Related papers: Dynamical Sampling: A Survey
In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a…
Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…
We review some of the recent developments and prove new results concerning frames and Bessel systems generated by iterations of the form $\{A^ng: g\in G,\, n=0,1,2,\dots \}$, where $A$ is a bounded linear operators on a separable complex…
We consider the problem of spatiotemporal sampling in which an initial state $f$ of an evolution process $f_t=A_tf$ is to be recovered from a combined set of coarse samples from varying time levels $\{t_1,\dots,t_N\}$. This new way of…
The dynamical sampling problem is centered around reconstructing signals that evolve over time according to a dynamical process, from spatial-temporal samples that may be noisy. This topic has been thoroughly explored for one-dimensional…
Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…
This paper considers some designs for sampling and interventions in dynamic networks and spatial temporal settings. The sample spreads through the population largely by tracing network links, although random sampling or spatial designs may…
Deep metric learning maps visually similar images onto nearby locations and visually dissimilar images apart from each other in an embedding manifold. The learning process is mainly based on the supplied image negative and positive training…
Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
In this contribution we establish a dictionary between terms in two different areas in order to show that many of the topics studied are common ones - just with a different terminology. We further analyze the relations between the…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
Recently there has been much work on selective sampling, an online active learning setting, in which algorithms work in rounds. On each round an algorithm receives an input and makes a prediction. Then, it can decide whether to query a…
Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry, and partly from…
In this paper, we study the problem of sampling from a graphical model when the model itself is changing dynamically with time. This problem derives its interest from a variety of inference, learning, and sampling settings in machine…
Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning…
Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts…
Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and…
This paper investigates the problem of dynamical sampling for graph signals influenced by a constant source term. We consider signals evolving over time according to a linear dynamical system on a graph, where both the initial state and the…
Given an unknown dynamical system, what is the minimum number of samples needed for effective learning of its governing laws and accurate prediction of its future evolution behavior, and how to select these critical samples? In this work,…