The rapidly advancing fields of machine learning and mathematical modeling, greatly enhanced by the recent growth in artificial intelligence, are the focus of this special issue. This issue compiles extensively revise...
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The rapidly advancing fields of machine learning and mathematical modeling, greatly enhanced by the recent growth in artificial intelligence, are the focus of this special issue. This issue compiles extensively revised and improved versions of the top papers from the workshop on mathematical Modeling and Problem Solving at PDPTA'23, the 29th International conference on Parallel and Distributed Processing Techniques and Applications. Covering fundamental research in matrix operations and heuristic searches to real-world applications in computer vision and drug discovery, the issue underscores the crucial role of supercomputing and parallel and distributed computing infrastructure in research. Featuring nine key studies, this issue pushes forward computational technologies in mathematical modeling, refines techniques for analyzing images and time-series data, and introduces new methods in pharmaceutical and materials science, making significant contributions to these areas.
We develop an analogue of eigenvalue methods to construct solutions of systems of tropical polynomial equalities and inequalities. We show that solutions can be obtained by solving parametric mean payoff games, arisin...
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ISBN:
(纸本)9783031645280;9783031645297
We develop an analogue of eigenvalue methods to construct solutions of systems of tropical polynomial equalities and inequalities. We show that solutions can be obtained by solving parametric mean payoff games, arising to approriate linearizations of the systems using tropical Macaulay matrices. We implemented specific algorithms adapted to the large scale parametric games that arise in this way, and present numerical experiments.
The 'Automated Math Equation Recognition and Problem Solving with computer Vision' research work is to develop a framework that utilizes computer vision methods to consequently recognize mathematical equations...
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This paper addresses mathematicalmethods to reduce or segment the search space for big data solutions into distinct subspaces with partial solutions. It is achieved by using a data organization structure of 'm-tu...
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The paper proposes an approach to the numerical solving the problem of determining the parameters of a two-dimensional mathematical model of oil filtration. The parameters are determined on the class of piecewise cons...
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ISBN:
(纸本)9783031734168;9783031734175
The paper proposes an approach to the numerical solving the problem of determining the parameters of a two-dimensional mathematical model of oil filtration. The parameters are determined on the class of piecewise constant functions. It is important that in this case the problem is not only to identify parameters values, but also to identify the parameters constancy boundaries. The approach is based on reducing the initial identification problem to a finite-dimensional optimization problem of a network structure. To solve this finite-dimensional optimization problem we obtain formulas for the gradient of the functional in the space of coefficient values that determine the process parameters and the domain of constancy of the coefficients. These formulas allow to use effective first-order optimization methods, in particular, the gradient method. Some of the results of the carried out computer experiments are given. The obtained results show the efficiency of the proposed approach to the numerical solving the identification problem.
We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical alge...
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ISBN:
(纸本)9783031645280;9783031645297
We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may be represented as a constrained neural network. This allows us to then use machine learning methods to further optimise the heuristic, leading to new networks of similar size, representing new heuristics of similar complexity as the original human-designed one. We present this as a form of ante-hoc explainability for use in computer algebra development.
Computational birational geometry is one of the key playing fields in an algorithmic approach to algebraic geometry, since birational maps are the fundamental way to relate algebraic varieties (or schemes). An importa...
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ISBN:
(纸本)9783031645280;9783031645297
Computational birational geometry is one of the key playing fields in an algorithmic approach to algebraic geometry, since birational maps are the fundamental way to relate algebraic varieties (or schemes). An important application is an algorithmic approach to the Minimal Model Program (MMP), which aims to classify algebraic varieties with mild singularities by finding simple birational models of such varieties in their birational equivalence class. This note presents work towards parallel methods to solve problems in birational geometry. Making use of a representation of algebraic schemes in terms of charts allows for a parallel computational approach for handling both the varieties and rational maps between them. In this note, we illustrate this approach on examples.
The aim of the study is computer modeling and solving the linear programming problem to intensify the use of limited resources. The research used methods of system analysis, mathematical modeling and programming. The ...
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The application of computer software technology has played a very important role in the development of the information society. With the development of computerscience and network communications and other disciplines...
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This paper describes work towards an approach to using massively parallel methods for computing syzygies and free resolutions of finitely generated modules over polynomial rings over fields. Our primary focus here is ...
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ISBN:
(纸本)9783031645280;9783031645297
This paper describes work towards an approach to using massively parallel methods for computing syzygies and free resolutions of finitely generated modules over polynomial rings over fields. Our primary focus here is Schreyer's resolution. Our method exploits the inherent parallelism of the algorithm, primarily utilizing Petri nets, within the GPI-Space [10] framework as our language for parallel workflows. GPI-Space is a task-based workflow management system that employs Petri nets as its coordination layer, while the computation is carried out by the computer algebra system Singular [9]. We outline how the algorithm is modeled through a Petri net, explaining the coordination of tasks and data structures within the parallel computing environment.
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