10:45.660> are<00:10:45.959> all<00:10:46.079> trying<00:10:46.320> to<00:10:46.500> get<00:10:46.620> a 00:10:46.790 --> 00:10:46.800 align:start position:0% Searchers are all trying to get a 00:10:46.800 --> 00:10:48.829 align:start position:0% Searchers are all trying to get a specific<00:10:47.160> liquidation<00:10:47.700> only<00:10:48.360> one<00:10:48.660> of<00:10:48.720> them 00:10:48.829 --> 00:10:48.839 align:start position:0% specific liquidation only one of them 00:10:48.839 --> 00:10:51.050 align:start position:0% specific liquidation only one of them can<00:10:49.079> get<00:10:49.260> that<00:10:49.380> liquidation<00:10:49.920> and<00:10:50.700> this<00:10:50.880> can 00:10:51.050 --> 00:10:51.060 align:start position:0% can get that liquidation and this can 00:10:51.060 --> 00:10:53.210 align:start position:0% can get that liquidation and this can also<00:10:51.360> be<00:10:51.480> encoded<00:10:51.959> in<00:10:52.140> this<00:10:52.320> set<00:10:52.500> so<00:10:52.740> this<00:10:52.920> is<00:10:52.980> a 00:10:53.210 --> 00:10:53.220 align:start position:0% also be encoded in this set so this is a 00:10:53.220 --> 00:10:55.130 align:start position:0% also be encoded in this set so this is a very<00:10:53.339> general<00:10:53.579> kind<00:10:54.000> of<00:10:54.120> object<00:10:54.480> that<00:10:54.959> just 00:10:55.130 --> 00:10:55.140 align:start position:0% very general kind of object that just 00:10:55.140 --> 00:10:57.230 align:start position:0% very general kind of object that just says<00:10:55.380> what<00:10:55.680> transactions<00:10:56.279> are<00:10:56.459> okay 00:10:57.230 --> 00:10:57.240 align:start position:0% says what transactions are okay 00:10:57.240 --> 00:10:59.210 align:start position:0% says what transactions are okay we're<00:10:57.839> going<00:10:58.019> to<00:10:58.140> do<00:10:58.320> a<00:10:58.500> this<00:10:58.740> is<00:10:58.860> kind<00:10:58.980> of<00:10:59.100> the 00:10:59.210 --> 00:10:59.220 align:start position:0% we're going to do a this is kind of the 00:10:59.220 --> 00:11:00.829 align:start position:0% we're going to do a this is kind of the first<00:10:59.399> mathematical<00:11:00.000> trick<00:11:00.300> that<00:11:00.480> we<00:11:00.660> play 00:11:00.829 --> 00:11:00.839 align:start position:0% first mathematical trick that we play 00:11:00.839 --> 00:11:01.670 align:start position:0% first mathematical trick that we play here 00:11:01.670 --> 00:11:01.680 align:start position:0% here 00:11:01.680 --> 00:11:03.110 align:start position:0% here um and<00:11:01.860> this<00:11:01.980> isn't<00:11:02.220> that<00:11:02.399> important<00:11:02.760> but 00:11:03.110 --> 00:11:03.120 align:start position:0% um and this isn't that important but 00:11:03.120 --> 00:11:05.210 align:start position:0% um and this isn't that important but it's<00:11:03.360> uh<00:11:03.660> essentially<00:11:04.320> instead<00:11:05.100> of 00:11:05.210 --> 00:11:05.220 align:start position:0% it's uh essentially instead of 00:11:05.220 --> 00:11:06.889 align:start position:0% it's uh essentially instead of considering<00:11:05.640> s<00:11:05.880> we<00:11:06.180> consider<00:11:06.420> What's<00:11:06.660> called 00:11:06.889 --> 00:11:06.899 align:start position:0% considering s we consider What's called 00:11:06.899 --> 00:11:09.530 align:start position:0% considering s we consider What's called the<00:11:07.200> convex<00:11:07.620> Hall<00:11:07.800> of<00:11:08.040> us<00:11:08.279> this<00:11:09.000> just<00:11:09.180> means 00:11:09.530 --> 00:11:09.540 align:start position:0% the convex Hall of us this just means 00:11:09.540 --> 00:11:11.810 align:start position:0% the convex Hall of us this just means that<00:11:09.720> instead<00:11:10.079> of<00:11:10.200> forcing<00:11:10.740> X<00:11:10.980> to<00:11:11.220> be<00:11:11.339> zero<00:11:11.700> or 00:11:11.810 --> 00:11:11.820 align:start position:0% that instead of forcing X to be zero or 00:11:11.820 --> 00:11:14.810 align:start position:0% that instead of forcing X to be zero or one<00:11:12.060> we<00:11:12.660> allow<00:11:12.899> X<00:11:13.140> to<00:11:13.440> be<00:11:13.620> a<00:11:14.040> fractional<00:11:14.579> value 00:11:14.810 --> 00:11:14.820 align:start position:0% one we allow X to be a fractional value 00:11:14.820 --> 00:11:17.329 align:start position:0% one we allow X to be a fractional value between<00:11:15.240> zero<00:11:15.779> and<00:11:15.899> one<00:11:16.079> so<00:11:16.800> the<00:11:16.980> way<00:11:17.100> to<00:11:17.220> think 00:11:17.329 --> 00:11:17.339 align:start position:0% between zero and one so the way to think 00:11:17.339 --> 00:11:18.590 align:start position:0% between zero and one so the way to think about<00:11:17.459> this<00:11:17.700> and<00:11:17.880> the<00:11:18.000> way<00:11:18.120> this<00:11:18.300> kind<00:11:18.480> of 00:11:18.590 --> 00:11:18.600 align:start position:0% about this and the way this kind of 00:11:18.600 --> 00:11:19.910 align:start position:0% about this and the way this kind of makes<00:11:18.779> sense<00:11:19.079> is<00:11:19.440> from<00:11:19.620> the<00:11:19.800> network 00:11:19.910 --> 00:11:19.920 align:start position:0% makes sense is from the network 00:11:19.920 --> 00:11:22.370 align:start position:0% makes sense is from the network designer's<00:11:20.640> perspective<00:11:21.060> uh<00:11:21.779> you<00:11:21.959> care<00:11:22.140> more 00:11:22.370 --> 00:11:22.380 align:start position:0% designer's perspective uh you care more 00:11:22.380 --> 00:11:24.769 align:start position:0% designer's perspective uh you care more about<00:11:22.560> the<00:11:22.860> average<00:11:23.040> case<00:11:23.519> or<00:11:24.240> the<00:11:24.540> average 00:11:24.769 --> 00:11:24.779 align:start position:0% about the average case or the average 00:11:24.779 --> 00:11:27.110 align:start position:0% about the average case or the average kind<00:11:25.140> of<00:11:25.260> usage<00:11:25.560> of<00:11:25.740> the<00:11:25.860> network<00:11:26.040> not<00:11:26.579> one 00:11:27.110 --> 00:11:27.120 align:start position:0% kind of usage of the network not one 00:11:27.120 --> 00:11:30.350 align:start position:0% kind of usage of the network not one particular<00:11:27.480> block<00:11:27.779> so<00:11:28.680> say<00:11:28.980> if<00:11:29.279> XJ<00:11:30.000> is<00:11:30.240> a 00:11:30.350 --> 00:11:30.360 align:start position:0% particular block so say if XJ is a 00:11:30.360 --> 00:11:32.389 align:start position:0% particular block so say if XJ is a fraction<00:11:30.660> that<00:11:31.440> would<00:11:31.560> just<00:11:31.740> say<00:11:31.860> that<00:11:32.100> we 00:11:32.389 --> 00:11:32.399 align:start position:0% fraction that would just say that we 00:11:32.399 --> 00:11:34.970 align:start position:0% fraction that would just say that we include<00:11:32.880> that<00:11:33.060> transaction<00:11:33.540> after<00:11:33.899> roughly<00:11:34.740> 1 00:11:34.970 --> 00:11:34.980 align:start position:0% include that transaction after roughly 1 00:11:34.980 --> 00:11:37.370 align:start position:0% include that transaction after roughly 1 over<00:11:35.160> x<00:11:35.399> j<00:11:35.640> blocks<00:11:36.180> and<00:11:36.720> we'll<00:11:36.839> see<00:11:37.019> that<00:11:37.140> we 00:11:37.370 --> 00:11:37.380 align:start position:0% over x j blocks and we'll see that we 00:11:37.380 --> 00:11:39.230 align:start position:0% over x j blocks and we'll see that we can<00:11:37.500> actually<00:11:37.680> remove<00:11:38.040> this<00:11:38.459> constraint<00:11:38.880> in<00:11:39.060> a 00:11:39.230 --> 00:11:39.240 align:start position:0% can actually remove this constraint in a 00:11:39.240 --> 00:11:41.090 align:start position:0% can actually remove this constraint in a little<00:11:39.300> bit<00:11:39.480> but<00:11:40.140> again<00:11:40.320> this<00:11:40.560> is<00:11:40.620> just<00:11:40.800> to<00:11:40.920> set 00:11:41.090 --> 00:11:41.100 align:start position:0% little bit but again this is just to set 00:11:41.100 --> 00:11:43.190 align:start position:0% little bit but again this is just to set up<00:11:41.279> kind<00:11:41.459> of<00:11:41.579> the<00:11:41.700> mathematical<00:11:42.180> formalism<00:11:42.720> so 00:11:43.190 --> 00:11:43.200 align:start position:0% up kind of the mathematical formalism so 00:11:43.200 --> 00:11:45.110 align:start position:0% up kind of the mathematical formalism so this<00:11:43.740> doesn't<00:11:43.920> really<00:11:44.160> matter<00:11:44.399> this<00:11:44.940> won't 00:11:45.110 --> 00:11:45.120 align:start position:0% this doesn't really matter this won't 00:11:45.120 --> 00:11:47.150 align:start position:0% this doesn't really matter this won't really<00:11:45.300> matter<00:11:45.600> in<00:11:45.959> a<00:11:46.079> bit<00:11:46.200> but<00:11:46.800> I<00:11:46.980> just<00:11:47.040> want 00:11:47.150 --> 00:11:47.160 align:start position:0% really matter in a bit but I just want 00:11:47.160 --> 00:11:48.829 align:start position:0% really matter in a bit but I just want to<00:11:47.279> be<00:11:47.399> complete<00:11:47.820> all<00:11:48.060> right<00:11:48.240> the<00:11:48.480> final<00:11:48.600> thing 00:11:48.829 --> 00:11:48.839 align:start position:0% to be complete all right the final thing 00:11:48.839 --> 00:11:51.050 align:start position:0% to be complete all right the final thing that<00:11:49.019> we<00:11:49.200> need<00:11:49.320> is<00:11:49.920> we<00:11:50.100> want<00:11:50.279> to<00:11:50.399> know<00:11:50.579> how<00:11:50.940> much 00:11:51.050 --> 00:11:51.060 align:start position:0% that we need is we want to know how much 00:11:51.060 --> 00:11:54.410 align:start position:0% that we need is we want to know how much utility<00:11:51.480> a<00:11:51.779> given<00:11:52.079> transaction<00:11:52.500> gives<00:11:53.399> to<00:11:54.180> the 00:11:54.410 --> 00:11:54.420 align:start position:0% utility a given transaction gives to the 00:11:54.420 --> 00:11:57.410 align:start position:0% utility a given transaction gives to the Joint<00:11:55.140> user<00:11:55.980> and<00:11:56.100> validator<00:11:56.579> set 00:11:57.410 --> 00:11:57.420 align:start position:0% Joint user and validator set 00:11:57.420 --> 00:11:59.990 align:start position:0% Joint user and validator set we<00:11:58.019> group<00:11:58.260> these<00:11:59.100> two 00:11:59.990 --> 00:12:00.000 align:start position:0% we group these two 00:12:00.000 --> 00:12:02.569 align:start position:0% we group these two um these<00:12:00.720> two<00:12:00.839> parties<00:12:01.320> together<00:12:01.560> into<00:12:02.160> what 00:12:02.569 --> 00:12:02.579 align:start position:0% um these two parties together into what 00:12:02.579 --> 00:12:04.550 align:start position:0% um these two parties together into what we<00:12:02.640> call<00:12:02.760> the<00:12:02.940> transaction<00:12:03.360> producers<00:12:04.019> and 00:12:04.550 --> 00:12:04.560 align:start position:0% we call the transaction producers and 00:12:04.560 --> 00:12:05.810 align:start position:0% we call the transaction producers and the<00:12:04.680> reason<00:12:04.740> we<00:12:04.980> do<00:12:05.100> this<00:12:05.220> is<00:12:05.459> because<00:12:05.579> we 00:12:05.810 --> 00:12:05.820 align:start position:0% the reason we do this is because we 00:12:05.820 --> 00:12:07.130 align:start position:0% the reason we do this is because we don't<00:12:05.940> want<00:12:06.120> to<00:12:06.240> deal<00:12:06.360> with<00:12:06.540> kind<00:12:06.720> of<00:12:06.839> the<00:12:06.959> game 00:12:07.130 --> 00:12:07.140 align:start position:0% don't want to deal with kind of the game 00:12:07.140 --> 00:12:10.370 align:start position:0% don't want to deal with kind of the game theoretic<00:12:07.860> analysis<00:12:08.459> of<00:12:09.240> uh<00:12:09.540> looking<00:12:09.720> at<00:12:09.959> bids 00:12:10.370 --> 00:12:10.380 align:start position:0% theoretic analysis of uh looking at bids 00:12:10.380 --> 00:12:12.769 align:start position:0% theoretic analysis of uh looking at bids and<00:12:10.500> auctions<00:12:10.980> and<00:12:11.339> that<00:12:11.579> type<00:12:11.760> of<00:12:11.940> thing 00:12:12.769 --> 00:12:12.779 align:start position:0% and auctions and that type of thing 00:12:12.779 --> 00:12:14.930 align:start position:0% and auctions and that type of thing um<00:12:12.839> so<00:12:13.079> we<00:12:13.260> assume<00:12:13.560> that<00:12:13.680> kind<00:12:13.860> of<00:12:13.980> these<00:12:14.339> this 00:12:14.930 --> 00:12:14.940 align:start position:0% um so we assume that kind of these this 00:12:14.940 --> 00:12:16.790 align:start position:0% um so we assume that kind of these this group<00:12:15.180> of<00:12:15.360> people<00:12:15.540> is<00:12:15.839> together<00:12:16.079> they're 00:12:16.790 --> 00:12:16.800 align:start position:0% group of people is together they're 00:12:16.800 --> 00:12:19.009 align:start position:0% group of people is together they're submitting<00:12:17.279> transactions<00:12:17.940> and<00:12:18.420> those<00:12:18.600> have<00:12:18.839> a 00:12:19.009 --> 00:12:19.019 align:start position:0% submitting transactions and those have a 00:12:19.019 --> 00:12:21.050 align:start position:0% submitting transactions and those have a specific<00:12:19.260> type<00:12:19.500> of<00:12:19.680> utility<00:12:19.980> you'll<00:12:20.760> see<00:12:20.880> that 00:12:21.050 --> 00:12:21.060 align:start position:0% specific type of utility you'll see that 00:12:21.060 --> 00:12:23.090 align:start position:0% specific type of utility you'll see that our<00:12:21.180> mechanism<00:12:21.660> actually<00:12:22.079> doesn't<00:12:22.440> matter<00:12:22.860> it 00:12:23.090 --> 00:12:23.100 align:start position:0% our mechanism actually doesn't matter it 00:12:23.100 --> 00:12:24.530 align:start position:0% our mechanism actually doesn't matter it doesn't<00:12:23.279> matter<00:12:23.519> that<00:12:23.820> we<00:12:24.000> group<00:12:24.180> these 00:12:24.530 --> 00:12:24.540 align:start position:0% doesn't matter that we group these 00:12:24.540 --> 00:12:26.090 align:start position:0% doesn't matter that we group these things<00:12:24.660> into<00:12:24.959> the<00:12:25.140> transaction<00:12:25.500> producers 00:12:26.090 --> 00:12:26.100 align:start position:0% things into the transaction producers 00:12:26.100 --> 00:12:28.430 align:start position:0% things into the transaction producers but<00:12:26.760> this<00:12:26.940> does<00:12:27.120> present<00:12:27.540> an<00:12:27.720> area<00:12:27.899> for<00:12:28.200> future 00:12:28.430 --> 00:12:28.440 align:start position:0% but this does present an area for future 00:12:28.440 --> 00:12:29.990 align:start position:0% but this does present an area for future work 00:12:29.990 --> 00:12:30.000 align:start position:0% work 00:12:30.000 --> 00:12:32.509 align:start position:0% work and<00:12:30.899> I'd<00:12:31.440> like<00:12:31.560> to<00:12:31.680> point<00:12:31.800> out<00:12:31.920> that<00:12:32.100> we<00:12:32.279> almost 00:12:32.509 --> 00:12:32.519 align:start position:0% and I'd like to point out that we almost 00:12:32.519 --> 00:12:34.490 align:start position:0% and I'd like to point out that we almost never<00:12:32.760> know<00:12:33.000> Q<00:12:33.180> in<00:12:33.420> practice<00:12:33.660> it's<00:12:34.140> more<00:12:34.380> or 00:12:34.490 --> 00:12:34.500 align:start position:0% never know Q in practice it's more or 00:12:34.500 --> 00:12:36.650 align:start position:0% never know Q in practice it's more or less<00:12:34.560> impossible<00:12:35.100> to<00:12:35.339> know<00:12:35.459> that<00:12:35.700> however<00:12:36.360> we 00:12:36.650 --> 00:12:36.660 align:start position:0% less impossible to know that however we 00:12:36.660 --> 00:12:37.970 align:start position:0% less impossible to know that however we will<00:12:36.839> see<00:12:37.079> that<00:12:37.260> this<00:12:37.440> actually<00:12:37.680> doesn't 00:12:37.970 --> 00:12:37.980 align:start position:0% will see that this actually doesn't 00:12:37.980 --> 00:12:39.650 align:start position:0% will see that this actually doesn't matter<00:12:38.279> once<00:12:38.820> we<00:12:38.940> write<00:12:39.060> out<00:12:39.240> this<00:12:39.420> problem 00:12:39.650 --> 00:12:39.660 align:start position:0% matter once we write out this problem 00:12:39.660 --> 00:12:43.430 align:start position:0% matter once we write out this problem okay<00:12:40.440> so<00:12:41.220> a<00:12:41.640> lot<00:12:41.820> of<00:12:42.060> setup<00:12:42.300> I'm<00:12:42.540> sorry 00:12:43.430 --> 00:12:43.440 align:start position:0% okay so a lot of setup I'm sorry 00:12:43.440 --> 00:12:44.870 align:start position:0% okay so a lot of setup I'm sorry um<00:12:43.500> but<00:12:43.740> this<00:12:43.920> is<00:12:43.980> kind<00:12:44.160> of<00:12:44.220> where<00:12:44.399> we<00:12:44.639> get<00:12:44.760> to 00:12:44.870 --> 00:12:44.880 align:start position:0% um but this is kind of where we get to 00:12:44.880 --> 00:12:46.370 align:start position:0% um but this is kind of where we get to so<00:12:45.180> what<00:12:45.420> is<00:12:45.540> the<00:12:45.600> resource<00:12:45.959> allocation 00:12:46.370 --> 00:12:46.380 align:start position:0% so what is the resource allocation 00:12:46.380 --> 00:12:49.009 align:start position:0% so what is the resource allocation problem<00:12:46.680> it<00:12:47.399> is<00:12:47.579> to<00:12:47.880> maximize<00:12:48.300> the<00:12:48.540> utility<00:12:48.839> of 00:12:49.009 --> 00:12:49.019 align:start position:0% problem it is to maximize the utility of 00:12:49.019 --> 00:12:51.769 align:start position:0% problem it is to maximize the utility of transactions<00:12:49.740> minus<00:12:50.579> the<00:12:50.820> loss<00:12:51.180> that<00:12:51.600> the 00:12:51.769 --> 00:12:51.779 align:start position:0% transactions minus the loss that the 00:12:51.779 --> 00:12:53.150 align:start position:0% transactions minus the loss that the network 00:12:53.150 --> 00:12:53.160 align:start position:0% network 00:12:53.160 --> 00:12:56.210 align:start position:0% network um<00:12:53.279> that<00:12:53.940> the<00:12:54.060> network<00:12:54.180> has<00:12:54.680> subject<00:12:55.680> to<00:12:55.920> kind 00:12:56.210 --> 00:12:56.220 align:start position:0% um that the network has subject to kind 00:12:56.220 --> 00:12:57.769 align:start position:0% um that the network has subject to kind of<00:12:56.279> the<00:12:56.399> resource<00:12:56.760> utilization<00:12:57.300> being 00:12:57.769 --> 00:12:57.779 align:start position:0% of the resource utilization being 00:12:57.779 --> 00:13:00.290 align:start position:0% of the resource utilization being defined<00:12:58.200> by<00:12:58.380> the<00:12:58.560> included<00:12:58.920> transactions<00:12:59.639> and 00:13:00.290 --> 00:13:00.300 align:start position:0% defined by the included transactions and 00:13:00.300 --> 00:13:02.810 align:start position:0% defined by the included transactions and the<00:13:00.540> transactions<00:13:01.079> being<00:13:01.320> allowable<00:13:01.800> so<00:13:02.639> this 00:13:02.810 --> 00:13:02.820 align:start position:0% the transactions being allowable so this 00:13:02.820 --> 00:13:05.030 align:start position:0% the transactions being allowable so this is<00:13:02.940> the<00:13:03.240> ideal<00:13:03.540> kind<00:13:03.839> of<00:13:03.959> best<00:13:04.200> case<00:13:04.440> scenario 00:13:05.030 --> 00:13:05.040 align:start position:0% is the ideal kind of best case scenario 00:13:05.040 --> 00:13:06.889 align:start position:0% is the ideal kind of best case scenario of<00:13:05.339> what<00:13:05.519> we<00:13:05.639> would<00:13:05.820> actually<00:13:06.000> like<00:13:06.360> to<00:13:06.600> solve 00:13:06.889 --> 00:13:06.899 align:start position:0% of what we would actually like to solve 00:13:06.899 --> 00:13:08.569 align:start position:0% of what we would actually like to solve for<00:13:07.320> all<00:13:07.500> the<00:13:07.620> reasons<00:13:07.860> I<00:13:08.040> mentioned<00:13:08.279> earlier 00:13:08.569 --> 00:13:08.579 align:start position:0% for all the reasons I mentioned earlier 00:13:08.579 --> 00:13:09.889 align:start position:0% for all the reasons I mentioned earlier this<00:13:08.940> is<00:13:09.060> not<00:13:09.240> something<00:13:09.420> that<00:13:09.660> we<00:13:09.839> can 00:13:09.889 --> 00:13:09.899 align:start position:0% this is not something that we can 00:13:09.899 --> 00:13:11.629 align:start position:0% this is not something that we can actually<00:13:10.139> solve<00:13:10.500> in<00:13:10.680> practice<00:13:10.920> but<00:13:11.279> we'll<00:13:11.399> see 00:13:11.629 --> 00:13:11.639 align:start position:0% actually solve in practice but we'll see 00:13:11.639 --> 00:13:13.190 align:start position:0% actually solve in practice but we'll see that<00:13:11.820> it<00:13:11.940> turns<00:13:12.180> out<00:13:12.300> to<00:13:12.480> be<00:13:12.600> a<00:13:12.779> very<00:13:12.899> useful 00:13:13.190 --> 00:13:13.200 align:start position:0% that it turns out to be a very useful 00:13:13.200 --> 00:13:14.629 align:start position:0% that it turns out to be a very useful starting<00:13:13.500> point 00:13:14.629 --> 00:13:14.639 align:start position:0% starting point 00:13:14.639 --> 00:13:16.129 align:start position:0% starting point um<00:13:14.700> and<00:13:14.880> again<00:13:15.000> this<00:13:15.360> is<00:13:15.480> because<00:13:15.660> you<00:13:16.019> know 00:13:16.129 --> 00:13:16.139 align:start position:0% um and again this is because you know 00:13:16.139 --> 00:13:18.230 align:start position:0% um and again this is because you know the<00:13:16.560> network<00:13:16.680> designer<00:13:17.220> doesn't<00:13:17.399> include<00:13:17.880> say 00:13:18.230 --> 00:13:18.240 align:start position:0% the network designer doesn't include say 00:13:18.240 --> 00:13:20.329 align:start position:0% the network designer doesn't include say which<00:13:18.480> transactions<00:13:19.079> are<00:13:19.260> included<00:13:19.680> Q<00:13:20.100> is 00:13:20.329 --> 00:13:20.339 align:start position:0% which transactions are included Q is 00:13:20.339 --> 00:13:21.949 align:start position:0% which transactions are included Q is unknowable<00:13:20.820> you<00:13:21.180> can't<00:13:21.240> partially<00:13:21.600> include 00:13:21.949 --> 00:13:21.959 align:start position:0% unknowable you can't partially include 00:13:21.959 --> 00:13:24.290 align:start position:0% unknowable you can't partially include transactions<00:13:22.620> all<00:13:22.920> of<00:13:23.040> these<00:13:23.279> issues<00:13:23.639> however 00:13:24.290 --> 00:13:24.300 align:start position:0% transactions all of these issues however 00:13:24.300 --> 00:13:26.210 align:start position:0% transactions all of these issues however we'll<00:13:24.540> see<00:13:24.720> that<00:13:24.839> we<00:13:24.959> can<00:13:25.079> actually<00:13:25.260> pull<00:13:25.680> from 00:13:26.210 --> 00:13:26.220 align:start position:0% we'll see that we can actually pull from 00:13:26.220 --> 00:13:28.490 align:start position:0% we'll see that we can actually pull from a<00:13:26.700> branch<00:13:27.060> of<00:13:27.180> math<00:13:27.360> called<00:13:27.600> convex<00:13:27.959> analysis 00:13:28.490 --> 00:13:28.500 align:start position:0% a branch of math called convex analysis 00:13:28.500 --> 00:13:30.829 align:start position:0% a branch of math called convex analysis and<00:13:28.740> specifically<00:13:29.100> Duality<00:13:29.579> Theory<00:13:30.120> to<00:13:30.660> take 00:13:30.829 --> 00:13:30.839 align:start position:0% and specifically Duality Theory to take 00:13:30.839 --> 00:13:33.350 align:start position:0% and specifically Duality Theory to take this<00:13:31.139> problem<00:13:31.320> and<00:13:32.040> turn<00:13:32.279> it<00:13:32.399> into<00:13:32.700> a<00:13:33.060> way<00:13:33.180> to 00:13:33.350 --> 00:13:33.360 align:start position:0% this problem and turn it into a way to 00:13:33.360 --> 00:13:36.230 align:start position:0% this problem and turn it into a way to set<00:13:33.540> prices<00:13:33.839> so<00:13:34.740> that<00:13:35.040> the<00:13:35.459> validators<00:13:36.000> and 00:13:36.230 --> 00:13:36.240 align:start position:0% set prices so that the validators and 00:13:36.240 --> 00:13:37.870 align:start position:0% set prices so that the validators and users<00:13:36.540> or<00:13:36.779> the<00:13:36.899> transaction<00:13:37.260> producers 00:13:37.870 --> 00:13:37.880 align:start position:0% users or the transaction producers 00:13:37.880 --> 00:13:40.790 align:start position:0% users or the transaction producers implicitly<00:13:38.880> solve<00:13:39.540> that<00:13:40.260> optimization 00:13:40.790 --> 00:13:40.800 align:start position:0% implicitly solve that optimization 00:13:40.800 --> 00:13:43.069 align:start position:0% implicitly solve that optimization problem<00:13:41.160> without<00:13:42.060> the<00:13:42.420> network<00:13:42.540> designer 00:13:43.069 --> 00:13:43.079 align:start position:0% problem without the network designer 00:13:43.079 --> 00:13:45.110 align:start position:0% problem without the network designer needing<00:13:43.380> to<00:13:43.500> really<00:13:43.620> do<00:13:43.860> anything<00:13:44.120> just 00:13:45.110 --> 00:13:45.120 align:start position:0% needing to really do anything just 00:13:45.120 --> 00:13:48.110 align:start position:0% needing to really do anything just update<00:13:45.720> prices<00:13:45.959> in<00:13:46.320> a<00:13:46.440> very<00:13:46.500> simple<00:13:46.680> way 00:13:48.110 --> 00:13:48.120 align:start position:0% update prices in a very simple way 00:13:48.120 --> 00:13:50.690 align:start position:0% update prices in a very simple way all<00:13:48.540> right<00:13:48.720> so<00:13:49.079> the<00:13:49.260> the<00:13:49.519> 30-second<00:13:50.519> version 00:13:50.690 --> 00:13:50.700 align:start position:0% all right so the the 30-second version 00:13:50.700 --> 00:13:52.430 align:start position:0% all right so the the 30-second version of<00:13:50.880> Duality<00:13:51.360> theory<00:13:51.720> is<00:13:51.959> essentially<00:13:52.260> it 00:13:52.430 --> 00:13:52.440 align:start position:0% of Duality theory is essentially it 00:13:52.440 --> 00:13:54.829 align:start position:0% of Duality theory is essentially it allows<00:13:52.800> us<00:13:52.980> a<00:13:53.399> way<00:13:53.519> to<00:13:53.880> relax<00:13:54.060> constraints 00:13:54.829 --> 00:13:54.839 align:start position:0% allows us a way to relax constraints 00:13:54.839 --> 00:13:57.590 align:start position:0% allows us a way to relax constraints into<00:13:55.139> penalties<00:13:55.740> so<00:13:56.459> I<00:13:56.820> can<00:13:56.940> say<00:13:57.120> that<00:13:57.360> you 00:13:57.590 --> 00:13:57.600 align:start position:0% into penalties so I can say that you 00:13:57.600 --> 00:13:59.870 align:start position:0% into penalties so I can say that you actually<00:13:57.720> don't<00:13:58.139> have<00:13:58.440> to<00:13:58.860> satisfy<00:13:59.639> this 00:13:59.870 --> 00:13:59.880 align:start position:0% actually don't have to satisfy this 00:13:59.880 --> 00:14:01.790 align:start position:0% actually don't have to satisfy this constraint<00:14:00.240> you<00:14:00.959> just<00:14:01.079> have<00:14:01.200> to<00:14:01.320> pay<00:14:01.500> for 00:14:01.790 --> 00:14:01.800 align:start position:0% constraint you just have to pay for 00:14:01.800 --> 00:14:03.650 align:start position:0% constraint you just have to pay for every<00:14:01.980> unit<00:14:02.160> of<00:14:02.459> violation 00:14:03.650 --> 00:14:03.660 align:start position:0% every unit of violation 00:14:03.660 --> 00:14:06.710 align:start position:0% every unit of violation and<00:14:04.200> this<00:14:04.320> allows<00:14:04.680> us<00:14:04.920> to<00:14:05.279> take<00:14:05.579> Y<00:14:06.240> which<00:14:06.540> is 00:14:06.710 --> 00:14:06.720 align:start position:0% and this allows us to take Y which is 00:14:06.720 --> 00:14:08.210 align:start position:0% and this allows us to take Y which is what<00:14:06.959> the<00:14:07.139> network<00:14:07.260> designer<00:14:07.800> cares<00:14:08.100> about 00:14:08.210 --> 00:14:08.220 align:start position:0% what the network designer cares about 00:14:08.220 --> 00:14:09.889 align:start position:0% what the network designer cares about that's<00:14:08.519> the<00:14:08.760> throughput 00:14:09.889 --> 00:14:09.899 align:start position:0% that's the throughput 00:14:09.899 --> 00:14:13.069 align:start position:0% that's the throughput and<00:14:10.440> decouple<00:14:10.980> it<00:14:11.160> from<00:14:11.820> the<00:14:12.360> transactions 00:14:13.069 --> 00:14:13.079 align:start position:0% and decouple it from the transactions 00:14:13.079 --> 00:14:15.530 align:start position:0% and decouple it from the transactions that<00:14:13.620> uh<00:14:14.160> are<00:14:14.519> actually<00:14:14.700> included<00:14:15.180> in<00:14:15.420> the 00:14:15.530 --> 00:14:15.540 align:start position:0% that uh are actually included in the 00:14:15.540 --> 00:14:17.269 align:start position:0% that uh are actually included in the block<00:14:15.660> there's<00:14:16.260> just<00:14:16.500> going<00:14:16.560> to<00:14:16.680> be<00:14:16.740> a<00:14:16.920> penalty 00:14:17.269 --> 00:14:17.279 align:start position:0% block there's just going to be a penalty 00:14:17.279 --> 00:14:19.069 align:start position:0% block there's just going to be a penalty for<00:14:17.700> these<00:14:18.060> two<00:14:18.180> things<00:14:18.360> not<00:14:18.660> matching 00:14:19.069 --> 00:14:19.079 align:start position:0% for these two things not matching 00:14:19.079 --> 00:14:22.009 align:start position:0% for these two things not matching exactly<00:14:19.620> however<00:14:20.579> what<00:14:21.300> strong<00:14:21.480> Duality 00:14:22.009 --> 00:14:22.019 align:start position:0% exactly however what strong Duality 00:14:22.019 --> 00:14:24.170 align:start position:0% exactly however what strong Duality tells<00:14:22.440> us<00:14:22.560> is<00:14:22.980> that<00:14:23.160> if<00:14:23.279> we<00:14:23.399> correctly<00:14:23.760> set<00:14:23.940> the 00:14:24.170 --> 00:14:24.180 align:start position:0% tells us is that if we correctly set the 00:14:24.180 --> 00:14:25.970 align:start position:0% tells us is that if we correctly set the penalty<00:14:24.600> this<00:14:25.019> penalty<00:14:25.380> being<00:14:25.560> the<00:14:25.860> prices 00:14:25.970 --> 00:14:25.980 align:start position:0% penalty this penalty being the prices 00:14:25.980 --> 00:14:28.069 align:start position:0% penalty this penalty being the prices then<00:14:26.820> the<00:14:27.000> Dual<00:14:27.120> problem<00:14:27.420> is<00:14:27.720> going<00:14:27.899> to<00:14:28.019> be 00:14:28.069 --> 00:14:28.079 align:start position:0% then the Dual problem is going to be 00:14:28.079 --> 00:14:29.750 align:start position:0% then the Dual problem is going to be equivalent<00:14:28.500> to<00:14:28.680> their<00:14:28.800> original<00:14:28.980> the 00:14:29.750 --> 00:14:29.760 align:start position:0% equivalent to their original the 00:14:29.760 --> 00:14:31.370 align:start position:0% equivalent to their original the original<00:14:29.940> being<00:14:30.300> this<00:14:30.600> problem<00:14:30.899> which<00:14:31.260> is 00:14:31.370 --> 00:14:31.380 align:start position:0% original being this problem which is 00:14:31.380 --> 00:14:33.590 align:start position:0% original being this problem which is what<00:14:31.560> we<00:14:31.740> actually<00:14:31.860> want<00:14:32.160> to<00:14:32.279> solve<00:14:32.579> and<00:14:33.360> these 00:14:33.590 --> 00:14:33.600 align:start position:0% what we actually want to solve and these 00:14:33.600 --> 00:14:34.970 align:start position:0% what we actually want to solve and these two<00:14:33.720> utilizations<00:14:34.260> are<00:14:34.500> going<00:14:34.620> to<00:14:34.740> be<00:14:34.800> equal 00:14:34.970 --> 00:14:34.980 align:start position:0% two utilizations are going to be equal 00:14:34.980 --> 00:14:36.170 align:start position:0% two utilizations are going to be equal and<00:14:35.459> they're<00:14:35.579> going<00:14:35.700> to<00:14:35.820> have<00:14:35.880> the<00:14:36.060> same 00:14:36.170 --> 00:14:36.180 align:start position:0% and they're going to have the same 00:14:36.180 --> 00:14:38.810 align:start position:0% and they're going to have the same optimal<00:14:36.600> value<00:14:36.779> so<00:14:37.560> again<00:14:37.680> this<00:14:38.040> tells<00:14:38.339> us<00:14:38.399> we 00:14:38.810 --> 00:14:38.820 align:start position:0% optimal value so again this tells us we 00:14:38.820 --> 00:14:41.150 align:start position:0% optimal value so again this tells us we correctly<00:14:39.180> set<00:14:39.420> the<00:14:39.600> prices<00:14:39.779> and<00:14:40.620> we<00:14:40.800> solve 00:14:41.150 --> 00:14:41.160 align:start position:0% correctly set the prices and we solve 00:14:41.160 --> 00:14:42.889 align:start position:0% correctly set the prices and we solve this<00:14:41.339> problem<00:14:41.639> without<00:14:42.060> you<00:14:42.420> know<00:14:42.540> having<00:14:42.720> to 00:14:42.889 --> 00:14:42.899 align:start position:0% this problem without you know having to 00:14:42.899 --> 00:14:44.629 align:start position:0% this problem without you know having to know<00:14:43.079> q<00:14:43.380> without<00:14:43.860> caring<00:14:44.279> about<00:14:44.399> the 00:14:44.629 --> 00:14:44.639 align:start position:0% know q without caring about the 00:14:44.639 --> 00:14:46.490 align:start position:0% know q without caring about the fractional<00:14:45.000> transactions<00:14:45.660> without<00:14:46.079> all<00:14:46.380> the 00:14:46.490 --> 00:14:46.500 align:start position:0% fractional transactions without all the 00:14:46.500 --> 00:14:48.650 align:start position:0% fractional transactions without all the things<00:14:46.680> that<00:14:46.920> I<00:14:47.040> mentioned<00:14:47.279> are<00:14:47.399> issues<00:14:47.880> all 00:14:48.650 --> 00:14:48.660 align:start position:0% things that I mentioned are issues all 00:14:48.660 --> 00:14:50.750 align:start position:0% things that I mentioned are issues all right<00:14:48.839> so<00:14:49.260> kind<00:14:49.920> of<00:14:50.040> turn<00:14:50.160> the<00:14:50.339> crank<00:14:50.459> of<00:14:50.639> the 00:14:50.750 --> 00:14:50.760 align:start position:0% right so kind of turn the crank of the 00:14:50.760 --> 00:14:52.790 align:start position:0% right so kind of turn the crank of the math<00:14:50.880> a<00:14:51.060> little<00:14:51.180> bit<00:14:51.300> and<00:14:51.720> you<00:14:51.899> can<00:14:52.019> decompose 00:14:52.790 --> 00:14:52.800 align:start position:0% math a little bit and you can decompose 00:14:52.800 --> 00:14:56.329 align:start position:0% math a little bit and you can decompose this<00:14:53.579> uh<00:14:54.120> dual<00:14:54.660> problem<00:14:54.959> so<00:14:55.680> the<00:14:55.860> Dual<00:14:56.100> problem 00:14:56.329 --> 00:14:56.339 align:start position:0% this uh dual problem so the Dual problem 00:14:56.339 --> 00:14:58.069 align:start position:0% this uh dual problem so the Dual problem is<00:14:56.579> to<00:14:56.820> maximize<00:14:57.180> this<00:14:57.480> thing<00:14:57.600> or<00:14:57.779> sorry<00:14:57.899> to 00:14:58.069 --> 00:14:58.079 align:start position:0% is to maximize this thing or sorry to 00:14:58.079 --> 00:14:59.930 align:start position:0% is to maximize this thing or sorry to minimize<00:14:58.440> this<00:14:58.680> thing<00:14:58.860> into<00:14:59.459> a<00:14:59.820> network 00:14:59.930 --> 00:14:59.940 align:start position:0% minimize this thing into a network 00:14:59.940 --> 00:15:02.689 align:start position:0% minimize this thing into a network problem<00:15:00.240> and<00:15:00.600> a<00:15:00.720> block<00:15:00.839> building<00:15:01.079> problem<00:15:01.699> and 00:15:02.689 --> 00:15:02.699 align:start position:0% problem and a block building problem and 00:15:02.699 --> 00:15:04.490 align:start position:0% problem and a block building problem and P<00:15:03.120> is<00:15:03.360> going<00:15:03.540> to<00:15:03.600> be<00:15:03.720> the<00:15:03.899> Dual<00:15:04.079> variable 00:15:04.490 --> 00:15:04.500 align:start position:0% P is going to be the Dual variable 00:15:04.500 --> 00:15:06.769 align:start position:0% P is going to be the Dual variable that's<00:15:04.920> going<00:15:05.160> to<00:15:05.279> connect<00:15:05.660> these<00:15:06.660> two 00:15:06.769 --> 00:15:06.779 align:start position:0% that's going to connect these two 00:15:06.779 --> 00:15:09.170 align:start position:0% that's going to connect these two problems<00:15:07.380> together<00:15:07.560> so<00:15:08.279> again<00:15:08.399> those<00:15:08.820> are<00:15:09.000> the 00:15:09.170 --> 00:15:09.180 align:start position:0% problems together so again those are the 00:15:09.180 --> 00:15:11.329 align:start position:0% problems together so again those are the prices<00:15:09.300> and<00:15:09.839> the<00:15:10.320> prices<00:15:10.500> are<00:15:10.800> essentially<00:15:11.100> a 00:15:11.329 --> 00:15:11.339 align:start position:0% prices and the prices are essentially a 00:15:11.339 --> 00:15:13.250 align:start position:0% prices and the prices are essentially a penalty<00:15:11.699> that<00:15:11.880> we<00:15:12.060> pay<00:15:12.180> per<00:15:12.540> unit<00:15:12.720> violation 00:15:13.250 --> 00:15:13.260 align:start position:0% penalty that we pay per unit violation 00:15:13.260 --> 00:15:15.769 align:start position:0% penalty that we pay per unit violation of<00:15:13.500> this<00:15:13.620> constraint<00:15:14.459> this<00:15:15.240> first<00:15:15.420> term<00:15:15.600> here 00:15:15.769 --> 00:15:15.779 align:start position:0% of this constraint this first term here 00:15:15.779 --> 00:15:17.389 align:start position:0% of this constraint this first term here is<00:15:15.899> actually<00:15:16.139> easy<00:15:16.380> to<00:15:16.620> evaluate<00:15:17.040> you'll 00:15:17.389 --> 00:15:17.399 align:start position:0% is actually easy to evaluate you'll 00:15:17.399 --> 00:15:18.710 align:start position:0% is actually easy to evaluate you'll probably<00:15:17.519> just<00:15:17.699> have<00:15:17.820> to<00:15:18.000> trust<00:15:18.240> me<00:15:18.360> on<00:15:18.540> this 00:15:18.710 --> 00:15:18.720 align:start position:0% probably just have to trust me on this 00:15:18.720 --> 00:15:20.509 align:start position:0% probably just have to trust me on this it's<00:15:19.260> this<00:15:19.500> object<00:15:19.980> called<00:15:20.220> the<00:15:20.339> central 00:15:20.509 --> 00:15:20.519 align:start position:0% it's this object called the central 00:15:20.519 --> 00:15:22.370 align:start position:0% it's this object called the central conjugate<00:15:21.180> it's<00:15:21.540> something<00:15:21.779> that<00:15:21.959> we<00:15:22.139> have<00:15:22.260> in 00:15:22.370 --> 00:15:22.380 align:start position:0% conjugate it's something that we have in 00:15:22.380 --> 00:15:24.050 align:start position:0% conjugate it's something that we have in closed<00:15:22.800> form<00:15:22.980> and<00:15:23.579> that<00:15:23.699> means<00:15:23.940> that 00:15:24.050 --> 00:15:24.060 align:start position:0% closed form and that means that 00:15:24.060 --> 00:15:26.629 align:start position:0% closed form and that means that essentially<00:15:24.420> this<00:15:24.600> can<00:15:24.779> be<00:15:24.839> run<00:15:25.019> on<00:15:25.260> chain 00:15:26.629 --> 00:15:26.639 align:start position:0% essentially this can be run on chain 00:15:26.639 --> 00:15:28.370 align:start position:0% essentially this can be run on chain however<00:15:27.060> the<00:15:27.360> second<00:15:27.480> term<00:15:27.779> is<00:15:28.019> a<00:15:28.199> little<00:15:28.260> bit 00:15:28.370 --> 00:15:28.380 align:start position:0% however the second term is a little bit 00:15:28.380 --> 00:15:29.990 align:start position:0% however the second term is a little bit more<00:15:28.620> interesting<00:15:28.980> so<00:15:29.220> let's<00:15:29.399> look<00:15:29.579> at<00:15:29.760> it<00:15:29.880> in 00:15:29.990 --> 00:15:30.000 align:start position:0% more interesting so let's look at it in 00:15:30.000 --> 00:15:32.030 align:start position:0% more interesting so let's look at it in a<00:15:30.180> little<00:15:30.300> bit<00:15:30.420> more<00:15:30.600> detail<00:15:31.079> what<00:15:31.800> does<00:15:31.920> the 00:15:32.030 --> 00:15:32.040 align:start position:0% a little bit more detail what does the 00:15:32.040 --> 00:15:33.650 align:start position:0% a little bit more detail what does the second<00:15:32.160> term<00:15:32.399> actually<00:15:32.699> saying<00:15:33.240> well<00:15:33.420> it's 00:15:33.650 --> 00:15:33.660 align:start position:0% second term actually saying well it's 00:15:33.660 --> 00:15:36.530 align:start position:0% second term actually saying well it's saying<00:15:34.019> maximize<00:15:34.920> the<00:15:35.339> utility<00:15:35.699> minus<00:15:36.420> the 00:15:36.530 --> 00:15:36.540 align:start position:0% saying maximize the utility minus the 00:15:36.540 --> 00:15:38.810 align:start position:0% saying maximize the utility minus the cost<00:15:36.720> so<00:15:36.959> this<00:15:37.199> is<00:15:37.260> the<00:15:37.380> net<00:15:37.560> utility<00:15:37.980> subject 00:15:38.810 --> 00:15:38.820 align:start position:0% cost so this is the net utility subject 00:15:38.820 --> 00:15:40.310 align:start position:0% cost so this is the net utility subject to<00:15:39.000> the<00:15:39.180> transactions<00:15:39.779> that<00:15:39.959> we<00:15:40.079> can<00:15:40.199> actually 00:15:40.310 --> 00:15:40.320 align:start position:0% to the transactions that we can actually 00:15:40.320 --> 00:15:42.590 align:start position:0% to the transactions that we can actually include<00:15:40.800> this<00:15:41.699> actually<00:15:42.060> has<00:15:42.300> the<00:15:42.480> same 00:15:42.590 --> 00:15:42.600 align:start position:0% include this actually has the same 00:15:42.600 --> 00:15:44.870 align:start position:0% include this actually has the same optimal<00:15:43.079> value<00:15:43.320> if<00:15:43.620> we<00:15:43.800> just<00:15:43.920> use<00:15:44.100> S<00:15:44.399> instead 00:15:44.870 --> 00:15:44.880 align:start position:0% optimal value if we just use S instead 00:15:44.880 --> 00:15:48.590 align:start position:0% optimal value if we just use S instead of<00:15:45.000> the<00:15:45.839> convex<00:15:46.199> Hall<00:15:46.380> of<00:15:46.560> s<00:15:47.060> and<00:15:48.060> this<00:15:48.480> is 00:15:48.590 --> 00:15:48.600 align:start position:0% of the convex Hall of s and this is 00:15:48.600 --> 00:15:50.210 align:start position:0% of the convex Hall of s and this is exactly<00:15:49.019> the<00:15:49.199> problem<00:15:49.380> that<00:15:49.680> is<00:15:49.800> solved<00:15:50.100> by 00:15:50.210 --> 00:15:50.220 align:start position:0% exactly the problem that is solved by 00:15:50.220 --> 00:15:52.189 align:start position:0% exactly the problem that is solved by the<00:15:50.339> block<00:15:50.519> producers<00:15:51.120> so<00:15:51.720> what<00:15:51.899> does<00:15:52.079> this 00:15:52.189 --> 00:15:52.199 align:start position:0% the block producers so what does this 00:15:52.199 --> 00:15:53.810 align:start position:0% the block producers so what does this mean<00:15:52.320> the<00:15:52.560> network<00:15:52.680> never<00:15:52.980> has<00:15:53.220> to<00:15:53.399> solve<00:15:53.699> this 00:15:53.810 --> 00:15:53.820 align:start position:0% mean the network never has to solve this 00:15:53.820 --> 00:15:55.670 align:start position:0% mean the network never has to solve this problem<00:15:54.060> it<00:15:54.480> could<00:15:54.600> just<00:15:54.779> observe<00:15:55.320> from<00:15:55.500> the 00:15:55.670 --> 00:15:55.680 align:start position:0% problem it could just observe from the 00:15:55.680 --> 00:15:57.530 align:start position:0% problem it could just observe from the previous<00:15:55.800> block<00:15:56.279> which<00:15:56.699> transactions<00:15:57.300> were 00:15:57.530 --> 00:15:57.540 align:start position:0% previous block which transactions were 00:15:57.540 --> 00:15:59.509 align:start position:0% previous block which transactions were actually<00:15:57.660> included<00:15:58.260> and<00:15:59.040> then<00:15:59.160> it<00:15:59.279> kind<00:15:59.459> of 00:15:59.509 --> 00:15:59.519 align:start position:0% actually included and then it kind of 00:15:59.519 --> 00:16:01.670 align:start position:0% actually included and then it kind of gets<00:15:59.820> the<00:15:59.880> solution<00:16:00.180> of<00:16:00.420> this<00:16:00.540> for<00:16:00.779> free<00:16:00.959> from 00:16:01.670 --> 00:16:01.680 align:start position:0% gets the solution of this for free from 00:16:01.680 --> 00:16:03.590 align:start position:0% gets the solution of this for free from kind<00:16:01.920> of<00:16:02.040> you<00:16:02.220> know<00:16:02.339> the<00:16:02.579> decentralized<00:16:03.240> block 00:16:03.590 --> 00:16:03.600 align:start position:0% kind of you know the decentralized block 00:16:03.600 --> 00:16:05.629 align:start position:0% kind of you know the decentralized block Builders<00:16:04.079> so<00:16:04.500> what<00:16:04.620> do<00:16:04.740> we<00:16:04.860> get<00:16:04.920> at<00:16:05.040> optimality 00:16:05.629 --> 00:16:05.639 align:start position:0% Builders so what do we get at optimality 00:16:05.639 --> 00:16:07.970 align:start position:0% Builders so what do we get at optimality well<00:16:06.120> if<00:16:06.420> we<00:16:06.540> assume<00:16:06.899> the<00:16:07.079> prices<00:16:07.320> are<00:16:07.800> set 00:16:07.970 --> 00:16:07.980 align:start position:0% well if we assume the prices are set 00:16:07.980 --> 00:16:09.670 align:start position:0% well if we assume the prices are set correctly<00:16:08.399> so<00:16:08.639> that's<00:16:08.820> going<00:16:09.000> to<00:16:09.120> be<00:16:09.180> P<00:16:09.360> star 00:16:09.670 --> 00:16:09.680 align:start position:0% correctly so that's going to be P star 00:16:09.680 --> 00:16:12.470 align:start position:0% correctly so that's going to be P star and<00:16:10.680> then<00:16:10.800> the<00:16:11.100> block<00:16:11.220> Builders<00:16:11.760> use<00:16:12.180> those 00:16:12.470 --> 00:16:12.480 align:start position:0% and then the block Builders use those 00:16:12.480 --> 00:16:14.689 align:start position:0% and then the block Builders use those prices<00:16:12.720> to<00:16:13.260> include<00:16:13.620> essentially<00:16:14.399> the 00:16:14.689 --> 00:16:14.699 align:start position:0% prices to include essentially the 00:16:14.699 --> 00:16:17.389 align:start position:0% prices to include essentially the transactions<00:16:15.360> that<00:16:15.600> are<00:16:15.720> optimal<00:16:16.620> then<00:16:17.160> what 00:16:17.389 --> 00:16:17.399 align:start position:0% transactions that are optimal then what 00:16:17.399 --> 00:16:19.670 align:start position:0% transactions that are optimal then what do<00:16:17.579> we<00:16:17.639> get<00:16:17.760> well<00:16:18.000> we<00:16:18.240> get<00:16:18.360> that<00:16:18.600> the<00:16:19.019> uh 00:16:19.670 --> 00:16:19.680 align:start position:0% do we get well we get that the uh 00:16:19.680 --> 00:16:21.829 align:start position:0% do we get well we get that the uh resource<00:16:20.160> utilization<00:16:20.639> of<00:16:20.940> the<00:16:21.060> network<00:16:21.240> is 00:16:21.829 --> 00:16:21.839 align:start position:0% resource utilization of the network is 00:16:21.839 --> 00:16:24.530 align:start position:0% resource utilization of the network is exactly<00:16:22.320> equal<00:16:22.620> to<00:16:23.100> that<00:16:23.220> of<00:16:23.399> the<00:16:23.579> block<00:16:23.760> again 00:16:24.530 --> 00:16:24.540 align:start position:0% exactly equal to that of the block again 00:16:24.540 --> 00:16:26.990 align:start position:0% exactly equal to that of the block again that's<00:16:25.019> back<00:16:25.320> to<00:16:25.980> what<00:16:26.220> I<00:16:26.399> was<00:16:26.459> saying<00:16:26.699> earlier 00:16:26.990 --> 00:16:27.000 align:start position:0% that's back to what I was saying earlier 00:16:27.000 --> 00:16:29.150 align:start position:0% that's back to what I was saying earlier is<00:16:27.600> that<00:16:27.839> we<00:16:28.139> essentially<00:16:28.440> get<00:16:28.680> that<00:16:28.920> this 00:16:29.150 --> 00:16:29.160 align:start position:0% is that we essentially get that this 00:16:29.160 --> 00:16:32.210 align:start position:0% is that we essentially get that this constraint<00:16:29.579> does<00:16:29.940> hold<00:16:30.180> an<00:16:30.420> optimality<00:16:30.980> and<00:16:31.980> Y 00:16:32.210 --> 00:16:32.220 align:start position:0% constraint does hold an optimality and Y 00:16:32.220 --> 00:16:34.189 align:start position:0% constraint does hold an optimality and Y satisfies<00:16:32.880> this<00:16:33.180> which<00:16:33.480> we<00:16:33.660> can<00:16:33.779> look<00:16:33.899> in<00:16:34.019> a 00:16:34.189 --> 00:16:34.199 align:start position:0% satisfies this which we can look in a 00:16:34.199 --> 00:16:36.290 align:start position:0% satisfies this which we can look in a little<00:16:34.320> bit<00:16:34.440> more<00:16:34.560> detail 00:16:36.290 --> 00:16:36.300 align:start position:0% little bit more detail 00:16:36.300 --> 00:16:38.329 align:start position:0% little bit more detail um<00:16:36.420> what<00:16:37.079> this<00:16:37.199> means<00:16:37.560> is<00:16:37.800> essentially<00:16:38.160> the 00:16:38.329 --> 00:16:38.339 align:start position:0% um what this means is essentially the 00:16:38.339 --> 00:16:40.970 align:start position:0% um what this means is essentially the prices<00:16:38.579> that<00:16:39.240> minimize<00:16:39.720> G<00:16:40.019> so<00:16:40.560> this<00:16:40.740> is<00:16:40.860> the 00:16:40.970 --> 00:16:40.980 align:start position:0% prices that minimize G so this is the 00:16:40.980 --> 00:16:43.069 align:start position:0% prices that minimize G so this is the Dual<00:16:41.160> problem<00:16:41.459> charge<00:16:42.420> the<00:16:42.660> transaction 00:16:43.069 --> 00:16:43.079 align:start position:0% Dual problem charge the transaction 00:16:43.079 --> 00:16:45.290 align:start position:0% Dual problem charge the transaction producers<00:16:43.680> exactly<00:16:44.579> the<00:16:44.759> marginal<00:16:45.120> cost 00:16:45.290 --> 00:16:45.300 align:start position:0% producers exactly the marginal cost 00:16:45.300 --> 00:16:47.509 align:start position:0% producers exactly the marginal cost faced<00:16:45.779> by<00:16:45.839> the<00:16:46.019> network<00:16:46.139> so<00:16:46.920> if<00:16:47.040> you<00:16:47.160> set<00:16:47.339> the 00:16:47.509 --> 00:16:47.519 align:start position:0% faced by the network so if you set the 00:16:47.519 --> 00:16:49.910 align:start position:0% faced by the network so if you set the prices<00:16:47.699> optimally<00:16:48.420> for<00:16:49.259> whatever<00:16:49.440> loss 00:16:49.910 --> 00:16:49.920 align:start position:0% prices optimally for whatever loss 00:16:49.920 --> 00:16:51.829 align:start position:0% prices optimally for whatever loss function<00:16:50.100> that<00:16:50.279> you<00:16:50.459> define<00:16:50.639> the<00:16:51.480> marginal 00:16:51.829 --> 00:16:51.839 align:start position:0% function that you define the marginal 00:16:51.839 --> 00:16:54.290 align:start position:0% function that you define the marginal cost<00:16:52.139> of<00:16:52.440> like<00:16:52.680> using<00:16:53.279> more<00:16:53.459> of<00:16:53.579> that<00:16:53.759> resource 00:16:54.290 --> 00:16:54.300 align:start position:0% cost of like using more of that resource 00:16:54.300 --> 00:16:56.569 align:start position:0% cost of like using more of that resource is<00:16:54.899> exactly<00:16:55.320> what<00:16:55.560> the<00:16:55.680> price<00:16:55.860> is<00:16:56.100> that<00:16:56.399> you 00:16:56.569 --> 00:16:56.579 align:start position:0% is exactly what the price is that you 00:16:56.579 --> 00:16:58.910 align:start position:0% is exactly what the price is that you charge<00:16:56.820> furthermore 00:16:58.910 --> 00:16:58.920 align:start position:0% charge furthermore 00:16:58.920 --> 00:17:00.710 align:start position:0% charge furthermore these<00:16:59.579> prices<00:16:59.699> are<00:17:00.060> going<00:17:00.180> to<00:17:00.300> be<00:17:00.360> the<00:17:00.480> ones 00:17:00.710 --> 00:17:00.720 align:start position:0% these prices are going to be the ones 00:17:00.720 --> 00:17:02.030 align:start position:0% these prices are going to be the ones that<00:17:00.899> incentivize<00:17:01.440> the<00:17:01.680> transaction 00:17:02.030 --> 00:17:02.040 align:start position:0% that incentivize the transaction 00:17:02.040 --> 00:17:04.370 align:start position:0% that incentivize the transaction producers<00:17:02.639> to<00:17:03.180> include<00:17:03.480> transactions<00:17:04.140> that 00:17:04.370 --> 00:17:04.380 align:start position:0% producers to include transactions that 00:17:04.380 --> 00:17:07.069 align:start position:0% producers to include transactions that maximize<00:17:04.799> welfare<00:17:05.280> generated<00:17:05.900> minus<00:17:06.900> the 00:17:07.069 --> 00:17:07.079 align:start position:0% maximize welfare generated minus the 00:17:07.079 --> 00:17:08.870 align:start position:0% maximize welfare generated minus the loss<00:17:07.319> incurred<00:17:07.679> by<00:17:07.799> the<00:17:07.919> network<00:17:08.040> so<00:17:08.640> that's 00:17:08.870 --> 00:17:08.880 align:start position:0% loss incurred by the network so that's 00:17:08.880 --> 00:17:11.030 align:start position:0% loss incurred by the network so that's back<00:17:09.299> to<00:17:09.600> uh<00:17:09.839> that<00:17:10.199> original<00:17:10.319> optimization 00:17:11.030 --> 00:17:11.040 align:start position:0% back to uh that original optimization 00:17:11.040 --> 00:17:13.309 align:start position:0% back to uh that original optimization problem<00:17:11.339> that<00:17:11.699> we<00:17:11.819> saw<00:17:12.059> you<00:17:12.720> correctly<00:17:13.140> set 00:17:13.309 --> 00:17:13.319 align:start position:0% problem that we saw you correctly set 00:17:13.319 --> 00:17:15.350 align:start position:0% problem that we saw you correctly set prices<00:17:13.620> you<00:17:14.040> solve<00:17:14.339> that<00:17:14.520> problem<00:17:14.760> the 00:17:15.350 --> 00:17:15.360 align:start position:0% prices you solve that problem the 00:17:15.360 --> 00:17:16.610 align:start position:0% prices you solve that problem the network<00:17:15.480> designer<00:17:16.020> doesn't<00:17:16.199> need<00:17:16.380> to<00:17:16.500> know 00:17:16.610 --> 00:17:16.620 align:start position:0% network designer doesn't need to know 00:17:16.620 --> 00:17:18.829 align:start position:0% network designer doesn't need to know the<00:17:16.799> utilities<00:17:17.160> or<00:17:17.400> anything<00:17:17.579> like<00:17:17.880> that<00:17:18.120> all 00:17:18.829 --> 00:17:18.839 align:start position:0% the utilities or anything like that all 00:17:18.839 --> 00:17:21.169 align:start position:0% the utilities or anything like that all right<00:17:18.959> so<00:17:19.380> okay<00:17:19.799> that's<00:17:20.040> great<00:17:20.339> I<00:17:21.059> still 00:17:21.169 --> 00:17:21.179 align:start position:0% right so okay that's great I still 00:17:21.179 --> 00:17:22.370 align:start position:0% right so okay that's great I still haven't<00:17:21.299> told<00:17:21.540> you<00:17:21.660> how<00:17:21.839> to<00:17:21.959> choose<00:17:22.199> prices 00:17:22.370 --> 00:17:22.380 align:start position:0% haven't told you how to choose prices 00:17:22.380 --> 00:17:24.350 align:start position:0% haven't told you how to choose prices I've<00:17:22.860> just<00:17:23.040> kind<00:17:23.160> of<00:17:23.280> talked<00:17:23.640> around<00:17:23.760> this<00:17:24.059> for 00:17:24.350 --> 00:17:24.360 align:start position:0% I've just kind of talked around this for 00:17:24.360 --> 00:17:25.909 align:start position:0% I've just kind of talked around this for a<00:17:24.419> while<00:17:24.540> so<00:17:24.959> how<00:17:25.140> do<00:17:25.260> you<00:17:25.380> actually<00:17:25.500> do<00:17:25.740> this 00:17:25.909 --> 00:17:25.919 align:start position:0% a while so how do you actually do this 00:17:25.919 --> 00:17:28.370 align:start position:0% a while so how do you actually do this well<00:17:26.579> we<00:17:26.819> can<00:17:26.939> compute<00:17:27.240> the<00:17:27.360> gradient<00:17:27.720> exactly 00:17:28.370 --> 00:17:28.380 align:start position:0% well we can compute the gradient exactly 00:17:28.380 --> 00:17:29.570 align:start position:0% well we can compute the gradient exactly and 00:17:29.570 --> 00:17:29.580 align:start position:0% and 00:17:29.580 --> 00:17:31.850 align:start position:0% and um<00:17:29.940> what<00:17:30.600> is<00:17:30.720> this<00:17:30.900> well<00:17:31.200> essentially<00:17:31.620> the 00:17:31.850 --> 00:17:31.860 align:start position:0% um what is this well essentially the 00:17:31.860 --> 00:17:34.610 align:start position:0% um what is this well essentially the network<00:17:31.980> can<00:17:32.280> determine<00:17:32.760> this<00:17:33.540> y<00:17:33.720> star<00:17:33.960> and<00:17:34.500> I 00:17:34.610 --> 00:17:34.620 align:start position:0% network can determine this y star and I 00:17:34.620 --> 00:17:35.510 align:start position:0% network can determine this y star and I said<00:17:34.799> earlier<00:17:35.100> that<00:17:35.280> this<00:17:35.460> is 00:17:35.510 --> 00:17:35.520 align:start position:0% said earlier that this is 00:17:35.520 --> 00:17:37.250 align:start position:0% said earlier that this is computationally<00:17:36.059> easy 00:17:37.250 --> 00:17:37.260 align:start position:0% computationally easy 00:17:37.260 --> 00:17:40.250 align:start position:0% computationally easy then<00:17:37.919> this<00:17:38.280> x-star<00:17:38.760> at<00:17:39.419> some<00:17:39.660> current<00:17:39.900> price 00:17:40.250 --> 00:17:40.260 align:start position:0% then this x-star at some current price 00:17:40.260 --> 00:17:42.650 align:start position:0% then this x-star at some current price is<00:17:41.039> found<00:17:41.220> by<00:17:41.460> observing<00:17:41.820> the<00:17:42.059> transactions 00:17:42.650 --> 00:17:42.660 align:start position:0% is found by observing the transactions 00:17:42.660 --> 00:17:44.810 align:start position:0% is found by observing the transactions in<00:17:43.020> the<00:17:43.140> previous<00:17:43.260> block<00:17:43.740> so<00:17:44.280> then<00:17:44.400> all<00:17:44.520> we<00:17:44.640> do 00:17:44.810 --> 00:17:44.820 align:start position:0% in the previous block so then all we do 00:17:44.820 --> 00:17:46.430 align:start position:0% in the previous block so then all we do is<00:17:44.940> we<00:17:45.120> apply<00:17:45.419> our<00:17:45.660> favorite<00:17:45.780> optimization 00:17:46.430 --> 00:17:46.440 align:start position:0% is we apply our favorite optimization 00:17:46.440 --> 00:17:48.710 align:start position:0% is we apply our favorite optimization method<00:17:46.799> like<00:17:47.039> gradient<00:17:47.460> descent<00:17:47.880> and<00:17:48.539> we 00:17:48.710 --> 00:17:48.720 align:start position:0% method like gradient descent and we 00:17:48.720 --> 00:17:51.049 align:start position:0% method like gradient descent and we update<00:17:49.020> the<00:17:49.260> prices<00:17:49.440> using<00:17:50.220> this<00:17:50.340> gradient<00:17:50.820> up 00:17:51.049 --> 00:17:51.059 align:start position:0% update the prices using this gradient up 00:17:51.059 --> 00:17:52.909 align:start position:0% update the prices using this gradient up here<00:17:51.179> there's<00:17:51.900> a<00:17:52.020> lot<00:17:52.140> of<00:17:52.200> other<00:17:52.320> optimization 00:17:52.909 --> 00:17:52.919 align:start position:0% here there's a lot of other optimization 00:17:52.919 --> 00:17:54.169 align:start position:0% here there's a lot of other optimization methods<00:17:53.340> that<00:17:53.520> you<00:17:53.640> could<00:17:53.700> choose<00:17:54.000> here 00:17:54.169 --> 00:17:54.179 align:start position:0% methods that you could choose here 00:17:54.179 --> 00:17:55.190 align:start position:0% methods that you could choose here they're<00:17:54.600> going<00:17:54.780> to<00:17:54.900> have<00:17:54.960> different 00:17:55.190 --> 00:17:55.200 align:start position:0% they're going to have different 00:17:55.200 --> 00:17:57.409 align:start position:0% they're going to have different convergence<00:17:55.980> behavior<00:17:56.520> and<00:17:57.240> different 00:17:57.409 --> 00:17:57.419 align:start position:0% convergence behavior and different 00:17:57.419 --> 00:17:59.210 align:start position:0% convergence behavior and different trades-offs<00:17:58.080> between<00:17:58.200> say<00:17:58.559> convergence<00:17:59.039> and 00:17:59.210 --> 00:17:59.220 align:start position:0% trades-offs between say convergence and 00:17:59.220 --> 00:18:00.890 align:start position:0% trades-offs between say convergence and complexity<00:17:59.700> this<00:18:00.240> is<00:18:00.299> all<00:18:00.419> stuff<00:18:00.660> that<00:18:00.780> we 00:18:00.890 --> 00:18:00.900 align:start position:0% complexity this is all stuff that we 00:18:00.900 --> 00:18:02.330 align:start position:0% complexity this is all stuff that we leave<00:18:01.080> for<00:18:01.260> future<00:18:01.440> work 00:18:02.330 --> 00:18:02.340 align:start position:0% leave for future work 00:18:02.340 --> 00:18:04.070 align:start position:0% leave for future work just<00:18:02.700> to<00:18:02.820> go<00:18:02.940> through<00:18:03.059> simple<00:18:03.360> examples<00:18:03.780> of 00:18:04.070 --> 00:18:04.080 align:start position:0% just to go through simple examples of 00:18:04.080 --> 00:18:06.710 align:start position:0% just to go through simple examples of what<00:18:04.260> I<00:18:04.380> saw<00:18:04.559> showed<00:18:05.220> earlier<00:18:05.520> so<00:18:06.059> let's<00:18:06.539> say 00:18:06.710 --> 00:18:06.720 align:start position:0% what I saw showed earlier so let's say 00:18:06.720 --> 00:18:08.510 align:start position:0% what I saw showed earlier so let's say you<00:18:07.080> had<00:18:07.200> this<00:18:07.500> loss<00:18:07.740> function<00:18:07.980> looks<00:18:08.280> kind<00:18:08.400> of 00:18:08.510 --> 00:18:08.520 align:start position:0% you had this loss function looks kind of 00:18:08.520 --> 00:18:10.250 align:start position:0% you had this loss function looks kind of silly<00:18:08.820> you<00:18:09.120> actually<00:18:09.240> do<00:18:09.480> get<00:18:09.660> somewhat<00:18:09.960> of<00:18:10.140> a 00:18:10.250 --> 00:18:10.260 align:start position:0% silly you actually do get somewhat of a 00:18:10.260 --> 00:18:12.590 align:start position:0% silly you actually do get somewhat of a reasonable<00:18:10.559> update<00:18:10.980> so<00:18:11.760> this<00:18:12.000> is<00:18:12.120> looks<00:18:12.539> like 00:18:12.590 --> 00:18:12.600 align:start position:0% reasonable update so this is looks like 00:18:12.600 --> 00:18:14.390 align:start position:0% reasonable update so this is looks like the<00:18:12.780> residual<00:18:13.260> so<00:18:13.679> you<00:18:13.860> essentially<00:18:14.160> just 00:18:14.390 --> 00:18:14.400 align:start position:0% the residual so you essentially just 00:18:14.400 --> 00:18:16.850 align:start position:0% the residual so you essentially just update<00:18:14.820> your<00:18:15.299> prices<00:18:15.480> by<00:18:16.200> some<00:18:16.500> you<00:18:16.799> know 00:18:16.850 --> 00:18:16.860 align:start position:0% update your prices by some you know 00:18:16.860 --> 00:18:19.430 align:start position:0% update your prices by some you know fraction<00:18:17.460> of<00:18:17.700> the<00:18:17.820> residual<00:18:18.240> if<00:18:18.960> you<00:18:19.080> use<00:18:19.200> this 00:18:19.430 --> 00:18:19.440 align:start position:0% fraction of the residual if you use this 00:18:19.440 --> 00:18:21.230 align:start position:0% fraction of the residual if you use this one<00:18:19.559> where<00:18:19.860> you're<00:18:20.039> only<00:18:20.280> unhappy<00:18:20.940> if<00:18:21.120> you're 00:18:21.230 --> 00:18:21.240 align:start position:0% one where you're only unhappy if you're 00:18:21.240 --> 00:18:24.049 align:start position:0% one where you're only unhappy if you're over<00:18:21.419> the<00:18:21.660> utilization<00:18:22.220> you<00:18:23.220> have<00:18:23.460> the<00:18:23.820> same 00:18:24.049 --> 00:18:24.059 align:start position:0% over the utilization you have the same 00:18:24.059 --> 00:18:26.750 align:start position:0% over the utilization you have the same update<00:18:24.900> except<00:18:25.440> you<00:18:25.679> essentially<00:18:26.160> make<00:18:26.460> it<00:18:26.580> so 00:18:26.750 --> 00:18:26.760 align:start position:0% update except you essentially make it so 00:18:26.760 --> 00:18:28.549 align:start position:0% update except you essentially make it so these<00:18:27.059> are<00:18:27.179> non-negative<00:18:27.720> so<00:18:28.140> if<00:18:28.320> any<00:18:28.440> of 00:18:28.549 --> 00:18:28.559 align:start position:0% these are non-negative so if any of 00:18:28.559 --> 00:18:30.710 align:start position:0% these are non-negative so if any of these<00:18:28.740> are<00:18:28.860> negative<00:18:29.100> you<00:18:29.400> zero<00:18:29.760> them<00:18:29.880> out<00:18:30.120> and 00:18:30.710 --> 00:18:30.720 align:start position:0% these are negative you zero them out and 00:18:30.720 --> 00:18:31.970 align:start position:0% these are negative you zero them out and so<00:18:30.840> this<00:18:30.960> you<00:18:31.200> can<00:18:31.320> actually<00:18:31.440> see<00:18:31.620> that<00:18:31.799> this 00:18:31.970 --> 00:18:31.980 align:start position:0% so this you can actually see that this 00:18:31.980 --> 00:18:34.789 align:start position:0% so this you can actually see that this makes<00:18:32.160> sense<00:18:32.460> here<00:18:33.000> in<00:18:33.539> this<00:18:33.660> first<00:18:33.900> loss 00:18:34.789 --> 00:18:34.799 align:start position:0% makes sense here in this first loss 00:18:34.799 --> 00:18:36.169 align:start position:0% makes sense here in this first loss function<00:18:35.039> we're<00:18:35.280> unhappy<00:18:35.700> if<00:18:35.880> we're<00:18:36.000> under 00:18:36.169 --> 00:18:36.179 align:start position:0% function we're unhappy if we're under 00:18:36.179 --> 00:18:38.330 align:start position:0% function we're unhappy if we're under the<00:18:36.419> utilization<00:18:36.960> so<00:18:37.620> this<00:18:37.740> means<00:18:38.039> that<00:18:38.160> we 00:18:38.330 --> 00:18:38.340 align:start position:0% the utilization so this means that we 00:18:38.340 --> 00:18:40.669 align:start position:0% the utilization so this means that we might<00:18:38.460> actually<00:18:38.700> want<00:18:39.059> negative<00:18:39.539> prices<00:18:39.840> to 00:18:40.669 --> 00:18:40.679 align:start position:0% might actually want negative prices to 00:18:40.679 --> 00:18:42.230 align:start position:0% might actually want negative prices to incentivize<00:18:41.160> people<00:18:41.400> to<00:18:41.580> use<00:18:41.760> more<00:18:42.000> of<00:18:42.120> a 00:18:42.230 --> 00:18:42.240 align:start position:0% incentivize people to use more of a 00:18:42.240 --> 00:18:45.169 align:start position:0% incentivize people to use more of a particular<00:18:42.539> resource<00:18:43.280> here<00:18:44.280> though<00:18:44.760> we 00:18:45.169 --> 00:18:45.179 align:start position:0% particular resource here though we 00:18:45.179 --> 00:18:46.490 align:start position:0% particular resource here though we actually<00:18:45.299> don't<00:18:45.660> care<00:18:45.840> if<00:18:46.140> we're<00:18:46.260> under 00:18:46.490 --> 00:18:46.500 align:start position:0% actually don't care if we're under 00:18:46.500 --> 00:18:49.010 align:start position:0% actually don't care if we're under utilizing<00:18:47.160> based<00:18:47.880> on<00:18:47.940> our<00:18:48.059> Target<00:18:48.299> so<00:18:48.900> we're 00:18:49.010 --> 00:18:49.020 align:start position:0% utilizing based on our Target so we're 00:18:49.020 --> 00:18:50.990 align:start position:0% utilizing based on our Target so we're never<00:18:49.200> going<00:18:49.380> to<00:18:49.440> have<00:18:49.559> negative<00:18:49.919> prices<00:18:50.160> and 00:18:50.990 --> 00:18:51.000 align:start position:0% never going to have negative prices and 00:18:51.000 --> 00:18:52.430 align:start position:0% never going to have negative prices and again<00:18:51.179> this<00:18:51.480> is<00:18:51.600> to<00:18:51.780> kind<00:18:51.900> of<00:18:51.960> get<00:18:52.080> to<00:18:52.260> the 00:18:52.430 --> 00:18:52.440 align:start position:0% again this is to kind of get to the 00:18:52.440 --> 00:18:54.049 align:start position:0% again this is to kind of get to the point<00:18:52.559> that<00:18:52.860> the<00:18:53.039> network<00:18:53.100> designer<00:18:53.640> chooses 00:18:54.049 --> 00:18:54.059 align:start position:0% point that the network designer chooses 00:18:54.059 --> 00:18:56.090 align:start position:0% point that the network designer chooses the<00:18:54.240> loss<00:18:54.539> function<00:18:54.780> and<00:18:55.500> the<00:18:55.620> loss<00:18:55.860> function 00:18:56.090 --> 00:18:56.100 align:start position:0% the loss function and the loss function 00:18:56.100 --> 00:18:58.130 align:start position:0% the loss function and the loss function encodes<00:18:56.460> exactly<00:18:56.940> what<00:18:57.240> your<00:18:57.360> unhappiness<00:18:57.960> is 00:18:58.130 --> 00:18:58.140 align:start position:0% encodes exactly what your unhappiness is 00:18:58.140 --> 00:19:00.010 align:start position:0% encodes exactly what your unhappiness is with<00:18:58.440> a<00:18:58.620> particular<00:18:58.919> resource<00:18:59.460> utilization 00:19:00.010 --> 00:19:00.020 align:start position:0% with a particular resource utilization 00:19:00.020 --> 00:19:02.810 align:start position:0% with a particular resource utilization and<00:19:01.020> then<00:19:01.140> once<00:19:01.440> you<00:19:01.500> do<00:19:01.679> that<00:19:01.919> up<00:19:02.280> update 00:19:02.810 --> 00:19:02.820 align:start position:0% and then once you do that up update 00:19:02.820 --> 00:19:04.970 align:start position:0% and then once you do that up update rules<00:19:03.179> that<00:19:03.539> will<00:19:03.900> maximum<00:19:04.559> or<00:19:04.740> sorry 00:19:04.970 --> 00:19:04.980 align:start position:0% rules that will maximum or sorry 00:19:04.980 --> 00:19:07.010 align:start position:0% rules that will maximum or sorry minimize<00:19:05.460> that<00:19:05.640> loss<00:19:06.000> function<00:19:06.240> will<00:19:06.840> fall 00:19:07.010 --> 00:19:07.020 align:start position:0% minimize that loss function will fall 00:19:07.020 --> 00:19:09.650 align:start position:0% minimize that loss function will fall out<00:19:07.260> of<00:19:07.380> it<00:19:07.500> so<00:19:08.280> it<00:19:08.580> comes<00:19:08.880> down<00:19:09.000> to<00:19:09.240> instead<00:19:09.600> of 00:19:09.650 --> 00:19:09.660 align:start position:0% out of it so it comes down to instead of 00:19:09.660 --> 00:19:11.390 align:start position:0% out of it so it comes down to instead of choosing<00:19:09.960> what<00:19:10.140> the<00:19:10.260> update<00:19:10.559> rule<00:19:10.860> is<00:19:10.980> you're 00:19:11.390 --> 00:19:11.400 align:start position:0% choosing what the update rule is you're 00:19:11.400 --> 00:19:13.430 align:start position:0% choosing what the update rule is you're choosing<00:19:11.760> what<00:19:11.880> the<00:19:12.000> loss<00:19:12.299> function<00:19:12.539> is 00:19:13.430 --> 00:19:13.440 align:start position:0% choosing what the loss function is 00:19:13.440 --> 00:19:14.570 align:start position:0% choosing what the loss function is all<00:19:13.860> right 00:19:14.570 --> 00:19:14.580 align:start position:0% all right 00:19:14.580 --> 00:19:17.270 align:start position:0% all right um so<00:19:14.880> this<00:19:15.120> is<00:19:15.240> a<00:19:15.480> lot<00:19:15.600> of<00:19:15.720> math<00:19:15.900> we<00:19:16.740> did<00:19:16.860> some 00:19:17.270 --> 00:19:17.280 align:start position:0% um so this is a lot of math we did some 00:19:17.280 --> 00:19:19.250 align:start position:0% um so this is a lot of math we did some numerical<00:19:17.820> work<00:19:18.059> to<00:19:18.360> kind<00:19:18.539> of<00:19:18.600> see<00:19:18.780> how<00:19:19.080> this 00:19:19.250 --> 00:19:19.260 align:start position:0% numerical work to kind of see how this 00:19:19.260 --> 00:19:21.230 align:start position:0% numerical work to kind of see how this would<00:19:19.440> work<00:19:19.620> and<00:19:19.980> very<00:19:20.220> simple 00:19:21.230 --> 00:19:21.240 align:start position:0% would work and very simple 00:19:21.240 --> 00:19:24.470 align:start position:0% would work and very simple um<00:19:21.299> very<00:19:21.840> simple<00:19:21.960> examples<00:19:22.559> so<00:19:23.460> here<00:19:23.880> we<00:19:24.299> have 00:19:24.470 --> 00:19:24.480 align:start position:0% um very simple examples so here we have 00:19:24.480 --> 00:19:26.150 align:start position:0% um very simple examples so here we have kind<00:19:24.720> of<00:19:24.780> a<00:19:24.960> steady<00:19:25.140> state<00:19:25.380> behavior<00:19:25.799> of<00:19:25.980> a 00:19:26.150 --> 00:19:26.160 align:start position:0% kind of a steady state behavior of a 00:19:26.160 --> 00:19:28.070 align:start position:0% kind of a steady state behavior of a network<00:19:26.280> with<00:19:27.179> only<00:19:27.419> one<00:19:27.720> type<00:19:27.900> of 00:19:28.070 --> 00:19:28.080 align:start position:0% network with only one type of 00:19:28.080 --> 00:19:29.930 align:start position:0% network with only one type of transaction<00:19:28.440> that's<00:19:28.740> being<00:19:28.980> submitted<00:19:29.460> you 00:19:29.930 --> 00:19:29.940 align:start position:0% transaction that's being submitted you 00:19:29.940 --> 00:19:31.730 align:start position:0% transaction that's being submitted you can<00:19:30.000> think<00:19:30.120> of<00:19:30.240> this<00:19:30.480> as<00:19:30.660> pretty<00:19:30.900> analogous<00:19:31.440> to 00:19:31.730 --> 00:19:31.740 align:start position:0% can think of this as pretty analogous to 00:19:31.740 --> 00:19:33.890 align:start position:0% can think of this as pretty analogous to that<00:19:31.919> example<00:19:32.340> that<00:19:32.640> I<00:19:33.000> showed<00:19:33.660> at<00:19:33.780> the 00:19:33.890 --> 00:19:33.900 align:start position:0% that example that I showed at the 00:19:33.900 --> 00:19:35.930 align:start position:0% that example that I showed at the beginning<00:19:34.020> of<00:19:34.320> the<00:19:34.440> talk<00:19:34.620> but<00:19:35.460> you<00:19:35.700> can<00:19:35.820> see 00:19:35.930 --> 00:19:35.940 align:start position:0% beginning of the talk but you can see 00:19:35.940 --> 00:19:37.750 align:start position:0% beginning of the talk but you can see that<00:19:36.179> one<00:19:36.360> dimensional<00:19:36.780> prices 00:19:37.750 --> 00:19:37.760 align:start position:0% that one dimensional prices 00:19:37.760 --> 00:19:40.610 align:start position:0% that one dimensional prices are<00:19:38.760> doing<00:19:39.059> about<00:19:39.299> 10<00:19:39.660> transactions<00:19:40.320> per 00:19:40.610 --> 00:19:40.620 align:start position:0% are doing about 10 transactions per 00:19:40.620 --> 00:19:42.710 align:start position:0% are doing about 10 transactions per block<00:19:40.860> and<00:19:41.460> multi-dimensional<00:19:42.120> prices<00:19:42.360> are 00:19:42.710 --> 00:19:42.720 align:start position:0% block and multi-dimensional prices are 00:19:42.720 --> 00:19:45.049 align:start position:0% block and multi-dimensional prices are able<00:19:42.900> to<00:19:43.020> eke<00:19:43.320> out<00:19:43.500> maybe<00:19:43.860> like<00:19:44.220> two<00:19:44.700> to<00:19:44.880> three 00:19:45.049 --> 00:19:45.059 align:start position:0% able to eke out maybe like two to three 00:19:45.059 --> 00:19:46.970 align:start position:0% able to eke out maybe like two to three more<00:19:45.299> transactions<00:19:45.840> per<00:19:46.020> block<00:19:46.260> but<00:19:46.679> this<00:19:46.860> is 00:19:46.970 --> 00:19:46.980 align:start position:0% more transactions per block but this is 00:19:46.980 --> 00:19:48.830 align:start position:0% more transactions per block but this is even<00:19:47.160> when<00:19:47.580> you<00:19:47.880> you<00:19:48.120> know<00:19:48.240> it's<00:19:48.360> the<00:19:48.660> same 00:19:48.830 --> 00:19:48.840 align:start position:0% even when you you know it's the same 00:19:48.840 --> 00:19:50.450 align:start position:0% even when you you know it's the same type<00:19:49.080> of<00:19:49.260> transaction<00:19:49.620> that's<00:19:49.980> going<00:19:50.160> through 00:19:50.450 --> 00:19:50.460 align:start position:0% type of transaction that's going through 00:19:50.460 --> 00:19:52.730 align:start position:0% type of transaction that's going through so<00:19:51.240> even<00:19:51.419> this<00:19:51.720> kind<00:19:51.900> of<00:19:51.960> like<00:19:52.020> the<00:19:52.320> simplest 00:19:52.730 --> 00:19:52.740 align:start position:0% so even this kind of like the simplest 00:19:52.740 --> 00:19:55.549 align:start position:0% so even this kind of like the simplest case<00:19:53.039> you<00:19:53.760> get<00:19:54.000> some<00:19:54.419> improvement<00:19:54.960> from<00:19:55.260> using 00:19:55.549 --> 00:19:55.559 align:start position:0% case you get some improvement from using 00:19:55.559 --> 00:19:57.710 align:start position:0% case you get some improvement from using these<00:19:55.740> multi-dimensional<00:19:56.460> prices 00:19:57.710 --> 00:19:57.720 align:start position:0% these multi-dimensional prices 00:19:57.720 --> 00:19:58.970 align:start position:0% these multi-dimensional prices um and<00:19:57.900> I'm<00:19:58.260> not<00:19:58.380> going<00:19:58.500> to<00:19:58.620> go<00:19:58.679> through<00:19:58.799> all 00:19:58.970 --> 00:19:58.980 align:start position:0% um and I'm not going to go through all 00:19:58.980 --> 00:20:00.529 align:start position:0% um and I'm not going to go through all the<00:19:59.100> details<00:19:59.520> of<00:19:59.760> kind<00:19:59.880> of<00:20:00.000> how<00:20:00.120> we<00:20:00.240> set<00:20:00.360> this 00:20:00.529 --> 00:20:00.539 align:start position:0% the details of kind of how we set this 00:20:00.539 --> 00:20:02.210 align:start position:0% the details of kind of how we set this up<00:20:00.660> but<00:20:00.900> I<00:20:01.140> would<00:20:01.260> encourage<00:20:01.740> you<00:20:01.860> to<00:20:02.039> look<00:20:02.100> at 00:20:02.210 --> 00:20:02.220 align:start position:0% up but I would encourage you to look at 00:20:02.220 --> 00:20:04.370 align:start position:0% up but I would encourage you to look at the<00:20:02.340> paper<00:20:02.520> for<00:20:02.880> that<00:20:03.000> however 00:20:04.370 --> 00:20:04.380 align:start position:0% the paper for that however 00:20:04.380 --> 00:20:06.350 align:start position:0% the paper for that however um<00:20:04.440> where<00:20:04.740> this<00:20:04.980> really<00:20:05.160> shines<00:20:05.580> is<00:20:06.000> when<00:20:06.179> we 00:20:06.350 --> 00:20:06.360 align:start position:0% um where this really shines is when we 00:20:06.360 --> 00:20:07.970 align:start position:0% um where this really shines is when we have<00:20:06.480> a<00:20:06.600> distribution<00:20:06.960> shift 00:20:07.970 --> 00:20:07.980 align:start position:0% have a distribution shift 00:20:07.980 --> 00:20:10.250 align:start position:0% have a distribution shift so<00:20:08.400> in<00:20:08.580> this<00:20:08.700> example<00:20:09.000> what<00:20:09.240> we<00:20:09.360> did<00:20:09.539> is<00:20:10.080> we 00:20:10.250 --> 00:20:10.260 align:start position:0% so in this example what we did is we 00:20:10.260 --> 00:20:12.049 align:start position:0% so in this example what we did is we have<00:20:10.440> this<00:20:10.620> type<00:20:10.799> 1<00:20:11.039> of<00:20:11.220> transactions<00:20:11.820> which 00:20:12.049 --> 00:20:12.059 align:start position:0% have this type 1 of transactions which 00:20:12.059 --> 00:20:14.330 align:start position:0% have this type 1 of transactions which you<00:20:12.179> saw<00:20:12.360> earlier<00:20:12.720> but<00:20:13.200> we<00:20:13.440> add<00:20:13.620> this<00:20:13.860> type<00:20:14.039> 2 00:20:14.330 --> 00:20:14.340 align:start position:0% you saw earlier but we add this type 2 00:20:14.340 --> 00:20:16.130 align:start position:0% you saw earlier but we add this type 2 transaction<00:20:14.940> which<00:20:15.480> has<00:20:15.660> a<00:20:15.840> much<00:20:15.960> different 00:20:16.130 --> 00:20:16.140 align:start position:0% transaction which has a much different 00:20:16.140 --> 00:20:18.049 align:start position:0% transaction which has a much different resource<00:20:16.740> profile<00:20:17.160> so<00:20:17.640> you<00:20:17.760> can<00:20:17.880> think<00:20:17.940> of 00:20:18.049 --> 00:20:18.059 align:start position:0% resource profile so you can think of 00:20:18.059 --> 00:20:20.390 align:start position:0% resource profile so you can think of this<00:20:18.240> like<00:20:18.419> an<00:20:18.539> nft<00:20:18.780> Mint<00:20:19.200> or<00:20:19.380> something<00:20:19.559> and 00:20:20.390 --> 00:20:20.400 align:start position:0% this like an nft Mint or something and 00:20:20.400 --> 00:20:23.090 align:start position:0% this like an nft Mint or something and they<00:20:20.520> come<00:20:20.700> at<00:20:20.880> about<00:20:21.059> block<00:20:21.360> 10.<00:20:22.320> so<00:20:22.799> the 00:20:23.090 --> 00:20:23.100 align:start position:0% they come at about block 10. so the 00:20:23.100 --> 00:20:24.650 align:start position:0% they come at about block 10. so the multi-dimensional<00:20:23.760> prices<00:20:24.000> are<00:20:24.299> the<00:20:24.480> purple 00:20:24.650 --> 00:20:24.660 align:start position:0% multi-dimensional prices are the purple 00:20:24.660 --> 00:20:26.330 align:start position:0% multi-dimensional prices are the purple and<00:20:24.900> blue<00:20:25.140> and<00:20:25.500> you<00:20:25.620> can<00:20:25.740> kind<00:20:25.860> of<00:20:25.980> see<00:20:26.100> that 00:20:26.330 --> 00:20:26.340 align:start position:0% and blue and you can kind of see that 00:20:26.340 --> 00:20:29.750 align:start position:0% and blue and you can kind of see that there's<00:20:26.520> this<00:20:26.880> nice<00:20:27.059> Spike<00:20:27.539> here<00:20:28.220> where<00:20:29.220> we<00:20:29.460> do 00:20:29.750 --> 00:20:29.760 align:start position:0% there's this nice Spike here where we do 00:20:29.760 --> 00:20:31.730 align:start position:0% there's this nice Spike here where we do less<00:20:29.940> of<00:20:30.179> type<00:20:30.299> 1<00:20:30.600> transaction<00:20:31.080> more<00:20:31.380> of<00:20:31.559> type 00:20:31.730 --> 00:20:31.740 align:start position:0% less of type 1 transaction more of type 00:20:31.740 --> 00:20:34.130 align:start position:0% less of type 1 transaction more of type 2<00:20:32.039> and<00:20:32.880> then<00:20:33.000> kind<00:20:33.240> of<00:20:33.360> once<00:20:33.660> we<00:20:33.720> go<00:20:33.900> through 00:20:34.130 --> 00:20:34.140 align:start position:0% 2 and then kind of once we go through 00:20:34.140 --> 00:20:37.310 align:start position:0% 2 and then kind of once we go through all<00:20:34.380> of<00:20:34.500> these<00:20:34.740> we<00:20:35.039> return<00:20:35.220> to<00:20:35.520> zero<00:20:35.940> and<00:20:36.600> we 00:20:37.310 --> 00:20:37.320 align:start position:0% all of these we return to zero and we 00:20:37.320 --> 00:20:39.289 align:start position:0% all of these we return to zero and we clear<00:20:37.559> some<00:20:37.919> backlog<00:20:38.460> after<00:20:38.820> we've<00:20:39.179> gone 00:20:39.289 --> 00:20:39.299 align:start position:0% clear some backlog after we've gone 00:20:39.299 --> 00:20:41.210 align:start position:0% clear some backlog after we've gone through<00:20:39.539> these<00:20:39.840> you<00:20:40.440> could<00:20:40.559> also<00:20:40.799> see<00:20:40.919> on<00:20:41.160> the 00:20:41.210 --> 00:20:41.220 align:start position:0% through these you could also see on the 00:20:41.220 --> 00:20:42.169 align:start position:0% through these you could also see on the right<00:20:41.340> here<00:20:41.520> these<00:20:42.000> are<00:20:42.059> the 00:20:42.169 --> 00:20:42.179 align:start position:0% right here these are the 00:20:42.179 --> 00:20:44.210 align:start position:0% right here these are the multi-dimensional<00:20:42.840> prices<00:20:43.020> so<00:20:43.679> once<00:20:43.980> we<00:20:44.039> hit 00:20:44.210 --> 00:20:44.220 align:start position:0% multi-dimensional prices so once we hit 00:20:44.220 --> 00:20:46.310 align:start position:0% multi-dimensional prices so once we hit block<00:20:44.460> 10<00:20:44.760> and<00:20:45.120> the<00:20:45.360> distribution<00:20:45.660> shifts<00:20:46.200> a 00:20:46.310 --> 00:20:46.320 align:start position:0% block 10 and the distribution shifts a 00:20:46.320 --> 00:20:49.010 align:start position:0% block 10 and the distribution shifts a lot<00:20:46.440> this<00:20:47.280> uh<00:20:47.580> light<00:20:47.880> blue<00:20:48.120> price<00:20:48.419> goes<00:20:48.840> down 00:20:49.010 --> 00:20:49.020 align:start position:0% lot this uh light blue price goes down 00:20:49.020 --> 00:20:51.409 align:start position:0% lot this uh light blue price goes down the<00:20:49.500> other<00:20:49.620> price<00:20:49.860> goes<00:20:50.340> up<00:20:50.520> quite<00:20:50.760> a<00:20:50.880> bit<00:20:51.000> and 00:20:51.409 --> 00:20:51.419 align:start position:0% the other price goes up quite a bit and 00:20:51.419 --> 00:20:52.970 align:start position:0% the other price goes up quite a bit and then<00:20:51.539> they<00:20:51.660> return<00:20:51.900> to<00:20:52.200> steady<00:20:52.500> state<00:20:52.740> a 00:20:52.970 --> 00:20:52.980 align:start position:0% then they return to steady state a 00:20:52.980 --> 00:20:54.890 align:start position:0% then they return to steady state a little<00:20:53.039> bit<00:20:53.160> long<00:20:53.520> a<00:20:53.880> little<00:20:54.179> bit 00:20:54.890 --> 00:20:54.900 align:start position:0% little bit long a little bit 00:20:54.900 --> 00:20:56.750 align:start position:0% little bit long a little bit afterwards 00:20:56.750 --> 00:20:56.760 align:start position:0% afterwards 00:20:56.760 --> 00:20:59.690 align:start position:0% afterwards um again<00:20:57.260> the<00:20:58.260> uniform<00:20:58.679> prices<00:20:58.980> are<00:20:59.520> still 00:20:59.690 --> 00:20:59.700 align:start position:0% um again the uniform prices are still 00:20:59.700 --> 00:21:02.150 align:start position:0% um again the uniform prices are still able<00:21:00.000> to<00:21:00.179> adjust<00:21:00.419> to<00:21:00.720> a<00:21:00.900> certain<00:21:01.020> extent<00:21:01.380> but 00:21:02.150 --> 00:21:02.160 align:start position:0% able to adjust to a certain extent but 00:21:02.160 --> 00:21:04.850 align:start position:0% able to adjust to a certain extent but it's<00:21:02.460> going<00:21:03.120> to<00:21:03.240> be<00:21:03.299> less<00:21:03.480> throughput<00:21:03.960> overall 00:21:04.850 --> 00:21:04.860 align:start position:0% it's going to be less throughput overall 00:21:04.860 --> 00:21:06.890 align:start position:0% it's going to be less throughput overall and<00:21:05.580> back<00:21:06.059> to<00:21:06.299> what<00:21:06.419> I<00:21:06.539> was<00:21:06.660> talking<00:21:06.780> about 00:21:06.890 --> 00:21:06.900 align:start position:0% and back to what I was talking about 00:21:06.900 --> 00:21:09.049 align:start position:0% and back to what I was talking about earlier<00:21:07.320> where<00:21:07.740> you<00:21:08.039> have<00:21:08.280> some<00:21:08.880> Target 00:21:09.049 --> 00:21:09.059 align:start position:0% earlier where you have some Target 00:21:09.059 --> 00:21:11.210 align:start position:0% earlier where you have some Target utilization<00:21:09.660> that<00:21:09.960> you<00:21:10.080> want<00:21:10.140> to<00:21:10.320> use<00:21:10.440> you<00:21:11.160> can 00:21:11.210 --> 00:21:11.220 align:start position:0% utilization that you want to use you can 00:21:11.220 --> 00:21:13.370 align:start position:0% utilization that you want to use you can see<00:21:11.340> here<00:21:11.580> in<00:21:11.820> the<00:21:12.000> second<00:21:12.179> example<00:21:12.660> the 00:21:13.370 --> 00:21:13.380 align:start position:0% see here in the second example the 00:21:13.380 --> 00:21:15.169 align:start position:0% see here in the second example the dashed<00:21:13.740> lines<00:21:13.980> are<00:21:14.160> going<00:21:14.340> to<00:21:14.400> be<00:21:14.520> the<00:21:14.700> targets 00:21:15.169 --> 00:21:15.179 align:start position:0% dashed lines are going to be the targets 00:21:15.179 --> 00:21:18.470 align:start position:0% dashed lines are going to be the targets so<00:21:15.840> the<00:21:16.500> uh<00:21:16.919> multi-dimensional<00:21:17.700> prices<00:21:17.940> which 00:21:18.470 --> 00:21:18.480 align:start position:0% so the uh multi-dimensional prices which 00:21:18.480 --> 00:21:20.750 align:start position:0% so the uh multi-dimensional prices which is<00:21:18.600> the<00:21:18.840> top<00:21:19.020> deviate<00:21:19.740> from<00:21:19.919> the<00:21:20.039> target<00:21:20.220> for<00:21:20.640> a 00:21:20.750 --> 00:21:20.760 align:start position:0% is the top deviate from the target for a 00:21:20.760 --> 00:21:22.669 align:start position:0% is the top deviate from the target for a short<00:21:21.000> period<00:21:21.299> of<00:21:21.480> time<00:21:21.660> to<00:21:21.960> handle<00:21:22.260> kind<00:21:22.559> of 00:21:22.669 --> 00:21:22.679 align:start position:0% short period of time to handle kind of 00:21:22.679 --> 00:21:25.370 align:start position:0% short period of time to handle kind of the<00:21:22.980> big<00:21:23.460> spike<00:21:23.760> in<00:21:23.940> transactions<00:21:24.660> but<00:21:25.200> then 00:21:25.370 --> 00:21:25.380 align:start position:0% the big spike in transactions but then 00:21:25.380 --> 00:21:26.870 align:start position:0% the big spike in transactions but then the<00:21:25.559> network<00:21:25.740> returns<00:21:26.280> to<00:21:26.460> steady<00:21:26.700> state 00:21:26.870 --> 00:21:26.880 align:start position:0% the network returns to steady state 00:21:26.880 --> 00:21:29.690 align:start position:0% the network returns to steady state afterwards<00:21:27.539> in<00:21:28.320> the<00:21:28.500> uniform<00:21:28.919> prices<00:21:29.220> where 00:21:29.690 --> 00:21:29.700 align:start position:0% afterwards in the uniform prices where 00:21:29.700 --> 00:21:30.649 align:start position:0% afterwards in the uniform prices where you<00:21:29.820> can<00:21:29.940> think<00:21:30.000> of<00:21:30.120> you<00:21:30.240> have<00:21:30.419> less 00:21:30.649 --> 00:21:30.659 align:start position:0% you can think of you have less 00:21:30.659 --> 00:21:33.169 align:start position:0% you can think of you have less dimensions<00:21:31.200> for<00:21:31.500> this<00:21:31.740> controller<00:21:32.280> you 00:21:33.169 --> 00:21:33.179 align:start position:0% dimensions for this controller you 00:21:33.179 --> 00:21:34.310 align:start position:0% dimensions for this controller you essentially<00:21:33.480> get<00:21:33.659> this<00:21:33.900> oscillating 00:21:34.310 --> 00:21:34.320 align:start position:0% essentially get this oscillating 00:21:34.320 --> 00:21:35.990 align:start position:0% essentially get this oscillating behavior<00:21:34.799> and<00:21:35.039> you<00:21:35.159> eventually<00:21:35.460> return<00:21:35.700> to 00:21:35.990 --> 00:21:36.000 align:start position:0% behavior and you eventually return to 00:21:36.000 --> 00:21:37.909 align:start position:0% behavior and you eventually return to somewhat<00:21:36.299> of<00:21:36.480> a<00:21:36.600> steady<00:21:36.780> state<00:21:37.020> but<00:21:37.620> you<00:21:37.799> kind 00:21:37.909 --> 00:21:37.919 align:start position:0% somewhat of a steady state but you kind 00:21:37.919 --> 00:21:39.890 align:start position:0% somewhat of a steady state but you kind of<00:21:38.039> get<00:21:38.159> a<00:21:38.340> lot<00:21:38.400> of<00:21:38.520> a<00:21:38.700> mess<00:21:38.880> right<00:21:39.419> here<00:21:39.600> as 00:21:39.890 --> 00:21:39.900 align:start position:0% of get a lot of a mess right here as 00:21:39.900 --> 00:21:42.710 align:start position:0% of get a lot of a mess right here as your<00:21:40.080> trans<00:21:40.320> as<00:21:40.919> the<00:21:41.100> distribution<00:21:41.640> shifts 00:21:42.710 --> 00:21:42.720 align:start position:0% your trans as the distribution shifts 00:21:42.720 --> 00:21:43.970 align:start position:0% your trans as the distribution shifts cool 00:21:43.970 --> 00:21:43.980 align:start position:0% cool 00:21:43.980 --> 00:21:45.110 align:start position:0% cool um<00:21:44.039> so 00:21:45.110 --> 00:21:45.120 align:start position:0% um so 00:21:45.120 --> 00:21:46.789 align:start position:0% um so there's<00:21:45.659> a<00:21:45.780> lot<00:21:45.840> of<00:21:45.900> future<00:21:46.020> work<00:21:46.320> to<00:21:46.500> be<00:21:46.620> done 00:21:46.789 --> 00:21:46.799 align:start position:0% there's a lot of future work to be done 00:21:46.799 --> 00:21:47.870 align:start position:0% there's a lot of future work to be done here 00:21:47.870 --> 00:21:47.880 align:start position:0% here 00:21:47.880 --> 00:21:49.850 align:start position:0% here um one<00:21:48.659> thing<00:21:48.780> that<00:21:49.020> we<00:21:49.140> didn't<00:21:49.260> do<00:21:49.440> is<00:21:49.679> super 00:21:49.850 --> 00:21:49.860 align:start position:0% um one thing that we didn't do is super 00:21:49.860 --> 00:21:51.710 align:start position:0% um one thing that we didn't do is super extensive<00:21:50.340> numerical<00:21:50.820> examples<00:21:51.240> and<00:21:51.480> you<00:21:51.600> can 00:21:51.710 --> 00:21:51.720 align:start position:0% extensive numerical examples and you can 00:21:51.720 --> 00:21:53.990 align:start position:0% extensive numerical examples and you can imagine<00:21:51.840> that<00:21:52.200> using<00:21:52.500> real<00:21:52.679> data<00:21:53.100> here<00:21:53.340> might 00:21:53.990 --> 00:21:54.000 align:start position:0% imagine that using real data here might 00:21:54.000 --> 00:21:55.850 align:start position:0% imagine that using real data here might lead<00:21:54.240> to<00:21:54.419> valuable<00:21:54.780> insights<00:21:55.380> that<00:21:55.500> allow<00:21:55.799> you 00:21:55.850 --> 00:21:55.860 align:start position:0% lead to valuable insights that allow you 00:21:55.860 --> 00:21:57.770 align:start position:0% lead to valuable insights that allow you to<00:21:56.039> tweak<00:21:56.280> the<00:21:56.460> framework<00:21:56.820> in<00:21:57.000> specific<00:21:57.360> ways 00:21:57.770 --> 00:21:57.780 align:start position:0% to tweak the framework in specific ways 00:21:57.780 --> 00:22:00.289 align:start position:0% to tweak the framework in specific ways in<00:21:58.440> addition<00:21:58.620> like<00:21:58.980> I<00:21:59.159> mentioned<00:21:59.400> earlier<00:21:59.760> we 00:22:00.289 --> 00:22:00.299 align:start position:0% in addition like I mentioned earlier we 00:22:00.299 --> 00:22:02.750 align:start position:0% in addition like I mentioned earlier we grouped<00:22:00.659> the<00:22:00.780> transaction<00:22:01.140> producers<00:22:01.799> or<00:22:02.580> we 00:22:02.750 --> 00:22:02.760 align:start position:0% grouped the transaction producers or we 00:22:02.760 --> 00:22:04.490 align:start position:0% grouped the transaction producers or we group<00:22:02.880> The<00:22:03.059> users<00:22:03.299> and<00:22:03.419> validators<00:22:03.900> into<00:22:04.200> that 00:22:04.490 --> 00:22:04.500 align:start position:0% group The users and validators into that 00:22:04.500 --> 00:22:07.730 align:start position:0% group The users and validators into that transaction<00:22:04.919> producer<00:22:05.580> kind<00:22:06.299> of<00:22:06.419> set<00:22:06.740> and 00:22:07.730 --> 00:22:07.740 align:start position:0% transaction producer kind of set and 00:22:07.740 --> 00:22:09.470 align:start position:0% transaction producer kind of set and there<00:22:07.860> is<00:22:07.980> some<00:22:08.159> work<00:22:08.340> on<00:22:08.820> the<00:22:09.059> dynamical 00:22:09.470 --> 00:22:09.480 align:start position:0% there is some work on the dynamical 00:22:09.480 --> 00:22:10.909 align:start position:0% there is some work on the dynamical behavior<00:22:09.900> of<00:22:10.080> like<00:22:10.260> essentially<00:22:10.559> how<00:22:10.740> do<00:22:10.860> we 00:22:10.909 --> 00:22:10.919 align:start position:0% behavior of like essentially how do we 00:22:10.919 --> 00:22:13.250 align:start position:0% behavior of like essentially how do we make<00:22:11.100> the<00:22:11.340> strategy<00:22:11.760> proof<00:22:12.120> how<00:22:12.539> do<00:22:12.659> we<00:22:13.200> um 00:22:13.250 --> 00:22:13.260 align:start position:0% make the strategy proof how do we um 00:22:13.260 --> 00:22:15.409 align:start position:0% make the strategy proof how do we um kind<00:22:14.220> of<00:22:14.340> you<00:22:14.520> know<00:22:14.580> we<00:22:14.880> just<00:22:15.059> talked<00:22:15.299> about 00:22:15.409 --> 00:22:15.419 align:start position:0% kind of you know we just talked about 00:22:15.419 --> 00:22:16.789 align:start position:0% kind of you know we just talked about essentially<00:22:15.840> the<00:22:15.960> amount<00:22:16.200> that<00:22:16.320> was<00:22:16.500> burned 00:22:16.789 --> 00:22:16.799 align:start position:0% essentially the amount that was burned 00:22:16.799 --> 00:22:19.070 align:start position:0% essentially the amount that was burned by<00:22:16.980> the<00:22:17.100> network<00:22:17.280> in<00:22:17.940> our<00:22:18.120> prices<00:22:18.299> so<00:22:18.720> how<00:22:18.960> do 00:22:19.070 --> 00:22:19.080 align:start position:0% by the network in our prices so how do 00:22:19.080 --> 00:22:20.510 align:start position:0% by the network in our prices so how do we<00:22:19.200> kind<00:22:19.380> of<00:22:19.440> you<00:22:19.620> know<00:22:19.740> make<00:22:19.919> this<00:22:20.100> into<00:22:20.280> an 00:22:20.510 --> 00:22:20.520 align:start position:0% we kind of you know make this into an 00:22:20.520 --> 00:22:22.190 align:start position:0% we kind of you know make this into an entire<00:22:20.820> system 00:22:22.190 --> 00:22:22.200 align:start position:0% entire system 00:22:22.200 --> 00:22:25.610 align:start position:0% entire system um also<00:22:22.799> I<00:22:23.400> mentioned<00:22:23.700> earlier<00:22:24.059> that<00:22:24.600> uh<00:22:25.320> the 00:22:25.610 --> 00:22:25.620 align:start position:0% um also I mentioned earlier that uh the 00:22:25.620 --> 00:22:27.110 align:start position:0% um also I mentioned earlier that uh the update<00:22:25.860> rule<00:22:26.159> while<00:22:26.400> I<00:22:26.580> chose<00:22:26.760> gradient 00:22:27.110 --> 00:22:27.120 align:start position:0% update rule while I chose gradient 00:22:27.120 --> 00:22:28.430 align:start position:0% update rule while I chose gradient descent<00:22:27.480> here<00:22:27.720> there's<00:22:28.020> a<00:22:28.140> lot<00:22:28.200> of<00:22:28.320> other 00:22:28.430 --> 00:22:28.440 align:start position:0% descent here there's a lot of other 00:22:28.440 --> 00:22:29.870 align:start position:0% descent here there's a lot of other things<00:22:28.679> that<00:22:28.860> you<00:22:29.039> could<00:22:29.100> do<00:22:29.280> you<00:22:29.820> could 00:22:29.870 --> 00:22:29.880 align:start position:0% things that you could do you could 00:22:29.880 --> 00:22:31.789 align:start position:0% things that you could do you could actually<00:22:30.059> choose<00:22:30.360> the<00:22:30.539> update<00:22:30.780> rule<00:22:31.140> in<00:22:31.260> a<00:22:31.740> way 00:22:31.789 --> 00:22:31.799 align:start position:0% actually choose the update rule in a way 00:22:31.799 --> 00:22:33.529 align:start position:0% actually choose the update rule in a way that<00:22:32.220> gets<00:22:32.580> you<00:22:32.640> something<00:22:32.820> that<00:22:33.059> looks<00:22:33.360> very 00:22:33.529 --> 00:22:33.539 align:start position:0% that gets you something that looks very 00:22:33.539 --> 00:22:35.750 align:start position:0% that gets you something that looks very very<00:22:33.720> similar<00:22:34.200> to<00:22:34.620> what<00:22:34.799> was<00:22:34.919> proposed<00:22:35.400> on<00:22:35.640> the 00:22:35.750 --> 00:22:35.760 align:start position:0% very similar to what was proposed on the 00:22:35.760 --> 00:22:37.669 align:start position:0% very similar to what was proposed on the ethereum<00:22:36.179> research<00:22:36.539> forums<00:22:36.900> back<00:22:37.200> in<00:22:37.320> January 00:22:37.669 --> 00:22:37.679 align:start position:0% ethereum research forums back in January 00:22:37.679 --> 00:22:39.529 align:start position:0% ethereum research forums back in January and<00:22:38.340> there's<00:22:38.460> a<00:22:38.640> question<00:22:38.760> of<00:22:39.000> okay<00:22:39.240> well 00:22:39.529 --> 00:22:39.539 align:start position:0% and there's a question of okay well 00:22:39.539 --> 00:22:41.210 align:start position:0% and there's a question of okay well which<00:22:39.900> update<00:22:40.200> rules<00:22:40.440> are<00:22:40.620> good<00:22:40.740> which<00:22:40.919> update 00:22:41.210 --> 00:22:41.220 align:start position:0% which update rules are good which update 00:22:41.220 --> 00:22:43.070 align:start position:0% which update rules are good which update rules<00:22:41.520> are<00:22:41.640> the<00:22:41.820> most<00:22:41.940> useful<00:22:42.299> and<00:22:42.720> how<00:22:42.900> do<00:22:42.960> you 00:22:43.070 --> 00:22:43.080 align:start position:0% rules are the most useful and how do you 00:22:43.080 --> 00:22:44.510 align:start position:0% rules are the most useful and how do you trade<00:22:43.260> off<00:22:43.380> between<00:22:43.679> say<00:22:44.039> convergence 00:22:44.510 --> 00:22:44.520 align:start position:0% trade off between say convergence 00:22:44.520 --> 00:22:45.890 align:start position:0% trade off between say convergence Behavior 00:22:45.890 --> 00:22:45.900 align:start position:0% Behavior 00:22:45.900 --> 00:22:48.110 align:start position:0% Behavior um and<00:22:46.200> complexity<00:22:46.740> so<00:22:47.100> how<00:22:47.460> quickly<00:22:47.760> kind<00:22:48.000> of 00:22:48.110 --> 00:22:48.120 align:start position:0% um and complexity so how quickly kind of 00:22:48.120 --> 00:22:50.029 align:start position:0% um and complexity so how quickly kind of your<00:22:48.179> prices<00:22:48.419> can<00:22:48.720> adjust<00:22:48.960> and<00:22:49.559> how<00:22:49.740> much<00:22:49.860> work 00:22:50.029 --> 00:22:50.039 align:start position:0% your prices can adjust and how much work 00:22:50.039 --> 00:22:52.070 align:start position:0% your prices can adjust and how much work that<00:22:50.220> you're<00:22:50.400> doing<00:22:50.520> on<00:22:50.880> chain<00:22:51.059> then<00:22:51.960> of 00:22:52.070 --> 00:22:52.080 align:start position:0% that you're doing on chain then of 00:22:52.080 --> 00:22:53.810 align:start position:0% that you're doing on chain then of course<00:22:52.200> on<00:22:52.440> the<00:22:52.559> system<00:22:52.620> designer<00:22:53.220> side<00:22:53.400> so<00:22:53.700> if 00:22:53.810 --> 00:22:53.820 align:start position:0% course on the system designer side so if 00:22:53.820 --> 00:22:54.950 align:start position:0% course on the system designer side so if you're<00:22:53.940> actually<00:22:54.059> trying<00:22:54.299> to<00:22:54.419> use<00:22:54.600> this<00:22:54.780> in 00:22:54.950 --> 00:22:54.960 align:start position:0% you're actually trying to use this in 00:22:54.960 --> 00:22:57.590 align:start position:0% you're actually trying to use this in practice<00:22:55.400> there's<00:22:56.400> a<00:22:56.700> lot<00:22:56.820> of<00:22:56.940> questions<00:22:57.120> that 00:22:57.590 --> 00:22:57.600 align:start position:0% practice there's a lot of questions that 00:22:57.600 --> 00:22:59.149 align:start position:0% practice there's a lot of questions that this<00:22:57.840> General<00:22:58.020> framework<00:22:58.500> doesn't<00:22:58.740> totally 00:22:59.149 --> 00:22:59.159 align:start position:0% this General framework doesn't totally 00:22:59.159 --> 00:23:01.730 align:start position:0% this General framework doesn't totally answer<00:22:59.460> so<00:23:00.120> for<00:23:00.299> example<00:23:00.600> like<00:23:01.020> you<00:23:01.440> know<00:23:01.500> what 00:23:01.730 --> 00:23:01.740 align:start position:0% answer so for example like you know what 00:23:01.740 --> 00:23:03.169 align:start position:0% answer so for example like you know what should<00:23:01.919> the<00:23:02.100> actual<00:23:02.280> resources<00:23:02.700> be<00:23:02.880> in<00:23:03.059> a 00:23:03.169 --> 00:23:03.179 align:start position:0% should the actual resources be in a 00:23:03.179 --> 00:23:04.610 align:start position:0% should the actual resources be in a given<00:23:03.419> system<00:23:03.600> and<00:23:03.900> how<00:23:04.080> do<00:23:04.140> you<00:23:04.260> trade<00:23:04.440> off 00:23:04.610 --> 00:23:04.620 align:start position:0% given system and how do you trade off 00:23:04.620 --> 00:23:06.649 align:start position:0% given system and how do you trade off kind<00:23:04.860> of<00:23:04.980> the<00:23:05.100> complexity<00:23:05.580> pricing<00:23:06.299> every<00:23:06.419> op 00:23:06.649 --> 00:23:06.659 align:start position:0% kind of the complexity pricing every op 00:23:06.659 --> 00:23:08.390 align:start position:0% kind of the complexity pricing every op code<00:23:06.840> every<00:23:07.140> sequence<00:23:07.500> of<00:23:07.620> op<00:23:07.740> codes<00:23:07.980> and<00:23:08.220> so 00:23:08.390 --> 00:23:08.400 align:start position:0% code every sequence of op codes and so 00:23:08.400 --> 00:23:10.190 align:start position:0% code every sequence of op codes and so on<00:23:08.580> and<00:23:09.000> the<00:23:09.120> ease<00:23:09.299> of<00:23:09.419> use<00:23:09.600> of<00:23:09.780> these<00:23:10.020> things 00:23:10.190 --> 00:23:10.200 align:start position:0% on and the ease of use of these things 00:23:10.200 --> 00:23:11.930 align:start position:0% on and the ease of use of these things and<00:23:10.860> then<00:23:10.919> of<00:23:11.100> course<00:23:11.159> how<00:23:11.460> do<00:23:11.520> you<00:23:11.580> determine 00:23:11.930 --> 00:23:11.940 align:start position:0% and then of course how do you determine 00:23:11.940 --> 00:23:13.789 align:start position:0% and then of course how do you determine a<00:23:12.120> loss<00:23:12.419> function<00:23:12.659> for<00:23:13.200> the<00:23:13.380> desired 00:23:13.789 --> 00:23:13.799 align:start position:0% a loss function for the desired 00:23:13.799 --> 00:23:15.770 align:start position:0% a loss function for the desired performance<00:23:14.159> characteristics<00:23:14.880> again<00:23:15.480> kind 00:23:15.770 --> 00:23:15.780 align:start position:0% performance characteristics again kind 00:23:15.780 --> 00:23:17.870 align:start position:0% performance characteristics again kind of<00:23:15.900> the<00:23:15.960> very<00:23:16.200> important<00:23:16.559> Point<00:23:16.860> here<00:23:17.100> is<00:23:17.640> that 00:23:17.870 --> 00:23:17.880 align:start position:0% of the very important Point here is that 00:23:17.880 --> 00:23:19.310 align:start position:0% of the very important Point here is that system<00:23:18.059> designers<00:23:18.659> should<00:23:18.900> be<00:23:19.080> thinking 00:23:19.310 --> 00:23:19.320 align:start position:0% system designers should be thinking 00:23:19.320 --> 00:23:21.230 align:start position:0% system designers should be thinking about<00:23:19.500> these<00:23:19.919> questions<00:23:20.100> but<00:23:20.820> should<00:23:21.059> not 00:23:21.230 --> 00:23:21.240 align:start position:0% about these questions but should not 00:23:21.240 --> 00:23:22.789 align:start position:0% about these questions but should not necessarily<00:23:21.659> be<00:23:21.780> thinking<00:23:22.080> about<00:23:22.200> okay<00:23:22.500> well 00:23:22.789 --> 00:23:22.799 align:start position:0% necessarily be thinking about okay well 00:23:22.799 --> 00:23:25.310 align:start position:0% necessarily be thinking about okay well like<00:23:23.039> how<00:23:23.460> do<00:23:23.580> I<00:23:23.700> do<00:23:23.880> the<00:23:24.179> exact<00:23:24.480> update<00:23:24.960> rule 00:23:25.310 --> 00:23:25.320 align:start position:0% like how do I do the exact update rule 00:23:25.320 --> 00:23:26.810 align:start position:0% like how do I do the exact update rule for<00:23:25.500> prices 00:23:26.810 --> 00:23:26.820 align:start position:0% for prices 00:23:26.820 --> 00:23:28.549 align:start position:0% for prices um<00:23:26.880> because<00:23:27.179> in<00:23:27.480> this<00:23:27.659> framework<00:23:28.020> if<00:23:28.380> you 00:23:28.549 --> 00:23:28.559 align:start position:0% um because in this framework if you 00:23:28.559 --> 00:23:29.990 align:start position:0% um because in this framework if you think<00:23:28.679> about<00:23:28.799> these<00:23:29.220> questions<00:23:29.340> then<00:23:29.760> the 00:23:29.990 --> 00:23:30.000 align:start position:0% think about these questions then the 00:23:30.000 --> 00:23:32.450 align:start position:0% think about these questions then the update<00:23:30.240> rule<00:23:30.539> falls<00:23:30.720> out<00:23:30.960> quite<00:23:31.260> naturally 00:23:32.450 --> 00:23:32.460 align:start position:0% update rule falls out quite naturally 00:23:32.460 --> 00:23:34.190 align:start position:0% update rule falls out quite naturally all<00:23:33.000> right<00:23:33.059> and<00:23:33.419> I<00:23:33.600> encourage<00:23:33.900> you<00:23:33.960> to<00:23:34.080> check 00:23:34.190 --> 00:23:34.200 align:start position:0% all right and I encourage you to check 00:23:34.200 --> 00:23:36.590 align:start position:0% all right and I encourage you to check out<00:23:34.320> the<00:23:34.559> paper<00:23:34.679> which<00:23:35.100> has<00:23:35.280> a<00:23:35.580> lot<00:23:35.940> more<00:23:36.179> and 00:23:36.590 --> 00:23:36.600 align:start position:0% out the paper which has a lot more and 00:23:36.600 --> 00:23:38.810 align:start position:0% out the paper which has a lot more and is<00:23:36.780> kind<00:23:36.960> of<00:23:37.080> like<00:23:37.200> 38<00:23:37.860> pages<00:23:38.280> that<00:23:38.580> goes 00:23:38.810 --> 00:23:38.820 align:start position:0% is kind of like 38 pages that goes 00:23:38.820 --> 00:23:39.830 align:start position:0% is kind of like 38 pages that goes through<00:23:38.940> this<00:23:39.179> entire<00:23:39.419> thing<00:23:39.600> and 00:23:39.830 --> 00:23:39.840 align:start position:0% through this entire thing and 00:23:39.840 --> 00:23:41.630 align:start position:0% through this entire thing and excruciating<00:23:40.380> detail 00:23:41.630 --> 00:23:41.640 align:start position:0% excruciating detail 00:23:41.640 --> 00:23:43.070 align:start position:0% excruciating detail um<00:23:41.700> and<00:23:41.820> happy<00:23:42.000> to<00:23:42.179> take<00:23:42.299> any<00:23:42.419> questions<00:23:42.659> thank 00:23:43.070 --> 00:23:43.080 align:start position:0% um and happy to take any questions thank 00:23:43.080 --> 00:23:44.270 align:start position:0% um and happy to take any questions thank you 00:23:44.270 --> 00:23:44.280 align:start position:0% you 00:23:44.280 --> 00:23:47.630 align:start position:0% you yeah<00:23:45.500> seeing<00:23:46.500> as<00:23:46.620> your<00:23:46.799> your<00:23:47.039> models<00:23:47.520> you're 00:23:47.630 --> 00:23:47.640 align:start position:0% yeah seeing as your your models you're 00:23:47.640 --> 00:23:49.610 align:start position:0% yeah seeing as your your models you're willing<00:23:47.880> to<00:23:48.000> give<00:23:48.240> a<00:23:48.480> different<00:23:48.780> cost<00:23:49.320> to 00:23:49.610 --> 00:23:49.620 align:start position:0% willing to give a different cost to 00:23:49.620 --> 00:23:51.590 align:start position:0% willing to give a different cost to different<00:23:49.860> op<00:23:50.460> code<00:23:50.640> and<00:23:50.880> resources<00:23:51.360> and 00:23:51.590 --> 00:23:51.600 align:start position:0% different op code and resources and 00:23:51.600 --> 00:23:53.870 align:start position:0% different op code and resources and everything<00:23:51.799> uh<00:23:52.799> I<00:23:53.159> think<00:23:53.340> something<00:23:53.640> that 00:23:53.870 --> 00:23:53.880 align:start position:0% everything uh I think something that 00:23:53.880 --> 00:23:56.350 align:start position:0% everything uh I think something that could<00:23:54.059> be<00:23:54.179> interesting<00:23:54.539> to<00:23:54.780> see<00:23:54.960> is<00:23:55.559> um 00:23:56.350 --> 00:23:56.360 align:start position:0% could be interesting to see is um 00:23:56.360 --> 00:23:59.510 align:start position:0% could be interesting to see is um the<00:23:57.360> order<00:23:57.659> of<00:23:58.080> a<00:23:58.260> transaction<00:23:58.559> itself<00:23:58.919> if<00:23:59.340> I 00:23:59.510 --> 00:23:59.520 align:start position:0% the order of a transaction itself if I 00:23:59.520 --> 00:24:00.710 align:start position:0% the order of a transaction itself if I have<00:23:59.640> different<00:23:59.760> costs<00:24:00.059> on<00:24:00.120> items<00:24:00.480> specific 00:24:00.710 --> 00:24:00.720 align:start position:0% have different costs on items specific 00:24:00.720 --> 00:24:03.289 align:start position:0% have different costs on items specific of<00:24:01.200> storage<00:24:01.380> like<00:24:02.159> for<00:24:02.280> example<00:24:02.520> Nova<00:24:03.059> semi 00:24:03.289 --> 00:24:03.299 align:start position:0% of storage like for example Nova semi 00:24:03.299 --> 00:24:05.210 align:start position:0% of storage like for example Nova semi visa<00:24:03.659> thing<00:24:03.840> and<00:24:04.140> generally<00:24:04.620> speaking<00:24:04.919> if<00:24:05.100> you 00:24:05.210 --> 00:24:05.220 align:start position:0% visa thing and generally speaking if you 00:24:05.220 --> 00:24:07.370 align:start position:0% visa thing and generally speaking if you eat<00:24:05.340> a<00:24:05.520> storage<00:24:05.760> slot<00:24:06.240> earlier<00:24:06.600> it<00:24:06.900> does<00:24:07.140> much 00:24:07.370 --> 00:24:07.380 align:start position:0% eat a storage slot earlier it does much 00:24:07.380 --> 00:24:08.810 align:start position:0% eat a storage slot earlier it does much more<00:24:07.559> potential<00:24:07.919> value<00:24:08.100> because<00:24:08.340> this<00:24:08.640> menu 00:24:08.810 --> 00:24:08.820 align:start position:0% more potential value because this menu 00:24:08.820 --> 00:24:11.210 align:start position:0% more potential value because this menu being<00:24:09.059> settled<00:24:09.480> first<00:24:09.679> what<00:24:10.679> would<00:24:10.919> be<00:24:11.100> the 00:24:11.210 --> 00:24:11.220 align:start position:0% being settled first what would be the 00:24:11.220 --> 00:24:14.510 align:start position:0% being settled first what would be the impact<00:24:11.460> of<00:24:11.940> costing<00:24:12.480> differently<00:24:12.960> uh<00:24:13.380> storage 00:24:14.510 --> 00:24:14.520 align:start position:0% impact of costing differently uh storage 00:24:14.520 --> 00:24:17.149 align:start position:0% impact of costing differently uh storage uh<00:24:15.240> of<00:24:15.480> code<00:24:15.720> depending<00:24:16.380> on<00:24:16.500> where<00:24:16.740> you<00:24:16.860> are<00:24:17.039> in 00:24:17.149 --> 00:24:17.159 align:start position:0% uh of code depending on where you are in 00:24:17.159 --> 00:24:18.529 align:start position:0% uh of code depending on where you are in the<00:24:17.280> block<00:24:17.400> and<00:24:17.820> generally<00:24:18.120> speaking<00:24:18.480> in 00:24:18.529 --> 00:24:18.539 align:start position:0% the block and generally speaking in 00:24:18.539 --> 00:24:20.450 align:start position:0% the block and generally speaking in terms<00:24:18.780> of<00:24:18.780> resourcedurization<00:24:19.440> to<00:24:19.679> anything 00:24:20.450 --> 00:24:20.460 align:start position:0% terms of resourcedurization to anything 00:24:20.460 --> 00:24:22.250 align:start position:0% terms of resourcedurization to anything that<00:24:20.820> happened<00:24:20.940> earlier<00:24:21.360> in<00:24:21.480> the<00:24:21.659> chain<00:24:21.840> is 00:24:22.250 --> 00:24:22.260 align:start position:0% that happened earlier in the chain is 00:24:22.260 --> 00:24:23.750 align:start position:0% that happened earlier in the chain is more<00:24:22.380> costly<00:24:22.740> for<00:24:22.919> the<00:24:23.039> network<00:24:23.159> as<00:24:23.460> a<00:24:23.640> whole 00:24:23.750 --> 00:24:23.760 align:start position:0% more costly for the network as a whole 00:24:23.760 --> 00:24:25.430 align:start position:0% more costly for the network as a whole because<00:24:24.240> you<00:24:24.419> need<00:24:24.539> to<00:24:24.659> store<00:24:24.780> it<00:24:24.960> for<00:24:25.080> longer 00:24:25.430 --> 00:24:25.440 align:start position:0% because you need to store it for longer 00:24:25.440 --> 00:24:29.210 align:start position:0% because you need to store it for longer and<00:24:26.340> uh<00:24:26.840> I<00:24:27.840> don't<00:24:28.020> think<00:24:28.260> your<00:24:28.679> framework<00:24:29.100> is 00:24:29.210 --> 00:24:29.220 align:start position:0% and uh I don't think your framework is 00:24:29.220 --> 00:24:31.070 align:start position:0% and uh I don't think your framework is straight<00:24:29.460> up<00:24:29.580> compatible<00:24:30.120> with<00:24:30.419> this<00:24:30.659> costing 00:24:31.070 --> 00:24:31.080 align:start position:0% straight up compatible with this costing 00:24:31.080 --> 00:24:32.570 align:start position:0% straight up compatible with this costing because<00:24:31.260> it's<00:24:31.440> missing<00:24:31.799> one<00:24:31.860> dimension<00:24:32.340> on 00:24:32.570 --> 00:24:32.580 align:start position:0% because it's missing one dimension on 00:24:32.580 --> 00:24:34.970 align:start position:0% because it's missing one dimension on the<00:24:32.760> Vector<00:24:33.659> cost<00:24:33.960> Maybe<00:24:34.200> I'm<00:24:34.440> Wrong<00:24:34.620> yeah 00:24:34.970 --> 00:24:34.980 align:start position:0% the Vector cost Maybe I'm Wrong yeah 00:24:34.980 --> 00:24:37.070 align:start position:0% the Vector cost Maybe I'm Wrong yeah that's<00:24:35.700> actually<00:24:36.000> a<00:24:36.240> great<00:24:36.299> question<00:24:36.960> um<00:24:36.960> I 00:24:37.070 --> 00:24:37.080 align:start position:0% that's actually a great question um I 00:24:37.080 --> 00:24:38.390 align:start position:0% that's actually a great question um I think<00:24:37.200> it's<00:24:37.320> compatible<00:24:37.679> with<00:24:37.799> the<00:24:38.039> first<00:24:38.159> but 00:24:38.390 --> 00:24:38.400 align:start position:0% think it's compatible with the first but 00:24:38.400 --> 00:24:40.190 align:start position:0% think it's compatible with the first but not<00:24:38.580> necessarily<00:24:39.000> the<00:24:39.419> second<00:24:39.600> or<00:24:39.900> the<00:24:40.080> second 00:24:40.190 --> 00:24:40.200 align:start position:0% not necessarily the second or the second 00:24:40.200 --> 00:24:41.990 align:start position:0% not necessarily the second or the second one<00:24:40.440> you<00:24:40.740> could<00:24:40.860> probably<00:24:41.100> put<00:24:41.460> into<00:24:41.640> it<00:24:41.880> but 00:24:41.990 --> 00:24:42.000 align:start position:0% one you could probably put into it but 00:24:42.000 --> 00:24:43.070 align:start position:0% one you could probably put into it but it<00:24:42.120> would<00:24:42.179> be<00:24:42.299> a<00:24:42.419> little<00:24:42.419> bit<00:24:42.600> harder<00:24:42.900> this 00:24:43.070 --> 00:24:43.080 align:start position:0% it would be a little bit harder this 00:24:43.080 --> 00:24:45.230 align:start position:0% it would be a little bit harder this kind<00:24:43.320> of<00:24:43.380> multi-block<00:24:43.860> one<00:24:44.159> however<00:24:44.880> for<00:24:45.059> a 00:24:45.230 --> 00:24:45.240 align:start position:0% kind of multi-block one however for a 00:24:45.240 --> 00:24:46.909 align:start position:0% kind of multi-block one however for a single<00:24:45.480> block<00:24:46.080> um<00:24:46.140> you<00:24:46.320> could<00:24:46.380> actually<00:24:46.559> view 00:24:46.909 --> 00:24:46.919 align:start position:0% single block um you could actually view 00:24:46.919 --> 00:24:49.669 align:start position:0% single block um you could actually view you<00:24:47.220> know<00:24:47.340> that<00:24:48.059> set<00:24:48.240> s<00:24:48.600> can<00:24:48.960> saying<00:24:49.380> like<00:24:49.500> you 00:24:49.669 --> 00:24:49.679 align:start position:0% you know that set s can saying like you 00:24:49.679 --> 00:24:51.110 align:start position:0% you know that set s can saying like you know<00:24:49.799> this<00:24:49.980> transaction<00:24:50.400> goes<00:24:50.700> before<00:24:50.820> this 00:24:51.110 --> 00:24:51.120 align:start position:0% know this transaction goes before this 00:24:51.120 --> 00:24:52.730 align:start position:0% know this transaction goes before this one<00:24:51.240> or<00:24:51.419> this<00:24:51.600> transaction<00:24:51.900> goes<00:24:52.320> after<00:24:52.440> this 00:24:52.730 --> 00:24:52.740 align:start position:0% one or this transaction goes after this 00:24:52.740 --> 00:24:54.470 align:start position:0% one or this transaction goes after this one<00:24:52.980> and<00:24:53.460> then<00:24:53.580> perhaps<00:24:53.940> if<00:24:54.120> you're<00:24:54.299> the 00:24:54.470 --> 00:24:54.480 align:start position:0% one and then perhaps if you're the 00:24:54.480 --> 00:24:56.450 align:start position:0% one and then perhaps if you're the second<00:24:54.720> uh<00:24:55.500> transaction<00:24:55.980> in<00:24:56.220> the<00:24:56.340> block 00:24:56.450 --> 00:24:56.460 align:start position:0% second uh transaction in the block 00:24:56.460 --> 00:24:57.950 align:start position:0% second uh transaction in the block you're<00:24:57.059> actually<00:24:57.299> using<00:24:57.659> a<00:24:57.840> different 00:24:57.950 --> 00:24:57.960 align:start position:0% you're actually using a different 00:24:57.960 --> 00:24:59.630 align:start position:0% you're actually using a different resource<00:24:58.440> so<00:24:58.620> you're<00:24:58.740> using<00:24:59.039> like<00:24:59.220> the<00:24:59.460> second 00:24:59.630 --> 00:24:59.640 align:start position:0% resource so you're using like the second 00:24:59.640 --> 00:25:01.370 align:start position:0% resource so you're using like the second read<00:24:59.940> so<00:25:00.539> that<00:25:00.720> should<00:25:00.840> be<00:25:00.960> extremely 00:25:01.370 --> 00:25:01.380 align:start position:0% read so that should be extremely 00:25:01.380 --> 00:25:02.870 align:start position:0% read so that should be extremely beneficial<00:25:01.799> on<00:25:01.980> field<00:25:02.159> from<00:25:02.340> a<00:25:02.460> network<00:25:02.580> if 00:25:02.870 --> 00:25:02.880 align:start position:0% beneficial on field from a network if 00:25:02.880 --> 00:25:04.310 align:start position:0% beneficial on field from a network if you<00:25:03.000> can<00:25:03.059> convince<00:25:03.360> more<00:25:03.539> people<00:25:03.720> of<00:25:04.020> going 00:25:04.310 --> 00:25:04.320 align:start position:0% you can convince more people of going 00:25:04.320 --> 00:25:05.990 align:start position:0% you can convince more people of going this<00:25:04.559> direction<00:25:04.799> because<00:25:05.220> this<00:25:05.520> means<00:25:05.820> lower 00:25:05.990 --> 00:25:06.000 align:start position:0% this direction because this means lower 00:25:06.000 --> 00:25:08.029 align:start position:0% this direction because this means lower cost<00:25:06.240> for<00:25:06.600> everyone<00:25:06.720> and<00:25:07.440> better<00:25:07.559> reputation 00:25:08.029 --> 00:25:08.039 align:start position:0% cost for everyone and better reputation 00:25:08.039 --> 00:25:10.490 align:start position:0% cost for everyone and better reputation first<00:25:08.400> one<00:25:08.640> so<00:25:08.820> very<00:25:09.600> good<00:25:09.900> direction<00:25:10.140> I'm 00:25:10.490 --> 00:25:10.500 align:start position:0% first one so very good direction I'm 00:25:10.500 --> 00:25:12.590 align:start position:0% first one so very good direction I'm very<00:25:10.860> happy<00:25:11.039> to<00:25:11.340> see<00:25:11.520> I'm<00:25:12.240> not<00:25:12.299> saying<00:25:12.480> it's 00:25:12.590 --> 00:25:12.600 align:start position:0% very happy to see I'm not saying it's 00:25:12.600 --> 00:25:14.450 align:start position:0% very happy to see I'm not saying it's easy<00:25:12.780> to<00:25:12.960> implement<00:25:13.200> though 00:25:14.450 --> 00:25:14.460 align:start position:0% easy to implement though 00:25:14.460 --> 00:25:16.669 align:start position:0% easy to implement though very<00:25:14.880> difficult<00:25:15.120> to<00:25:15.360> implement<00:25:15.539> but<00:25:15.960> if<00:25:16.380> even 00:25:16.669 --> 00:25:16.679 align:start position:0% very difficult to implement but if even 00:25:16.679 --> 00:25:18.409 align:start position:0% very difficult to implement but if even if<00:25:16.919> here<00:25:17.100> it<00:25:17.280> breaks<00:25:17.580> like<00:25:17.760> implementation<00:25:18.299> is 00:25:18.409 --> 00:25:18.419 align:start position:0% if here it breaks like implementation is 00:25:18.419 --> 00:25:21.250 align:start position:0% if here it breaks like implementation is not<00:25:18.539> going<00:25:18.659> to<00:25:18.720> be<00:25:18.780> possible<00:25:19.020> thank<00:25:19.860> you 00:25:21.250 --> 00:25:21.260 align:start position:0% not going to be possible thank you 00:25:21.260 --> 00:25:24.230 align:start position:0% not going to be possible thank you so<00:25:22.260> do<00:25:22.860> you<00:25:23.039> see<00:25:23.100> this<00:25:23.400> research<00:25:23.880> being 00:25:24.230 --> 00:25:24.240 align:start position:0% so do you see this research being 00:25:24.240 --> 00:25:27.529 align:start position:0% so do you see this research being applied<00:25:24.900> directly<00:25:25.740> for<00:25:26.039> example<00:25:26.340> in<00:25:26.700> ethereum 00:25:27.529 --> 00:25:27.539 align:start position:0% applied directly for example in ethereum 00:25:27.539 --> 00:25:30.890 align:start position:0% applied directly for example in ethereum in<00:25:28.320> like<00:25:28.620> I<00:25:28.919> don't<00:25:29.039> know<00:25:29.159> 50<00:25:29.460> years<00:25:29.700> or<00:25:30.600> maybe 00:25:30.890 --> 00:25:30.900 align:start position:0% in like I don't know 50 years or maybe 00:25:30.900 --> 00:25:32.990 align:start position:0% in like I don't know 50 years or maybe sooner<00:25:31.320> uh<00:25:31.980> I<00:25:32.159> think<00:25:32.279> there's<00:25:32.460> probably<00:25:32.760> some 00:25:32.990 --> 00:25:33.000 align:start position:0% sooner uh I think there's probably some 00:25:33.000 --> 00:25:34.070 align:start position:0% sooner uh I think there's probably some people<00:25:33.120> in<00:25:33.299> this<00:25:33.419> room<00:25:33.600> that<00:25:33.840> could<00:25:33.960> answer 00:25:34.070 --> 00:25:34.080 align:start position:0% people in this room that could answer 00:25:34.080 --> 00:25:37.370 align:start position:0% people in this room that could answer that<00:25:34.320> better<00:25:34.500> than<00:25:34.740> I<00:25:34.980> can<00:25:35.159> but<00:25:36.480> um<00:25:36.539> I<00:25:36.900> think<00:25:37.200> we 00:25:37.370 --> 00:25:37.380 align:start position:0% that better than I can but um I think we 00:25:37.380 --> 00:25:39.049 align:start position:0% that better than I can but um I think we we've<00:25:37.740> gotten<00:25:37.980> a<00:25:38.100> lot<00:25:38.159> of<00:25:38.279> interest<00:25:38.400> from 00:25:39.049 --> 00:25:39.059 align:start position:0% we've gotten a lot of interest from 00:25:39.059 --> 00:25:40.909 align:start position:0% we've gotten a lot of interest from different<00:25:39.480> protocols<00:25:40.080> that<00:25:40.380> are<00:25:40.559> you<00:25:40.860> know 00:25:40.909 --> 00:25:40.919 align:start position:0% different protocols that are you know 00:25:40.919 --> 00:25:43.070 align:start position:0% different protocols that are you know Roll-Ups<00:25:42.240> um 00:25:43.070 --> 00:25:43.080 align:start position:0% Roll-Ups um 00:25:43.080 --> 00:25:45.049 align:start position:0% Roll-Ups um Etc<00:25:43.200> that<00:25:43.679> are<00:25:43.799> interested<00:25:44.279> in<00:25:44.340> us<00:25:44.580> and<00:25:44.820> from 00:25:45.049 --> 00:25:45.059 align:start position:0% Etc that are interested in us and from 00:25:45.059 --> 00:25:47.330 align:start position:0% Etc that are interested in us and from the<00:25:45.179> ethereum<00:25:45.600> research<00:25:45.900> team<00:25:46.140> as<00:25:46.380> well 00:25:47.330 --> 00:25:47.340 align:start position:0% the ethereum research team as well 00:25:47.340 --> 00:25:48.950 align:start position:0% the ethereum research team as well um<00:25:47.400> I<00:25:47.760> can't<00:25:48.000> speak<00:25:48.240> to<00:25:48.539> development 00:25:48.950 --> 00:25:48.960 align:start position:0% um I can't speak to development 00:25:48.960 --> 00:25:50.750 align:start position:0% um I can't speak to development timelines<00:25:49.559> though<00:25:49.860> and<00:25:50.100> when<00:25:50.340> this<00:25:50.520> stuff 00:25:50.750 --> 00:25:50.760 align:start position:0% timelines though and when this stuff 00:25:50.760 --> 00:25:52.610 align:start position:0% timelines though and when this stuff would<00:25:50.940> be<00:25:51.120> like<00:25:51.360> I<00:25:51.539> said<00:25:51.659> there's<00:25:52.260> definitely 00:25:52.610 --> 00:25:52.620 align:start position:0% would be like I said there's definitely 00:25:52.620 --> 00:25:54.230 align:start position:0% would be like I said there's definitely quite<00:25:52.860> a<00:25:53.039> bit<00:25:53.100> of<00:25:53.220> future<00:25:53.340> work<00:25:53.640> that<00:25:53.940> has<00:25:54.120> to 00:25:54.230 --> 00:25:54.240 align:start position:0% quite a bit of future work that has to 00:25:54.240 --> 00:25:56.810 align:start position:0% quite a bit of future work that has to go<00:25:54.419> into<00:25:54.600> making<00:25:54.960> this<00:25:55.260> production<00:25:55.559> ready 00:25:56.810 --> 00:25:56.820 align:start position:0% go into making this production ready 00:25:56.820 --> 00:26:00.350 align:start position:0% go into making this production ready um<00:25:56.880> and<00:25:57.059> I<00:25:57.179> imagine<00:25:57.360> that<00:25:57.900> uh<00:25:58.679> you<00:25:59.340> know<00:25:59.460> newer 00:26:00.350 --> 00:26:00.360 align:start position:0% um and I imagine that uh you know newer 00:26:00.360 --> 00:26:04.490 align:start position:0% um and I imagine that uh you know newer newer<00:26:00.779> chains<00:26:01.200> that<00:26:01.679> maybe<00:26:01.980> aren't<00:26:02.460> as<00:26:03.000> uh 00:26:04.490 --> 00:26:04.500 align:start position:0% newer chains that maybe aren't as uh 00:26:04.500 --> 00:26:06.590 align:start position:0% newer chains that maybe aren't as uh don't<00:26:04.980> have<00:26:05.220> to<00:26:05.580> pressure<00:26:05.880> test<00:26:06.179> their 00:26:06.590 --> 00:26:06.600 align:start position:0% don't have to pressure test their 00:26:06.600 --> 00:26:08.330 align:start position:0% don't have to pressure test their changes<00:26:06.960> quite<00:26:07.260> as<00:26:07.440> much<00:26:07.620> we'll<00:26:08.039> probably 00:26:08.330 --> 00:26:08.340 align:start position:0% changes quite as much we'll probably 00:26:08.340 --> 00:26:09.769 align:start position:0% changes quite as much we'll probably adopt<00:26:09.059> something<00:26:09.179> like<00:26:09.419> this<00:26:09.539> before 00:26:09.769 --> 00:26:09.779 align:start position:0% adopt something like this before 00:26:09.779 --> 00:26:11.570 align:start position:0% adopt something like this before ethereum<00:26:10.380> would 00:26:11.570 --> 00:26:11.580 align:start position:0% ethereum would 00:26:11.580 --> 00:26:13.010 align:start position:0% ethereum would you 00:26:13.010 --> 00:26:13.020 align:start position:0% you 00:26:13.020 --> 00:26:14.570 align:start position:0% you um so<00:26:13.260> in<00:26:13.500> the<00:26:13.620> interest<00:26:13.679> of<00:26:13.980> keeping<00:26:14.220> this<00:26:14.340> a 00:26:14.570 --> 00:26:14.580 align:start position:0% um so in the interest of keeping this a 00:26:14.580 --> 00:26:16.669 align:start position:0% um so in the interest of keeping this a convex<00:26:15.059> optimization<00:26:15.600> problem<00:26:15.960> are<00:26:16.500> there 00:26:16.669 --> 00:26:16.679 align:start position:0% convex optimization problem are there 00:26:16.679 --> 00:26:18.830 align:start position:0% convex optimization problem are there any<00:26:16.799> limitations<00:26:17.580> this<00:26:17.940> puts<00:26:18.240> on<00:26:18.360> how<00:26:18.539> we<00:26:18.720> can 00:26:18.830 --> 00:26:18.840 align:start position:0% any limitations this puts on how we can 00:26:18.840 --> 00:26:20.990 align:start position:0% any limitations this puts on how we can construct<00:26:19.260> different<00:26:20.039> parts<00:26:20.340> of<00:26:20.580> the<00:26:20.760> problem 00:26:20.990 --> 00:26:21.000 align:start position:0% construct different parts of the problem 00:26:21.000 --> 00:26:24.049 align:start position:0% construct different parts of the problem so<00:26:21.299> such<00:26:21.539> as<00:26:21.659> the<00:26:21.720> Lost<00:26:21.900> landscape<00:26:22.380> or<00:26:23.340> have<00:26:23.880> I 00:26:24.049 --> 00:26:24.059 align:start position:0% so such as the Lost landscape or have I 00:26:24.059 --> 00:26:25.430 align:start position:0% so such as the Lost landscape or have I missed<00:26:24.299> something<00:26:24.419> and<00:26:24.659> is<00:26:24.840> there<00:26:25.020> kind<00:26:25.260> of<00:26:25.320> a 00:26:25.430 --> 00:26:25.440 align:start position:0% missed something and is there kind of a 00:26:25.440 --> 00:26:27.110 align:start position:0% missed something and is there kind of a chance<00:26:25.559> we<00:26:25.799> can<00:26:25.919> land<00:26:26.039> in<00:26:26.279> a<00:26:26.460> local<00:26:26.580> Optimum 00:26:27.110 --> 00:26:27.120 align:start position:0% chance we can land in a local Optimum 00:26:27.120 --> 00:26:29.930 align:start position:0% chance we can land in a local Optimum rather<00:26:27.360> than<00:26:27.539> a<00:26:27.779> global<00:26:28.080> Optimum<00:26:28.500> here 00:26:29.930 --> 00:26:29.940 align:start position:0% rather than a global Optimum here 00:26:29.940 --> 00:26:31.669 align:start position:0% rather than a global Optimum here um also<00:26:30.360> a<00:26:30.419> good<00:26:30.539> question<00:26:30.720> well<00:26:30.960> so<00:26:31.260> the<00:26:31.440> loss 00:26:31.669 --> 00:26:31.679 align:start position:0% um also a good question well so the loss 00:26:31.679 --> 00:26:34.070 align:start position:0% um also a good question well so the loss function<00:26:31.919> has<00:26:32.100> to<00:26:32.220> be<00:26:32.279> convex<00:26:32.820> uh<00:26:33.480> so<00:26:33.659> there's 00:26:34.070 --> 00:26:34.080 align:start position:0% function has to be convex uh so there's 00:26:34.080 --> 00:26:36.230 align:start position:0% function has to be convex uh so there's you<00:26:34.440> know<00:26:34.500> one<00:26:34.740> immediate<00:26:35.220> thing<00:26:35.880> that<00:26:36.059> you 00:26:36.230 --> 00:26:36.240 align:start position:0% you know one immediate thing that you 00:26:36.240 --> 00:26:38.510 align:start position:0% you know one immediate thing that you have<00:26:36.360> from<00:26:36.720> con<00:26:37.020> and<00:26:37.380> you<00:26:37.919> can<00:26:37.980> imagine<00:26:38.159> that 00:26:38.510 --> 00:26:38.520 align:start position:0% have from con and you can imagine that 00:26:38.520 --> 00:26:40.549 align:start position:0% have from con and you can imagine that maybe<00:26:38.700> I<00:26:39.059> don't<00:26:39.120> know<00:26:39.240> if<00:26:39.480> there's<00:26:39.720> two<00:26:40.320> states 00:26:40.549 --> 00:26:40.559 align:start position:0% maybe I don't know if there's two states 00:26:40.559 --> 00:26:41.810 align:start position:0% maybe I don't know if there's two states that<00:26:40.799> you<00:26:40.860> want<00:26:40.980> to<00:26:41.100> run<00:26:41.220> in<00:26:41.400> and<00:26:41.640> maybe 00:26:41.810 --> 00:26:41.820 align:start position:0% that you want to run in and maybe 00:26:41.820 --> 00:26:43.370 align:start position:0% that you want to run in and maybe sometimes<00:26:42.240> you<00:26:42.360> want<00:26:42.539> to<00:26:42.659> go<00:26:42.720> hit<00:26:43.020> for<00:26:43.260> one 00:26:43.370 --> 00:26:43.380 align:start position:0% sometimes you want to go hit for one 00:26:43.380 --> 00:26:44.630 align:start position:0% sometimes you want to go hit for one target<00:26:43.559> sometimes<00:26:43.980> you<00:26:44.100> want<00:26:44.279> to<00:26:44.340> hit<00:26:44.460> another 00:26:44.630 --> 00:26:44.640 align:start position:0% target sometimes you want to hit another 00:26:44.640 --> 00:26:46.909 align:start position:0% target sometimes you want to hit another that<00:26:45.360> wouldn't<00:26:45.480> be<00:26:45.720> convex<00:26:46.260> if<00:26:46.500> you<00:26:46.620> kind<00:26:46.799> of 00:26:46.909 --> 00:26:46.919 align:start position:0% that wouldn't be convex if you kind of 00:26:46.919 --> 00:26:48.470 align:start position:0% that wouldn't be convex if you kind of your<00:26:47.100> landscape<00:26:47.520> looks<00:26:47.880> like<00:26:48.000> something<00:26:48.179> like 00:26:48.470 --> 00:26:48.480 align:start position:0% your landscape looks like something like 00:26:48.480 --> 00:26:49.490 align:start position:0% your landscape looks like something like this 00:26:49.490 --> 00:26:49.500 align:start position:0% this 00:26:49.500 --> 00:26:50.750 align:start position:0% this um so<00:26:49.679> there<00:26:49.799> definitely<00:26:50.039> are<00:26:50.220> limitations 00:26:50.750 --> 00:26:50.760 align:start position:0% um so there definitely are limitations 00:26:50.760 --> 00:26:53.090 align:start position:0% um so there definitely are limitations the<00:26:51.240> other<00:26:51.299> thing<00:26:51.480> here<00:26:51.779> is<00:26:52.440> um<00:26:52.440> we<00:26:52.919> kind<00:26:53.039> of 00:26:53.090 --> 00:26:53.100 align:start position:0% the other thing here is um we kind of 00:26:53.100 --> 00:26:55.549 align:start position:0% the other thing here is um we kind of have<00:26:53.279> this<00:26:53.640> uh<00:26:53.940> the<00:26:54.240> resource<00:26:54.659> part<00:26:55.140> is<00:26:55.320> very 00:26:55.549 --> 00:26:55.559 align:start position:0% have this uh the resource part is very 00:26:55.559 --> 00:26:57.769 align:start position:0% have this uh the resource part is very general<00:26:55.799> and<00:26:56.580> to<00:26:56.760> the<00:26:56.880> question<00:26:57.059> earlier<00:26:57.480> that 00:26:57.769 --> 00:26:57.779 align:start position:0% general and to the question earlier that 00:26:57.779 --> 00:26:59.149 align:start position:0% general and to the question earlier that you<00:26:57.960> can<00:26:58.020> kind<00:26:58.200> of<00:26:58.260> have<00:26:58.440> these<00:26:58.740> resources 00:26:59.149 --> 00:26:59.159 align:start position:0% you can kind of have these resources 00:26:59.159 --> 00:27:01.010 align:start position:0% you can kind of have these resources that<00:26:59.520> are<00:26:59.820> dependent<00:27:00.360> so<00:27:00.600> like<00:27:00.779> one 00:27:01.010 --> 00:27:01.020 align:start position:0% that are dependent so like one 00:27:01.020 --> 00:27:02.930 align:start position:0% that are dependent so like one transaction<00:27:01.559> can<00:27:02.100> be<00:27:02.279> dependent<00:27:02.640> on<00:27:02.760> another 00:27:02.930 --> 00:27:02.940 align:start position:0% transaction can be dependent on another 00:27:02.940 --> 00:27:06.649 align:start position:0% transaction can be dependent on another however<00:27:03.840> we<00:27:04.620> do<00:27:04.740> encode<00:27:05.159> this<00:27:05.400> all<00:27:05.640> in<00:27:06.120> like<00:27:06.419> an 00:27:06.649 --> 00:27:06.659 align:start position:0% however we do encode this all in like an 00:27:06.659 --> 00:27:08.330 align:start position:0% however we do encode this all in like an additive<00:27:07.020> linear<00:27:07.440> way 00:27:08.330 --> 00:27:08.340 align:start position:0% additive linear way 00:27:08.340 --> 00:27:10.490 align:start position:0% additive linear way um<00:27:08.400> and<00:27:08.760> there's<00:27:09.240> it's<00:27:09.779> probably<00:27:10.020> not<00:27:10.260> the 00:27:10.490 --> 00:27:10.500 align:start position:0% um and there's it's probably not the 00:27:10.500 --> 00:27:12.110 align:start position:0% um and there's it's probably not the most<00:27:10.620> efficient<00:27:10.980> thing<00:27:11.159> to<00:27:11.400> do 00:27:12.110 --> 00:27:12.120 align:start position:0% most efficient thing to do 00:27:12.120 --> 00:27:13.190 align:start position:0% most efficient thing to do um<00:27:12.179> for<00:27:12.419> the<00:27:12.539> reasons<00:27:12.779> that<00:27:12.900> I<00:27:13.020> talked<00:27:13.200> about 00:27:13.190 --> 00:27:13.200 align:start position:0% um for the reasons that I talked about 00:27:13.200 --> 00:27:14.269 align:start position:0% um for the reasons that I talked about earlier<00:27:13.500> is<00:27:13.620> you<00:27:13.799> kind<00:27:13.919> of<00:27:13.980> get<00:27:14.100> this 00:27:14.269 --> 00:27:14.279 align:start position:0% earlier is you kind of get this 00:27:14.279 --> 00:27:16.130 align:start position:0% earlier is you kind of get this exploding<00:27:14.820> complexity 00:27:16.130 --> 00:27:16.140 align:start position:0% exploding complexity 00:27:16.140 --> 00:27:17.630 align:start position:0% exploding complexity um as<00:27:16.320> you<00:27:16.440> do<00:27:16.620> that<00:27:16.740> however<00:27:17.039> if<00:27:17.400> you<00:27:17.460> don't 00:27:17.630 --> 00:27:17.640 align:start position:0% um as you do that however if you don't 00:27:17.640 --> 00:27:19.549 align:start position:0% um as you do that however if you don't do<00:27:17.820> that<00:27:18.000> you<00:27:18.419> get<00:27:18.659> to<00:27:19.080> kind<00:27:19.320> of<00:27:19.380> the 00:27:19.549 --> 00:27:19.559 align:start position:0% do that you get to kind of the 00:27:19.559 --> 00:27:23.029 align:start position:0% do that you get to kind of the non-convex<00:27:20.279> world<00:27:20.460> so<00:27:21.240> it<00:27:22.020> might<00:27:22.200> be<00:27:22.440> a<00:27:22.679> more 00:27:23.029 --> 00:27:23.039 align:start position:0% non-convex world so it might be a more 00:27:23.039 --> 00:27:26.090 align:start position:0% non-convex world so it might be a more succinct<00:27:23.580> or<00:27:23.820> lower<00:27:24.059> like<00:27:24.600> uh<00:27:25.080> complexity<00:27:25.740> way 00:27:26.090 --> 00:27:26.100 align:start position:0% succinct or lower like uh complexity way 00:27:26.100 --> 00:27:28.250 align:start position:0% succinct or lower like uh complexity way of<00:27:26.340> describing<00:27:26.940> what<00:27:27.659> it<00:27:27.779> is<00:27:27.900> that<00:27:28.020> you<00:27:28.140> want 00:27:28.250 --> 00:27:28.260 align:start position:0% of describing what it is that you want 00:27:28.260 --> 00:27:29.690 align:start position:0% of describing what it is that you want to<00:27:28.380> do<00:27:28.440> but<00:27:28.679> you<00:27:28.740> won't<00:27:28.860> actually<00:27:28.980> be<00:27:29.159> able<00:27:29.580> to 00:27:29.690 --> 00:27:29.700 align:start position:0% to do but you won't actually be able to 00:27:29.700 --> 00:27:32.810 align:start position:0% to do but you won't actually be able to solve<00:27:30.000> it<00:27:30.320> and<00:27:31.320> this<00:27:31.799> entire<00:27:32.039> framework<00:27:32.460> does 00:27:32.810 --> 00:27:32.820 align:start position:0% solve it and this entire framework does 00:27:32.820 --> 00:27:35.269 align:start position:0% solve it and this entire framework does rely<00:27:33.179> on<00:27:33.360> strong<00:27:33.600> Duality<00:27:34.140> which<00:27:34.860> you<00:27:35.100> only 00:27:35.269 --> 00:27:35.279 align:start position:0% rely on strong Duality which you only 00:27:35.279 --> 00:27:37.850 align:start position:0% rely on strong Duality which you only really<00:27:35.640> get<00:27:35.880> in<00:27:36.059> convex<00:27:36.480> on<00:27:36.720> you<00:27:37.440> mostly<00:27:37.679> only 00:27:37.850 --> 00:27:37.860 align:start position:0% really get in convex on you mostly only 00:27:37.860 --> 00:27:39.950 align:start position:0% really get in convex on you mostly only get<00:27:38.100> in<00:27:38.220> convex<00:27:38.700> optimization<00:27:39.240> problems<00:27:39.779> or 00:27:39.950 --> 00:27:39.960 align:start position:0% get in convex optimization problems or 00:27:39.960 --> 00:27:42.110 align:start position:0% get in convex optimization problems or it's<00:27:40.140> very<00:27:40.500> rare<00:27:40.799> to<00:27:41.039> get<00:27:41.159> it<00:27:41.340> in<00:27:41.520> non-convex 00:27:42.110 --> 00:27:42.120 align:start position:0% it's very rare to get it in non-convex 00:27:42.120 --> 00:27:44.210 align:start position:0% it's very rare to get it in non-convex problems<00:27:42.600> and<00:27:42.779> that<00:27:42.900> that<00:27:43.080> allows<00:27:43.440> us<00:27:43.559> to<00:27:43.860> look 00:27:44.210 --> 00:27:44.220 align:start position:0% problems and that that allows us to look 00:27:44.220 --> 00:27:46.070 align:start position:0% problems and that that allows us to look at<00:27:44.400> the<00:27:44.580> prices<00:27:44.760> which<00:27:45.240> is<00:27:45.360> kind<00:27:45.539> of<00:27:45.600> the<00:27:45.779> Dual 00:27:46.070 --> 00:27:46.080 align:start position:0% at the prices which is kind of the Dual 00:27:46.080 --> 00:27:48.830 align:start position:0% at the prices which is kind of the Dual of<00:27:46.860> that<00:27:47.220> instead<00:27:48.000> of<00:27:48.059> looking<00:27:48.179> at<00:27:48.360> like<00:27:48.539> what 00:27:48.830 --> 00:27:48.840 align:start position:0% of that instead of looking at like what 00:27:48.840 --> 00:27:50.510 align:start position:0% of that instead of looking at like what transactions<00:27:49.380> do<00:27:49.500> I<00:27:49.620> include<00:27:49.860> I<00:27:50.159> look<00:27:50.279> at<00:27:50.400> how 00:27:50.510 --> 00:27:50.520 align:start position:0% transactions do I include I look at how 00:27:50.520 --> 00:27:52.370 align:start position:0% transactions do I include I look at how do<00:27:50.700> I<00:27:50.820> set<00:27:50.940> prices<00:27:51.179> but<00:27:51.900> that's<00:27:52.080> a<00:27:52.260> great 00:27:52.370 --> 00:27:52.380 align:start position:0% do I set prices but that's a great 00:27:52.380 --> 00:27:53.149 align:start position:0% do I set prices but that's a great question 00:27:53.149 --> 00:27:53.159 align:start position:0% question 00:27:53.159 --> 00:27:54.590 align:start position:0% question thank<00:27:53.820> you 00:27:54.590 --> 00:27:54.600 align:start position:0% thank you 00:27:54.600 --> 00:27:55.970 align:start position:0% thank you the<00:27:55.080> video 00:27:55.970 --> 00:27:55.980 align:start position:0% the video 00:27:55.980 --> 00:27:57.789 align:start position:0% the video thank<00:27:56.460> you 00:27:57.789 --> 00:27:57.799 align:start position:0% thank you 00:27:57.799 --> 00:28:00.409 align:start position:0% thank you and<00:27:58.799> now<00:27:58.919> people<00:27:59.159> let's<00:27:59.520> go<00:27:59.700> to<00:27:59.820> the<00:28:00.000> top<00:28:00.179> of 00:28:00.409 --> 00:28:00.419 align:start position:0% and now people let's go to the top of 00:28:00.419 --> 00:28:02.450 align:start position:0% and now people let's go to the top of the<00:28:00.779> mountain<00:28:01.020> to<00:28:01.500> find<00:28:01.679> where<00:28:02.039> is<00:28:02.220> going<00:28:02.340> to 00:28:02.450 --> 00:28:02.460 align:start position:0% the mountain to find where is going to 00:28:02.460 --> 00:28:05.900 align:start position:0% the mountain to find where is going to be<00:28:02.580> defcom7<00:28:03.299> see<00:28:03.600> you<00:28:03.779> there