Gröbner bases are the computational method par excellence for studying polynomial systems. In the case of parametric polynomial systems one has to determine the reduced Gröbner basis in dependence of the values of the parameters. In this article, we present the algorithm GröbnerCover which has as inputs a finite set of parametric polynomials, and outputs a finite partition of the parameter spac...

In the paper, we describe Drinfel'd double structure of $n$-rank Taft algebra and all its simple modules, then endow $R$-matrices with some application to knot invariants. The invariants get is a generalization Jones polynomial, in particular, it recovers polynomial rank $1$ case, while $2$ one-parameter specialization two-parameter unframed Dubrovnik higher case composite ($n$-power) polynomial.

In this paper the accuracy of two machine learning algorithms including SVM and Bayesian Network are investigated as two important algorithms in diagnosis of Parkinson’s disease. We use Parkinson's disease data in the University of California, Irvine (UCI). In order to optimize the SVM algorithm, different kernel functions and C parameters have been used and our results show that SVM with C par...

In recent years, moment-closure approximations (MAs) of the chemical master equation have become a popular method for the study of stochastic effects in chemical reaction systems. Several different MA methods have been proposed and applied in the literature, but it remains unclear how they perform with respect to each other. In this paper, we study the normal, Poisson, log-normal, and central-m...

The circular Dyson Brownian motion model refers to the stochastic dynamics of the log-gas on a circle. It also specifies the eigenvalues of certain parameter-dependent ensembles of unitary random matrices. This model is considered with the initial condition that the particles are non-interacting (Poisson statistics). Jack polynomial theory is used to derive a simple exact expression for the den...

Abstract Single-machine scheduling where jobs have a penalty for being late or rejected altogether is an important (sub)problem in manufacturing, logistics, and satellite scheduling. It known to be NP-hard the strong sense, there no polynomial-time algorithm that can guarantee constant-factor approximation (unless P=NP). We provide exact fixed-parameter tractable slack maximum number of time wi...

This paper describes a multiple time interval (“multi-interval”) parameter estimation method. The multi-interval parameter estimation method estimates a parameter from a new multi-interval prediction error polynomial that can simultaneously consider multiple time intervals. The root of the multi-interval prediction error polynomial includes the effect on each time interval, and the important mo...

The parametric lattice-point counting problem is as follows: Given an integer matrix A ∈ Zm×n , compute an explicit formula parameterized by b ∈ R that determines the number of integer points in the polyhedron {x ∈R : Ax É b}. In the last decade, this counting problem has received considerable attention in the literature. Several variants of Barvinok’s algorithm have been shown to solve this pr...

The notions of cutwidth and pathwidth of digraphs play a central role in the containment theory for tournaments, or more generally semi-complete digraphs, developed in a recent series of papers by Chudnovsky, Fradkin, Kim, Scott, and Seymour [2, 3, 4, 8, 9, 11]. In this work we introduce a new approach to computing these width measures on semi-complete digraphs, via degree orderings. Using the ...

Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an extremely efficient method to solve numerous polynomial systems that differ only in coefficients, not monomials. This technique is frequently used for solving a parameterized family of polynomial systems at multiple par...