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We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve…
Deep neural networks (DNNs) have been widely and successfully applied to various applications, but they require large amounts of memory and computational power. This severely restricts their deployment on resource-limited devices. To…
We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
Classical Cellular Automata (CCAs) are a powerful computational framework for modeling global spatio-temporal dynamics with local interactions. While CCAs have been applied across numerous scientific fields, identifying the local rule that…
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…
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…
We have improved an algorithm generating synchronizing automata with a large length of the shortest reset words. This has been done by refining some known results concerning bounds on the reset length. Our improvements make possible to…
We study one-dimensional reversible and number-conserving cellular automata (RNCCA) that have both properties of reversibility and number-conservation. In the case of 2-neighbor RNCCA, Garc\'ia-Ramos proved that every RNCCA shows trivial…
The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between…
We propose a characteristic representation ofone-dimensional and 2-state, 3-neighbor cellular automaton rules, which describes an effective form of each rule after many time steps. Simulated results of the representation show that complex…
The exploration of the densest sphere packings is a fundamental problem in mathematics and a wide variety of sciences including materials science. We present our exhaustive computational exploration of the densest ternary sphere packings…
Cellular automata (CA) are fully discrete alternatives to partial differential equations (PDE). For PDEs, one often considers the Cauchy problem, or initial value problem: find the solution of the PDE satisfying a given initial condition.…
High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…
Classification with a large number of classes is a key problem in machine learning and corresponds to many real-world applications like tagging of images or textual documents in social networks. If one-vs-all methods usually reach top…
The cellular tree classifier model addresses a fundamental problem in the design of classifiers for a parallel or distributed computing world: Given a data set, is it sufficient to apply a majority rule for classification, or shall one…
Cellular automata (CA) is an important modelling paradigm for complex systems. In the design of cellular automata, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
In this paper, we consider the problem of recursively designing uniquely decodable ternary code sets for highly overloaded synchronous code-division multiple-access (CDMA) systems. The proposed code set achieves larger number of users $K <…
A Cellular Automata (CA) is a computing model of complex System using simple rule. In CA the problem space into number of cell and each cell can be one or several final state. Cells are affected by neighbours' to the simple rule. Cellular…
Generalized product codes (GPCs) are extensions of product codes (PCs) where code symbols are protected by two component codes but not necessarily arranged in a rectangular array. We consider a deterministic construction of GPCs (as opposed…