We consider the sequence of integers whose nth term has base-p expansion given by row Pascal’s triangle modulo p (where is a prime number). first present and generalize well-known relations concerning this sequence. Then, with great help Sloane’s On-Line Encyclopedia Integer Sequences, we show that it appears naturally as subsequence 2-regular Its study provides interesting surprisingly involve...

A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the linear. Each players has a quadratic functional on its own disposal, which should be minimized. case where weight matrices in control costs one player are singular both functionals studied. Hence, under consideration singular. novel definition Nash equilibrium this (a sequence) proposed. solved by appl...

Motif analysis has long been an important method to characterize biological functionality and the current growth of sequencing-based genomics experiments further extends its potential. These diverse experiments often generate sequence lists ranked by some functional property. There is therefore a growing need for motif analysis methods that can exploit this coupled data structure and be tailore...

This paper provides a framework for the extraction of frequent sequences satisfying a given regular expression (RE) constraint. We take advantage of the information contained in the hierarchical representation of an RE by abstract syntax trees (AST). Interestingly, pruning can be based on the anti-monotonicity of the minimal frequency constraint, but also on the RE constraint, even though this ...

Finding motifs and the corresponding binding sites is a critical and challenging problem in studying the process of gene expression. String and matrix representations are two popular models to represent a motif. However, both representations share an important weakness by assuming that the occurrence of a nucleotide in a binding site is independent of other nucleotides. More complicated represe...

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

We present a method for identifying errors in EHRs caused by copying and pasting text containing relative dates. Our method utilizes a sequence alignment method for recognizing instances of copy/paste, and regular expressions for relative dates. We furthermore present an analysis of our method on the MIMIC-II dataset. Introduction Electronic health records (EHR) are a powerful enabling technolo...

numeration systems are a natural generalization of positional numeration systems whose set of representations of all the integers is a regular language. They were introduced five years ago by P. Lecomte and myself [3] and are defined in the following way. Consider any infinite regular language L over a totally ordered alphabet (A,<). An abstract numeration system is thus simply given by the tri...

While considerable effort and some progress has been made on developing an analytic formula for the probability of an approximate match, such work has not achieved fruition [4, 6, 2, 1]. Therefore, we consider here the development of an unbiased estimation procedure for determining said probability given a specific string P ∈ Σ and a specific cost function δ for weighting edit operations. Probl...