SIAM Journal on Applied Algebra and Geometry最新文献_第5页

Second-Order Cone Representation for Convex Sets in the Plane 平面上凸集的二阶锥表示

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-01-01 DOI: 10.1137/20M133717X

C. Scheiderer

引用次数: 2

Orbit Computation for Atomically Generated Subgroups of Isometries of Zn 原子生成Zn等距子群的轨道计算

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-01-01 DOI: 10.1137/20M1375127

Haizi Yu, Igor Mineyev, L. Varshney

引用次数: 2

Koszul-type determinantal formulas for families of mixed multilinear systems 混合多线性系统族的koszul型行列式公式

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-01-01 DOI: 10.1137/20m1332190

M. Bender, J. Faugère, Angelos Mantzaflaris, Elias P. Tsigaridas

{"title":"Koszul-type determinantal formulas for families of mixed multilinear systems","authors":"M. Bender, J. Faugère, Angelos Mantzaflaris, Elias P. Tsigaridas","doi":"10.1137/20m1332190","DOIUrl":"https://doi.org/10.1137/20m1332190","url":null,"abstract":"Effective computation of resultants is a central problem in elimination theory and polynomial system solving. Commonly, we compute the resultant as a quotient of determinants of matrices and we say that there exists a determinantal formula when we can express it as a determinant of a matrix whose elements are the coefficients of the input polynomials. We study the resultant in the context of mixed multilinear polynomial systems, that is multilinear systems with polynomials having different supports, on which determinantal formulas were not known. We construct determinantal formulas for two kind of multilinear systems related to the Multiparameter Eigenvalue Problem (MEP): first, when the polynomials agree in all but one block of variables; second, when the polynomials are bilinear with different supports, related to a bipartite graph. We use the Weyman complex to construct Koszul-type determinantal formulas that generalize Sylvester-type formulas. We can use the matrices associated to these formulas to solve square systems without computing the resultant. The combination of the resultant matrices with the eigenvalue and eigenvector criterion for polynomial systems leads to a new approach for solving MEP.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77818604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

Maximum Likelihood Degree, Complete Quadrics, and ℂ*-Action 极大似然度，完全二次函数，和*-作用

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-01-01 DOI: 10.1137/20M1335960

M. Michałek, Leonid Monin, Jaroslaw A. Wisniewski

引用次数: 24

Computing the nc-Rank via Discrete Convex Optimization on CAT(0) Spaces 在CAT(0)空间上用离散凸优化计算nc秩

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2020-12-26 DOI: 10.1137/20m138836x

Masaki Hamada, H. Hirai

引用次数: 15

Multi-experiment parameter identifiability of ODEs and model theory ode的多实验参数可辨识性与模型理论

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2020-11-21 DOI: 10.1137/21m1389845

A. Ovchinnikov, A. Pillay, G. Pogudin, T. Scanlon

{"title":"Multi-experiment parameter identifiability of ODEs and model theory","authors":"A. Ovchinnikov, A. Pillay, G. Pogudin, T. Scanlon","doi":"10.1137/21m1389845","DOIUrl":"https://doi.org/10.1137/21m1389845","url":null,"abstract":"Structural identifiability is a property of an ODE model with parameters that allows for the parameters to be determined from continuous noise-free data. This is natural prerequisite for practical identifiability. Conducting multiple independent experiments could make more parameters or functions of parameters identifiable, which is a desirable property to have. How many experiments are sufficient? In the present paper, we provide an algorithm to determine the exact number of experiments for multi-experiment local identifiability and obtain an upper bound that is off at most by one for the number of experiments for multi-experiment global identifiability. Interestingly, the main theoretical ingredient of the algorithm has been discovered and proved using model theory (in the sense of mathematical logic). We hope that this unexpected connection will stimulate interactions between applied algebra and model theory, and we provide a short introduction to model theory in the context of parameter identifiability. As another related application of model theory in this area, we construct a nonlinear ODE system with one output such that single-experiment and mutiple-experiment identifiability are different for the system. This contrasts with recent results about single-output linear systems. We also present a Monte Carlo randomized version of the algorithm with a polynomial arithmetic complexity. Implementation of the algorithm is provided and its performance is demonstrated on several examples. The source code is available at https://github.com/pogudingleb/ExperimentsBound.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2020-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76864317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 11

Existence of Two View Chiral Reconstructions 两视图手性重构的存在性

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2020-11-14 DOI: 10.1137/20m1381848

Andrew Pryhuber, Rainer Sinn, Rekha R. Thomas

引用次数: 4

Common Complements of Linear Subspaces and the Sparseness of MRD Codes 线性子空间的公补与MRD码的稀疏性

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2020-11-05 DOI: 10.1137/21m1428947

Anina Gruica, A. Ravagnani

{"title":"Common Complements of Linear Subspaces and the Sparseness of MRD Codes","authors":"Anina Gruica, A. Ravagnani","doi":"10.1137/21m1428947","DOIUrl":"https://doi.org/10.1137/21m1428947","url":null,"abstract":"We consider the problem of estimating the number of common complements of a family of subspaces over a finite field, in terms of the cardinality of the family and its intersection structure. We derive upper and lower bounds for this number, along with their asymptotic versions as the field size tends to infinity. We use these bounds to describe the general behavior of common complements with respect to sparsity and density, showing that the decisive property is whether or not the number of spaces to be complemented is negligible with respect to the field size. The proof techniques are based on the study of isolated vertices in certain bipartite graphs. By specializing our results to matrix spaces, we answer an open question in coding theory, proving that MRD codes in the rank metric are sparse for all parameter sets as the field grows, with only very few exceptions. We also investigate the density of MRD codes as their column length tends to infinity, obtaining a new asymptotic bound. Using properties of the Euler function from number theory, we then show that our bound improves on known results for most parameter sets. We conclude the paper by establishing two structural properties of the density function of rank-metric codes.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2020-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76447637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 14

Sums of Squares and Sparse Semidefinite Programming 平方和与稀疏半定规划

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2020-10-21 DOI: 10.1137/20m1376170

Grigoriy Blekherman, Kevin Shu

引用次数: 4

Edit Distance and Persistence Diagrams Over Lattices 编辑格上的距离和持久性图

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2020-10-14 DOI: 10.1137/20M1373700

Alex McCleary, A. Patel

引用次数: 31