Related papers: Calculs effectifs de congruences entre caract\`ere…
Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string…
In this paper, we shall explore the Mosco convergence on regular subspaces of one-dimensional irreducible and strongly local Dirichlet forms. We find that if the characteristic sets of regular subspaces are convergent, then their associated…
In this paper, we revisit the old problem of compact finite difference approximations of the homogeneous Dirichlet problem in dimension 1. We design a large and natural set of schemes of arbitrary high order, and we equip this set with an…
In this paper, we present a fast and strong neural approach for general purpose text matching applications. We explore what is sufficient to build a fast and well-performed text matching model and propose to keep three key features…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
The approximate string matching is a fundamental and recurrent problem that arises in most computer science fields. This problem can be defined as follows: Let $D=\{x_1,x_2,\ldots x_d\}$ be a set of $d$ words defined on an alphabet…
The main result establishes the existence of a solution in a generalized sense for a nonlinear Dirichlet problem driven by a competing operator and exhibiting a convection term composed with an intrinsic operator. A finite dimensional…
Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…
We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…
We prove a result related to Dirichlet spectrum for simultaneous approximation to two real numbers in Euclidean norm and badly or very well approximability.
In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.
This paper proposes to use distributed representation of words (word embeddings) in cross-language textual similarity detection. The main contributions of this paper are the following: (a) we introduce new cross-language similarity…
We present an algorithm to approximate the real trilogarithm for a real argument with IEEE 754-1985 double precision accuracy. The approximation is structured such that it can make use of instruction-level parallelism when executed on…
We present some variations on some of the main open problems on character degrees. We collect some of the methods that have proven to be very useful to work on these problems. These methods are also useful to solve certain problems on zeros…
The aim of the paper is to show that L. Friedlander's results on the relation between Dirichlet and Neumann counting functions (Arch. Ration. Mech. Anal. 116, 1991) remain valid in abstract setting.
We give an explicit upper bound for non-principal Dirichlet $L$-functions on the line $s=1+it$. This result can be applied to improve the error in the zero-counting formulae for these functions.
In this paper, we propose a novel deep coherence model (DCM) using a convolutional neural network architecture to capture the text coherence. The text coherence problem is investigated with a new perspective of learning sentence…
Ontologies usually suffer from the semantic heterogeneity when simultaneously used in information sharing, merging, integrating and querying processes. Therefore, the similarity identification between ontologies being used becomes a…
If $\lambda$ and $\mu$ are two non-empty Young diagrams with the same number of squares, and $\boldsymbol\lambda$ and $\boldsymbol\mu$ are obtained by dividing each square into $d^2$ congruent squares, then the corresponding character value…
In this paper, we give criteria for infinitely many sign changes of the coefficients of any Dirichlet series if the coefficients are real numbers. We also provide examples where our criteria are applicable.