The change-point detection problem is cast into a delay estimation. Using a local piecewise polynomial representation and some elementary algebraic manipulations, we give an explicit characterization of a change-point as a solution of a given polynomial equation. A key feature of this polynomial equation is its coefficients being composed by short time window iterated integrals of the noisy sig...

A preliminary study of p-refinement with vector finite elements is reported. Results suggest that improved accuracy can be obtained from representations employing a mixture of polynomial orders instead of a uniform polynomial order. Results also suggest that it might be possible to jump directly from the local error in a p=0 expansion to a final representation employing 5 or more polynomial ord...

We study the problem of dictionary learning for signals that can be represented as polynomials or polynomial matrices, such as convolutive signals with time delays or acoustic impulse responses. Recently, we developed a method for polynomial dictionary learning based on the fact that a polynomial matrix can be expressed as a polynomial with matrix coefficients, where the coefficient of the poly...

we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

A matrix representation of iterative methods is presented which includes almost all those based on polynomial methods. A simple lemma and corollaries are established which show that the order of convergence of the iteration is the spectral radius of the matrix representation. A number of old and new methods, particularly those adapted to parallel computation, are analyzed using this representat...

Most digital systems operate on a positional representation of data, such as binary radix. A positional representation is a compact way to encode signal values: in binary radix, 2 distinct values can be represented with n bits. However, operating on it requires complex logic: in each operation such as addition or multiplication, the signal must be “decoded,” with the higher order bits weighted ...

Algorithms invented in the past 25 years make it possible on a computer to efficiently factor a polynomial in one, several, or many variables with coefficients from a certain field, such as a finite field or the rational, real, or complex numbers. I have surveyed work up to 1986 in the papers (Kaltofen 1982 and 1990a). This article discusses important developments of the past five years; I also...

Motivated by the definition of the edge elimination polynomial of a graph we define the covered components polynomial counting spanning subgraphs with respect to their number of components, edges and covered components. We prove a recurrence relation, which shows that both graph polynomials are substitution instances of each other. We give some properties of the covered components polynomial an...

The Pontryagin dual of the twisted Alexander module for a dcomponent link and GLNZ representation is an algebraic dynamical system with an elementary description in terms of colorings of a diagram. In the case of a knot, its associated topological entropy is the logarithmic growth rate of the number of torsion elements in the twisted first-homology group of r-fold cyclic covers of the knot comp...

Let G be a finite cover of a closed connected transpose-stable subgroup of GL(n,R) with complexified Lie algebra g. Let K be a maximal compact subgroup of G, and assume that G and K have equal rank. We prove a translation principle for the Dirac index of virtual (g,K)-modules. As a byproduct, to each coherent family of such modules, we attach a polynomial on the dual of the compact Cartan subal...