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We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…
We study the parametrization of the moduli space Bun_2(C)_L of rank 2 bundles over a curve C with fixed determinant, provided by Hecke modifications at fixed points of the trivial bundle. This parametrization is closely related to the…
Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate the system matrices. An application to stabilization via algebraic Riccati equations is included. The approach is…
The lattice regularization of QCD provides us with the most systematic way of computing non-perturbative properties of hadrons directly from the first principles of QCD. The recent rapid development of parallel computers has enabled us to…
Integrable discretizations are introduced for the rational and hyperbolic spin Ruijsenaars--Schneider models. These discrete dynamical systems are demonstrated to belong to the same integrable hierarchies as their continuous--time…
The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical…
In this paper we propose a novel approach to identify dynamical systems. The method estimates the model structure and the parameters of the model simultaneously, automating the critical decisions involved in identification such as model…
In this short survey, we describe our approach for constructing hierarchies of Poisson brackets for classical integrable systems using its' spectral curves.
We provide an explicit quantization of dynamical r-matrices for semisimple Lie algebras, classified earlier by the third author, which includes the Belavin-Drinfeld r-matrices. We do so by constructing an appropriate (dynamical) twist in…
We generalize a recent result stating that all analytic quantum dynamics can be represented exactly as the reduction of unitary dynamics generated by a time-dependent Hamiltonian. More precisely, we prove that the partial trace over…
Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…
The paper addresses a novel model of metamaterial structure. A system of spinners has been embedded into a two-dimensional periodic lattice system. The equations of motion of spinners are used to derive the expression for the chiral term in…
In this paper we study the monomial dynamical systems of dimension one over finite fields from the viewpoints of arithmetic and graph theory. We give formulas for the number of periodic points with period r and cycles with length r. Then we…
Continuation of algebraic structures in families of dynamical systems is described using category theory, sheaves, and lattice algebras. Well-known concepts in dynamics, such as attractors or invariant sets, are formulated as functors on…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
We propose a high dimensional generalisation of the standard Klein bottle, going beyond those considered previously. We address the problem of generating continuous scalar fields (distributions) and dynamical systems (flows) on such state…
This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention…
Two outer automorphisms of infinite-dimensional representations of $sl(2)$ algebra are considered. The similar constructions for the loop algebras and yangians are presented. The corresponding linear and quadratic $R$-brackets include the…
We derive a new representation for the Weyl function associated with the complex Jacobi matrix in the finite and semi-infinite cases. In our approach we exploit connections to the discrete-time dynamical system associated with these…
A dynamical scheme of quantization of symplectic manifolds is described. It is based on intrinsic Schr\"odinger and Heisenberg type nonlinear evolutionary equations with multidimensional time running over the manifold. This is the…