arXiv research

The paper sets sample complexity bounds for identifying LTI systems from a finite set.

Category theory generalizes finite type invariants using diagrams systems.

Finite-gap solutions approximate jets of initial data for certain BKM systems.

Simplified proof for approximations of set systems.

Study on self-similar sets on Riemannian manifolds with new separation conditions.

Study shows finiteness of magnetic hypersurfaces on closed manifolds.

The study describes metrics geodesically compatible with Nijenhuis operators and their applications to integrable systems.

Deep neural networks with memory learn reduced equations from partial data.

We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann sphere due to the automatic coopeartion of many kinds of maps in the system, ev…

New bounds show current methods overestimate system parameter errors.

Stabilization of linear systems with unknown dynamics is a canonical problem in adaptive control. Since the lack of knowledge of system parameters can cause it to become destabilized, an adaptive stabilization procedure is needed prior to regulation. Therefore, the adaptive stabilization needs to be completed in finite…

The paper analyzes deep neural networks using control theory to set a time limit for their convergence.

Autostackability for finitely generated groups is defined via a topological property of the associated Cayley graph which can be encoded in a finite state automaton. Autostackable groups have solvable word problem and an effective inductive procedure for constructing van Kampen diagrams with respect to a canonical fini…

New scalable MARL framework for dynamic networked systems.

We prove that finite Morse index solutions to the Allen-Cahn equation in $\R^2$ have {\bf finitely many ends} and {\bf linear energy growth}. The main tool is a {\bf curvature decay estimate} on level sets of these finite Morse index solutions, which in turn is reduced to a problem on the uniform second order regularit…

Study connects bank default models using dynamic contagion.

Convex geometry has recently attracted great attention as a framework to formulate general probabilistic theories. In this framework, convex sets and affine maps represent the state spaces of physical systems and the possible dynamics, respectively. In the first part of this paper, we present a result on separation of …

Unified framework for solving fixed-point equations in deterministic and stochastic settings.

We define a new class of racks, called finitely stable racks, which, to some extent, share various flavors with Abelian groups. Characterization of finitely stable Alexander quandles is established. Further, we study twisted rack dynamical systems, construct their cross-products, and introduce representation theory of …

Paper reduces sample complexity for bilinear systems identification to nearly constant.

Let $Λ$ be the limit set of a conformal dynamical system, i.e. a Kleinian group acting on either finite- or infinite-dimensional real Hilbert space, a conformal iterated function system, or a rational function. We give an easily expressible sufficient condition, requiring that the limit set is not too much bigger than …

Constructs initial data for Einstein vacuum equations involving multiple localized gravitational sources.

Guaranteed reachable set for unknown nonlinear systems on manifolds.

The paper solves integrable systems of PDEs, including famous equations.

End-to-end algorithm for controlling bilinear systems with probabilistic noise.

The paper surveys open problems and questions related to different aspects of integrable systems with finitely many degrees of freedom. Many of the open problems were suggested by the participants of the conference "Finite-dimensional Integrable Systems, FDIS 2017" held at CRM, Barcelona in July 2017.

Temporal-difference (TD) networks are a class of predictive state representations that use well-established TD methods to learn models of partially observable dynamical systems. Previous research with TD networks has dealt only with dynamical systems with finite sets of observations and actions. We present an algorithm…

Study applies inverse scattering to BKM systems, linking spectra and integrable systems.

Market equilibrium price proven in a large-agent model.

The paper extends log-Sobolev inequalities to matrix-valued settings using combinatorial methods.

Meta-learning control algorithm with finite-time guarantees for unknown systems.

New bounds for adaptive control in high dimensions without fixed state space.

Flow approach solves Toda system equations.

A new stochastic algorithm approximates optimal distributions without requiring propagation of chaos.

In this paper, we show that the boundary $\partialΣ(W,S)$ of a right-angled Coxeter system $(W,S)$ is minimal if and only if $W_{\tilde{S}}$ is irreducible, where $W_{\tilde{S}}$ is the minimum parabolic subgroup of finite index in $W$. We also provide several applications and remarks. In particular, we obtain that for…

We show that the set of the equivalence classes of multifoliate structures is in one-to-one correspondence with the set of equivalence classes of finite complete projective systems of vector space epimorphisms. After that we give the complete description of all product preserving bundle functors on the categories of mu…

In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples. The evolution equations of the involved observables are obtained in each example…

Open, connected, saturated sets W without holonomy in codimension one foliations play key roles as fundamental building blocks. Here, for the case of foliated 3-manifolds, we produce a finite system of closed, convex, non-overlapping polyhedral cones in the first cohomology of W with real coefficients such that the iso…

A quantum system can be entirely described by the Kähler structure of the projective space P(H) associated to the Hilbert space H of possible states; this is the so-called geometrical formulation of quantum mechanics. In this paper, we give an explicit link between the geometrical formulation (of finite dimensional qua…

CASP selects reliable policies for two-stage recommender systems by considering both value and support.

Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping: the so-called superposition rule. Apart from this fundamental property…

Smooth fractal trees via analytic generators, preserving combinatorial and geometric properties.

Study stationary measures and orbit closures for non-abelian actions on surfaces.

Paper solves convertible bond valuation using finite elements with penalty method.

QENDy learns quadratic dynamics from nonlinear systems data.

In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without external inputs. The objective is to recover the system parameters as well as the Kalm…

The paper studies random dynamical systems of polynomial automorphisms on C^2 and finds mean stability.

Simplified proof of mass center system's uniqueness and generalized Pappus' theorem across Euclidean, spherical, and hyperbolic geometries.