Related papers: Characterizing and Testing Configuration Stability…
Two types of stability boundaries exist for any planetary system consisting of one star and two planets. Lagrange stability requires that the planets remain bound to the star, conserves the ordering of the distance from the star, and limits…
We present an extension to the robust phase estimation protocol, which can identify incorrect results that would otherwise lie outside the expected statistical range. Robust phase estimation is increasingly a method of choice for…
A new thresholding method, based on L-statistics and called order thresholding, is proposed as a technique for improving the power when testing against high-dimensional alternatives. The new method allows great flexibility in the choice of…
This paper studies the well-posedness and regularity of safe stabilizing optimization-based controllers for control-affine systems in the presence of model uncertainty. When the system dynamics contain unknown parameters, a finite set of…
Neural Cellular Automata (NCAs) offer a way to study the growth of two-dimensional artificial organisms from a single seed cell. From the outset, NCA-grown organisms have had issues with stability, their natural boundary often breaking down…
Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and…
In pattern-forming systems, competition between patterns with different wave numbers can lead to domain structures, which consist of regions with differing wave numbers separated by domain walls. For domain structures well above threshold…
We have determined families of two-dimensional deterministic totalistic cellular automaton rules whose stationary density of active sites exhibits a period two in time. Each family of deterministic rules is characterized by an ``average…
Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
Stability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schr\"odinger equations with boundary…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
We elaborate a scheme of trapping-expulsion management (TEM), in the form of the quadratic potential periodically switching between confinement and expulsion, as a means of stabilization of two-dimensional dynamical states against the…
In this paper, we investigate constrained control of continuous-time linear stochastic systems. We show that for certain system parameter settings, constrained control policies can never achieve stabilization. Specifically, we explore a…
Algorithmic stability is a classical framework for analyzing the generalization error of learning algorithms. It predicts that an algorithm has small generalization error if it is insensitive to small perturbations in the training set such…
It is shown that for the N-neighbor and K-state cellular automata, the class II, class III and class IV patterns coexist at least in the range $\frac{1}{K} \le \lambda \le 1-\frac{1}{K} $. The mechanism which determines the difference…
Threshold automata are a formalism for modeling fault-tolerant distributed algorithms. The main feature of threshold automata is the notion of a threshold guard, which allows us to compare the number of received messages with the total…
A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the…
In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different…