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A dynamic backstepping method is proposed to design controllers for nonlinear systems in the pure-feedback form, for which the traditional backstepping method suffers from solving the implicit nonlinear algebraic equation. The idea of this…

We develop a Markov process viewpoint for discrete circular distributions motivated by directional-statistics settings where angles are observed on a finite grid and evolve over time. On the $m$-point discrete circle, the cycle graph, we…

We study the thermodynamic properties of spin systems on small-world hypergraphs, obtained by superimposing sparse Poisson random graphs with p-spin interactions onto a one-dimensional Ising chain with nearest-neighbor interactions. We use…

Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…

We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the…

We present a method, the dynamical cumulant expansion, that allows to calculate quantum corrections for time-dependent quantities of interacting spin systems or single spins with anisotropy. This method is applied to the quantum-spin model…

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…

In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using…

We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under…

Dynamics of information flow in adaptively interacting stochastic processes is studied. We give an extended form of game dynamics for Markovian processes and study its behavior to observe information flow through the system. Examples of the…

We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical…

The folded node is a singularity associated with loss of normal hyperbolicity in systems where mixtures of slow and fast timescales arise due to singular perturbations. Canards are special solutions that reveal a counteractive feature of…

We consider a discrete-time dynamical process on graphs, firstly introduced in connection with a protocol for controlling large networks of spin 1/2 quantum mechanical particles [Phys. Rev. Lett. 99, 100501 (2007)]. A description is as…

Closure modeling - the statistical modeling of missing dynamics in the natural sciences and engineering - is a growing and active area of research. Existing methods for closure modeling are often computationally prohibitive, lack…

We discuss convergence and coupling of Markov chains, and present general relations between the transfer matrices describing these two processes. We then analyze a recently developed local-patch algorithm, which computes rigorous upper…

This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a…

We introduce jump processes in R^k, called density-profile process, to model biological signaling networks. They describe the macroscopic evolution of finite-size spin-flip models with k types of spins interacting through a non-reversible…

A stochastic representation of the dynamics of open quantum systems, suitable for non-perturbative system-reservoir interaction, non-Markovian effects and arbitrarily driven systems is presented. It includes the case of driving on…

In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…

In the study of dynamics on networks, moment closure is a commonly used method to obtain low-dimensional evolution equations amenable to analysis. The variables in the evolution equations are mean counts of subgraph states and are referred…