Related papers: An analytical formulation for roughness based on c…
A system comprised of an elastic solid and its response to an external random force sequence is shown to behave based on the principles of the theory of algorithmic complexity and randomness. The solid distorts the randomness of an input…
Many methods of estimating causal models do not provide estimates of confidence in the resulting model. In this work, a metric is proposed for validating the output of a causal model fit; the robustness of the model structure with resampled…
Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect…
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…
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
Defining the density flow of perturbations moving at a given speed for cellular automata, we establish equalities and inequalities between the measurable entropy of a cellular automaton and the measurable entropy of its associated shift.
The friction and adhesion between elastic bodies are strongly influenced by the roughness of the surfaces in contact. Here we develop a multiscale molecular dynamics approach to contact mechanics, which can be used also when the surfaces…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…
Finite cellular automata (FCA) are widely used in simulating nonlinear complex systems, and their reversibility is closely related to information loss during the evolution. However, only a relatively small portion of their reversibility…
Cellular automata are a famous model of computation, yet it is still a challenging task to assess the computational capacity of a given automaton; especially when it comes to showing negative results. In this paper, we focus on studying…
We study several probability distributions relevant to the avalanche dynamics of elastic interfaces driven on a random substrate: The distribution of size, duration, lateral extension or area, as well as velocities. Results from the…
We investigate the statistical evidence for the use of `rough' fractional processes with Hurst exponent $H< 0.5$ for the modeling of volatility of financial assets, using a model-free approach. We introduce a non-parametric method for…
We present a practical approach for constructing meshes of general rough surfaces with given autocorrelation functions based on the unstructured meshes of nominally smooth surfaces. The approach builds on a well-known method to construct…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
In this paper we propose an approach for measuring growth of complexity of emerging patterns in complex systems such as cellular automata. We discuss several ways how a metric for measuring the complexity growth can be defined. This…
In this paper, connections between surface roughness and directed polymers in random medium are studied, when the surface is considered as a directed line undergoing stochastic oscillations. This is performed by studying the influence of a…
We present a preliminary results of our Galactic Habitable Zone (GHZ) 2D probabilistic cellular automata models. The relevant time-scales (emergence of life, it's diversification and evolution influenced with the global risk function) are…
Machine learning methods have significantly improved in their predictive capabilities, but at the same time they are becoming more complex and less transparent. As a result, explainers are often relied on to provide interpretability to…