Journal of Symbolic Computation最新文献_第2页

Asymptotics of solutions of special second-order linear recurrencies with polynomial coefficients and boundary effects of polynomial filters 具有多项式系数的特殊二阶线性回归方程解的渐近性和多项式滤波器的边界效应

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-09-26 DOI: 10.1016/j.jsc.2024.102386

Alexey A. Kytmanov , Sergey P. Tsarev

引用次数: 0

Symbolic-numeric algorithm for parameter estimation in discrete-time models with exp 离散时间模型参数估计的符号-数字算法

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-09-26 DOI: 10.1016/j.jsc.2024.102387

Yosef Berman , Joshua Forrest , Matthew Grote , Alexey Ovchinnikov , Sonia L. Rueda

{"title":"Symbolic-numeric algorithm for parameter estimation in discrete-time models with exp","authors":"Yosef Berman , Joshua Forrest , Matthew Grote , Alexey Ovchinnikov , Sonia L. Rueda","doi":"10.1016/j.jsc.2024.102387","DOIUrl":"10.1016/j.jsc.2024.102387","url":null,"abstract":"<div><div>Dynamic models describe phenomena across scientific disciplines, yet to make these models useful in application the unknown parameter values of the models must be determined. Discrete-time dynamic models are widely used to model biological processes, but it is often difficult to determine these parameters. In this paper, we propose a symbolic-numeric approach for parameter estimation in discrete-time models that involve univariate non-algebraic (locally) analytic functions such as exp. We illustrate the performance (precision) of our approach by applying our approach to two archetypal discrete-time models in biology (the flour beetle ‘LPA’ model and discrete Lotka-Volterra competition model). Unlike optimization-based methods, our algorithm guarantees to find all solutions of the parameter values up to a specified precision given time-series data for the measured variables provided that there are finitely many parameter values that fit the data and that the used polynomial system solver can find all roots of the associated polynomial system with interval coefficients.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142422637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Algorithm for globally identifiable reparametrizations of ODEs 全局可识别的 ODEs 重参数化算法

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-09-10 DOI: 10.1016/j.jsc.2024.102385

Sebastian Falkensteiner , Alexey Ovchinnikov , J. Rafael Sendra

引用次数: 0

Subresultants of several univariate polynomials in Newton basis 几个单变量多项式在牛顿基上的子结果

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-30 DOI: 10.1016/j.jsc.2024.102378

Weidong Wang, Jing Yang

引用次数: 0

D-algebraic functions D 代函数

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-28 DOI: 10.1016/j.jsc.2024.102377

Rida Ait El Manssour , Anna-Laura Sattelberger , Bertrand Teguia Tabuguia

引用次数: 0

Invariant neural architecture for learning term synthesis in instantiation proving 在实例化证明中学习术语合成的不变神经架构

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-28 DOI: 10.1016/j.jsc.2024.102375

Jelle Piepenbrock , Josef Urban , Konstantin Korovin , Miroslav Olšák , Tom Heskes , Mikoláš Janota

{"title":"Invariant neural architecture for learning term synthesis in instantiation proving","authors":"Jelle Piepenbrock , Josef Urban , Konstantin Korovin , Miroslav Olšák , Tom Heskes , Mikoláš Janota","doi":"10.1016/j.jsc.2024.102375","DOIUrl":"10.1016/j.jsc.2024.102375","url":null,"abstract":"<div><p>The development of strong CDCL-based propositional (SAT) solvers has greatly advanced several areas of automated reasoning (AR). One of the directions in AR is therefore to make use of SAT solvers in expressive formalisms such as first-order logic, for which large corpora of general mathematical problems exist today. This is possible due to Herbrand's theorem, which allows reduction of first-order problems to propositional problems by instantiation. The core challenge is synthesizing the appropriate instances from the typically infinite Herbrand universe.</p><p>In this work, we develop a machine learning system targeting this task, addressing its combinatorial and invariance properties. In particular, we develop a GNN2RNN architecture based on a graph neural network (GNN) that learns from problems and their solutions independently of many symmetries and symbol names (addressing the abundance of Skolems), combined with a recurrent neural network (RNN) that proposes for each clause its instantiations. The architecture is then combined with an efficient ground solver and, starting with zero knowledge, iteratively trained on a large corpus of mathematical problems. We show that the system is capable of solving many problems by such educated guessing, finding proofs for 32.12% of the training set. The final trained system solves 19.74% of the unseen test data on its own. We also observe that the trained system finds solutions that the iProver and CVC5 systems did not find.</p></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0747717124000798/pdfft?md5=03f2c9a993930436ebd44dced50d3406&pid=1-s2.0-S0747717124000798-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142150873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Graph sequence learning for premise selection 用于前提选择的图序列学习

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-27 DOI: 10.1016/j.jsc.2024.102376

Edvard K. Holden, Konstantin Korovin

引用次数: 0

Symmetric SAGE and SONC forms, exactness and quantitative gaps 对称 SAGE 和 SONC 形式、精确性和数量差距

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-13 DOI: 10.1016/j.jsc.2024.102374

Philippe Moustrou , Cordian Riener , Thorsten Theobald , Hugues Verdure

引用次数: 0

A short proof for the parameter continuation theorem 参数延续定理的简短证明

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-03 DOI: 10.1016/j.jsc.2024.102373

Viktoriia Borovik, Paul Breiding

引用次数: 0

Fast evaluation and root finding for polynomials with floating-point coefficients 浮点系数多项式的快速求值和求根

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-07-20 DOI: 10.1016/j.jsc.2024.102372

Rémi Imbach , Guillaume Moroz

{"title":"Fast evaluation and root finding for polynomials with floating-point coefficients","authors":"Rémi Imbach , Guillaume Moroz","doi":"10.1016/j.jsc.2024.102372","DOIUrl":"10.1016/j.jsc.2024.102372","url":null,"abstract":"<div><p>Evaluating or finding the roots of a polynomial <span><math><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>d</mi></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> with floating-point number coefficients is a ubiquitous problem. By using a piecewise approximation of <em>f</em> obtained with a careful use of the Newton polygon of <em>f</em>, we improve state-of-the-art upper bounds on the number of operations to evaluate and find the roots of a polynomial. In particular, if the coefficients of <em>f</em> are given with <em>m</em> significant bits, we provide for the first time an algorithm that finds all the roots of <em>f</em> with a relative condition number lower than <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>m</mi></mrow></msup></math></span>, using a number of bit operations quasi-linear in the bit-size of the floating-point representation of <em>f</em>. Notably, our new approach handles efficiently polynomials with coefficients ranging from <span><math><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo><mi>d</mi></mrow></msup></math></span> to <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>d</mi></mrow></msup></math></span>, both in theory and in practice.</p></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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