Research
Research
Research
Research
227+ open-access research outputs.
In this paper, we study generating functions of Erd\'{e}lyi's multivariate Laguerre polynomials $L_{n_1,\cdots,n_k}^{(\alpha)}(x_1,\cdots,x_k)$ with a varying complex parameter. Our main result is a m…
Agentic AI systems integrating large language models (LLMs) with reasoning and tooluse capabilities are transforming various domains - in particular, software development. In contrast, their applicati…
These notes are based on a short course delivered at the Summer School EUR MINT 2025 "Control, Inverse Problems and Spectral Theory", held in June 2025 in Toulouse, France. The course presents three i…
This report documents the program of the second Toulouse Tensor Workshop which took place at the University of Toulouse on September 17-19, 2025, and summarizes the main points of discussion. This wor…
The lack of GPS data limits the ability to reconstruct the actual routes taken by cyclists in urban areas. This article introduces an inference method based solely on trip durations and origin-destina…
Spatially varying coefficients (SVC) models allow for marginal effects to be non-stationary over space and thus offer a higher degree of flexibility with respect to standard geostatistical models with…
Lecture Notes based on the course given at Toulouse School of Economics, on Fall 2024. It contains a quick introduction to the field of bilevel optimization, following a perspective from Variational A…
Modeling realistic human behaviour to understand people's mode choices in order to propose personalised mobility solutions remains challenging. This paper presents an architecture for modeling realist…
The quantum Fisher information, the quantum analogue of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing due to its connection to parameter estimation a…
This article is a continuation of my previous paper on miraculous pentagrams published in Annales Scientifiques de Facult\'e des Sciences de Toulouse in 2013. We discuss the moduli space of miraculous…
Let $X$ be a Riemann surface and $K_X \rightarrow X$ the canonical bundle. For each integer $r \geq 2$, each $q \in H^0(K_X^r)$, and each choice of the square root $K_X^{1/2}$ of the canonical bundle,…
Virtual Reality (VR) offers promising avenues for innovative therapeutic interventions in populations with intellectual disabilities (ID). This paper presents the design, development, and evaluation o…
The perceptron has served as a prototypical neuronal learning machine in the physics community interested in neural networks and artificial intelligence, which included G\'erard Toulouse as one of its…
The paper deals with fine volume growth estimates on metric measures spaces supporting various Sobolev-type inequalities. Given a generic metric measure space, we first prove a quantitative volume gro…
Spin-orbit coupling (SOC) is one of the crucial factors that affect the chiral symmetry of matter by causing the spatial symmetry breaking of the system. We find that Raman-induced SOC can induce a ch…
In 1977, G\'erard Toulouse has proposed a new concept termed as "frustration" in spin systems. Using this definition, several frustrated models have been created and studied, among them we can mention…
Atomic diffusion with radiative levitation is a major transport process to consider to explain abundance anomalies in Am stars. Radiative accelerations vary from one species to another, yielding diffe…
In this paper, we establish monotonicity formulas for capillary surfaces in the half-space $\mathbb{R}^3_+$ and in the unit ball $\mathbb{B}^3$ and extend the result of Volkmann (Comm. Anal. Geom.24(2…
We prove the representation given by a stable $\alpha_1$-cyclic parabolic $\mathrm{SO}_0(2,3)$-Higgs bundle through the non-Abelian Hodge correspondence is $\{\alpha_2\}$-almost dominated. This is a g…
We give an explicit geometric structures interpretation of the $G_2'$-Hitchin component $Hit(S, G_2') \subset \chi(\pi_1S,G_2')$ of a closed oriented surface $S$ of genus $g \geq 2$. In particular, we…
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