Let F be the class of all 1-periodic real functions with absolutely convergent Fourier series expansion and let (xn)n≥0 be the van der Corput sequence. In this paper results on the boundedness of ∑N−1 n=0 f(xn) for f ∈ F are given. We give a criterion on the convergence rate of the Fourier coefficients of f such that the above sum is bounded independently of N . Further we show that our result ...

We present an automated, system-internal evaluation technique for linguistic representations in a large-scale, multilingual MT system. We use machine-learned classifiers to recognize the differences between linguistic representations generated from transfer in an MT context from representations that are produced by "native" analysis of the target language. In the MT scenario, convergence of the...

An implementable proximal point algorithm is established for the smooth nonconvex unconstrained minimization problem. At each iteration, the algorithm minimizes approximately a general quadratic by a truncated strategy with step length control. The main contributions are: (i) a framework for updating the proximal parameter; (ii) inexact criteria for approximately solving the subproblems; (iii) ...

In most of the commonly used approaches, the ranking of generalized fuzzy numbers is calculated based on the only one criterion i.e., rank criteria. However, there are some weaknesses associated with this criterion. In this paper, we discuss the insufficiency of considering only rank for the ordering of generalized fuzzy numbers. Some shortcomings in existing ranking methods have been pointed o...

The paper presents a new (to the best of the authors’ knowledge) estimator of probability called the “Eph√2 completeness estimator” along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in ...

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior variance in Bayesian quadrature. We then show that sequential Bayesian quadrature ca...

A criterion for the maximum possible pointwise convergence rate in Birkhoff’s ergodic theorem semiflows a Lebesgue space is obtained. It proved that higher rates of this are impossible.

Abstmct This study discusses the mathematical structure of the dominant AHP and the concurrent convergence method which were originally developed by Kinoshita and Nakanishi. They introduced a new concept of a regulating alternative into an analyzing tool for a simple evaluation problem with a criterion set and an alternative set. Although the original idea of the dominant AHP and the concurrent...

The Fisher-EM algorithm has been recently proposed in [4] for the simultaneous visualization and clustering of high-dimensional data. It is based on a latent mixture model which fits the data into a latent discriminative subspace with a low intrinsic dimension. Although the Fisher-EM algorithm is based on the EM algorithm, it does not respect at a first glance all conditions of the EM convergen...

Using the criterion of convergence branched continued fractions special form with positive elements, effective sufficient criteria for these are established. To study parabolic regions convergence, element and value technique was used. In particular, half-planes considered as regions. A multidimensional analogue Tron's twin is The obtained results made it possible to establish conditions $S$-fr...