Related papers: Diddy: a Python toolbox for infinite discrete dyna…
A sequential dynamical system, or SDS, consists of an undirected graph Y, a vertex-indexed list of local functions F_Y, and a permutation pi of the vertex set (or more generally, a word w over the vertex set) that describes the order in…
The sparse identification of nonlinear dynamics (SINDy) has been established as an effective method to learn interpretable models of dynamical systems from data. However, for high-dimensional slow-fast dynamical systems, the regression…
This paper gives a summary of basic concepts of density-functional theory (DFT) and its use in state-of-the-art computations of complex processes in condensed matter physics and materials science. In particular we discuss how microscopic…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…
This thesis is divided into three parts. In the first part, we give an introduction to J. Harrison's theory of differential chains. In the second part, we apply these tools to generalize the Cauchy theorems in complex analysis. Instead of…
The fixed point construction is a method for designing tile sets and cellular automata with highly nontrivial dynamical and computational properties. It produces an infinite hierarchy of systems where each layer simulates the next one. The…
Since the 1980s, many exact results have been discovered in $2d$ CFT, from critical exponents to correlation functions to complete solutions of certain models. In $d>2$, there is a wealth of numerical results as well as promising analytic…
We introduce topological differential testing (TDT), an approach to extracting the consensus behavior of a set of programs on a corpus of inputs. TDT uses the topological notion of a simplicial complex (and implicitly draws on richer…
Understanding and predicting the thermodynamic properties of point defects in semiconductors and insulators would greatly aid in the design of novel materials and allow tuning the properties of existing ones. As a matter of fact,…
This is an overview of the basic tools of nonsmooth analysis which are grounded on nonstandard models of set theory. By way of illustration we give a criterion for an infinitesimally optimal path of a general discrete dynamic system.
Differentiable programming has facilitated numerous methodological advances in scientific computing. Physics engines supporting automatic differentiation have simpler code, accelerating the development process and reducing the maintenance…
Data-driven methodologies are nowadays ubiquitous. Their rapid development and spread have led to applications even beyond the traditional fields of science. As far as dynamical systems and differential equations are concerned, neural…
A simple mathematical expression for the universal map for cellular automata is found in closed form with the help of a digit function, whose most basic properties are established. This result is found after proving a theorem on the…
Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept…
We study existence and uniqueness of the fixed points solutions of a large class of non-linear variable discounted transfer operators associated to a sequential decision-making process. We establish regularity properties of these solutions,…
New tools are needed to handle the growth of data in astrophysics delivered by recent and upcoming surveys. We aim to build open-source, light, flexible, and interactive software designed to visualize extensive three-dimensional (3D)…
Gradually-typed languages feature a dynamic type that supports implicit coercions, greatly weakening the type system but making types easier to adopt. Understanding how developers use this dynamic type is a critical question for the design…
Behavioral studies using personal digital devices typically produce rich longitudinal datasets of mixed data types. These data provide information about the behavior of users of these devices in real-time and in the users' natural…
An open source symbolic tool for vector fields analysis 'SymFields' is developed in Python. The SymFields module is constructed upon Python symbolic module sympy, which could only conduct scaler field analysis. With SymFields module, you…