Related papers: Local Nash Realizations
We give a classification of connected abelian locally (real) Nash groups of dimension two. We first consider Painlev\'e's description of meromorphic maps admitting an Algebraic Addition Theorem and analyse the algebraic dependence of such…
We classify semi-algebraic surfaces in $\mathbb{R}^n$ with isolated singularities up to bi-Lipschitz homeomorphisms with respect to the inner distance. In particular, we obtain complete classifications for the Nash surfaces and the complex…
Finding, counting, or determining the existence of Nash equilibria, where players must play optimally given each others' actions, are known to be computational intractable problems. We ask whether weakening optimality to the requirement…
We investigate a hierarchical control problem for a one-dimensional Stefan system with localized distributed controls. The setting combines a Stackelberg strategy with a Nash equilibrium among multiple followers, yielding a multi-objective…
We prove a realisation theorem for irreducible hypergeometric local systems defined over the rational numbers in terms of families of affine varieties in algebraic tori. The families we consider have been studied extensively in the…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
Individual choices often depend on the order in which the decisions are made. In this paper, we expose a general theory of measurable systems (an example of which is an individual's preferences) allowing for incompatible (non-commuting)…
We introduce a multiplicative neural network architecture in which multiplicative interactions constitute the fundamental representation, rather than appearing as auxiliary components within an additive model. We establish a universal…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
We develop realizability models of intensional type theory, based on groupoids, wherein realizers themselves carry non-trivial (non-discrete) homotopical structure. In the spirit of realizability, this is intended to formalize a homotopical…
We consider graphical $n$-person games with perfect information that have no Nash equilibria in pure stationary strategies. Solving these games in mixed strategies, we introduce probabilistic distributions in all non-terminal positions. The…
Locality-sensitive hashing (LSH) is a fundamental technique for similarity search and similarity estimation in high-dimensional spaces. The basic idea is that similar objects should produce hash collisions with probability significantly…
This paper presents a novel algorithm for reachability analysis of nonlinear discrete-time systems. The proposed method combines constrained zonotopes (CZs) with polyhedral relaxations of factorable representations of nonlinear functions to…
Numerous complex systems, such as those arisen in ecological networks, genomic contact networks, and social networks, exhibit higher-order and time-varying characteristics, which can be effectively modeled using temporal hypergraphs.…
In this paper we study a criterion for the viability of stochastic semilinear control systems on a real, separable Hilbert space. The necessary and sufficient conditions are given using the notion of stochastic quasi-tangency. As a…
Contemporary applications of machine learning in two-team e-sports and the superior expressivity of multi-agent generative adversarial networks raise important and overlooked theoretical questions regarding optimization in two-team games.…
We consider the problem of under and over-approximating the image of general vector-valued functions over bounded sets, and apply the proposed solution to the estimation of reachable sets of uncertain non-linear discrete-time dynamical…
We study well-posedness, local and global, existence of solutions for a general class of physically meaningful nonlinear Schr\"odinger systems with magnetic field involving local and nonlocal nonlinearities.
This paper deals with diagnosability of discrete-time nonlinear systems with unknown inputs and quantized outputs. We propose a novel notion of diagnosability that we term approximate diagnosability, corresponding to the possibility of…