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role="tablist"><li class="nav-chip active" role="presentation"><a data-section-name="" data-toggle="tab" href="#all" role="tab">all</a></li><li class="nav-chip" role="presentation"><a class="js-profile-docs-nav-section u-textTruncate" data-click-track="profile-works-tab" data-section-name="Papers" data-toggle="tab" href="#papers" role="tab" title="Papers"><span>13</span> <span class="ds2-5-body-sm-bold">Papers</span></a></li><li class="nav-chip" role="presentation"><a class="js-profile-docs-nav-section u-textTruncate" data-click-track="profile-works-tab" data-section-name="Expositions" data-toggle="tab" href="#expositions" role="tab" title="Expositions"><span>1</span> <span class="ds2-5-body-sm-bold">Expositions</span></a></li><li class="nav-chip" role="presentation"><a class="js-profile-docs-nav-section u-textTruncate" data-click-track="profile-works-tab" data-section-name="Theses" data-toggle="tab" href="#theses" role="tab" title="Theses"><span>2</span> <span class="ds2-5-body-sm-bold">Theses</span></a></li><li class="nav-chip" role="presentation"><a class="js-profile-docs-nav-section u-textTruncate" data-click-track="profile-works-tab" data-section-name="Undergraduate-Work" data-toggle="tab" href="#undergraduatework" role="tab" title="Undergraduate Work"><span>1</span> <span class="ds2-5-body-sm-bold">Undergraduate Work</span></a></li></ul></div><div class="divider ds-divider-16" style="margin: 0px;"></div><div class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Joshua A Grochow</h3></div><div class="js-work-strip profile--work_container" data-work-id="24813434"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/24813434/Polynomial_Time_Isomorphism_Test_of_Groups_that_are_Tame_Extensions"><img alt="Research paper thumbnail of Polynomial-Time Isomorphism Test of Groups that are Tame Extensions" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/24813434/Polynomial_Time_Isomorphism_Test_of_Groups_that_are_Tame_Extensions">Polynomial-Time Isomorphism Test of Groups that are Tame Extensions</a></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2015</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813434"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813434"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813434; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=24813434]").text(description); $(".js-view-count[data-work-id=24813434]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x 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dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=24813434]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":24813434,"title":"Polynomial-Time Isomorphism Test of Groups that are Tame Extensions","internal_url":"https://www.academia.edu/24813434/Polynomial_Time_Isomorphism_Test_of_Groups_that_are_Tame_Extensions","owner_id":47488207,"coauthors_can_edit":false,"owner":{"id":47488207,"first_name":"Joshua","middle_initials":"A","last_name":"Grochow","page_name":"JoshuaGrochow","domain_name":"santafe","created_at":"2016-04-21T10:28:03.547-07:00","display_name":"Joshua A Grochow","url":"https://santafe.academia.edu/JoshuaGrochow"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813432"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813432/A_framework_for_optimal_high_level_descriptions_in_science_and_engineering_preliminary_report"><img alt="Research paper thumbnail of A framework for optimal high-level descriptions in science and engineering---preliminary report" class="work-thumbnail" src="https://attachments.academia-assets.com/45140144/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813432/A_framework_for_optimal_high_level_descriptions_in_science_and_engineering_preliminary_report">A framework for optimal high-level descriptions in science and engineering---preliminary report</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Both science and engineering rely on the use of high-level descriptions. These go under various n...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Both science and engineering rely on the use of high-level descriptions. These go under various names, including &quot;macrostates,&quot; &quot;coarse-grainings,&quot; and &quot;effective theories&quot;. The ideal gas is a high-level description of a large collection of point particles, just as a a set of interacting firms is a high-level description of individuals participating in an economy and just as a cell a high-level description of a set of biochemical interactions. Typically, these descriptions are constructed in an $\mathit{ad~hoc}$ manner, without an explicit understanding of their purpose. Here, we formalize and quantify that purpose as a combination of the need to accurately predict observables of interest, and to do so efficiently and with bounded computational resources. This State Space Compression framework makes it possible to solve for the optimal high-level description of a given dynamical system, rather than relying on human intuition alone. In this preliminary r...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="5cf81eddee0fe9911a0fe2b07f68c734" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140144,"asset_id":24813432,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140144/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813432"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813432"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813432; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=24813432]").text(description); $(".js-view-count[data-work-id=24813432]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 24813432; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='24813432']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "5cf81eddee0fe9911a0fe2b07f68c734" } } $('.js-work-strip[data-work-id=24813432]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":24813432,"title":"A framework for optimal high-level descriptions in science and engineering---preliminary report","internal_url":"https://www.academia.edu/24813432/A_framework_for_optimal_high_level_descriptions_in_science_and_engineering_preliminary_report","owner_id":47488207,"coauthors_can_edit":false,"owner":{"id":47488207,"first_name":"Joshua","middle_initials":"A","last_name":"Grochow","page_name":"JoshuaGrochow","domain_name":"santafe","created_at":"2016-04-21T10:28:03.547-07:00","display_name":"Joshua A Grochow","url":"https://santafe.academia.edu/JoshuaGrochow"},"attachments":[{"id":45140144,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/45140144/thumbnails/1.jpg","file_name":"A_framework_for_optimal_high-level_descr20160427-25546-1w52r8q.pdf","download_url":"https://www.academia.edu/attachments/45140144/download_file","bulk_download_file_name":"A_framework_for_optimal_high_level_descr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/45140144/A_framework_for_optimal_high-level_descr20160427-25546-1w52r8q-libre.pdf?1461777101=\u0026response-content-disposition=attachment%3B+filename%3DA_framework_for_optimal_high_level_descr.pdf\u0026Expires=1740485236\u0026Signature=YBZNpxwFYda3zp6AkmupeFYsn4S7PGB-qSqAdCSB23yZSisfswuQbmz0EvC3fCwz18tJnVHpHktp5chKkvza5A6jayjMi73iCN7S5Z85XACJF9Mo1IT3xuYrMNofcpD--oOL04Svtp5E-sVHPPJVAzpoyCmJoyL86eWTLQZ6Q9sTV1O3SoPPZ7BWwvoL2pOhsXdzF-Y--lI4dXjZdaKNIaB2vH7i~mz1nQoWG053BdKoem97ITruFoQacV9UvvvqR8KucbOLXBdmT6P8OmN9zKVCiufhoUwgSptyhggz~9SnPFu~kg-J2ZKvibIzcTxN2VMFVVZmv9l-ESDJiZy3Cw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813427"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813427/Circuit_Complexity_Proof_Complexity_and_Polynomial_Identity_Testing"><img alt="Research paper thumbnail of Circuit Complexity, Proof Complexity, and Polynomial Identity Testing" class="work-thumbnail" src="https://attachments.academia-assets.com/45140139/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813427/Circuit_Complexity_Proof_Complexity_and_Polynomial_Identity_Testing">Circuit Complexity, Proof Complexity, and Polynomial Identity Testing</a></div><div class="wp-workCard_item"><span>2014 IEEE 55th Annual Symposium on Foundations of Computer Science</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We introduce a new and very natural algebraic proof system, which has tight connections to (algeb...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We introduce a new and very natural algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent does not have polynomialsize algebraic circuits (VNP = VP). As a corollary to the proof, we also show that superpolynomial lower bounds on the number of lines in Polynomial Calculus proofs (as opposed to the usual measure of number of monomials) imply the Permanent versus Determinant Conjecture. Note that, prior to our work, there was no proof system for which lower bounds on an arbitrary tautology implied any computational lower bound.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="417cb5ff343a2b201d36d92d33e2014d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140139,"asset_id":24813427,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140139/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813427"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813427"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813427; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=24813427]").text(description); $(".js-view-count[data-work-id=24813427]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 24813427; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='24813427']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24636778"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24636778/Algorithms_for_Group_Isomorphism_via_Group_Extensions_and_Cohomology"><img alt="Research paper thumbnail of Algorithms for Group Isomorphism via Group Extensions and Cohomology" class="work-thumbnail" src="https://attachments.academia-assets.com/44963617/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24636778/Algorithms_for_Group_Isomorphism_via_Group_Extensions_and_Cohomology">Algorithms for Group Isomorphism via Group Extensions and Cohomology</a></div><div class="wp-workCard_item"><span>2014 IEEE 29th Conference on Computational Complexity (CCC)</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The isomorphism problem for groups given by their multiplication tables (GpI) has long been known...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The isomorphism problem for groups given by their multiplication tables (GpI) has long been known to be solvable in n O(log n) time, but until the last few years little progress towards a polynomial-time algorithm had been achieved. Recently, Babai et al. (ICALP 2012) gave a polynomial-time algorithm for groups with no abelian normal subgroups. Thus, at present it is crucial to understand groups with abelian normal subgroups to develop n o(log n) -time algorithms.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4b334529b6aee37cb0ac212bf6b52318" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":44963617,"asset_id":24636778,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/44963617/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24636778"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24636778"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24636778; 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Lie algebras arise centrally in areas as di...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley--Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices such that $A, B\in L$ implies $AB - BA \in L$. Two matrix Lie algebras are conjugate if there is an invertible matrix $M$ such that $L_1 = M L_2 M^{-1}$. We show that certain cases of Lie algebra conjugacy are equivalent to graph isomorphism. On the other hand, we give polynomial-time algorithms for other cases of Lie algebra conjugacy, which allow us to essentially derandomize a recent result of Kayal on affine equivalence of polynomials. Affine equivalence is related to many complexity problems such as factoring integers, graph isomorphism, matrix multiplication, and permanent versus determinant. Specifically, we show: Abelian Lie algebra conjugacy is equivalent to the code equivalence problem, and hence is as hard as...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="968970fb9fee143f0d5edff4a5388096" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140134,"asset_id":24813430,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140134/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813430"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813430"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813430; 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Lie algebras arise centrally in areas as di...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley-Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices such that M 1 , M 2 ∈ L =⇒ M 1 M 2 − M 2 M 1 ∈ L. Two matrix Lie algebras are conjugate if there is an invertible matrix M such that</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="09bb3f950a585569d5dfd357ebd2c291" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140136,"asset_id":24813420,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140136/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813420"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813420"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813420; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813419"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/24813419/Matrix_isomorphism_of_matrix_lie_algebras"><img alt="Research paper thumbnail of Matrix isomorphism of matrix lie algebras" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/24813419/Matrix_isomorphism_of_matrix_lie_algebras">Matrix isomorphism of matrix lie algebras</a></div><div class="wp-workCard_item"><span>Proceedings of the Annual IEEE Conference on Computational Complexity</span><span>, 2012</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813419"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813419"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813419; 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=24813419]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":24813419,"title":"Matrix isomorphism of matrix lie algebras","internal_url":"https://www.academia.edu/24813419/Matrix_isomorphism_of_matrix_lie_algebras","owner_id":47488207,"coauthors_can_edit":false,"owner":{"id":47488207,"first_name":"Joshua","middle_initials":"A","last_name":"Grochow","page_name":"JoshuaGrochow","domain_name":"santafe","created_at":"2016-04-21T10:28:03.547-07:00","display_name":"Joshua A Grochow","url":"https://santafe.academia.edu/JoshuaGrochow"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813435"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813435/Complexity_classes_of_equivalence_problems_revisited"><img alt="Research paper thumbnail of Complexity classes of equivalence problems revisited" class="work-thumbnail" src="https://attachments.academia-assets.com/45140142/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813435/Complexity_classes_of_equivalence_problems_revisited">Complexity classes of equivalence problems revisited</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://santafe.academia.edu/JoshuaGrochow">Joshua A Grochow</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://northwestern.academia.edu/Lancefortnow">Lance Fortnow</a></span></div><div class="wp-workCard_item"><span>Information and Computation</span><span>, Apr 1, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Blass and Gurevich (SIAM J. Comput., 1984) ask whether these conditions on equivalence relations ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Blass and Gurevich (SIAM J. Comput., 1984) ask whether these conditions on equivalence relations -- having an FP canonical form, having an FP complete invariant, and simply being in P -- are in fact different. They showed that this question requires non-relativizing techniques to resolve. Here we extend their results, and give new connections to probabilistic and quantum computation.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="814bccc461c02a93880feac967b61a2c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140142,"asset_id":24813435,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140142/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813435"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813435"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813435; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813428"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/24813428/Code_Equivalence_and_Group_Isomorphism"><img alt="Research paper thumbnail of Code Equivalence and Group Isomorphism" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/24813428/Code_Equivalence_and_Group_Isomorphism">Code Equivalence and Group Isomorphism</a></div><div class="wp-workCard_item"><span>Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT The isomorphism problem for groups given by their multiplication tables has long been kn...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT The isomorphism problem for groups given by their multiplication tables has long been known to be solvable in time nlog n+O(1). The decades-old quest for a polynomial-time algorithm has focused on the very difficult case of class-2 nilpotent groups (groups whose quotient by their center is abelian), with little success. In this paper we consider the opposite end of the spectrum and initiate a more hopeful program to find a polynomial-time algorithm for semisimple groups, defined as groups without abelian normal subgroups. First we prove that the isomorphism problem for this class can be solved in time nO(log log n). We then identify certain bottlenecks to polynomial-time solvability and give a polynomial-time solution to a rich subclass, namely the semisimple groups where each minimal normal subgroup has a bounded number of simple factors. We relate the results to the filtration of groups introduced by Babai and Beals (1999). One of our tools is an algorithm for equivalence of (not necessarily linear) codes in simply-exponential time in the length of the code, obtained by modifying Luks&amp;#39;s algorithm for hypergraph isomorphism in simply-exponential time in the number of vertices (FOCS 1999). We comment on the complexity of the closely related problem of permutational isomorphism of permutation groups.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813428"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813428"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813428; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=24813428]").text(description); $(".js-view-count[data-work-id=24813428]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 24813428; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='24813428']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=24813428]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":24813428,"title":"Code Equivalence and Group Isomorphism","internal_url":"https://www.academia.edu/24813428/Code_Equivalence_and_Group_Isomorphism","owner_id":47488207,"coauthors_can_edit":false,"owner":{"id":47488207,"first_name":"Joshua","middle_initials":"A","last_name":"Grochow","page_name":"JoshuaGrochow","domain_name":"santafe","created_at":"2016-04-21T10:28:03.547-07:00","display_name":"Joshua A Grochow","url":"https://santafe.academia.edu/JoshuaGrochow"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813433"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813433/Genomic_analysis_reveals_a_tight_link_between_transcription_factor_dynamics_and_regulatory_network_architecture"><img alt="Research paper thumbnail of Genomic analysis reveals a tight link between transcription factor dynamics and regulatory network architecture" class="work-thumbnail" src="https://attachments.academia-assets.com/45140137/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813433/Genomic_analysis_reveals_a_tight_link_between_transcription_factor_dynamics_and_regulatory_network_architecture">Genomic analysis reveals a tight link between transcription factor dynamics and regulatory network architecture</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://santafe.academia.edu/JoshuaGrochow">Joshua A Grochow</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/TPrzytycka">T. Przytycka</a></span></div><div class="wp-workCard_item"><span>Molecular Systems Biology</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Although several studies have provided important insights into the general principles of biologic...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Although several studies have provided important insights into the general principles of biological networks, the link between network organization and the genome-scale dynamics of the underlying entities (genes, mRNAs, and proteins) and its role in systems behavior remain unclear. Here we show that transcription factor (TF) dynamics and regulatory network organization are tightly linked. By classifying TFs in the yeast regulatory network into three hierarchical layers (top, core, and bottom) and integrating diverse genome-scale datasets, we find that the TFs have static and dynamic properties that are similar within a layer and different across layers. At the protein level, the top-layer TFs are relatively abundant, long-lived, and noisy compared with the core- and bottom-layer TFs. Although variability in expression of top-layer TFs might confer a selective advantage, as this permits at least some members in a clonal cell population to initiate a response to changing conditions, t...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="cb2804b86963e12563a8d5351510bf78" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140137,"asset_id":24813433,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140137/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813433"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813433"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813433; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24636779"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24636779/Network_Motif_Discovery_Using_Subgraph_Enumeration_and_Symmetry_Breaking"><img alt="Research paper thumbnail of Network Motif Discovery Using Subgraph Enumeration and Symmetry-Breaking" class="work-thumbnail" src="https://attachments.academia-assets.com/44963619/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24636779/Network_Motif_Discovery_Using_Subgraph_Enumeration_and_Symmetry_Breaking">Network Motif Discovery Using Subgraph Enumeration and Symmetry-Breaking</a></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2007</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The study of biological networks and network motifs can yield significant new insights into syste...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The study of biological networks and network motifs can yield significant new insights into systems biology. Previous methods of discovering network motifs -network-centric subgraph enumeration and sampling -have been limited to motifs of 6 to 8 nodes, revealing only the smallest network components. New methods are necessary to identify larger network sub-structures and functional motifs.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ba219379b618fd51d05a040f0532c7cc" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":44963619,"asset_id":24636779,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/44963619/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24636779"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24636779"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24636779; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="profile--tab_heading_container js-section-heading" data-section="Expositions" id="Expositions"><h3 class="profile--tab_heading_container">Expositions by Joshua A Grochow</h3></div><div class="js-work-strip profile--work_container" data-work-id="24813431"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813431/Report_on_Mathematical_Aspects_of_P_vs_NP_and_its_Variants"><img alt="Research paper thumbnail of Report on "Mathematical Aspects of P vs. NP and its Variants" class="work-thumbnail" src="https://attachments.academia-assets.com/45140138/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813431/Report_on_Mathematical_Aspects_of_P_vs_NP_and_its_Variants">Report on "Mathematical Aspects of P vs. NP and its Variants</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://santafe.academia.edu/JoshuaGrochow">Joshua A Grochow</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KorbenRusek">Korben Rusek</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This is a report on a workshop held August 1 to August 5, 2011 at the Institute for Computational...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This is a report on a workshop held August 1 to August 5, 2011 at the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University, Providence, Rhode Island, organized by Saugata Basu, Joseph M. Landsberg, and J. Maurice Rojas. We provide overviews of the more recent results presented at the workshop, including some works-in-progress as well as tentative and intriguing ideas for new directions. The main themes we discuss are representation theory and geometry in the Mulmuley-Sohoni Geometric Complexity Theory Program, and number theory and other ideas in the Blum-Shub-Smale model.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="3be4bdf5f16224fd4be35e438e0c506b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140138,"asset_id":24813431,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140138/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813431"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813431"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813431; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="profile--tab_heading_container js-section-heading" data-section="Theses" id="Theses"><h3 class="profile--tab_heading_container">Theses by Joshua A Grochow</h3></div><div class="js-work-strip profile--work_container" data-work-id="24813425"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/24813425/The_Complexity_of_Equivalence_Relations"><img alt="Research paper thumbnail of The Complexity of Equivalence Relations" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/24813425/The_Complexity_of_Equivalence_Relations">The Complexity of Equivalence Relations</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">To determine if two given lists of numbers are the same set, we would sort both lists and see if ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">To determine if two given lists of numbers are the same set, we would sort both lists and see if we get the same result. The sorted list is a canonical form for the equivalence relation of set equality. Other canonical forms for equivalences arise in graph isomorphism and its variants, and the equality of permutation groups given by generators.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813425"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813425"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813425; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=24813425]").text(description); $(".js-view-count[data-work-id=24813425]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 24813425; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='24813425']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=24813425]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":24813425,"title":"The Complexity of Equivalence Relations","internal_url":"https://www.academia.edu/24813425/The_Complexity_of_Equivalence_Relations","owner_id":47488207,"coauthors_can_edit":false,"owner":{"id":47488207,"first_name":"Joshua","middle_initials":"A","last_name":"Grochow","page_name":"JoshuaGrochow","domain_name":"santafe","created_at":"2016-04-21T10:28:03.547-07:00","display_name":"Joshua A Grochow","url":"https://santafe.academia.edu/JoshuaGrochow"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813429"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813429/On_the_structure_and_evolution_of_protein_interaction_networks"><img alt="Research paper thumbnail of On the structure and evolution of protein interaction networks" class="work-thumbnail" src="https://attachments.academia-assets.com/45140135/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813429/On_the_structure_and_evolution_of_protein_interaction_networks">On the structure and evolution of protein interaction networks</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Comp...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Includes bibliographical references (p. 107-114). The study of protein interactions from the networks point of view has yielded new insights into systems biology [Bar03, MA03, RSM+02, WS98]. In particular, &quot;network motifs&quot; become apparent as a useful and systematic tool for describing and exploring networks [BP06, MKFV06, MSOI+02, SOMMA02, SV06]. Finding motifs has involved either exact counting (e.g. [MSOI+02]) or subgraph sampling (e.g. [BP06, KIMA04a, MZW05]). In this thesis we develop an algorithm to count all instances of a particular subgraph, which can be used to query whether a given subgraph is a significant motif. This method can be used to perform exact counting of network motifs faster and with less mem...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="900aeccdd78355fbc319fb9f0b173c24" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140135,"asset_id":24813429,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140135/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813429"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813429"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813429; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=24813429]").text(description); $(".js-view-count[data-work-id=24813429]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 24813429; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='24813429']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="profile--tab_heading_container js-section-heading" data-section="Undergraduate Work" id="Undergraduate Work"><h3 class="profile--tab_heading_container">Undergraduate Work by Joshua A Grochow</h3></div><div class="js-work-strip profile--work_container" data-work-id="24813499"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813499/Robust_Methods_of_Synchronization_in_Amorphous_Networks"><img alt="Research paper thumbnail of Robust Methods of Synchronization in Amorphous Networks" class="work-thumbnail" src="https://attachments.academia-assets.com/45140203/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813499/Robust_Methods_of_Synchronization_in_Amorphous_Networks">Robust Methods of Synchronization in Amorphous Networks</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">“Amorphous computing is the development of organizational principles and programming languages fo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">“Amorphous computing is the development of organizational principles and programming languages for obtaining coherent behavior from the cooperation of myriads of unreliable parts that are interconnected in unknown, irregular, and time-varying ways [Abelson, et. al. Amorphous Computer. White Paper, 1999.].” One of these principles is temporal control, and a very basic form of temporal control is synchronization. I present a method of synchronization in an ad-hoc network (such as an amorphous computer) which is similar to the Network Time Protocol (used to<br />synchronize the internet) in its method of error estimation. The resulting error between any two processors in the network is worst case \sqrt{2 d \sigma}, where d is the diameter of the network and \sigma is the standard deviation of error between<br />two adjacent processors.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="df5728a6721fa92d48f384f709782e92" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140203,"asset_id":24813499,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140203/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813499"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813499"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813499; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=24813499]").text(description); $(".js-view-count[data-work-id=24813499]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 24813499; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='24813499']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "df5728a6721fa92d48f384f709782e92" } } $('.js-work-strip[data-work-id=24813499]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":24813499,"title":"Robust Methods of Synchronization in Amorphous Networks","internal_url":"https://www.academia.edu/24813499/Robust_Methods_of_Synchronization_in_Amorphous_Networks","owner_id":47488207,"coauthors_can_edit":false,"owner":{"id":47488207,"first_name":"Joshua","middle_initials":"A","last_name":"Grochow","page_name":"JoshuaGrochow","domain_name":"santafe","created_at":"2016-04-21T10:28:03.547-07:00","display_name":"Joshua A Grochow","url":"https://santafe.academia.edu/JoshuaGrochow"},"attachments":[{"id":45140203,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/45140203/thumbnails/1.jpg","file_name":"joshuag-final.pdf","download_url":"https://www.academia.edu/attachments/45140203/download_file","bulk_download_file_name":"Robust_Methods_of_Synchronization_in_Amo.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/45140203/joshuag-final-libre.pdf?1461777245=\u0026response-content-disposition=attachment%3B+filename%3DRobust_Methods_of_Synchronization_in_Amo.pdf\u0026Expires=1740485236\u0026Signature=RUHGY-DARFgv59fJuBl22ELORDhvPZaZHjsZSWYY~ngWcpMZbQp4c54qM9NdJIxz5f-VVLUus4vwLBiPBytd-psU1Zi0WFFuA~wv~tFtcc2fu1GHHN7Bd8gQsOBMad3mjUAZiFj3QpH5rl-akJfQGXuwggavj7C6LB0vRRyj-8TjLZwBUrwmKPQpydO-p5DM7~w7eopA2I7SmACewrqvj2N4r8AepadBLXFTBU3JnRCR76MkML2TdcwCOCl6xGurLVaXd53gk36wOvsXnGnG1uUWyhVVKMJORiNbCbYUWKgRBKSupO2EPIxkbLqlGw08SA6cyqMA0PHcMnhLjZUpkw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":45140202,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/45140202/thumbnails/1.jpg","file_name":"joshuag-final.pdf","download_url":"https://www.academia.edu/attachments/45140202/download_file","bulk_download_file_name":"Robust_Methods_of_Synchronization_in_Amo.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/45140202/joshuag-final-libre.pdf?1461777245=\u0026response-content-disposition=attachment%3B+filename%3DRobust_Methods_of_Synchronization_in_Amo.pdf\u0026Expires=1740485236\u0026Signature=JvOun5cdjUZC7u1q5TvNKUzbKp18ZfrBTYZyndW-p1w8dxjY3tGr4OqwiHRJ98bP2GLdH1GQPoWZVVQRj3aXziLdpoThP49FOyFzvzyHrHzZ~WNq6b9H7Y2J3BBRygafLF4~YE~YYL3OJ3dOe~n~runacWubeSP2lqRyDQ2BVb9E~8X~YBBNF90rHURNa~oe4MgzjiG8oIimBr3Z3gMYYkcTY0KNJHx71kQzcPef6zAA-WGr5Ov60dyMYA3VRtulczGic1l6M4IW3sJZVAo5MSucmpHGxA9-t5fYBn5Cgd-5hO9x2kCIFB9qoUbP98yzmh4L-fVmkC7WBqN4pUdW9g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="5083387" id="papers"><div class="js-work-strip profile--work_container" data-work-id="24813434"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/24813434/Polynomial_Time_Isomorphism_Test_of_Groups_that_are_Tame_Extensions"><img alt="Research paper thumbnail of Polynomial-Time Isomorphism Test of Groups that are Tame Extensions" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/24813434/Polynomial_Time_Isomorphism_Test_of_Groups_that_are_Tame_Extensions">Polynomial-Time Isomorphism Test of Groups that are Tame Extensions</a></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2015</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813434"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813434"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813434; 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These go under various n...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Both science and engineering rely on the use of high-level descriptions. These go under various names, including &quot;macrostates,&quot; &quot;coarse-grainings,&quot; and &quot;effective theories&quot;. The ideal gas is a high-level description of a large collection of point particles, just as a a set of interacting firms is a high-level description of individuals participating in an economy and just as a cell a high-level description of a set of biochemical interactions. Typically, these descriptions are constructed in an $\mathit{ad~hoc}$ manner, without an explicit understanding of their purpose. Here, we formalize and quantify that purpose as a combination of the need to accurately predict observables of interest, and to do so efficiently and with bounded computational resources. This State Space Compression framework makes it possible to solve for the optimal high-level description of a given dynamical system, rather than relying on human intuition alone. In this preliminary r...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="5cf81eddee0fe9911a0fe2b07f68c734" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140144,"asset_id":24813432,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140144/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813432"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813432"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813432; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813427"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813427/Circuit_Complexity_Proof_Complexity_and_Polynomial_Identity_Testing"><img alt="Research paper thumbnail of Circuit Complexity, Proof Complexity, and Polynomial Identity Testing" class="work-thumbnail" src="https://attachments.academia-assets.com/45140139/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813427/Circuit_Complexity_Proof_Complexity_and_Polynomial_Identity_Testing">Circuit Complexity, Proof Complexity, and Polynomial Identity Testing</a></div><div class="wp-workCard_item"><span>2014 IEEE 55th Annual Symposium on Foundations of Computer Science</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We introduce a new and very natural algebraic proof system, which has tight connections to (algeb...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We introduce a new and very natural algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent does not have polynomialsize algebraic circuits (VNP = VP). As a corollary to the proof, we also show that superpolynomial lower bounds on the number of lines in Polynomial Calculus proofs (as opposed to the usual measure of number of monomials) imply the Permanent versus Determinant Conjecture. Note that, prior to our work, there was no proof system for which lower bounds on an arbitrary tautology implied any computational lower bound.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="417cb5ff343a2b201d36d92d33e2014d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140139,"asset_id":24813427,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140139/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813427"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813427"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813427; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24636778"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24636778/Algorithms_for_Group_Isomorphism_via_Group_Extensions_and_Cohomology"><img alt="Research paper thumbnail of Algorithms for Group Isomorphism via Group Extensions and Cohomology" class="work-thumbnail" src="https://attachments.academia-assets.com/44963617/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24636778/Algorithms_for_Group_Isomorphism_via_Group_Extensions_and_Cohomology">Algorithms for Group Isomorphism via Group Extensions and Cohomology</a></div><div class="wp-workCard_item"><span>2014 IEEE 29th Conference on Computational Complexity (CCC)</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The isomorphism problem for groups given by their multiplication tables (GpI) has long been known...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The isomorphism problem for groups given by their multiplication tables (GpI) has long been known to be solvable in n O(log n) time, but until the last few years little progress towards a polynomial-time algorithm had been achieved. Recently, Babai et al. (ICALP 2012) gave a polynomial-time algorithm for groups with no abelian normal subgroups. Thus, at present it is crucial to understand groups with abelian normal subgroups to develop n o(log n) -time algorithms.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4b334529b6aee37cb0ac212bf6b52318" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":44963617,"asset_id":24636778,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/44963617/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24636778"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24636778"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24636778; 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Church</a></span></div><div class="wp-workCard_item"><span>International Mathematics Research Notices</span><span>, 2014</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813424"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813424"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813424; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=24813424]").text(description); 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Lie algebras arise centrally in areas as di...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley--Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices such that $A, B\in L$ implies $AB - BA \in L$. Two matrix Lie algebras are conjugate if there is an invertible matrix $M$ such that $L_1 = M L_2 M^{-1}$. We show that certain cases of Lie algebra conjugacy are equivalent to graph isomorphism. On the other hand, we give polynomial-time algorithms for other cases of Lie algebra conjugacy, which allow us to essentially derandomize a recent result of Kayal on affine equivalence of polynomials. Affine equivalence is related to many complexity problems such as factoring integers, graph isomorphism, matrix multiplication, and permanent versus determinant. Specifically, we show: Abelian Lie algebra conjugacy is equivalent to the code equivalence problem, and hence is as hard as...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="968970fb9fee143f0d5edff4a5388096" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140134,"asset_id":24813430,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140134/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813430"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813430"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813430; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813420"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813420/Lie_algebra_conjugacy"><img alt="Research paper thumbnail of Lie algebra conjugacy" class="work-thumbnail" src="https://attachments.academia-assets.com/45140136/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813420/Lie_algebra_conjugacy">Lie algebra conjugacy</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as di...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley-Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices such that M 1 , M 2 ∈ L =⇒ M 1 M 2 − M 2 M 1 ∈ L. Two matrix Lie algebras are conjugate if there is an invertible matrix M such that</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="09bb3f950a585569d5dfd357ebd2c291" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140136,"asset_id":24813420,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140136/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813420"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813420"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813420; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813419"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/24813419/Matrix_isomorphism_of_matrix_lie_algebras"><img alt="Research paper thumbnail of Matrix isomorphism of matrix lie algebras" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/24813419/Matrix_isomorphism_of_matrix_lie_algebras">Matrix isomorphism of matrix lie algebras</a></div><div class="wp-workCard_item"><span>Proceedings of the Annual IEEE Conference on Computational Complexity</span><span>, 2012</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813419"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813419"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813419; 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=24813419]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":24813419,"title":"Matrix isomorphism of matrix lie algebras","internal_url":"https://www.academia.edu/24813419/Matrix_isomorphism_of_matrix_lie_algebras","owner_id":47488207,"coauthors_can_edit":false,"owner":{"id":47488207,"first_name":"Joshua","middle_initials":"A","last_name":"Grochow","page_name":"JoshuaGrochow","domain_name":"santafe","created_at":"2016-04-21T10:28:03.547-07:00","display_name":"Joshua A Grochow","url":"https://santafe.academia.edu/JoshuaGrochow"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813435"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813435/Complexity_classes_of_equivalence_problems_revisited"><img alt="Research paper thumbnail of Complexity classes of equivalence problems revisited" class="work-thumbnail" src="https://attachments.academia-assets.com/45140142/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813435/Complexity_classes_of_equivalence_problems_revisited">Complexity classes of equivalence problems revisited</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://santafe.academia.edu/JoshuaGrochow">Joshua A Grochow</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://northwestern.academia.edu/Lancefortnow">Lance Fortnow</a></span></div><div class="wp-workCard_item"><span>Information and Computation</span><span>, Apr 1, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Blass and Gurevich (SIAM J. Comput., 1984) ask whether these conditions on equivalence relations ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Blass and Gurevich (SIAM J. Comput., 1984) ask whether these conditions on equivalence relations -- having an FP canonical form, having an FP complete invariant, and simply being in P -- are in fact different. They showed that this question requires non-relativizing techniques to resolve. Here we extend their results, and give new connections to probabilistic and quantum computation.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="814bccc461c02a93880feac967b61a2c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140142,"asset_id":24813435,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140142/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813435"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813435"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813435; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813428"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/24813428/Code_Equivalence_and_Group_Isomorphism"><img alt="Research paper thumbnail of Code Equivalence and Group Isomorphism" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/24813428/Code_Equivalence_and_Group_Isomorphism">Code Equivalence and Group Isomorphism</a></div><div class="wp-workCard_item"><span>Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT The isomorphism problem for groups given by their multiplication tables has long been kn...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT The isomorphism problem for groups given by their multiplication tables has long been known to be solvable in time nlog n+O(1). The decades-old quest for a polynomial-time algorithm has focused on the very difficult case of class-2 nilpotent groups (groups whose quotient by their center is abelian), with little success. In this paper we consider the opposite end of the spectrum and initiate a more hopeful program to find a polynomial-time algorithm for semisimple groups, defined as groups without abelian normal subgroups. First we prove that the isomorphism problem for this class can be solved in time nO(log log n). We then identify certain bottlenecks to polynomial-time solvability and give a polynomial-time solution to a rich subclass, namely the semisimple groups where each minimal normal subgroup has a bounded number of simple factors. We relate the results to the filtration of groups introduced by Babai and Beals (1999). One of our tools is an algorithm for equivalence of (not necessarily linear) codes in simply-exponential time in the length of the code, obtained by modifying Luks&amp;#39;s algorithm for hypergraph isomorphism in simply-exponential time in the number of vertices (FOCS 1999). We comment on the complexity of the closely related problem of permutational isomorphism of permutation groups.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813428"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813428"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813428; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=24813428]").text(description); $(".js-view-count[data-work-id=24813428]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 24813428; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='24813428']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=24813428]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":24813428,"title":"Code Equivalence and Group Isomorphism","internal_url":"https://www.academia.edu/24813428/Code_Equivalence_and_Group_Isomorphism","owner_id":47488207,"coauthors_can_edit":false,"owner":{"id":47488207,"first_name":"Joshua","middle_initials":"A","last_name":"Grochow","page_name":"JoshuaGrochow","domain_name":"santafe","created_at":"2016-04-21T10:28:03.547-07:00","display_name":"Joshua A Grochow","url":"https://santafe.academia.edu/JoshuaGrochow"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813433"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813433/Genomic_analysis_reveals_a_tight_link_between_transcription_factor_dynamics_and_regulatory_network_architecture"><img alt="Research paper thumbnail of Genomic analysis reveals a tight link between transcription factor dynamics and regulatory network architecture" class="work-thumbnail" src="https://attachments.academia-assets.com/45140137/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813433/Genomic_analysis_reveals_a_tight_link_between_transcription_factor_dynamics_and_regulatory_network_architecture">Genomic analysis reveals a tight link between transcription factor dynamics and regulatory network architecture</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://santafe.academia.edu/JoshuaGrochow">Joshua A Grochow</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/TPrzytycka">T. Przytycka</a></span></div><div class="wp-workCard_item"><span>Molecular Systems Biology</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Although several studies have provided important insights into the general principles of biologic...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Although several studies have provided important insights into the general principles of biological networks, the link between network organization and the genome-scale dynamics of the underlying entities (genes, mRNAs, and proteins) and its role in systems behavior remain unclear. Here we show that transcription factor (TF) dynamics and regulatory network organization are tightly linked. By classifying TFs in the yeast regulatory network into three hierarchical layers (top, core, and bottom) and integrating diverse genome-scale datasets, we find that the TFs have static and dynamic properties that are similar within a layer and different across layers. At the protein level, the top-layer TFs are relatively abundant, long-lived, and noisy compared with the core- and bottom-layer TFs. Although variability in expression of top-layer TFs might confer a selective advantage, as this permits at least some members in a clonal cell population to initiate a response to changing conditions, t...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="cb2804b86963e12563a8d5351510bf78" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140137,"asset_id":24813433,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140137/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813433"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813433"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813433; 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Previous methods of discovering network motifs -network-centric subgraph enumeration and sampling -have been limited to motifs of 6 to 8 nodes, revealing only the smallest network components. New methods are necessary to identify larger network sub-structures and functional motifs.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ba219379b618fd51d05a040f0532c7cc" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":44963619,"asset_id":24636779,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/44963619/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24636779"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24636779"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24636779; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="5120244" id="expositions"><div class="js-work-strip profile--work_container" data-work-id="24813431"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813431/Report_on_Mathematical_Aspects_of_P_vs_NP_and_its_Variants"><img alt="Research paper thumbnail of Report on "Mathematical Aspects of P vs. NP and its Variants" class="work-thumbnail" src="https://attachments.academia-assets.com/45140138/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813431/Report_on_Mathematical_Aspects_of_P_vs_NP_and_its_Variants">Report on "Mathematical Aspects of P vs. NP and its Variants</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://santafe.academia.edu/JoshuaGrochow">Joshua A Grochow</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KorbenRusek">Korben Rusek</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This is a report on a workshop held August 1 to August 5, 2011 at the Institute for Computational...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This is a report on a workshop held August 1 to August 5, 2011 at the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University, Providence, Rhode Island, organized by Saugata Basu, Joseph M. Landsberg, and J. Maurice Rojas. We provide overviews of the more recent results presented at the workshop, including some works-in-progress as well as tentative and intriguing ideas for new directions. The main themes we discuss are representation theory and geometry in the Mulmuley-Sohoni Geometric Complexity Theory Program, and number theory and other ideas in the Blum-Shub-Smale model.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="3be4bdf5f16224fd4be35e438e0c506b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140138,"asset_id":24813431,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140138/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813431"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813431"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813431; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="5120243" id="theses"><div class="js-work-strip profile--work_container" data-work-id="24813425"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/24813425/The_Complexity_of_Equivalence_Relations"><img alt="Research paper thumbnail of The Complexity of Equivalence Relations" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/24813425/The_Complexity_of_Equivalence_Relations">The Complexity of Equivalence Relations</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">To determine if two given lists of numbers are the same set, we would sort both lists and see if ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">To determine if two given lists of numbers are the same set, we would sort both lists and see if we get the same result. The sorted list is a canonical form for the equivalence relation of set equality. Other canonical forms for equivalences arise in graph isomorphism and its variants, and the equality of permutation groups given by generators.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813425"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813425"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813425; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=24813425]").text(description); $(".js-view-count[data-work-id=24813425]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 24813425; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='24813425']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=24813425]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":24813425,"title":"The Complexity of Equivalence Relations","internal_url":"https://www.academia.edu/24813425/The_Complexity_of_Equivalence_Relations","owner_id":47488207,"coauthors_can_edit":false,"owner":{"id":47488207,"first_name":"Joshua","middle_initials":"A","last_name":"Grochow","page_name":"JoshuaGrochow","domain_name":"santafe","created_at":"2016-04-21T10:28:03.547-07:00","display_name":"Joshua A Grochow","url":"https://santafe.academia.edu/JoshuaGrochow"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="24813429"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813429/On_the_structure_and_evolution_of_protein_interaction_networks"><img alt="Research paper thumbnail of On the structure and evolution of protein interaction networks" class="work-thumbnail" src="https://attachments.academia-assets.com/45140135/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813429/On_the_structure_and_evolution_of_protein_interaction_networks">On the structure and evolution of protein interaction networks</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Comp...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Includes bibliographical references (p. 107-114). The study of protein interactions from the networks point of view has yielded new insights into systems biology [Bar03, MA03, RSM+02, WS98]. In particular, &quot;network motifs&quot; become apparent as a useful and systematic tool for describing and exploring networks [BP06, MKFV06, MSOI+02, SOMMA02, SV06]. Finding motifs has involved either exact counting (e.g. [MSOI+02]) or subgraph sampling (e.g. [BP06, KIMA04a, MZW05]). In this thesis we develop an algorithm to count all instances of a particular subgraph, which can be used to query whether a given subgraph is a significant motif. This method can be used to perform exact counting of network motifs faster and with less mem...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="900aeccdd78355fbc319fb9f0b173c24" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140135,"asset_id":24813429,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140135/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813429"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813429"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813429; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=24813429]").text(description); $(".js-view-count[data-work-id=24813429]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 24813429; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='24813429']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="5120247" id="undergraduatework"><div class="js-work-strip profile--work_container" data-work-id="24813499"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/24813499/Robust_Methods_of_Synchronization_in_Amorphous_Networks"><img alt="Research paper thumbnail of Robust Methods of Synchronization in Amorphous Networks" class="work-thumbnail" src="https://attachments.academia-assets.com/45140203/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/24813499/Robust_Methods_of_Synchronization_in_Amorphous_Networks">Robust Methods of Synchronization in Amorphous Networks</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">“Amorphous computing is the development of organizational principles and programming languages fo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">“Amorphous computing is the development of organizational principles and programming languages for obtaining coherent behavior from the cooperation of myriads of unreliable parts that are interconnected in unknown, irregular, and time-varying ways [Abelson, et. al. Amorphous Computer. White Paper, 1999.].” One of these principles is temporal control, and a very basic form of temporal control is synchronization. I present a method of synchronization in an ad-hoc network (such as an amorphous computer) which is similar to the Network Time Protocol (used to<br />synchronize the internet) in its method of error estimation. The resulting error between any two processors in the network is worst case \sqrt{2 d \sigma}, where d is the diameter of the network and \sigma is the standard deviation of error between<br />two adjacent processors.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="df5728a6721fa92d48f384f709782e92" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":45140203,"asset_id":24813499,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/45140203/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="24813499"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="24813499"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 24813499; 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