Related papers: Large value estimates in number theory, harmonic a…
In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…
As the amount of economic and other data generated worldwide increases vastly, a challenge for future generations of econometricians will be to master efficient algorithms for inference in empirical models with large information sets. This…
Evaluating a polynomial on a set of points is a fundamental task in computer algebra. In this work, we revisit a particular variant called trimmed multipoint evaluation: given an $n$-variate polynomial with bounded individual degree $d$ and…
We give a number of theoretical and practical methods related to the computation of L-functions, both in the local case (counting points on varieties over finite fields, involving in particular a detailed study of Gauss and Jacobi sums),…
In this note, convergence of random variables will be revisited. We will give the answers to 5 questions among the 6 open questions introduced in (Convergence rates in the law of large numbers and new kinds of convergence of random…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
We consider the spectral structure of indefinite second order boundary-value problems on graphs. A variational formulation for such boundary-value problems on graphs is given and we obtain both full and half-range completeness results. This…
Large language models (LLMs) and transformer-based architectures are increasingly utilized for source code analysis. As software systems grow in complexity, integrating LLMs into code analysis workflows becomes essential for enhancing…
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
This paper examines the opportunities, limitations, and practical considerations associated with the use of large language models (LLMs) in qualitative research. Drawing on a multidisciplinary perspective that combines expertise in…
This is a survey of the diversity of problems in additive number theory. Equity requires the consideration of less currently popular problems, and suggests their inclusion in the additive canon. Of particular interest are problems about the…
This study explores the prediction of high-frequency price changes using deep learning models. Although state-of-the-art methods perform well, their complexity impedes the understanding of successful predictions. We found that an…
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
Estimating the volume of a convex body is a canonical problem in theoretical computer science. Its study has led to major advances in randomized algorithms, Markov chain theory, and computational geometry. In particular, determining the…
We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.
Algorithm selection, a critical process of automated machine learning, aims to identify the most suitable algorithm for solving a specific problem prior to execution. Mainstream algorithm selection techniques heavily rely on problem…
We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove…