This paper focuses on the use of sense clusters for classification and clustering of very short texts such as conference abstracts. Common keyword-based techniques are effective for very short documents only when the data pertain to different domains. In the case of conference abstracts, all the documents are from a narrow domain (i.e., share a similar terminology), that increases the difficult...

Hurwitz found the Fourier expansion of the Bernoulli polynomials over a century ago. In general, Fourier analysis can be fruitfully employed to obtain properties of the Bernoulli polynomials and related functions in a simple manner. In addition, applying the technique of Möbius inversion from analytic number theory to Fourier expansions, we derive identities involving Bernoulli polynomials, Ber...

Suppose that Y n is obtained by observing a uniform Bernoulli random vector X through a binary symmetric channel with crossover probability α. The “most informative Boolean function” conjecture postulates that the maximal mutual information between Y n and any Boolean function b(X) is attained by a dictator function. In this paper, we consider the “complementary” case in which the Boolean funct...

This paper explores the use of binary segmentation procedures in two applications. The first application is concerned with the estimation of nonparametric quantal response curves. With Bernoulli data and an assumed monotone increasing curve, this gives rise a change-point model where the change points are determined using a sequence of nested hypothesis tests of whether a change point exists. T...

Given a sample of binary random vectors with i.i.d. Bernoulli(p) components, that is equal to 1 (resp. 0) with probability p (resp. 1 − p), we first establish a formula for the mean of the size of the random Galois lattice built from this sample, and a more complex one for its variance. Then, noticing that closed α-frequent itemsets are in bijection with closed α-winning coalitions, we establis...

This paper introduces a new stepwise approach for predicting one specific binary relationship in a multi-relational setting. The approach includes a phase of initializing the components of a logistic additive model by matrix factorization and a phase of further optimizing the components with an additive restriction and the Bernoulli modelling assumption. By using low-rank approximations on a se...

Discovering causal relations among observed variables in a given data set is a main topic in studies of statistics and artificial intelligence. Recently, some techniques to discover an identifiable causal structure have been explored based on non-Gaussianity of the observed data distribution. However, most of these are limited to continuous data. In this paper, we present a novel causal model f...

the principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (iae) by using the bernoulli polynomials and the residual correction method. after implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown bernoulli coefficients. thismethod gives an analytic solution when t...

Kupershmidt and Tuenter have introduced reflection symmetries for the q-Bernoulli numbers and the Bernoulli polynomials in 2005 , 2001 , respectively. However, they have not dealt with congruence properties for these numbers entirely. Kupershmidt gave a quantization of the reflection symmetry for the classical Bernoulli polynomials. Tuenter derived a symmetry of power sum polynomials and the cl...