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In the rapidly evolving era of Artificial Intelligence (AI), synthetic data are widely used to accelerate innovation while preserving privacy and enabling broader data accessibility. However, the evaluation of synthetic data remains…
Many dynamical systems can be naturally represented as `Bratteli-Vershik' (or `adic') systems, which provide an appealing combinatorial description of their dynamics. If an adic system X satisfies two technical conditions (`focus' and…
The use of Digital Twins is set to transform the manufacturing sector by aiding monitoring and real-time decision making. For several applications in this sector, the system to be modeled consists of a mix of discrete-event and continuous…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
The method of synthetic controls is widely used for evaluating causal effects of policy changes in settings with observational data. Often, researchers aim to estimate the causal impact of policy interventions on a treated unit at an…
We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…
Direct Numerical Simulations (DNS) of the Navier Stokes equations is a valuable research tool in fluid dynamics, but there are very few publicly available codes and, due to heavy number crunching, codes are usually written in low-level…
We solve a problem, stated in [CGP10], showing that Sticky Datalog, defined in the cited paper as an element of the Datalog\pm project, has the finite controllability property. In order to do that, we develop a technique, which we believe…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate challenges of…
DisCoPy (Distributional Compositional Python) is an open source toolbox for computing with string diagrams and functors. In particular, the diagram data structure allows to encode various kinds of quantum processes, with functors for…
Synthesizing controllers for large, complex, and distributed systems is a challenging task. Numerous proposed methods exist in the literature, but it is difficult for practitioners to apply them -- most proposed synthesis methods lack…
We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…
This tutorial is about cellular automata that exhibit 'cold dynamics'. By this we mean zero entropy, stabilization of all orbits, trivial asymptotic dynamics, etc. These are purely transient irreversible dynamics, but they capture many…
Topological transitivity is a fundamental notion in topological dynamics and is widely regarded as a basic indicator of global dynamical complexity. For general cellular automata, topological transitivity is known to be undecidable. By…
A large part of modern machine learning theory often involves computing the high-dimensional expected trace of a rational expression of large rectangular random matrices. To symbolically compute such quantities using free probability…
We study the set of strictly periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but they not spatially periodic. This set turns out to be dense for…
Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…
Software that processes real-world data or that models a physical system must have some way of managing units. While simple approaches like the understood convention that all data are in a unit system (such as the MKS SI unit system) do…
Multiplexed imaging data are revolutionizing our understanding of the composition and organization of tissues and tumors. A critical aspect of such tissue profiling is quantifying the spatial relationship relationships among cells at…