Related papers: Max-Min Representation of Piecewise Linear Functio…
This paper concerns a method of selecting a subset of features for a sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer quadratic optimization formulation for solving the problem based on a quadratic approximation…
We consider the problem of minimising functions represented as a difference of lattice submodular functions. We propose analogues to the SupSub, SubSup and ModMod routines for lattice submodular functions. We show that our…
We give a description of the minimal exponent of a hypersurface using higher direct images of suitably twisted sheaves of log forms on a log resolution.
The article proves an assertion analogous to the Littlewood-Paley theorem for the orthoprojectors onto mutually orthogonal subspaces of piecewise polynomial functions on the cube $ I^d. $ This assertion provides an upper estimate for the…
In this paper we show that the piecewise linear map f(x) = px for x in [0,1/p], and sx-s/p for x in (1/p,1], p > 1, 0 < s < 1 which has an expanding, onto branch and a contracting branch is eventually piecewise expanding and exact.
We survey the main results of approximation theory for adaptive piecewise polynomial functions. In such methods, the partition on which the piecewise polynomial approximation is defined is not fixed in advance, but adapted to the given…
We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates of…
We propose a representation of boolean bent functions by bent rectangles, that is, by special matrices with restrictions on rows and columns. Using this representation, we exhibit new classes of bent functions, give an algorithm to…
A syntactical proof is given that all functions definable in a certain affine linear typed lambda-calculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be…
Given a function from $\mathbb{Z}_n$ to itself one can determine its polynomial representability by using Kempner function. In this paper we present an alternative characterization of polynomial functions over $\mathbb{Z}_n$ by constructing…
We present a procedure to approximate a plane contour by piecewise polynomial functions, depending on various parameters, such as degree, number of local patches, selection of knots. This procedure aims to be adopted to study how…
A new algorithm for solving non-homogeneous asymptotically linear and superlinear problems is proposed. The ground state solution of the problem, which in general is obtained as a mini-max of the associated functional, is obtained as the…
Sylvester showed that the partition function can be written as a sum of the polynomial term and quasiperiodic components called the Sylvester waves. Recently an explicit expression of the Sylvester wave as a finite sum over the Bernoulli…
Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of the incomplete gamma function over complex variables of the…
Wilson lines, being comparators that render non-local operator products gauge invariant, are extensively used in QCD calculations, especially in small-$x$ calculations, calculations concerning validation of factorisation schemes and in…
(NxN)-matrix is called additive when its elements are pair-wise sums of N real numbers. For a quadratic binary functional with an additive connection matrix we succeeded in finding the global minimum expressing it through external…
A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces is justified by the fact that, similarly as for polynomial…
In this article, I introduce a group-theoretical method to prove positivity of certain linear combinations (with coefficients generally lying in $\mathbb{C}$) of exponential functions under a set of semidefinite linear constraints. The…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking…