相关论文: Representative dynamics
A generalized fluctuation-response relation is found for thermal systems driven out of equilibrium. Its derivation is independent of many details of the dynamics, which is only required to be first-order. The result gives a correction to…
Stochastic representation for interaction of quantum systems is formulated which allows to replace some of them by equivalent but purely commutative random sources. The formalism is applied to two-level systems interacting with Gaussian…
In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response…
We show the equivalence of inverse problems for different dynamical systems and corresponding canonical systems. For canonical system with general Hamiltonian we outline the strategy of studying the dynamic inverse problem and procedure of…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
A key issue in complex systems regards the relationship between topology and dynamics. In this work, we use a recently introduced network property known as steering coefficient as a means to approach this issue with respect to different…
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…
We establish a connection between finite fields and finite dynamical systems. We show how this connection can be used to shed light on some problems in finite dynamical systems and in particular, in linear systems.
In this paper we give a brief review of the relation between microscopic dynamical properties and the Fourier law of heat conduction as well as the connection between anomalous conduction and anomalous diffusion. We then discuss the…
In this paper, we study the dynamical behavior of a linear control system on $\R^2$ when the associated matrix has real eigenvalues. Different from the complex case, we show that the position of the control zero relative to the control…
A recent approach to the control of underactuated systems is to look for control laws which will induce some specified structure on the closed loop system. This basic idea is used in several papers already. In this paper, we will describe…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
This paper considers two problems -- a dynamic team problem and a decentralized control problem. The problems we consider do not belong to the known classes of "simpler" dynamic team/decentralized control problems such as partially nested…
The brain is often called a computer and likened to a Turing machine, in part because the mind can manipulate discrete symbols such as numbers. But the brain is a dynamical system, more like a Watt governor than a Turing machine. Can a…
This paper provides rigorous definitions and analysis of the dynamics of weakly-coupled systems and gives sufficient conditions for an infinite dimensional quantum control system to be weakly-coupled. As an illustration we provide examples…
Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality…
In this paper we will discuss problems and techniques related to underactuated systems. We give a mathematical formulation of several problems arising from applications, review some standard and new techniques, and pose some interesting and…
We consider the inverse problem for the dynamical system with discrete Schr\"odinger operator and discrete time. As an inverse data we take a \emph{response operator}, the natural analog of the dynamical Dirichlet-to-Neumann map. We derive…
Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…