Related papers: Decomposing replicable functions
We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…
We give an elementary characterization of rational functions among meromorphic functions in the complex plane.
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
This article introduces an adaptive sorting algorithm that can relocate elements accurately by substituting their values into a function which we name it the guessing function. We focus on building this function which is the mapping…
By means of partial fraction method, we investigate the decomposition of rational functions. Several striking identities on harmonic numbers and generalized Apery numbers will be established, including the binomial-harmonic number identity…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
Let G=Aut_K (K(x)) be the Galois group of the transcendental degree one pure field extension K(x)/K. In this paper we describe polynomial time algorithms for computing the field Fix(H) fixed by a subgroup H < G and for computing the fixing…
We give a decomposition formula for computing the state polytope of a reducible variety in terms of the state polytopes of its components.
We define a ring whose elements are rational functions, whose addition is polynomial multiplication, and whose multiplication is a convolution operation. It is then show that this ring's endomorphisms exhibit a strong classification.…
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
In this paper, we give a theoretical analysis for the algorithms to compute functional decomposition for multivariate polynomials based on differentiation and homogenization which are proposed by Ye, Dai, Lam (1999) and Faug$\mu$ere, Perret…
We review the cumulant decomposition (a way of decomposing the expectation of a product of random variables (e.g. $\mathbb{E}[XYZ]$) into a sum of terms corresponding to partitions of these variables.) and the Wick decomposition (a way of…
We present a MATLAB/Octave toolbox to decompose finite dimensionial representations of compact groups. Surprisingly, little information about the group and the representation is needed to perform that task. We discuss applications to…
We present an algorithm for the decomposition of periodic financial return data into orthogonal factors of expected return and "systemic", "productive", and "nonproductive" risk. Generally, when the number of funds does not exceed the…
The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…
The powers of generating functions and its properties are analyzed. A new class of functions is introduced, based on the application of compositions of an integer $n$, called composita. The methods for obtaining reciprocal and reverse…
Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep…
A rational function $f(x)$ is rationally summable if there exists a rational function $g(x)$ such that $f(x)=g(x+1)-g(x)$. Detecting whether a given rational function is summable is an important and basic computational subproblem that…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…