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Erratum: A Counterexample to Comon’s Conjecture 勘误：科蒙猜想的一个反例
IF 1.2 2区 数学
SIAM Journal on Applied Algebra and Geometry Pub Date : 2024-03-29 DOI: 10.1137/23m1623781
J. Draisma
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引用次数: 0
Computing Geometric Feature Sizes for Algebraic Manifolds 计算代数流形的几何特征尺寸
2区 数学
SIAM Journal on Applied Algebra and Geometry Pub Date : 2023-11-09 DOI: 10.1137/22m1522656
Sandra Di Rocco, Parker B. Edwards, David Eklund, Oliver Gäfvert, Jonathan D. Hauenstein
{"title":"Computing Geometric Feature Sizes for Algebraic Manifolds","authors":"Sandra Di Rocco, Parker B. Edwards, David Eklund, Oliver Gäfvert, Jonathan D. Hauenstein","doi":"10.1137/22m1522656","DOIUrl":"https://doi.org/10.1137/22m1522656","url":null,"abstract":"","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135243099","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: 0
A Sum of Squares Characterization of Perfect Graphs 完美图的平方和刻划
2区 数学
SIAM Journal on Applied Algebra and Geometry Pub Date : 2023-10-16 DOI: 10.1137/22m1530410
Amir Ali Ahmadi, Cemil Dibek
{"title":"A Sum of Squares Characterization of Perfect Graphs","authors":"Amir Ali Ahmadi, Cemil Dibek","doi":"10.1137/22m1530410","DOIUrl":"https://doi.org/10.1137/22m1530410","url":null,"abstract":"We present an algebraic characterization of perfect graphs, i.e., graphs for which the clique number and the chromatic number coincide for every induced subgraph. We show that a graph is perfect if and only if certain nonnegative polynomials associated with the graph are sums of squares. As a byproduct, we obtain several infinite families of nonnegative polynomials that are not sums of squares through graph-theoretic constructions. We also characterize graphs for which the associated polynomials belong to certain structured subsets of sum of squares polynomials. Finally, we reformulate some well-known results from the theory of perfect graphs as statements about sum of squares proofs of nonnegativity of certain polynomials.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136077517","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: 0
Persistent Homology of Semialgebraic Sets 半代数集的持久同调
2区 数学
SIAM Journal on Applied Algebra and Geometry Pub Date : 2023-09-27 DOI: 10.1137/22m1494415
Saugata Basu, Negin Karisani
{"title":"Persistent Homology of Semialgebraic Sets","authors":"Saugata Basu, Negin Karisani","doi":"10.1137/22m1494415","DOIUrl":"https://doi.org/10.1137/22m1494415","url":null,"abstract":"We give an algorithm with singly exponential complexity for computing the barcodes up to dimension (for any fixed ) of the filtration of a given semialgebraic set by the sublevel sets of a given polynomial. Our algorithm is the first algorithm for this problem with singly exponential complexity and generalizes the corresponding results for computing the Betti numbers up to dimension of semialgebraic sets with no filtration present.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135579655","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: 4
Finiteness of Spatial Central Configurations with Fixed Subconfigurations 具有固定子构型的空间中心构型的有限性
IF 1.2 2区 数学
SIAM Journal on Applied Algebra and Geometry Pub Date : 2023-08-03 DOI: 10.1137/22m1490788
Yiyang Deng, M. Hampton
{"title":"Finiteness of Spatial Central Configurations with Fixed Subconfigurations","authors":"Yiyang Deng, M. Hampton","doi":"10.1137/22m1490788","DOIUrl":"https://doi.org/10.1137/22m1490788","url":null,"abstract":"","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88211447","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: 0
The Projectivization Matroid of a (boldsymbol{q}) -Matroid (boldsymbol{q}) -矩阵的投影矩阵
IF 1.2 2区 数学
SIAM Journal on Applied Algebra and Geometry Pub Date : 2023-05-23 DOI: 10.1137/22m1494567
Benjamin Jany
{"title":"The Projectivization Matroid of a (boldsymbol{q}) -Matroid","authors":"Benjamin Jany","doi":"10.1137/22m1494567","DOIUrl":"https://doi.org/10.1137/22m1494567","url":null,"abstract":"","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79795384","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: 0
Computing Circuit Polynomials in the Algebraic Rigidity Matroid 计算代数刚性矩阵中的电路多项式
2区 数学
SIAM Journal on Applied Algebra and Geometry Pub Date : 2023-05-23 DOI: 10.1137/21m1437986
Goran Malić, Ileana Streinu
{"title":"Computing Circuit Polynomials in the Algebraic Rigidity Matroid","authors":"Goran Malić, Ileana Streinu","doi":"10.1137/21m1437986","DOIUrl":"https://doi.org/10.1137/21m1437986","url":null,"abstract":"We present an algorithm for computing circuit polynomials in the algebraic rigidity matroid associated to the Cayley–Menger ideal for points in 2D. It relies on combinatorial resultants, a new operation on graphs that captures properties of the Sylvester resultant of two polynomials in this ideal. We show that every rigidity circuit has a construction tree from graphs based on this operation. Our algorithm performs an algebraic elimination guided by such a construction tree and uses classical resultants, factorization, and ideal membership. To highlight its effectiveness, we implemented the algorithm in Mathematica: it took less than 15 seconds on an example where a Gröbner basis calculation took 5 days and 6 hours. Additional speed-ups are obtained using non- generators of the Cayley–Menger ideal and simple variations on our main algorithm.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135140263","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: 1
Optimal Encodings to Elliptic Curves of (boldsymbol{j})-Invariants 0, 1728 椭圆曲线(boldsymbol{j})的最优编码-不变量0,1728
IF 1.2 2区 数学
SIAM Journal on Applied Algebra and Geometry Pub Date : 2022-12-09 DOI: 10.1137/21m1441602
D. Koshelev
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引用次数: 0
A Quiver Invariant Theoretic Approach to Radial Isotropy and the Paulsen Problem for Matrix Frames 矩阵框架径向各向同性和Paulsen问题的颤振不变量理论研究
IF 1.2 2区 数学
SIAM Journal on Applied Algebra and Geometry Pub Date : 2022-11-14 DOI: 10.1137/21m141470x
C. Chindris, Jasim Ismaeel
{"title":"A Quiver Invariant Theoretic Approach to Radial Isotropy and the Paulsen Problem for Matrix Frames","authors":"C. Chindris, Jasim Ismaeel","doi":"10.1137/21m141470x","DOIUrl":"https://doi.org/10.1137/21m141470x","url":null,"abstract":"In this dissertation, we view matrix frames as representations of quivers and study them within the general framework of Quiver Invariant Theory. We are particularly interested in radial isotropic and Parseval matrix frames. Using methods from Quiver Invariant Theory [CD21], we first prove a far-reaching generalization of Barthe's Theorem [Bar98] on vectors in radial isotropic position to the case of matrix frames (see Theorems 5.13(3) and 4.12). With this tool at our disposal, we generalize the Paulsen problem from frames (of vectors) to frames of matrices of arbitrary rank and size extending Hamilton-Moitra's upper bound [HM18]. Specifically, we show in Theorem 5.20 that for any given ε-nearly equal-norm Parseval frame F of n matrices with d rows there exists an equal-norm Parseval frame W of n matrices with d rows such that dist^2 (F,W) [less than or equal to] 46[epsilon]d^2. Finally, in Theorem 5.28 we address the constructive aspects of transforming a matrix frame into radial isotropic position which extend those in [Bar98, AKS20].","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75010828","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: 0
Irrational Quantum Walks 非理性量子漫步
IF 1.2 2区 数学
SIAM Journal on Applied Algebra and Geometry Pub Date : 2022-08-18 DOI: 10.1137/22m1521262
G. Coutinho, P. Baptista, C. Godsil, Thomás Jung Spier, R. Werner
{"title":"Irrational Quantum Walks","authors":"G. Coutinho, P. Baptista, C. Godsil, Thomás Jung Spier, R. Werner","doi":"10.1137/22m1521262","DOIUrl":"https://doi.org/10.1137/22m1521262","url":null,"abstract":"The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the behaviour of the walk is typically not periodic. In consequence we can usually only compute numerical approximations to parameters of the walk. In this paper, we develop theory to exactly study any quantum walk generated by an integral Hamiltonian. As a result, we provide exact methods to compute the average of the mixing matrices, and to decide whether pretty good (or almost) perfect state transfer occurs in a given graph. We also use our methods to study geometric properties of beautiful curves arising from entries of the quantum walk matrix, and discuss possible applications of these results.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79008405","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: 1
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