Related papers: An information-based classification of Elementary …
Exponential models of distributions are widely used in machine learning for classiffication and modelling. It is well known that they can be interpreted as maximum entropy models under empirical expectation constraints. In this work, we…
A population of neurons typically exhibits a broad diversity of responses to sensory inputs. The intuitive notion of functional classification is that cells can be clustered so that most of the diversity is captured in the identity of the…
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…
Modeling the immune system so that its essential functionalities stand out without the need for every molecular or cellular interaction to be taken into account has been challenging for many decades. Two competing approaches have been the…
Developmental patterning comprises processes that range from purely instructed, where external signals specify cell fates, to fully self-organized, where spatial patterns emerge autonomously through cellular interactions. We propose that…
We consider the problem of finding the density of 1's in a configuration obtained by $n$ iterations of a given cellular automaton (CA) rule, starting from disordered initial condition. While this problems is intractable in full generality…
Using Rule 126 elementary cellular automaton (ECA) we demonstrate that a chaotic discrete system --- when enriched with memory -- hence exhibits complex dynamics where such space exploits on an ample universe of periodic patterns induced…
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…
Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number…
A dynamic model for cell differentiation is studied, where cells with internal chemical reaction dynamics interact with each other and replicate. It leads to spontaneous differentiation of cells and determination, as is discussed in the…
A thermodynamic formalism describing the efficiency of information learning is proposed, which is applicable for stochastic thermodynamic systems with multiple internal degree of freedom. The learning rate, entropy production rate (EPR),…
A detail study on the In-degree Distribution (ID) of Cellular Automata is obtained by exact enumeration. The results indicate large deviation from multiscaling and classification according to ID are discussed. We further augment the…
Elementary cellular automata (ECA) are converted into multiplicative versions by using permuted n-dim Galois fields and octonion multiplication tables as binary pointers to each rule's Wolfram code truth table. This enables an extension of…
Cellular automata (CA) have long attracted attention as dynamical systems with local updating rules and yet can exhibit, for certain rules, complex, long space and time correlated patterns. This contrast with other rules which results in…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors…
Electric automation systems offer convenience and efficiency in controlling electrical circuits and devices. Traditionally, these systems rely on predefined commands for control, limiting flexibility and adaptability. In this paper, we…
Traffic models based on cellular automata have high computational efficiency because of their simplicity in describing unrealistic vehicular behavior and the versatility of cellular automata to be implemented on parallel processing. 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…
Rule 22 elementary cellular automaton (ECA) has a 3--cell neighborhood, binary cell states, where a cell takes state `1' if there is exactly one neighbor, including the cell itself, in state `1'. In Boolean terms the cell-state transition…