Related papers: Symbolic Dynamic Formulation for the Collatz Conje…
In this paper, we develop a novel approach to model the Internet round trip time using a recently proposed symbolic type neural network model called symbolic function network. The developed predictor is shown to have good generalization…
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…
Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in…
A digit function is presented which provides the $i$th-digit in base $p$ of any real number $x$. By means of this function, formulated within $\mathcal{B}$-calculus, the local, nonlocal and global dynamical behaviors of cellular automata…
This paper attempts to make feasible the evolutionary emergence of novelty in a supposedly deterministic world which behavior is associated with those of the mathematical dynamical systems. The work was motivated by the observation of…
We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…
Symbolic models have recently spurred the interest of the research community because they offer a correct-by-design approach to the control of embedded and cyber-physical systems. In this paper we address construction of symbolic models for…
We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string…
Much of dynamical algebraic combinatorics focuses on global dynamical systems defined via maps that are compositions of local toggle operators. The second author and Roby studied such maps that result from toggling independent sets of a…
A dynamical system is a pair $(X,f)$, where $X$ is a topological space and $f\colon X\to X$ is continuous. Kremer observed that the language of propositional linear temporal logic can be interpreted over the class of dynamical systems,…
Causal discovery from observational data is a challenging task that can only be solved up to a set of equivalent solutions, called an equivalence class. Such classes, which are often large in size, encode uncertainties about the orientation…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
We set up a geometrical theory for the study of the dynamics of reducible Pisot substitutions. It is based on certain Rauzy fractals generated by duals of higher dimensional extensions of substitutions. We obtain under certain hypotheses…
In the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical…
This work presents a step towards utilizing incrementally-improving symbolic perception knowledge of the robot's surroundings for provably correct reactive control synthesis applied to an autonomous driving problem. Combining abstract…
This work represents an in-depth study of the structural behavior of the Collatz sequences. We consider a finite arithmetic progression with a common difference is 2 and the number of terms in the sequence is equal to 2^n . After, we…
We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…
In the area of urban transportation networks, a growing number of day-to-day (DTD) traffic dynamic theories have been proposed to describe the network flow evolution, and an increasing amount of laboratory experiments have been conducted to…
A novel approach to automated learning of syntactic rules governing natural languages is proposed, based on using probabilities assigned to sentences (and potentially longer word sequences) by transformer neural network language models to…
The order of orbit generation in one-dimensional Lorenz-like maps is presented within a two letter symbolics scheme. This order is derived from the natural order of a set of fractions associated to the binary sequences. Its relation to the…