July 13–16, 2020 The International Congress on Mathematical Software (ICMS 2020) Braunschweig, Germany Virtual conference, due to the COVID-19 pandemic Organizers: General Chair: Michael Joswig (TU Berlin, Germany); Program Chairs: Anna Bigatti (Università di Genova, Italy), Folkmar Bornemann (TU München, Germany), and Jacques Carette (McMaster University, Canada) Website: http://icms-conference.org/2020/
{"title":"Recent and upcoming events","authors":"Staff","doi":"10.1145/3427218.3427227","DOIUrl":"https://doi.org/10.1145/3427218.3427227","url":null,"abstract":"July 13–16, 2020 The International Congress on Mathematical Software (ICMS 2020) Braunschweig, Germany Virtual conference, due to the COVID-19 pandemic Organizers: General Chair: Michael Joswig (TU Berlin, Germany); Program Chairs: Anna Bigatti (Università di Genova, Italy), Folkmar Bornemann (TU München, Germany), and Jacques Carette (McMaster University, Canada) Website: http://icms-conference.org/2020/","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"62 - 64"},"PeriodicalIF":0.1,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3427218.3427227","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44921899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marc Härkönen, Benjamin Hollering, Fatemeh Tarashi Kashani, J. Rodriguez
The Macaulay2 [5] package AlgebraicOptimization implements methods for determining the algebraic degree of an optimization problem. We describe the structure of an algebraic optimization problem and explain how the methods in this package may be used to determine the respective degrees. Special features include determining Euclidean distance degrees and maximum likelihood degrees. To our knowledge, this is the first comprehensive software package combining different methods in algebraic optimization. The package is available at https://github.com/Macaulay2/Workshop-2020-Cleveland/tree/ISSAC-AlgOpt/alg-stat/AlgebraicOptimization.
{"title":"Algebraic optimization degree","authors":"Marc Härkönen, Benjamin Hollering, Fatemeh Tarashi Kashani, J. Rodriguez","doi":"10.1145/3427218.3427222","DOIUrl":"https://doi.org/10.1145/3427218.3427222","url":null,"abstract":"The Macaulay2 [5] package AlgebraicOptimization implements methods for determining the algebraic degree of an optimization problem. We describe the structure of an algebraic optimization problem and explain how the methods in this package may be used to determine the respective degrees. Special features include determining Euclidean distance degrees and maximum likelihood degrees. To our knowledge, this is the first comprehensive software package combining different methods in algebraic optimization. The package is available at https://github.com/Macaulay2/Workshop-2020-Cleveland/tree/ISSAC-AlgOpt/alg-stat/AlgebraicOptimization.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"44 - 48"},"PeriodicalIF":0.1,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3427218.3427222","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49269990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work we present a new module for the computer algebraic topology system Kenzo computing the Eilenberg-Moore spectral sequence of fibrations between spaces with effective homology. These programs can be applied to determine the Eilenberg-Moore spectral sequence of extensions of finitely generated abelian groups.
{"title":"A new Kenzo module for computing the Eilenberg-Moore spectral sequence","authors":"A. Romero, J. Rubio, F. Sergeraert, Markus Szymik","doi":"10.1145/3427218.3427225","DOIUrl":"https://doi.org/10.1145/3427218.3427225","url":null,"abstract":"In this work we present a new module for the computer algebraic topology system Kenzo computing the Eilenberg-Moore spectral sequence of fibrations between spaces with effective homology. These programs can be applied to determine the Eilenberg-Moore spectral sequence of extensions of finitely generated abelian groups.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"57 - 60"},"PeriodicalIF":0.1,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3427218.3427225","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43856465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tolis Chalkis, Vissarion Fisikopoulos, Panagiotis Repouskos, Elias P. Tsigaridas
We present algorithmic, complexity, and implementation results on the problem of sampling points in the interior and the boundary of a spectrahedron, that is the feasible region of a semidefinite program. Our main tool is random walks. We define and analyze a set of primitive geometric operations that exploits the algebraic properties of spectrahedra and the polynomial eigenvalue problem and leads to the realization of a broad collection of efficient random walks. We demonstrate random walks that experimentally show faster mixing time than the ones used previously for sampling from spectrahedra in theory or applications, for example Hit and Run. Consecutively, the variety of random walks allows us to sample from general probability distributions, for example the family of log-concave distributions which arise frequently in numerous applications. We apply our tools to compute (i) the volume of a spectrahedron and (ii) the expectation of functions coming from robust optimal control. We provide a C++ open source implementation of our methods that scales efficiently up to dimension 200. We illustrate its efficiency on various data sets.
我们给出了在半定程序的可行域谱面体的内部和边界采样点问题的算法、复杂性和实现结果。我们的主要工具是随机行走。我们定义并分析了一组原始几何运算，这些运算利用了spectrahedra的代数性质和多项式特征值问题，并实现了广泛的有效随机游动集合。我们展示了随机行走，实验表明，与之前在理论或应用中（例如Hit and Run）从spectrahedra采样时使用的混合时间相比，混合时间更快。连续地，随机游动的多样性使我们能够从一般概率分布中进行采样，例如在许多应用中经常出现的对数凹分布族。我们应用我们的工具来计算（i）谱面体的体积和（ii）来自鲁棒最优控制的函数的期望。我们提供了我们方法的C++开源实现，该实现可以有效地扩展到维度200。我们在各种数据集上说明了它的效率。
{"title":"Sampling the feasible sets of SDPs and volume approximation","authors":"Tolis Chalkis, Vissarion Fisikopoulos, Panagiotis Repouskos, Elias P. Tsigaridas","doi":"10.1145/3457341.3457349","DOIUrl":"https://doi.org/10.1145/3457341.3457349","url":null,"abstract":"We present algorithmic, complexity, and implementation results on the problem of sampling points in the interior and the boundary of a spectrahedron, that is the feasible region of a semidefinite program. Our main tool is random walks. We define and analyze a set of primitive geometric operations that exploits the algebraic properties of spectrahedra and the polynomial eigenvalue problem and leads to the realization of a broad collection of efficient random walks. We demonstrate random walks that experimentally show faster mixing time than the ones used previously for sampling from spectrahedra in theory or applications, for example Hit and Run. Consecutively, the variety of random walks allows us to sample from general probability distributions, for example the family of log-concave distributions which arise frequently in numerous applications. We apply our tools to compute (i) the volume of a spectrahedron and (ii) the expectation of functions coming from robust optimal control. We provide a C++ open source implementation of our methods that scales efficiently up to dimension 200. We illustrate its efficiency on various data sets.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"114 - 118"},"PeriodicalIF":0.1,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3457341.3457349","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43872475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
During May 12-17, 2019, shall we celebrate the late famous mathematician Wen-Tsun Wu's centenary birthday. Professor Wen-Tsun Wu is one of the most internationally influential mathematicians in China, who brought far-reaching influence on both mathematics and computer research by his great contributions to the field of topology and the opening of the new area of Mathematics Mechanization. His research includes algebraic topology, di.erential topology, mathematics mechanization, algebraic geometry, game theory as well as the history of mathematics. His work has been regarded as among the greatest classical influential results in topology. In late 1970s, he opened the area of mathematics mechanization by the so-called "Wu method" which automatically proves geometric theorems using computers and was taken as the pioneer work in automatic reasoning. The symposium focuses on his achievements in topology, mathematics mechanization as well as the history of mathematics, and casts light on their future prospects and potential applications. Specific topics for the symposium include but are not limited to: •Algebraic topology •Automated reasoning •Computational algebraic geometry and optimization •Computational geometry and topology •Computational number theory •Coding theory and cryptology •Di.erential and di.erence algebras •History of mathematics •Polynomial equation solving •Symbolic or symbolic-numeric computation •Applications of mathematical mechanization
{"title":"International Symposium on Wen-Tsun Wu's Academic Thought and Mathematics Mechanization","authors":"Academy of Mathematics and Systems Science","doi":"10.1145/3388974.3388975","DOIUrl":"https://doi.org/10.1145/3388974.3388975","url":null,"abstract":"During May 12-17, 2019, shall we celebrate the late famous mathematician Wen-Tsun Wu's centenary birthday. Professor Wen-Tsun Wu is one of the most internationally influential mathematicians in China, who brought far-reaching influence on both mathematics and computer research by his great contributions to the field of topology and the opening of the new area of Mathematics Mechanization. His research includes algebraic topology, di.erential topology, mathematics mechanization, algebraic geometry, game theory as well as the history of mathematics. His work has been regarded as among the greatest classical influential results in topology. In late 1970s, he opened the area of mathematics mechanization by the so-called \"Wu method\" which automatically proves geometric theorems using computers and was taken as the pioneer work in automatic reasoning. The symposium focuses on his achievements in topology, mathematics mechanization as well as the history of mathematics, and casts light on their future prospects and potential applications. Specific topics for the symposium include but are not limited to: •Algebraic topology •Automated reasoning •Computational algebraic geometry and optimization •Computational geometry and topology •Computational number theory •Coding theory and cryptology •Di.erential and di.erence algebras •History of mathematics •Polynomial equation solving •Symbolic or symbolic-numeric computation •Applications of mathematical mechanization","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"53 1","pages":"155 - 181"},"PeriodicalIF":0.1,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3388974.3388975","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48504133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We are pleased to announce 15 open PhD Positions within the new European Network GRAPES: Learning, Processing and Optimising Shapes. GRAPES is a Marie Sk lodowska-Curie Innovative Training Network in the framework of H2020, started on December 1st, 2019, and lasting for 4 years. It includes 11 academic/industrial groups o.ering 15 PhD's, and 6 associated partners; it is coordinated by ATHENA Research & Innovation Center, Greece. GRAPES aims at advancing the state-of-the-art in Mathematics, Computer-Aided Design, and Machine Learning, in order to promote game changing approaches for generating, optimising, and learning 3D shapes, along with a multisectoral training for young researchers, supported by the active participation of SMEs. Recent advances in the above domains have solved numerous tasks concerning multimedia and 2D data. However, automation of 3D geometry processing and analysis lags severely behind, despite their importance in science, technology and everyday life, and some well-understood underlying mathematical principles. Concrete applications include simulation, manufacturing and 3D printing, visualisation and naval design, retrieval and mining, reconstruction and urban planning.
我们很高兴地宣布，在新的欧洲GRAPES网络中，有15个博士职位空缺：学习、加工和优化形状。GRAPES是一个基于H2020框架的Marie Sk lodowska Curie创新培训网络，始于2019年12月1日，持续4年。它包括11个学术/工业团体，获得15个博士学位，以及6个相关合作伙伴；它由希腊ATHENA研究与创新中心协调。GRAPES旨在推进数学、计算机辅助设计和机器学习领域的最先进技术，以促进生成、优化和学习3D形状的改变游戏规则的方法，并在中小企业的积极参与下为年轻研究人员提供多部门培训。上述领域的最新进展已经解决了与多媒体和2D数据有关的许多任务。然而，3D几何处理和分析的自动化严重落后，尽管它们在科学、技术和日常生活中很重要，并且有一些众所周知的基本数学原理。具体应用包括模拟、制造和3D打印、可视化和海军设计、检索和采矿、重建和城市规划。
{"title":"15 PhD positions in GRAPES","authors":"I. Emiris","doi":"10.1145/3388974.3388978","DOIUrl":"https://doi.org/10.1145/3388974.3388978","url":null,"abstract":"We are pleased to announce 15 open PhD Positions within the new European Network GRAPES: Learning, Processing and Optimising Shapes. GRAPES is a Marie Sk lodowska-Curie Innovative Training Network in the framework of H2020, started on December 1st, 2019, and lasting for 4 years. It includes 11 academic/industrial groups o.ering 15 PhD's, and 6 associated partners; it is coordinated by ATHENA Research & Innovation Center, Greece. GRAPES aims at advancing the state-of-the-art in Mathematics, Computer-Aided Design, and Machine Learning, in order to promote game changing approaches for generating, optimising, and learning 3D shapes, along with a multisectoral training for young researchers, supported by the active participation of SMEs. Recent advances in the above domains have solved numerous tasks concerning multimedia and 2D data. However, automation of 3D geometry processing and analysis lags severely behind, despite their importance in science, technology and everyday life, and some well-understood underlying mathematical principles. Concrete applications include simulation, manufacturing and 3D printing, visualisation and naval design, retrieval and mining, reconstruction and urban planning.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"53 1","pages":"189 - 189"},"PeriodicalIF":0.1,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3388974.3388978","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44827423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Maple Conference 2019 was held at the University of Waterloo in Waterloo, Ontario, Canada, on October 15 -- October 17, 2019.
2019年枫叶大会于2019年10月15日至10月17日在加拿大安大略省滑铁卢市的滑铁卢大学举行。
{"title":"Maple Conference 2019","authors":"J. Gerhard, I. Kotsireas","doi":"10.1145/3388974.3388976","DOIUrl":"https://doi.org/10.1145/3388974.3388976","url":null,"abstract":"The Maple Conference 2019 was held at the University of Waterloo in Waterloo, Ontario, Canada, on October 15 -- October 17, 2019.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"53 1","pages":"182 - 182"},"PeriodicalIF":0.1,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48440690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Each quarter we are pleased to present abstracts of recent doctoral dissertations in Computer Algebra and Symbolic Computation. We encourage all recent Ph.D. graduates who have defended in the past two years (and their supervisors), to submit their abstracts for publication in CCA.
{"title":"Abstracts of recent doctoral dissertations in computer algebra","authors":"CCA editors","doi":"10.1145/3388974.3388977","DOIUrl":"https://doi.org/10.1145/3388974.3388977","url":null,"abstract":"Each quarter we are pleased to present abstracts of recent doctoral dissertations in Computer Algebra and Symbolic Computation. We encourage all recent Ph.D. graduates who have defended in the past two years (and their supervisors), to submit their abstracts for publication in CCA.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"53 1","pages":"183 - 188"},"PeriodicalIF":0.1,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3388974.3388977","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47647130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Most numerical algorithms are designed for single or double precision floating point arithmetic, and their complexity is measured in terms of the total number of floating point operations. The resolution of problems with high condition numbers (e.g. when approaching a singularity or degeneracy) may require higher working precisions, in which case it is important to take the precision into account when doing complexity analyses. In this paper, we propose a new "ultimate complexity" model, which focuses on analyzing the cost of numerical algorithms for "sufficiently large" precisions. As an example application we will present an ultimately softly linear time algorithm for modular composition of univariate polynomials.
{"title":"Ultimate complexity for numerical algorithms","authors":"J. Hoeven, Grégoire Lecerf","doi":"10.1145/3419048.3419049","DOIUrl":"https://doi.org/10.1145/3419048.3419049","url":null,"abstract":"Most numerical algorithms are designed for single or double precision floating point arithmetic, and their complexity is measured in terms of the total number of floating point operations. The resolution of problems with high condition numbers (e.g. when approaching a singularity or degeneracy) may require higher working precisions, in which case it is important to take the precision into account when doing complexity analyses. In this paper, we propose a new \"ultimate complexity\" model, which focuses on analyzing the cost of numerical algorithms for \"sufficiently large\" precisions. As an example application we will present an ultimately softly linear time algorithm for modular composition of univariate polynomials.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"1 - 13"},"PeriodicalIF":0.1,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3419048.3419049","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46249452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The applications of solving systems of polynomial equations are legion: The real case permeates all of non-linear optimization as well as numerous problems in engineering. The p-adic case leads to many classical questions in number theory, and is close to many applications in cryptography, coding theory, and computational number theory. As such, it is important to understand the complexity of solving systems of polynomial equations over local fields. Furthermore, the complexity of solving structured systems --- such as those with a fixed number of monomial terms or invariance with respect to a group action --- arises naturally in many computational geometric applications and is closely related to a deeper understanding of circuit complexity (see, e.g., [8]). Clearly, if we are to fully understand the complexity of solving sparse polynomial systems, then we should at least be able to settle the univariate case, e.g., classify when it is possible to separate and approximate roots in deterministic time polynomial in the input size.
{"title":"A complexity chasm for solving sparse polynomial equations over p-adic fields","authors":"J. Rojas, Yuyu Zhu","doi":"10.1145/3457341.3457343","DOIUrl":"https://doi.org/10.1145/3457341.3457343","url":null,"abstract":"The applications of solving systems of polynomial equations are legion: The real case permeates all of non-linear optimization as well as numerous problems in engineering. The p-adic case leads to many classical questions in number theory, and is close to many applications in cryptography, coding theory, and computational number theory. As such, it is important to understand the complexity of solving systems of polynomial equations over local fields. Furthermore, the complexity of solving structured systems --- such as those with a fixed number of monomial terms or invariance with respect to a group action --- arises naturally in many computational geometric applications and is closely related to a deeper understanding of circuit complexity (see, e.g., [8]). Clearly, if we are to fully understand the complexity of solving sparse polynomial systems, then we should at least be able to settle the univariate case, e.g., classify when it is possible to separate and approximate roots in deterministic time polynomial in the input size.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"86 - 90"},"PeriodicalIF":0.1,"publicationDate":"2020-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3457341.3457343","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47380350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：