Related papers: Periods of the discretized Arnold Cat Map and its …
Models of discrete space and space-time that exhibit continuum-like behavior at large lengths could have profound implications for physics. They may tame the infinities that arise from quantizing gravity, and dispense with the machinery of…
Since their introduction the Trasformer architectures emerged as the dominating architectures for both natural language processing and, more recently, computer vision applications. An intrinsic limitation of this family of "fully-attentive"…
Label-free tomographic microscopy offers a compelling means to visualize three-dimensional (3D) refractive index (RI) distributions from two-dimensional (2D) intensity measurements. However, limited forward-model accuracy and the ill-posed…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
Period doubling H\'enon renormalization of strongly dissipative maps is generalized in arbitrary finite dimension. In particular, a small perturbation of toy model maps with dominated splitting has invariant $C^r$ surfaces embedded in…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
In this work, we investigate the discrete Calder\'{o}n problem on grid graphs of dimension three or higher, formed by hypercubic structures. The discrete Calder\'{o}n problem is concerned with determining whether the discrete…
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
In this article, we proposed new discrete maps with memory (DMM). These maps are derived from fractional differential equations (FDE) with the Hilfer fractional derivatives of non-integer orders and periodic sequence of kicks. The suggested…
Proximity maps and regions are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in…
This paper introduces Manhattan sampling in two and higher dimensions, and proves sampling theorems. In two dimensions, Manhattan sampling, which takes samples densely along a Manhattan grid of lines, can be viewed as sampling on the union…
The approximate discrete Radon transform (ADRT) is a hierarchical multiscale approximation of the Radon transform. In this paper, we factor the ADRT into a product of linear transforms that resemble convolutions and derive an explicit…
Due to the deterministic nature of chaotic systems, fluctuations in their trajectories arise solely from the choice of initial conditions. Some of these dynamical fluctuations may lead to extremely unlikely scenarios. Understanding the…
Identifying the discontinuous diffusion coefficient in an elliptic equation with observation data of the gradient of the solution is an important nonlinear and ill-posed inverse problem. Models with total variational (TV) regularization…
We study differentially private (DP) machine learning algorithms as instances of noisy fixed-point iterations, in order to derive privacy and utility results from this well-studied framework. We show that this new perspective recovers…
We study quasiperiodically forced circle endomorphisms, homotopic to the identity, and show that under suitable conditions these exhibit uncountably many minimal sets with a complicated structure, to which we refer to as `strangely…
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
We prove that every flat nonlinear discrete-time system can be decomposed by coordinate transformations into a smaller-dimensional subsystem and an endogenous dynamic feedback. For flat continuous-time systems, no comparable result is…
We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with…
The alternating direction method of multipliers (ADMM) has recently sparked interest as a flexible and efficient optimization tool for imaging inverse problems, namely deconvolution and reconstruction under non-smooth convex regularization.…