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We work out an exactly solvable hamiltonian model which retains all the features of realistic quantum measurements. In order to use an interaction process involving a system and an apparatus as a measurement, it is necessary that the…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
We extend our two-scale neural-network method for scalar singularly perturbed problems with one small parameter to dynamical systems with multiple small parameters. To accommodate multiple small parameters, we use a single effective scale…
We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…
Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small…
Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they…
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in…
We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of…
We introduce a new dynamical system, at the interface between second-order dynamics with inertia and Newton's method. This system extends the class of inertial Newton-like dynamics by featuring a time-dependent parameter in front of the…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
In the last decade it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the…
Quadratic systems of equations appear in several applications. The results in this paper are motivated by quadratic systems of equations that describe equilibrium behavior of physical infrastructure networks like the power and gas grids.…
We propose a general framework to extract microscopic interactions from raw configurations with deep neural networks. The approach replaces the modeling Hamiltonian by the neural networks, in which the interaction is encoded. It can be…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
We analyze multivariate ordered discrete response models with a lattice structure, modeling decision makers who narrowly bracket choices across multiple dimensions. These models map latent continuous processes into discrete responses using…
The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance,…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…