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A Symbolic-Numeric Approach for Parametrizing Ruled Surfaces
This paper presents symbolic algorithms to determine whether a given surface (implicitly or parametrically defined) is a rational ruled surface and...
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Algebraic Dynamical Systems in Machine Learning
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an...
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Congnitive Networks, Their Properties and Applications in Attack Detection and Prevention Systems
The paper considers real-time cyberattack detection methods based on an algebraic approach. The author has applied the algebraic matching method,...
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A computational status update for exact rational mixed integer programming
The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a...
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Glushkov’s Algorithmic Algebras and Automated Parallel Computing Design
An overview of the results obtained within the algebra of algorithms and tools for the automated development of programs for multiprocessor platforms...
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VerifyRealRoots: A Matlab Package for Computing Verified Real Solutions of Polynomials Systems of Equations and Inequalities
VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and inequalities. It calls Bertini...
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A Symbolic Dynamic Geometry System Using the Analytical Geometry Method
A symbolic geometry system such as Geometry Expressions can generate symbolic measurements in terms of indeterminate inputs from a geometric figure....
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Adaptive Deep Learning System for Investigating General Data
The paper presents an approach to analyzing large amounts of data lacking a clear relationship. The approach serves to identify at least some...
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Increasing the Semantic Storage Density of Sparse Distributed Memory
The integration of the compressive sensing (CS) method in the sparse distributed memory (SDM) implementation is proposed for increasing the storage...
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Signatureless Anomalous Behavior Detection in Information Systems
The early detection of cyber threats with cyber-attacks adapted to the nature of information systems is a crucial cybersecurity problem. This problem...
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On Fuzzy Nonlinear Two Coupled System of Differential Equations
The problem taken to solve in this manuscript is a kind of nonlinear differential equation. Many nonlinear systems will not give us an exact...
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Reachable Set Estimation and Safety Verification of Nonlinear Systems via Iterative Sums of Squares Programming
In this paper, the problems of forward reachable set estimation and safety verification of uncertain nonlinear systems with polynomial dynamics are...
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How to Do Maths with Words: Neural Machine Learning Applications to Mathematics and Their Philosophical Significance
Recent years have seen a remarkable development of deep neural network techniques for data analysis, along with their increasing application in...
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Symbolic computation for the qualitative theory of differential equations
This paper provides a survey on symbolic computational approaches for the analysis of qualitative behaviors of systems of ordinary differential...
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Domain Decomposition Algorithms for Neural Network Approximation of Partial Differential Equations
With the success of deep learning technology in many application areas, there have been pioneering approaches to approximate solutions of partial...
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Spatial best linear unbiased prediction: a computational mathematics approach for high dimensional massive datasets
With the advent of massive data sets, much of the computational science and engineering community has moved toward data-intensive approaches in...
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How to Do Maths with Words: Neural Machine Learning Applications to Mathematics and Their Philosophical Significance
Recent years have seen a remarkable development of deep neural network techniques for data analysis, along with their increasing application in...
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Isotopic Meshing of a Real Algebraic Space Curve
This paper presents a new algorithm for computing the topology of an algebraic space curve. Based on an efficient weak generic position-checking...