Study on sphere-valued maps, proving energy convergence and current limits.
problem Understanding the behavior of sphere-valued Sobolev maps as their energy grows.
method Proving Gamma-convergence of p-energies to the mass of an integral current. result Jacobian convergence to an area-minimizing current in a cobordism class.
New technique explains convergence in ML models with data modifications.
problem Understanding convergence of ML models under data changes.
method Analogue of Fatou's lemma and gamma-convergence.
result Relevance and applications in general ML tasks and domain adaptation.
Paper studies central bank's strategy to control systemic risk in interbank system.
problem Minimizing average distance between log-monetary reserves and target levels.
method Weak formulation, Ekeland's variational principle, Gamma-convergence, stochastic Fokker-Planck-Kolmogorov equation.
result Proves convergence of optimal strategies as number of banks increases.
We prove a Gamma-convergence result for a family of bending energies defined on smooth surfaces in R3 equipped with a director field. The energies strongly penalize the deviation of the director from the surface unit normal and control the derivatives of the director. Such type of energies for example arise…
Study proposes a nonlocal approximation of the Willmore functional using fractional Allen-Cahn energies.
problem Approximating the Willmore functional using nonlocal methods.
method Gamma-convergence and fractional Laplacian analysis in Fermi coordinates.
result Proves Γ-limsup estimate for the proposed nonlocal approximation. The paper proves Γ-convergence of discrete tangent-point energies to continuous energies and ropelength, with applications to biarc curves.
problem Proving convergence of discrete tangent-point energies to continuous energies and ropelength.
method Using biarc curves and interpolation, the paper proves Γ-convergence of discretized tangent-point energies to the continuous tangent-point energies and ropelength functional. result Discrete almost minimizing biarc curves converge to ropelength minimizers and minimizers of continuous tangent-point energies.
We introduce length dilatation structures on metric spaces, tempered dilatation structures and coherent projections and explore the relations between these objects and the Radon-Nikodym property and Gamma-convergence of length functionals. Then we show that the main properties of sub-riemannian spaces can be obtained f…
The paper proves consistency of GVI posteriors under minimal conditions.
problem Consistency of generalized variational inference posteriors.
method Proves consistency using Γ-convergence theory. result GVI posteriors are consistent and collapse to the population-optimal parameter value.
In this paper we are concerned with the learnability of energies from data obtained by observing time evolutions of their critical points starting at random initial equilibria. As a byproduct of our theoretical framework we introduce the novel concept of mean-field limit of critical point evolutions and of their energy…
Develops BV function and finite perimeter set theory on Riemannian manifolds.
problem Theory of BV functions and finite perimeter sets on arbitrary Riemannian manifolds.
method Localization framework combining Euclidean and metric measure space techniques.
result Recovery of key Euclidean results in Riemannian setting.
Generative AI connects to Schrödinger bridge problems with soft constraints for stability.
problem Stability issues in generative AI due to hard terminal constraints.
method Soft-constrained Schrödinger bridge formulation and convergence analysis.
result Existence and convergence of optimal solutions as penalty grows.