Related papers: Explicit formulae for stochastic equilibria
Similar to the role of Markov decision processes in reinforcement learning, Stochastic Games (SGs) lay the foundation for the study of multi-agent reinforcement learning (MARL) and sequential agent interactions. In this paper, we derive…
In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix $A$…
A stochastic dynamical system represented through a linear vector equation in idempotent algebra is considered. We propose simple bounds on the mean growth rate of the system state vector, and give an analysis of absolute error of a bound.…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the…
The concept of equilibrium is a general tool to fill the gap between macroscopic and mesoscopic information, both within kinetic systems and kinetic schemes. This work explores the use of equilibria to devise numerical boundary conditions…
We study the expectation of linear eigenvalue statistics of matrix models with any $\beta>0$, assuming that the potential $V$ is a real analytic function and that the corresponding equilibrium measure has a one-interval support. We obtain…
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…
Sylvester-type matrix equations have applications in areas including control theory, neural networks, and image processing. In this paper, we establish the necessary and sufficient conditions for the system of Sylvester-type quaternion…
Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with…
The process of alternately row scaling and column scaling a positive $n \times n$ matrix $A$ converges to a doubly stochastic positive $n \times n$ matrix $S(A)$, often called the \emph{Sinkhorn limit} of $A$. The main result in this paper…
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…
Despite being a key bottleneck in many machine learning tasks, the cost of solving large linear systems has proven challenging to quantify due to problem-dependent quantities such as condition numbers. To tackle this, we consider a…
We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…
We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are…
The explicit formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure for the solution of systems of linear equations is applied to error analysis. Stability conditions in terms of relative…