Mathematics
Path-dependent McKean--Vlasov (MKV) control models large interacting populations with history-dependent dynamics and costs. This paper develops a unified approximation-and-learning framework for continuous time path-dependent MKV problem…
We present a semidefinite programming framework for constructing time-varying Lyapunov densities for nonautonomous dynamical systems on a hypertorus. The formulation leverages Gram matrix representations of hybrid (real-trigonometric)…
Selecting a fixed number of representative points from a finite Pareto-front approximation is a fundamental post-processing task in multiobjective optimization. This paper studies this problem for the integral R2 indicator in three…
This paper addresses model-free continuous-time mean-field control in a setting where the population dynamics evolve continuously according to an unknown McKean-Vlasov stochastic differential equation, while only discrete-time transition…
Input convex neural networks (ICNNs) are increasingly used as surrogates for stability indices and embedded as constraints in power-system optimization. This letter clarifies two recurring formulation limitations that can negate ICNN…
This article shortly provides related proofs of the ergodic theorems of von Neumann, Birkhoff, Wiener, and Rokhlin's lemma for $Z^d$-actions with an invariant measure. It is shown how some deviations of ergodic averages can be structured.…
In this paper, we are dealing with constrained vector optimisation problems where the objective function acts between real linear-topological spaces. Our aim is to study the relationships between the sets of properly efficient solutions to…
Given a finite abelian group $G$ and a Sylow $p$-subgroup $N_p$, we prove that the $KU_G/p$-local sphere spectrum is equivalent to the homotopy fixed points of a $p$-complete $KO_{N_p}$-module spectrum. Then we compute the…
We propose Acc-Sinkhorn, a simple accelerated variant of Sinkhorn for entropy-regularized optimal transport (EOT). The method is derived from a bilevel optimization view: Sinkhorn row scaling solves the inner variable $u$ exactly and…
We investigate transient clustering dynamics in nonlocal aggregation-diffusion systems from an energetic perspective. Starting from a stochastic interacting particle system, we study the associated macroscopic McKean-Vlasov equation on the…
Recent literature shows that hypocoercivity properties of linear evolution equations (in particular their exponential decay and the sharp short time decay of their propagator norm) carry over to their discretization via the midpoint rule.…
Motivated by Berg's notion of quasi-disjointness for ergodic systems, we introduce and investigate the concept of quasi-disjointness for minimal systems. Several equivalent characterizations are provided. We prove that quasi-disjointness is…
We study the action of the Hecke triangle groups $G_q$ on $\lambda_q \mathbb{Q}(\lambda_q^2) \cup \{\infty\}$ with $\lambda_q = 2 \cos (\pi / q)$. When $q = 18$, we show the existence of infinitely many distinct orbits of fixed points of…
The asymptotic Karush-Kuhn-Tucker (AKKT) optimality conditions are distinguished from other approaches in the literature by virtue of their capacity to be effectively derived through numerical methods, such as the utilization of an…
This paper studies a type of rank-based mean field game in which competing agents strategically switch among multiple effort regimes. We propose an entropy regularized auxiliary problem where the switching decisions are randomized to the…
The term Gibbons conjecture is widely used in connection with symmetry results for the Allen-Cahn equation. However, its origin is less transparent than its frequent citation suggests. In this note, we revisit its emergence, tracing it to a…
Distributed online stochastic optimization has received extensive attention in large-scale distributed learning and other related fields due to its unique advantage in processing streaming data. However, information exchange through the…
Let $\mathfrak{g}$ be a symmetrizable Kac-Moody Lie algebra and let $\rho$ denote the sum of the fundamental weights. The irreducible highest weight representations $V(m\rho)$ occupy a distinguished position in representation theory due to…
Algebraic representations of time series are symbolic representations whose symbols belong to a finite group. Precisely, the framework of the present paper is the analysis of coupled time series in algebraic representations and, more…
Convection-dominated problems are known for their slow Kolmogorov $n$-width decays and are challenging for model order reduction (MOR). In this work, we propose a hybrid surrogate modeling approach and a non-intrusive variant that overcome…