We introduce a new class of functions that can be minimized in polynomial time in the value oracle model. These are functions f satisfying f(x) + f(y) ≥ f(x ⊓ y) + f(x ⊔ y) where the domain of each variable xi corresponds to nodes of a rooted binary tree, and operations ⊓,⊔ are defined with respect to this tree. Special cases include previously studied L-convex and bisubmodular functions, which...

This paper gives an algorithm to factor a polynomial f (in one variable) over rings like Z=rZ for r 2 Z or F q y]=rF q y] for r 2 F q y]. The Chinese Remainder Theorem reduces our problem to the case where r is a prime power. Then factorization is not unique, but if r does not divide the discriminant of f , our (probabilistic) algorithm produces a description of all (possibly exponentially many...

The one-dimensional functional equation g(y(t)) = cg(z(t)) with known functions y and z and constant c is considered. The indeterminacies are calculated, and an algorithm for approximating g given y and z at finitely many time instants is proposed. This linearization identification algorithm is applied to the postnonlinear blind source separation (BSS) problem in the case of independent sources...

We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion y ∈ T (x), where y is a perturbation element near 0 and T is a set-valued mapping acting from a Banach space X to a Banach space Y which is metrically regular around some point point (x̄, 0) in its graph. We study the behavior of the convergent iterates generated by the algorithm and we prove th...

Properties of Pisot numbers have long been of interest. One line of questioning, initiated by Erdős, Joó and Komornik in 1990, is the determination of l(q) for Pisot numbers q, where l(q) = inf(|y| : y = 0 + 1q + · · ·+ nq, i ∈ {±1, 0}, y 6= 0). Although the quantity l(q) is known for some Pisot numbers q, there has been no general method for computing l(q). This paper gives such an algorithm. ...

The Expectation Maximisation (EM) algorithm is a procedure that iteratively optimises parameters of a given model, to maximise the likelihood of observing a given (training) dataset. Assuming that our framework has unobserved data, X, observed data, Y , parameters Θ, and a likelihood function L(X,Y,Θ) = P(X,Y |Θ), we can derive the steps of the algorithm as follows: 1. Choose initial parameters...

Given an m x m image I and a smaller n x n image P, the computation of an (m-n+1) x (m-n+1) matrix C where C(i, j) is of the form C(i,j)=Sigma(k=0)(n-1)Sigma(k'=0)(n-1)f(I(i+k,j+k'), P(k,k')), 0= or <i, j= or <m-n for some function f, is often used in template matching. Frequent choices for the function f are f(x,y)=(x-y)(2) and f(x,y)=/m-y/. For the case when f(x,y)=(x-y)(2), it is well known ...

This is an annotated bibliography on fully dynamic algorithms for path problems on general directed graphs. In particular, we consider two fundamental problems: dynamic transitive closure and dynamic shortest paths. Although research on these problems spans over more than three decades, in the last couple of years many novel algorithmic techniques have been proposed. 1 Dynamic Path Problems A d...

The standard technique for obtaining the stability regions of numerical methods for ordinary diierential equations (ODEs) and delay diierential equations (DDEs) is the boundary-locus algorithm (BLA). However, in the case of the DDE y 0 (t) = y(t) + y(t ?) for & 2 R, the BLA often fails to map out the stability region correctly. In this paper we give a FORTRAN 77 listing of an alternative stabil...

We consider a special case of the problem of computing the Galois group of a system of linear ordinary differential equations Y ′ = MY, M ∈ C(x)n×n. We assume that C is a computable, characteristic-zero, algebraically closed constant field with factorization algorithm. There exists a decision procedure, due to Compoint and Singer, to compute the group in case the system is completely reducible....