Annals of Mathematics and Artificial Intelligence最新文献

Analysis and optimization of probabilities of beneficial mutation and crossover recombination in a Hamming space 汉明空间中有益突变和交叉重组概率的分析与优化

IF 1 4区计算机科学

Annals of Mathematics and Artificial Intelligence Pub Date : 2025-06-23 DOI: 10.1007/s10472-025-09987-5

Roman V. Belavkin

{"title":"Analysis and optimization of probabilities of beneficial mutation and crossover recombination in a Hamming space","authors":"Roman V. Belavkin","doi":"10.1007/s10472-025-09987-5","DOIUrl":"10.1007/s10472-025-09987-5","url":null,"abstract":"<div><p>Inspired by Fisher’s geometric approach to study beneficial mutations, we analyse probabilities of beneficial mutation and crossover recombination of strings in a general Hamming space with arbitrary finite alphabet. Mutations and recombinations that reduce the distance to an optimum are considered as beneficial. Geometric and combinatorial analysis is used to derive closed-form expressions for transition probabilities between spheres around an optimum giving a complete description of Markov evolution of distances from an optimum over multiple generations. This paves the way for optimization of parameters of mutation and recombination operators. Here we derive optimality conditions for mutation and recombination radii maximizing the probabilities of mutation and crossover into the optimum. The analysis highlights important differences between these evolutionary operators. While mutation can potentially reach any part of the search space, the probability of beneficial mutation decreases with distance to an optimum, and the optimal mutation radius or rate should also decrease resulting in a slow-down of evolution near the optimum. Crossover recombination, on the other hand, acts in a subspace of the search space defined by the current population of strings. However, probabilities of beneficial and deleterious crossover are balanced, and their characteristics, such as variance, are translation invariant in a Hamming space, suggesting that recombination may complement mutation and boost the rate of evolution near the optimum.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"94 1","pages":"127 - 161"},"PeriodicalIF":1.0,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10472-025-09987-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146082839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalization-based similarity Generalization-based相似

IF 1 4区计算机科学

Annals of Mathematics and Artificial Intelligence Pub Date : 2025-06-20 DOI: 10.1007/s10472-025-09989-3

Christian Antić

引用次数: 0

Foreword: special issue on formalisation of geometry, automated and interactive geometric reasoning 前言：关于几何形式化，自动和交互几何推理的特刊

IF 1 4区计算机科学

Annals of Mathematics and Artificial Intelligence Pub Date : 2025-06-19 DOI: 10.1007/s10472-025-09992-8

Zoltán Kovács, Pedro Quaresma

引用次数: 0

Preface special issue on agents and robots for reliable engineered autonomy (AREA 2023) 前言：用于可靠工程自主的代理和机器人特刊（AREA 2023）

IF 1 4区计算机科学

Annals of Mathematics and Artificial Intelligence Pub Date : 2025-06-18 DOI: 10.1007/s10472-025-09991-9

Angelo Ferrando, Rafael C. Cardoso

引用次数: 0

Relative-interior solution for the (incomplete) linear assignment problem with applications to the quadratic assignment problem （不完全）线性分配问题的相对内解及其在二次分配问题中的应用

IF 1 4区计算机科学

Annals of Mathematics and Artificial Intelligence Pub Date : 2025-05-21 DOI: 10.1007/s10472-025-09974-w

Tomáš Dlask, Bogdan Savchynskyy

{"title":"Relative-interior solution for the (incomplete) linear assignment problem with applications to the quadratic assignment problem","authors":"Tomáš Dlask, Bogdan Savchynskyy","doi":"10.1007/s10472-025-09974-w","DOIUrl":"10.1007/s10472-025-09974-w","url":null,"abstract":"<div><p>We study the set of optimal solutions of the dual linear programming formulation of the linear assignment problem (LAP) to propose a method for computing a solution from the relative interior of this set. Assuming that an arbitrary dual-optimal solution and an optimal assignment are available (for which many efficient algorithms already exist), our method computes a relative-interior solution in linear time. Since the LAP occurs as a subproblem in the linear programming (LP) relaxation of the quadratic assignment problem (QAP), we employ our method as a new component in the family of dual-ascent algorithms that provide bounds on the optimal value of the QAP. To make our results applicable to the incomplete QAP, which is of interest in practical use-cases, we also provide a linear-time reduction from the incomplete LAP to the complete LAP along with a mapping that preserves optimality and membership in the relative interior. Our experiments on publicly available benchmarks indicate that our approach with relative-interior solution can frequently provide bounds near the optimum of the LP relaxation and its runtime is much lower when compared to a commercial LP solver.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"94 1","pages":"19 - 62"},"PeriodicalIF":1.0,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10472-025-09974-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146082336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Automated analysis of the difficulty of secondary school geometry theorems 中学几何定理难度的自动分析

IF 1 4区计算机科学

Annals of Mathematics and Artificial Intelligence Pub Date : 2025-05-19 DOI: 10.1007/s10472-025-09983-9

Soma Bartha, András Kerekes, Zoltán Kovács, Tomás Recio

{"title":"Automated analysis of the difficulty of secondary school geometry theorems","authors":"Soma Bartha, András Kerekes, Zoltán Kovács, Tomás Recio","doi":"10.1007/s10472-025-09983-9","DOIUrl":"10.1007/s10472-025-09983-9","url":null,"abstract":"<div><p>We elaborate, as a benchmark, a list of geometry theorems that are regularly used in Hungarian high schools, in specialized tracks for mathematics. Then, these statements are implemented as GeoGebra files, and algebraically proven (with certification) in GeoGebra Discovery. Next, these files are imported in Java Geometry Expert (JGEX), and geometrically proven with the associated Geometry Deductive Database method. In both programs, through quite different approaches in each case, we define and implement an algorithmic measure of the difficulty of a geometric theorem. Then, we compute the corresponding measures on the selected list of statements, and we analyze the obtained collection of pairs of difficulty grades, finding a moderate positive correlation (0.51) between GeoGebra Discovery’s algebraic, and JGEX’s deductive difficulty formulations. A correlation that seems to support the adequacy of the chosen approximation in our on-going work to algorithmically establish some <i>ad-hoc</i> measure of the difficulty of geometric statements that could be reasonably coincidental with the appreciation of human expert users (e.g. teachers).</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"93 6","pages":"1011 - 1033"},"PeriodicalIF":1.0,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Reasoning with system W and infeasible worlds 用系统W和不可行的世界推理

IF 1 4区计算机科学

Annals of Mathematics and Artificial Intelligence Pub Date : 2025-05-15 DOI: 10.1007/s10472-025-09982-w

Jonas Haldimann, Christoph Beierle, Gabriele Kern-Isberner, Thomas Meyer

{"title":"Reasoning with system W and infeasible worlds","authors":"Jonas Haldimann, Christoph Beierle, Gabriele Kern-Isberner, Thomas Meyer","doi":"10.1007/s10472-025-09982-w","DOIUrl":"10.1007/s10472-025-09982-w","url":null,"abstract":"<div><p>System W is an inference method for conditional belief bases with some notable properties like capturing system Z while, in contrast to system Z, avoiding the <i>drowning problem</i>. This paper further investigates the properties of system W. We show how system W behaves with respect to postulates put forward for inference relations. We develop postulates ensuring compliance with syntax splitting for inference operators based on a full strict partial order on worlds. By observing that system W satisfies these axioms, it is proven that system W satisfies syntax splitting. We also explore how syntax splitting affects the strict partial order underlying system W and exploit this for answering certain types of queries without having to determine this strict partial order completely. However, the original definition of system W and the results above only consider inference from belief bases satisfying a strong notion of consistency. In the second part of this paper, we lift this limitation and extend system W to also cover inference from belief bases that only satisfy a weaker notion of consistency. We investigate the properties of the such extended system W. Especially, it is shown that extended system W complies with syntax splitting and retains the desireable properties of system W. Furthermore, we give an overview of the relations of extended system W to other inductive inference operators.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"93 5","pages":"665 - 698"},"PeriodicalIF":1.0,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10472-025-09982-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145449535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Encoding paths with binary arrays in a king’s graph for error-free data transmission 用国王图中的二进制数组编码路径，实现无差错数据传输

IF 1 4区计算机科学

Annals of Mathematics and Artificial Intelligence Pub Date : 2025-05-15 DOI: 10.1007/s10472-025-09985-7

Gökçe Çaylak Kayaturan, Alexei Vernitski

引用次数: 0

Using causal discovery and pattern mining methods for group-specific policy-making: An agent-based model analysis method 在群体决策中使用因果发现和模式挖掘方法：基于主体的模型分析方法

IF 1 4区计算机科学

Annals of Mathematics and Artificial Intelligence Pub Date : 2025-05-08 DOI: 10.1007/s10472-025-09984-8

Shuang Chang, Tatsuya Asai, Yusuke Koyanagi, Kento Uemura, Koji Maruhashi, Kotaro Ohori

{"title":"Using causal discovery and pattern mining methods for group-specific policy-making: An agent-based model analysis method","authors":"Shuang Chang, Tatsuya Asai, Yusuke Koyanagi, Kento Uemura, Koji Maruhashi, Kotaro Ohori","doi":"10.1007/s10472-025-09984-8","DOIUrl":"10.1007/s10472-025-09984-8","url":null,"abstract":"<div><p>An agent-based modelling approach is a powerful means of understanding social phenomena by modelling individual behaviours and interactions. However, the advancements in modelling pose challenges in the model analysis process for understanding the complex effects of input factors, especially when it comes to offering concrete policies for improving system outcomes. In this work, we propose a revised micro-dynamic analysis method that adopts pattern mining and causal discovery methods to enhance the model interpretation and to facilitate group-specific policy-making. It strengthens the explanation power of the conventional micro-dynamic analysis by eliminating ambiguity in the result interpretation and enabling a causal interpretation of a target phenomenon across subgroups. We applied our method to understand an agent-based model that evaluates the effects of a long-term care scheme on access to care. Our findings showed that the method can suggest policies for improving the equity of access more efficiently than the conventional scenario analysis.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"94 1","pages":"89 - 109"},"PeriodicalIF":1.0,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146082527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Formalization of gyrovector spaces as models of hyperbolic geometry and special relativity 作为双曲几何和狭义相对论模型的陀螺矢量空间的形式化

IF 1 4区计算机科学

Annals of Mathematics and Artificial Intelligence Pub Date : 2025-04-26 DOI: 10.1007/s10472-025-09979-5

Jelena Marković, Filip Marić

{"title":"Formalization of gyrovector spaces as models of hyperbolic geometry and special relativity","authors":"Jelena Marković, Filip Marić","doi":"10.1007/s10472-025-09979-5","DOIUrl":"10.1007/s10472-025-09979-5","url":null,"abstract":"<div><p>In this paper, we present an Isabelle/HOL formalization of noncommutative and nonassociative algebraic structures known as <i>gyrogroups</i> and <i>gyrovector spaces</i>. These concepts were introduced by Abraham A. Ungar and have deep connections to hyperbolic geometry and special relativity. Gyrovector spaces can be used to define models of hyperbolic geometry. Unlike other models, gyrovector spaces offer the advantage that all definitions exhibit remarkable syntactical similarities to standard Euclidean and Cartesian geometry (e.g., points on the line between <i>a</i> and <i>b</i> satisfy the parametric equation <span>( a oplus totimes (ominus a oplus b))</span>, for <span>(t in mathbb {R})</span>, while the hyperbolic Pythagorean theorem is expressed as <span>(a^2oplus b^2 = c^2)</span>, where <span>(otimes )</span>, <span>(oplus )</span>, and <span>(ominus )</span> represent gyro operations). We begin by formally defining gyrogroups and gyrovector spaces and proving their numerous properties. Next, we formalize Möbius and Einstein models of these abstract structures (formulated in the two-dimensional, complex plane), and then demonstrate that these are equivalent to the Poincaré and Klein-Beltrami models, satisfying Tarski’s geometry axioms for hyperbolic geometry.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"93 6","pages":"871 - 905"},"PeriodicalIF":1.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0