Related papers: Assessing complexity by means of maximum entropy m…
G. Edelman, O. Sporns, and G. Tononi introduced in theoretical biology the neural complexity of a family of random variables. This functional is a special case of intricacy, i.e., an average of the mutual information of subsystems whose…
We investigate expressiveness, a parameter of one-dimensional cellular automata, in the context of simulated biological systems. The development of elementary cellular automata is interpreted in terms of biological systems, and biologically…
Many unconventional computing models, including some that appear to be quite different from traditional ones such as Turing machines, happen to characterise either the complexity class P or PSPACE when working in deterministic polynomial…
A multispecies artificial ecosystem is formulated using cellular automata with species interactions and food chain hierarchy. The constructed finite state automaton can simulate the complexity and self-organized characteristics of the…
We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. We apply it in random matrix…
Classification is a ubiquitous and fundamental problem in artificial intelligence and machine learning, with extensive efforts dedicated to developing more powerful classifiers and larger datasets. However, the classification task is…
We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which 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…
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.
Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…
Computer-based modelling and simulation have become useful tools to facilitate humans to understand systems in different domains, such as physics, astrophysics, chemistry, biology, economics, engineering and social science. A complex system…
A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling…
We compute the asymptotic temporal behavior of the dynamical complexity associated with the maximum probability trajectories on Gaussian statistical manifolds in presence of correlations between the variables labeling the macrostates of the…
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms…
When constructing models of the world, we aim for optimal compressions: models that include as few details as possible while remaining as accurate as possible. But which details -- or features measured in data -- should we choose to include…
Data Science and Machine Learning have become fundamental assets for companies and research institutions alike. As one of its fields, supervised classification allows for class prediction of new samples, learning from given training data.…