Related papers: From eventually different functions to pandemic nu…
A recent article that combines normalized epidemic compartmental models and population games put forth a system theoretic approach to capture the coupling between a population's strategic behavior and the course of an epidemic. It…
We give examples of degree functions deg : R --> M, where R is a polynomial ring in 2 or 3 variables and M is either the integers or the natural numbers, whose behaviour with respect to derivations D : R --> R is pathological in the sense…
SIRS models capture transmission dynamics of infectious diseases for which immunity is not lifelong. Extending these models by a W compartment for individuals with waning immunity, the boosting of the immune system upon repeated exposure…
In Diagonally Non-Computable Functions and Bi-Immunity, Carl Jockusch and Andrew Lewis proved that every DNC function computes a bi-immune set. They asked whether every DNC function computes an effectively bi-immune set. We construct a DNC…
We present and study new definitions of universal and programmable universal unary functions and consider a new simplicity criterion: almost decidability of the halting set. A set of positive integers S is almost decidable if there exists a…
We introduce a novel approach to the automated termination analysis of computer programs: we use neural networks to represent ranking functions. Ranking functions map program states to values that are bounded from below and decrease as a…
We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…
Functional Data Analysis (FDA) is a statistical domain developed to handle functional data characterized by high dimensionality and complex data structures. Sequential Neural Networks (SNNs) are specialized neural networks capable of…
Deep neural networks (DNNs) achieve remarkable performance on a wide range of tasks, yet their mathematical analysis remains fragmented: stability and generalization are typically studied in disparate frameworks and on a case-by-case basis.…
In this manuscript, we develop a mobility-based Susceptible-Infectious-Recovered (SIR) model to elucidate the dynamics of pandemic propagation. While traditional SIR models within the field of epidemiology aptly characterize transitions…
We develop an extension of the Susceptible-Infected-Recovery (SIR) model to account for spatial variations in population as well as infection and recovery parameters. The equations are derived by taking the continuum limit of discrete…
We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural…
We study epidemic models where the infectivity of each individual is a random function of the infection age (the elapsed time of infection). To describe the epidemic evolution dynamics, we use a stochastic process that tracks the number of…
In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have been studied in the past only in particular cases, two of…
When an infectious disease propagates throughout society, the incidence function may rise at first due to an increase in pathogenicity and then decrease due to inhibitory effects until it reaches saturation. Effective vaccination and…
In this article we identify a general class of high-dimensional continuous functions that can be approximated by deep neural networks (DNNs) with the rectified linear unit (ReLU) activation without the curse of dimensionality. In other…
In the recent COVID-19 pandemic we assisted at a sequence of epidemic waves intertwined by anomalous fade-outs with periods of low but persistent epidemic prevalence. These long-living epidemic states complicate epidemic control and…
We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in…
Causal functions of sequences occur throughout computer science, from theory to hardware to machine learning. Mealy machines, synchronous digital circuits, signal flow graphs, and recurrent neural networks all have behaviour that can be…
We consider the \mnk{classical} problem of a controller activating (or sampling) sequentially from a finite number of $N \geq 2$ populations, specified by unknown distributions. Over some time horizon, at each time $n = 1, 2, \ldots$, the…