Related papers: Optimal linear response for expanding circle maps
The purpose of this paper is to prove a local optimality property of a recently proposed coherent feedback configuration for distributed generation of EPR entanglement using two nondegenerate optical parametric amplifiers (NOPAs) in the…
We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
We present a set-oriented graph-based computational framework for continuous-time optimal transport over nonlinear dynamical systems. We recover provably optimal control laws for steering a given initial distribution in phase space to a…
Let L/K be an extension of absolutely abelian number fields of equal conductor, n. The image of the ring of integers of L under the trace map from L to K is an ideal in the ring of integers in K. We compute the absolute norm of this ideal…
Recent advances in {matrix-mimetic} tensor frameworks have made it possible to preserve linear algebraic properties for multilinear data analysis and, as a result, to obtain optimal representations of multiway data. Matrix mimeticity arises…
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…
We study the problem of estimating a function $T$ given independent samples from a distribution $P$ and from the pushforward distribution $T_\sharp P$. This setting is motivated by applications in the sciences, where $T$ represents the…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
Distributional data have become increasingly prominent in modern signal processing, highlighting the necessity of computing optimal transport (OT) maps across multiple probability distributions. Nevertheless, recent studies on neural OT…
We derive an extremal equation for optimal completely-positive map which most closely approximates a given transformation between pure quantum states. Moreover, we also obtain an upper bound on the maximal mean fidelity that can be attained…
This paper considers two different problems in trajectory tracking control for linear systems. First, if the control is not unique which is most input energy efficient. Second, if exact tracking is infeasible which control performs most…
Optimal prediction methods compensate for a lack of resolution in the numerical solution of time-dependent differential equations through the use of prior statistical information. We present a new derivation of the basic methodology, show…
In order to adapt to the differentiable setting a formula for linear response proved by Pollicott and Vytnova in the analytic setting, we show a result of regularity of dynamical determinants of expanding maps of the circle. The main tool…
This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two…
The optimal controller design problem for a linear, first-order spatially-invariant distributed parameter system is considered. Through a case study of the Linear Quadratic Regulator (LQR) problem for the diffusion equation over the torus,…
In this paper, we consider the problem of recovering the $W_2$-optimal transport map T between absolutely continuous measures $\mu,\nu\in\mathcal{P}(\mathbb{R}^n)$ as the flow of a linear-control neural ODE, where the control depends only…
Using optimal transport we study some dynamical properties of expanding circle maps acting on measures by push-forward. Using the definition of the tangent space to the space of measures introduced by Gigli, their derivative at the unique…
Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…