Institut de Mathématiques de Toulouse

Scalable ground-state certification of quantum spin systems via structured noncommutative polynomial optimization

A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard variational approaches posit a wave-function ansatz and minimize over the possible states expressible by that ansatz, the problem can alternatively be form...

Gradient-enhanced global sensitivity analysis with Poincaré chaos expansions

Spectral methods, also known as chaos expansions, are widely used in global sensitivity analysis (GSA), as they leverage orthogonal bases of $L^2$ spaces to efficiently compute Sobol' indices, particularly in data-scarce settings. When derivatives of the model are available, a de...

Trend to Equilibrium and Diffusion Limit for the Inertial Kuramoto–Sakaguchi Equation

Abstract. In this paper, we study the inertial Kuramoto–Sakaguchi equation for interacting oscillatory systems. On the one hand, we prove the convergence toward corresponding phase-homogeneous stationary states in weighted Lebesgue norm sense when the coupling strength is small e...

Swarming by curvature control in arbitrary dimension

We consider an interacting particle system proposed in the literature to model fish behavior. In this model, the agents move at constant speed and control the curvature of their trajectory (i.e. the time-derivative of their velocity) so as to align their velocity with that of the...

Ground states on a fractured strip and one-dimensional reduction

We consider the nonlinear Schrödinger equation on a strip with Neumann boundary conditions and a delta condition at x = 0 . We first show the existence of ground states as minimizers of the action or of the energy under suitable constraints. We then prove that the energy minimize...

Refinements on higher order Weil–Oesterlé bounds via a Serre type argument

Abstract Weil's theorem gives the most standard bound on the maximum number of points of a curve of genus over a finite field . This bound was improved by Ihara and Oesterlé for larger genus. A recent point of view allows one to recover these bounds by solving a sequence of semi‐...

Convergence Rates for Polynomial Optimization on Set Products

Abstract. We consider polynomial optimization problems on Cartesian products of basic compact semialgebraic sets. The solution of such problems can be approximated as closely as desired by hierarchies of semidefinite programming relaxations, based on classical sums of squares cer...

Formal moduli problems and derived Lie algebras

We show that derived Lie algebras and restricted Lie algebras classify formal moduli problems on Artin divided power algebras and truncated algebras respectively. This article is part of the theme issue 'Derived Lie algebras in geometry and topology'.

Are exercise benefits in older adults clinically meaningful?: An ancillary and follow-up analysis of a multicenter randomized controlled trial

Physical exercise is beneficial for older adults, but little is known about inter-individual response variability or whether its effects reach clinical significance. We analyzed individual clinically meaningful responses to exercise in older adults. This is an ancillary analysis...