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Tradeoffs and Average-Case Equilibria in Selfish Routing

Martin Hoefer, Alexander Souza
<span title="2010-11-01">2010</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/o4i7rml3svgnppoghhzxfanmkm" style="color: black;">ACM Transactions on Computation Theory</a> </i> &nbsp;
Furthermore, our analyses of the expected prices are average-case analyses of a local search algorithm that computes Nash equilibria in polynomial time.  ...  We consider the price of selfish routing in terms of tradeoffs and from an average-case perspective.  ...  An immediate question is the applicability of the obtained results to the average-case performance of Nash equilibria in more general (network) congestion games.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1867719.1867721">doi:10.1145/1867719.1867721</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kck3itjaczdbblu364xdt6tdy4">fatcat:kck3itjaczdbblu364xdt6tdy4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829150555/https://www.uni-konstanz.de/mmsp/pubsys/publishedFiles/HoSo07.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/00/48/0048f800ddae8040d7f75a06616ca8004b132c75.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1867719.1867721"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Tradeoffs and Average-Case Equilibria in Selfish Routing [chapter]

Martin Hoefer, Alexander Souza
<i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uot5qmdbz5g6rasdd5kuoonkzu" style="color: black;">Algorithms – ESA 2007</a> </i> &nbsp;
Furthermore, our analyses of the expected prices are average-case analyses of a local search algorithm that computes Nash equilibria in polynomial time.  ...  We consider the price of selfish routing in terms of tradeoffs and from an average-case perspective.  ...  An immediate question is the applicability of the obtained results to the average-case performance of Nash equilibria in more general (network) congestion games.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-75520-3_8">doi:10.1007/978-3-540-75520-3_8</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/esa/HoeferS07.html">dblp:conf/esa/HoeferS07</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mx255icp5zdq5lk4td7jvjyexy">fatcat:mx255icp5zdq5lk4td7jvjyexy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829150555/https://www.uni-konstanz.de/mmsp/pubsys/publishedFiles/HoSo07.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/00/48/0048f800ddae8040d7f75a06616ca8004b132c75.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-75520-3_8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Stability and convergence for systems with switching equilibria

Silvia Mastellone, Dusan M. Stipanovic, Mark W. Spong
<span title="">2007</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wjd7b2sxyfahnaei4xvi46vwsu" style="color: black;">2007 46th IEEE Conference on Decision and Control</a> </i> &nbsp;
In the time-dependent switching case we highlight connections between the relaxation theorem corresponding to differential inclusions, Pulse-Width-Modulation (PWM) and averaging theory.  ...  We refer to those systems as systems with switching equilibria. To motivate our study, we describe a class of problems in engineering and biology that can be formulated using such systems.  ...  We extend some of the results from averaging theory (see [5] ) to the case of systems with switching equilibria.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2007.4434822">doi:10.1109/cdc.2007.4434822</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cdc/MastelloneSS07.html">dblp:conf/cdc/MastelloneSS07</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/crqpovehjrgovfn6jix6bzuoba">fatcat:crqpovehjrgovfn6jix6bzuoba</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130807074047/http://ise.illinois.edu/sites/default/files/documents/stability_and_convergence.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a2/69/a269df8fabe917fb011ea50c94b6adfeb2b1ae95.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2007.4434822"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Page 1301 of Cellular and Molecular Life Sciences Vol. 41, Issue 10 [page]

<span title="1985-10-15">1985</span> <i title="Springer Science &amp; Business Media"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_cellular-and-molecular-life-sciences" style="color: black;">Cellular and Molecular Life Sciences </a> </i> &nbsp;
The unstable case corresponds to the runaway process antici- pated by Fisher®**. In this case, the population evolves away from a line of unstable equilibria at ever increasing speed.  ...  The existence of a line of equilibria can be th A M2 | ~~ 74 Average female mate preference ZA LNA V7 Average male character b optimum is specified by the vertical dashed line. a Runaway sexual selec-  ... 
<span class="external-identifiers"> </span>
<a target="_blank" rel="noopener" href="https://archive.org/details/sim_cellular-and-molecular-life-sciences_1985-10-15_41_10/page/1301" title="read fulltext microfilm" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Archive [Microfilm] <div class="menu fulltext-thumbnail"> <img src="https://archive.org/serve/sim_cellular-and-molecular-life-sciences_1985-10-15_41_10/__ia_thumb.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>

Bifurcations of phase portraits of pendulum with vibrating suspension point

A.I. Neishtadt, K. Sheng
<span title="">2017</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/k7mu2abycrg6znsheqexp2qnwm" style="color: black;">Communications in nonlinear science &amp; numerical simulation</a> </i> &nbsp;
We give complete description of bifurcations of phase portraits of this averaged system.  ...  The averaged over the fast vibrations system is a Hamiltonian system with one degree of freedom depending on two parameters.  ...  Equations for equilibria of the averaged system in this case are obtained in [16] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cnsns.2016.11.003">doi:10.1016/j.cnsns.2016.11.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6pvt5nk74vh35b4z37kzft7c5a">fatcat:6pvt5nk74vh35b4z37kzft7c5a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190218104357/https://core.ac.uk/download/pdf/78909846.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/05/60/0560ff242724f3e36fb05aaca791c115311f7836.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cnsns.2016.11.003"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

On the Price of Anarchy and Stability of Correlated Equilibria of Linear Congestion Games,, [chapter]

George Christodoulou, Elias Koutsoupias
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We show that for the sum social cost, which corresponds to the average cost of the players, every linear congestion game has Nash and correlated price of stability at most 1.6.  ...  This matches the lower bounds given in [2, 4] for pure Nash equilibria. We also extend the results in [2] for weighted congestion games to correlated equilibria.  ...  We also left open some cases about the maximum cost or symmetric games.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11561071_8">doi:10.1007/11561071_8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ze2cjhlbprf65ngmu3gtivpfx4">fatcat:ze2cjhlbprf65ngmu3gtivpfx4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170306023722/http://cgi.di.uoa.gr/~gchristo/paper-ck05b.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/84/e3/84e39dcac742f35d21a54fe7c65c9478e89d12c6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11561071_8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On Lookahead Equilibria in Congestion Games [chapter]

Vittorio Bilò, Angelo Fanelli, Luca Moscardelli
<span title="">2013</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We show that in the worst-case model without consecutive moves, any symmetric singleton game always admits 2-lookahead equilibria. For the average-case model, instead, we show that symmetric single-  ...  In the average-case model, player p assumes that the next move after q is taken by a player selected uniformly at random.  ...  We first show that, in the worst-case model, for any linear congestion game, the price of anarchy is at most 8. For the average-case model, we obtain smaller bounds.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-45046-4_6">doi:10.1007/978-3-642-45046-4_6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jg5eoxygbvhyjnlgdht755mvsm">fatcat:jg5eoxygbvhyjnlgdht755mvsm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190228120058/http://pdfs.semanticscholar.org/91ac/adf351f9203772bddc5519cceb3aa8f62850.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/91/ac/91acadf351f9203772bddc5519cceb3aa8f62850.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-45046-4_6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On stability of planar solutions of double averaged restricted elliptic three-body problem [article]

Anatoly Neishtadt, Kaicheng Sheng, Vladislav Sidorenko
<span title="2018-04-04">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that these equilibria are stable in the linear approximation as equilibria of the double averaged spatial restricted elliptic three-body problem.  ...  Double averaged planar restricted elliptic three-body problem has a two-parametric family of stable equilibria.  ...  In this case one can use averaging over motions of the system star -planet and of the asteroid (double averaging).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.08847v2">arXiv:1803.08847v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6buprlxz6jcbhm6ksy5chn335m">fatcat:6buprlxz6jcbhm6ksy5chn335m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200825143357/https://arxiv.org/pdf/1803.08847v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cd/93/cd933ea2febd34d54fd8e61cb96e77ea1d063909.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.08847v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Pareto Efficient Nash Implementation Via Approval Voting [article]

Yakov Babichenko, Leonard J. Schulman
<span title="2017-03-03">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The characterization demonstrates a close connection between the approval voting mechanism and the notion of average fixed point, which is a point that is equal to the average of all points that it does  ...  Moreover, we provide an exact characterization of pure Nash equilibria profiles and outcomes of the mechanism.  ...  This basic fact remains true also in the case of weighted averages.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1502.05238v2">arXiv:1502.05238v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xgtmdgohifc6to2gkw4buwlfga">fatcat:xgtmdgohifc6to2gkw4buwlfga</a> </span>
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Quantal Response Equilibria in Binary Choice Games on Graphs [article]

Andrey Leonidov, Alexey Savvateev, Andrew G. Semenov
<span title="2019-12-19">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Static and dynamic equilibria in noisy binary choice games on graphs are considered.  ...  It is shown that in the special cases of complete graph and arbitrary noise distribution, and circular and star topology and logistic noise distribution the resulting equations can be cast in the form  ...  In the general case of interdependent random effects influencing agent's decisions these are correlated equilibria [1] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1912.09584v1">arXiv:1912.09584v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b4thbi4ddffhlnyaetbdgkzw7u">fatcat:b4thbi4ddffhlnyaetbdgkzw7u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200321073957/https://arxiv.org/pdf/1912.09584v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1912.09584v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Page 675 of Neural Computation Vol. 6, Issue 4 [page]

<span title="">1994</span> <i title="MIT Press Journals"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_neural-computation" style="color: black;">Neural Computation </a> </i> &nbsp;
For each case, we show the average effect of noise on the rate of information loss (memory retention).  ...  A point in gain-bias space fixes the number and location of equilibria and hence determines the stimulus ranges for which noise (on average) will improve retention.  ... 
<span class="external-identifiers"> </span>
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Page 2091 of Genetics Vol. 167, Issue 4 [page]

<span title="">2004</span> <i title="Genetics Society of America"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_genetics" style="color: black;">Genetics </a> </i> &nbsp;
In all cases of parameter values yielding three poly- morphic equilibria, two of them are stable and one is unstable.  ...  Although we suspect that the system precludes cases of one stable and two unstable equilibria we cannot reject the possibility that these exist in exceedingly rare numbers.  ... 
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Optimality and Equilibria in Stochastic Games

Roger Hartley
<span title="">1994</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fq4jrflj6zesjk7f4nb4otuwwy" style="color: black;">Journal of the Operational Research Society</a> </i> &nbsp;
Similar difficulties are encountered in the general-sum case, where existence of Nash equilibria was established in 1964 for discounted problems, but existence in the average cost case is still open.  ...  However, it was not until 1981 that the existence of a value in the average cost case was finally proved.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1057/jors.1994.13">doi:10.1057/jors.1994.13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6w5g75il4fecnpstcgldod2rpu">fatcat:6w5g75il4fecnpstcgldod2rpu</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/details/sim_journal-of-the-operational-research-society_1994-01_45_1/page/116" title="read fulltext microfilm" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Archive [Microfilm] <div class="menu fulltext-thumbnail"> <img src="https://archive.org/serve/sim_journal-of-the-operational-research-society_1994-01_45_1/__ia_thumb.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1057/jors.1994.13"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

A theoretical and numerical assessment of genetic variability

S Karlin, M W Feldman
<span title="">1981</span> <i title="The Genetics Society of America"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/j4jbzoikwjh4nhplkbx7xsr32y" style="color: black;">Genetics</a> </i> &nbsp;
Preliminary evidence shows that this is not the case for 16 alleles.  ...  Among the key conclusions are (1) equilibria that are most polymorphic do not usually have the highest mean fitness, (2) the more structure there is in the choice of the viability model, the greater is  ...  The exception to this appears in the distance random model, which averages 5.7 distinct stable equilibria for the 8 allele case.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/17249079">pmid:17249079</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC1214405/">pmcid:PMC1214405</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ic57bytnurdidfhcmfxcfb4d4q">fatcat:ic57bytnurdidfhcmfxcfb4d4q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808201153/http://www.genetics.org/content/genetics/97/2/475.full.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b4/cd/b4cd512dd02720efb702c667d51e242ddb0b9240.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1214405" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Factor graph-based structural equilibria in dynamical games

Liming Wang, Vikram Krishnamurthy, Dan Schonfeld
<span title="">2011</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rc5jnc4ldvhs3dswicq5wk3vsq" style="color: black;">2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</a> </i> &nbsp;
Such factor graph-based structural equilibria are more general than Nash equilibria and can model constrained dependencies than general correlated equilibria.  ...  Correlated equilibria are a generalization of Nash equilibria that permit agents to act in a correlated manner and can therefore, model learning in games.  ...  4 . 34 The average reward for player 2 under NE, CEThe average reward for player 3 under NE, CE, FGSE Table 1 . 1 Boolean functions of mammalian cell cycle.  ... 
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