Related papers: Identification of stochastic operators
A scalar valued random field is called operator-scaling if it satisfies a self-similarity property for some matrix E with positive real parts of the eigenvalues. We present a moving average and a harmonizable representation of stable…
A method to quantify the probabilistic controller taskload inherent to maintaining aircraft adherence to 4-D trajectories within flow corridors is presented. An Ornstein-Uhlenbeck model of the aircraft motion and a Poisson model of the flow…
We provide a general result for finding Stein operators for the product of two independent random variables whose Stein operators satisfy a certain assumption, extending a recent result of Gaunt, Mijoule and Swan \cite{gms18}. This…
We study stochastic graph optimization problems in a novel distributed setting. As in the standard centralized setting, a random subgraph $G^*$ of a known base graph $G$ is realized by including each edge $e$ independently with a known…
We consider bounded operators $A$ acting iteratively on a finite set of vectors $\{f_i : i\in I\}$ in a Hilbert space $\mathcal H$ and address the problem of providing necessary and sufficient conditions for the collection of iterates…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and…
Four-dimensional scanning transmission electron microscopy (4D-STEM) of local atomic diffraction patterns is emerging as a powerful technique for probing intricate details of atomic structure and atomic electric fields. However, efficient…
We present an operator learning approach for a class of evolution operators using a composition of a learned lift into the space of diffeomorphisms of the domain and the group action on the field space. In turn, this transforms the…
This paper addresses a distributed optimization problem in a communication network where nodes are active sporadically. Each active node applies some learning method to control its action to maximize the global utility function, which is…
Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from…
We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…
Distributed algorithms, particularly Diffusion Least Mean Square, are widely favored for their reliability, robustness, and fast convergence in various industries. However, limited observability of the target can compromise the integrity of…
We prove that deterministic motion in dissipative systems emerges as a strict geometric attractor of contact flow, not a statistical approximation. Building on the contact geometry of stochastic vector bundles, we develop time-dependent…
Detection transformers like DETR have recently shown promising performance on many object detection tasks, but the generalization ability of those methods is still quite challenging for cross-domain adaptation scenarios. To address the…
We introduce a framework to study the random entire function $\zeta_\beta$ whose zeros are given by the Sine$_\beta$ process, the bulk limit of beta ensembles. We present several equivalent characterizations, including an explicit power…
In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…
We study the recovery of operators with bandlimited Kohn-Nirenberg symbol from the action of such operators on a weighted impulse train, a procedure we refer to as operator sampling. Kailath, and later Kozek and the authors have shown that…
We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of $S$-matrix elements, in arbitrary spacetime dimensions and with…
The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential…