Related papers: Introduction to the Symbolic Integration System
This study extends the use of symbolic computation in Matrix Structural Analysis (MSA) to plane (2D) trusses, building on previous work that focused on continuous beams. An open-source MATLAB program, hosted on GitHub, was developed to…
Geometric algebra (GA) is a mathematical tool for geometric computing, providing a framework that allows a unified and compact approach to geometric relations which in other mathematical systems are typically described using different more…
In this paper we present efficient computational and symbolic algorithms for solving a nearly pentadiagonal linear systems. The implementation of the algorithms using Computer Algebra Systems (CAS)such as MAPLE, MACSYMA, MATHEMATICA, and…
Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce concepts of abstract modules and abstract modular systems to study…
Signal Processing (SP) and Machine Learning (ML) rely on good math and coding knowledge, in particular, linear algebra, probability, trigonometry, and complex numbers. A good grasp of these relies on scalar algebra learned in middle school.…
We present a review of the symbol map, a mathematical tool that can be useful in simplifying expressions among multiple polylogarithms, and recall its main properties. A recipe is given for how to obtain the symbol of a multiple…
Symbolic computation is an important approach in automated program analysis. Most state-of-the-art tools perform symbolic computation as interpreters and directly maintain symbolic data. In this paper, we show that it is feasible, and in…
Modality-agnostic Semantic Segmentation (MaSS) aims to achieve robust scene understanding across arbitrary combinations of input modality. Existing methods typically rely on explicit feature alignment to achieve modal homogenization, which…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python…
Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style…
Several approaches are proposed to deal with the problem of the Automatic Schema Matching (ASM). The challenges and difficulties caused by the complexity and uncertainty characterizing both the process and the outcome of Schema Matching…
The goal of this paper is to deliver the overview of the current state of the art, to provide experience report on developing quantum software tools, and to outline the perspective for developing quantum programming tools supporting…
The article highlights the promising ways of providing access to the mathematical software in higher educational institutions. It is emphasized that the cloud computing services implementation is the actual trend of modern ICT pedagogical…
In recent years, neural systems have demonstrated highly effective learning ability and superior perception intelligence. However, they have been found to lack effective reasoning and cognitive ability. On the other hand, symbolic systems…
In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…
We demonstrate a library for the integration of domain knowledge in deep learning architectures. Using this library, the structure of the data is expressed symbolically via graph declarations and the logical constraints over outputs or…
This article is intended to an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The effort of mathematicians in field of the group…
Vector Symbolic Architectures combine a high-dimensional vector space with a set of carefully designed operators in order to perform symbolic computations with large numerical vectors. Major goals are the exploitation of their…
Constraint answer set programming or CASP, for short, is a hybrid approach in automated reasoning putting together the advances of distinct research areas such as answer set programming, constraint processing, and satisfiability modulo…