Related papers: Higher-order response theory in optimal stochastic…
Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic…
An important problem in applied dynamical systems is to compute the external forcing that provokes the largest response of a desired observable quantity. For this, we investigate the perturbation theory of Markov matrices in connection with…
This paper is concerned with the design of a linear control law for linear systems with stationary additive disturbances. The objective is to find a state feedback gain that minimizes a quadratic stage cost function, while observing chance…
Researchers are often interested in drawing inferences regarding the order between two experimental groups on the basis of multivariate response data. Since standard multivariate methods are designed for two-sided alternatives, they may not…
The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
The design of specified nonlinear mechanical responses into a structure or material is a highly sought after capability, which would have a significant impact in areas such as wave tailoring in metamaterials, impact mitigation, soft…
The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…
We present a method to design driving protocols that achieve fast thermal equilibration of a system of interest using techniques inspired by machine learning training algorithms. For example, consider a Brownian particle manipulated by…
In this study, we describe a procedure of topology optimization in the framework of the linear Boltzmann equation, implemented using a reference Monte-Carlo particle transport code. This procedure can design complex structures that optimize…
We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the energy-based quasicontinuum approximation and the…
The reliability of physical theories depends on whether they agree with well established physical laws. In this work, we address the compatibility of the Hamiltonian formulation of linear-response theory with the Second Law of…
Linear response theory lies at the heart of quantum many-body physics because it builds up connections between the dynamical response to an external probe and correlation functions at equilibrium. Here we consider the dynamical response of…
Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global…
We propose an optimization strategy to control the dynamics of a stochastic system transferred from one thermal equilibrium to another and apply it experimentally to a Brownian particle in an optical trap under compression. Based on a…
The computation of a maximal order of an order in a semisimple algebra over a global field is a classical well-studied problem in algorithmic number theory. In this paper we consider the related problems of computing all minimal overorders…
We develop a theory for inferring equilibrium transition rates from trajectories driven by a time dependent force using results from stochastic thermodynamics. Applying the Kawasaki relation to approximate the nonequilibrium distribution…
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…
Robust control of complex engineered and biological systems hinges on the integration of feedforward and feedback mechanisms. This is exemplified in neural motor control, where feedforward muscle co-contraction complements sensory-driven…
This paper shows how the theory of nonlinear adaptive observers can be effectively used in the design of internal models for nonlinear output regulation. The theory substantially enhances the existing results in the context of {\em…