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At least 55 records · Page 3Linked to original sources
arXiv2009

The development of a fuzzy regulator with an entry and an output in Fislab

The present article is a sequel of the article "Fislab the Fuzzy Inference Tool-Box for Scilab" and it represents the practical application of:"The development of the Fuzzy regulator with an input and an output in Fislab". The article contains, besides this application, some functions to be used in the program, namely Scilab functions for the fuzzification of the firm information, functions for the operation of de-fuzzification and functions for the implementation of.

cs.MS↗
arXiv2009

WinBioinfTools: Bioinformatics Tools for Windows High Performance Computing Server 2008

Open source bioinformatics tools running under MS Windows are rare to find, and those running under Windows HPC cluster are almost non-existing. This is despite the fact that the Windows is the most popular operating system used among life scientists. Therefore, we introduce in this initiative WinBioinfTools, a toolkit containing a number of bioinformatics tools running under Windows High Performance Computing Server 2008. It is an open source code package, where users and developers can share and add to. We currently start with three programs from the area of sequence analysis: 1) CoCoNUT for pairwise genome comparison, 2) parallel BLAST for biological database search, and 3) parallel global pairwise sequence alignment. In this report, we focus on technical aspects concerning how some components of these tools were ported from Linux/Unix environment to run under Windows. We also show the advantages of using the Windows HPC Cluster 2008. We demonstrate by experiments the performance gain achieved when using a computer cluster against a single machine. Furthermore, we show the results of comparing the performance of WinBioinfTools on the Windows and Linux Cluster.

cs.MS↗
arXiv2009

Limits of Educational Soft "GeoGebra" in a Critical Constructive Review

Mathematical educational soft explore, investigating in a dynamical way, some algebraically, geometrically problems, the expected results being used to involve a lot of mathematical results. One such software soft is GeoGebra. The software is free and multi-platform dynamic mathematics software for learning and teaching, awards in Europe and the USA. This paper describes some critical but constructive investigation using the platform for graph functions and dynamic geometry.

cs.MS↗
arXiv2009

Iterative Methods for Systems' Solving - a C# approach

This work wishes to support various mathematical issues concerning the iterative methods with the help of new programming languages. We consider a way to show how problems in math have an answer by using different academic resources and different thoughts. Here we treat methods like Gauss-Seidel's, Cramer's and Gauss-Jordan's.

cs.MS↗
arXiv2009

Real Solution Isolation with Multiplicity of Zero-Dimensional Triangular Systems

Existing algorithms for isolating real solutions of zero-dimensional polynomial systems do not compute the multiplicities of the solutions. In this paper, we define in a natural way the multiplicity of solutions of zero-dimensional triangular polynomial systems and prove that our definition is equivalent to the classical definition of local (intersection) multiplicity. Then we present an effective and complete algorithm for isolating real solutions with multiplicities of zero-dimensional triangular polynomial systems using our definition. The algorithm is based on interval arithmetic and square-free factorization of polynomials with real algebraic coefficients. The computational results on some examples from the literature are presented.

cs.SC↗
arXiv2009

Asymmetric Quantum Cyclic Codes

It is recently conjectured in quantum information processing that phase-shift errors occur with high probability than qubit-flip errors, hence the former is more disturbing to quantum information than the later one. This leads us to construct asymmetric quantum error controlling codes to protect quantum information over asymmetric channels, $\Pr Z \geq \Pr X$. In this paper we present two generic methods to derive asymmetric quantum cyclic codes using the generator polynomials and defining sets of classical cyclic codes. Consequently, the methods allow us to construct several families of asymmetric quantum BCH, RS, and RM codes. Finally, the methods are used to construct families of asymmetric subsystem codes.

cs.IT↗
arXiv2009

Tensors and n-d Arrays:A Mathematics of Arrays (MoA), psi-Calculus and the Composition of Tensor and Array Operations

The Kronecker product is a key algorithm and is ubiquitous across the physical, biological, and computation social sciences. Thus considerations of optimal implementation are important. The need to have high performance and computational reproducibility is paramount. Moreover, due to the need to compose multiple Kronecker products, issues related to data structures, layout and indexing algebra require a new look at an old problem. This paper discusses the outer product/tensor product and a special case of the tensor product: the Kronecker product, along with optimal implementation when composed, and mapped to complex processor/memory hierarchies. We discuss how the use of ``A Mathematics of Arrays" (MoA), and the psi-Calculus, (a calculus of indexing with shapes), provides optimal, verifiable, reproducible, scalable, and portable implementations of both hardware and software.

cs.MS↗
arXiv2014

Computational Understanding and Manipulation of Symmetries

For natural and artificial systems with some symmetry structure, computational understanding and manipulation can be achieved without learning by exploiting the algebraic structure. Here we describe this algebraic coordinatization method and apply it to permutation puzzles. Coordinatization yields a structural understanding, not just solutions for the puzzles.

cs.AI↗
arXiv2009

Approximating Mathematical Semantic Web Services Using Approximation Formulas and Numerical Methods

Mathematical semantic web services are very useful in practice, but only a small number of research results are reported in this area. In this paper we present a method of obtaining an approximation of a mathematical semantic web service, from its semantic description, using existing mathematical semantic web services, approximation formulas, and numerical methods techniques. We also give a method for automatic comparison of two complexity functions. In addition, we present a method for classifying the numerical methods mathematical semantic web services from a library.

cs.MS↗
arXiv2010

Implementing Gröbner bases for operads

We present an implementation of the algorithm for computing Groebner bases for operads due to the first author and A. Khoroshkin. We discuss the actual algorithms, the choices made for the implementation platform and the data representation, and strengths and weaknesses of our approach.

cs.SC↗
arXiv2009

On the Different Shapes Arising in a Family of Rational Curves Depending on a Parameter

Given a family of rational curves depending on a real parameter, defined by its parametric equations, we provide an algorithm to compute a finite partition of the parameter space (${\Bbb R}$, in general) so that the shape of the family stays invariant along each element of the partition. So, from this partition the topology types in the family can be determined. The algorithm is based on a geometric interpretation of previous work (\cite{JGRS}) for the implicit case. However, in our case the algorithm works directly with the parametrization of the family, and the implicit equation does not need to be computed. Timings comparing the algorithm in the implicit and the parametric cases are given; these timings show that the parametric algorithm developed here provides in general better results than the known algorithm for the implicit case.

cs.SC↗
arXiv2009

Local Shape of Generalized Offsets to Algebraic Curves

In this paper we study the local behavior of an algebraic curve under a geometric construction which is a variation of the usual offsetting construction, namely the {\it generalized} offsetting process (\cite {SS99}). More precisely, here we discuss when and how this geometric construction may cause local changes in the shape of an algebraic curve, and we compare our results with those obtained for the case of classical offsets (\cite{JGS07}). For these purposes, we use well-known notions of Differential Geometry, and also the notion of {\it local shape} introduced in \cite{JGS07}.

cs.SC↗
arXiv2010

Transmission line inspires a new distributed algorithm to solve linear system of circuit

Transmission line, or wire, is always troublesome to integrated circuits designers, but it could be helpful to parallel computing researchers. This paper proposes the Virtual Transmission Method (VTM), which is a new distributed and stationary iterative algorithm to solve the linear system extracted from circuit. It tears the circuit by virtual transmission lines to achieve distributed computing. For the symmetric positive definite (SPD) linear system, VTM is proved to be convergent. For the unsymmetrical linear system, numerical experiments show that VTM is possible to achieve better convergence property than the traditional stationary algorithms. VTM could be accelerated by some preconditioning techniques, and the convergence speed of VTM is fast when its preconditioner is properly chosen.

cs.CE↗
arXiv2009

Parallel Computation of Finite Element Navier-Stokes codes using MUMPS Solver

The study deals with the parallelization of 2D and 3D finite element based Navier-Stokes codes using direct solvers. Development of sparse direct solvers using multifrontal solvers has significantly reduced the computational time of direct solution methods. Although limited by its stringent memory requirements, multifrontal solvers can be computationally efficient. First the performance of MUltifrontal Massively Parallel Solver (MUMPS) is evaluated for both 2D and 3D codes in terms of memory requirements and CPU times. The scalability of both Newton and modified Newton algorithms is tested.

cs.MS↗
arXiv2009

A Branch and Cut Algorithm for the Halfspace Depth Problem

The concept of \emph{data depth} in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. \emph{Halfspace depth} is a measure of data depth. Given a set $S$ of points and a point $p$, the halfspace depth (or rank) of $p$ is defined as the minimum number of points of $S$ contained in any closed halfspace with $p$ on its boundary. Computing halfspace depth is NP-hard, and it is equivalent to the Maximum Feasible Subsystem problem. In this paper a mixed integer program is formulated with the big-$M$ method for the halfspace depth problem. We suggest a branch and cut algorithm for these integer programs. In this algorithm, Chinneck's heuristic algorithm is used to find an upper bound and a related technique based on sensitivity analysis is used for branching. Irreducible Infeasible Subsystem (IIS) hitting set cuts are applied. We also suggest a binary search algorithm which may be more numerically stable. The algorithms are implemented with the BCP framework from the \textbf{COIN-OR} project.

cs.CG↗
arXiv2009

Isogenies of Elliptic Curves: A Computational Approach

Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the reducibility of the elliptic curve discrete logarithm problem. With such diverse uses, understanding these objects is important for anyone interested in the field of elliptic curve cryptography. This paper, targeted at an audience with a knowledge of the basic theory of elliptic curves, provides an introduction to the necessary theoretical background for understanding what isogenies are and their basic properties. This theoretical background is used to explain some of the basic computational tasks associated with isogenies. Herein, algorithms for computing isogenies are collected and presented with proofs of correctness and complexity analyses. As opposed to the complex analytic approach provided in most texts on the subject, the proofs in this paper are primarily algebraic in nature. This provides alternate explanations that some with a more concrete or computational bias may find more clear.

cs.CR↗
arXiv2011

Numerical Algebraic Geometry for Macaulay2

Numerical Algebraic Geometry uses numerical data to describe algebraic varieties. It is based on the methods of numerical polynomial homotopy continuation, an alternative to the classical symbolic approaches of computational algebraic geometry. We present a package, the driving idea behind which is to interlink the existing symbolic methods of Macaulay2 and the powerful engine of numerical approximate computations. The core procedures of the package exhibit performance competitive with the other homotopy continuation software.

math.AG↗