A. Martín del Rey

Modeling epidemics using cellular automata

Abstract The main goal of this work is to introduce a theoretical model, based on cellular automata, to simulate epidemic spreading. Specifically, it divides the population into three classes: susceptible, infected and recovered, and the state of each cell stands for the portion of these classes of individuals in the cell at every step of time. The effect of population vaccination is also considered. The proposed model can serve as a basis for the development of other algorithms to simulate real epidemics based on real data.

Simulation of forest fire fronts using cellular automata

In this work a new model for fire front spreading based on two-dimensional cellular automata is proposed. It is a more realistic modification of the model introduced by Karafyllidis and Thanailakis (see [Karafyllidis I, Thanailakis A. A model for predicting forest fire spreading using cellular automata. Ecol Model 1997;99:87-97]), which is based on the transfer of fractional burned area. Specifically, the model proposed in this work introduces a more accurate factor of propagation from a diagonal neighbor cell and includes, in a detailed form, the rate of fire spread. Moreover, the model is useful for both homogeneous and inhomogeneous environments. Some tests have been passed in order to determine the goodness of the method.

A secret sharing scheme based on cellular automata

A new secret sharing scheme based on a particular type of discrete delay dynamical systems: memory cellular automata, is proposed. Specifically, such scheme consists of a (k,n)-threshold scheme where the text to be shared is considered as one of the k initial conditions of the memory cellular automata and the n shares to be distributed are n consecutive configurations of the evolution of such cellular automata. It is also proved to be perfect and ideal.

A multisecret sharing scheme for color images based on cellular automata

In this work a new multisecret sharing scheme for secret color images among a set of users is proposed. The protocol allows that each participant in the scheme to share a secret color image with the rest of participants in such a way that all of them can recover all the secret color images only if the whole set of participants pools their shadows. The proposed scheme is based on the use of bidimensional reversible cellular automata with memory. The security of the scheme is studied and it is proved that the protocol is ideal and perfect and that it resists the most important statistical attacks.

Inverse rules of ECA with rule number 150

The explicit expressions of local transition functions of the inverse cellular automata of elementary cellular automata with rule number 150 and periodic boundary conditions are given. The procedure to obtain such local transition functions is based on the algebraic properties of elementary cellular automata.

A secure scheme to share secret color images

The main goal of this work is to study how discrete dynamical systems can be used to design secret sharing schemes. Specifically, the proposed scheme permits to share secret color images, and it is based on bidimensional cellular automata. The main idea is to analyze how a simple reversible model of computation allows one to compute the shares and then using the reverse computation in order to recover the secret image. Moreover, the proposed scheme exhibits good statistical properties.

Reversibility of linear cellular automata

In this paper the reversibility problem for linear cellular automata defined by a characteristic matrix of the form of a pentadiagonal matrix is tackled. Specifically, a criterion for the reversibility in terms of the number of cells is stated and, in these cases, the inverse cellular automata are explicitly computed.

A model based on cellular automata to simulate epidemic diseases

The main goal of this work is to introduce a mathematical model, based on two-dimensional cellular automata, to simulate epidemic diseases Specifically, each cell stands for a square portion of the ground where the epidemic is spreading, and its state is given by the fractions of susceptible, infected and recovered individuals.

On The Reversibility Of 150 Wolfram Cellular Automata

In this paper, the reversibility problem for 150 Wolfram cellular automata is tackled for null boundary conditions. It is explicitly shown that the reversibility depends on the number of cells of the cellular automaton. The inverse cellular automaton for each case is also computed.

Faá di Bruno's formula, lattices, and partitions

The coefficients of g(s) in expanding the rth derivative of the composite function g ○ f by Faa di Brunos formula, is determined by a Diophantine linear system, which is proved to be equivalent to the problem of enumerating partitions of a finite set of integers attached to r and s canonically.