Related papers: Higher-order response theory in optimal stochastic…

Perturbed projection for linear scaling solution of the coupled-perturbed self-consistent-field equations [Weber, Niklasson and Challacombe, Phys. Rev.\ Lett. {\bf 92}, 193002 (2004)] is extended to the computation of higher order static…

We derive equations of motion for higher order density response functions using the theory of thermodynamic Green's functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions.…

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…

The energetic optimization problem, e.g., searching for the optimal switch- ing protocol of certain system parameters to minimize the input work, has been extensively studied by stochastic thermodynamics. In current work, we study this…

The empirical success of machine learning models with many more parameters than measurements has generated an interest in the theory of overparameterisation, i.e., underdetermined models. This paradigm has recently been studied in domains…

We consider the problem of flexible modeling of higher order hidden Markov models when the number of latent states and the nature of the serial dependence, including the true order, are unknown. We propose Bayesian nonparametric methodology…

We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…

We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of non-linear control problems that can be formulated as a path integral and where the noise plays the role of…

We present a framework for constructing a first-order hyperbolic system whose solution approximates that of a desired higher-order evolution equation. Constructions of this kind have received increasing interest in recent years, and are…

In dynamical system theory, the process of obtaining a reduced-order approximation of the high-order model is called model order reduction. The closeness of the reduced-order model to the original model is generally gauged by using system…

We study the problem of policy optimization (PO) with linear temporal logic (LTL) constraints. The language of LTL allows flexible description of tasks that may be unnatural to encode as a scalar cost function. We consider LTL-constrained…

We study the thermodynamic cost associated with driving systems between different non-equilibrium steady states. In particular, we combine a linear-response framework for non-equilibrium Markov systems with Lagrangian techniques to minimize…

Nonlinear observer design for systems whose state space evolves on Lie groups is considered. The proposed method is similar to previously developed nonlinear observers in that it involves propagating the state estimate using a process model…

The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…

A molecular understanding of how protein function is related to protein structure will require an ability to understand large conformational changes between multiple states. Unfortunately these states are often separated by high free energy…

In the chemical, pharmaceutical, and food industries, sometimes the order of adding a set of components has an impact on the final product. These are instances of the order-of-addition (OofA) problem, which aims to find the optimal sequence…

Biochemical reactions involving three or more reactants, called higher-molecular reactions, play an important role in theoretical systems and synthetic biology. In particular, such reactions underpin a variety of important bio-dynamical…

Nonlinear density response theory is revisited focusing on the harmonically perturbed finite temperature uniform electron gas. Within the non-interacting limit, brute force quantum kinetic theory calculations for the quadratic, cubic,…

We consider linear elliptic equations in divergence form with stationary random coefficients of integrable correlations. We characterize the fluctuations of a macroscopic observable of a solution to relative order $\frac{d}{2}$, where $d$…

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…