G. Rodríguez Sánchez

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 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.

3D medical data security protection

A novel encryption method for 3D biomedical objects is introduced.It is based on the use of cellular automata, boolean functions and discretized chaotic maps.The protocol involves two phases that produce confusion and diffusion.The encryption method directly acts on the 3D structure of the object defined by voxels. A novel encryption protocol for 3D biomedical objects is introduced in this work. This method consists of two phases which are iteratively applied: the confusion phase and the diffusion phase. In the confusion phase the position of the voxels are permuted by means of a discretized chaotic map, whereas in the diffusion phase the value of each voxel is changed. The diffusion phase is divided into two sub phases: in the first one a memory reversible 3D cellular automata is applied using the 3D object as the initial conditions, and in the second sub phase, a discrete dynamical system with delay defined by a non-linear boolean function is applied to the output of the evolution of the cellular automaton. The protocol is shown to be secure against the most important cryptanalytic attacks.The impact and novelty of this method lies on directly ciphering the 3D objects and considering these objects as the aggregation of voxels. Moreover, this allows to design a new and efficient encryption algorithm which is the generalization of those methods to encrypt digital images that are based on the iteration of a confusion and a diffusion phase.The use of cellular automata and boolean transition rules in the diffusion phase opens new possibilities for the use of expert and intelligence systems in cryptography since cellular automata can be used and inference machines.

Encrypting digital images using cellular automata

In this paper a novel symmetric protocol to cipher digital images is introduced. The protocol proposed consists of two iterative phases: The confusion phase and the diffusion phase. The first stage permutes the pixels in the image using a discrete chaotic map (specifically, the Cat map), whereas in the second stage, the pixel values (that is, the color of each pixel) are modified sequentially by means of a reversible memory cellular automata. The proposed protocol is shown to be secure against the more important cryptanalytic attacks.

A DISCRETE MATHEMATICAL MODEL TO SIMULATE MALWARE SPREADING

With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.

On the boolean partial derivatives and their composition

Abstract The main goal of this work is to introduce the relation between the partial boolean derivatives of an n -variable boolean function and their directional boolean derivatives.

An image encryption algorithm based on 3D cellular automata and chaotic maps

A novel encryption algorithm to cipher digital images is presented in this work. The digital image is rendering into a three-dimensional (3D) lattice and the protocol consists of two phases: the confusion phase where 24 chaotic Cat maps are applied and the diffusion phase where a 3D cellular automata is evolved. The encryption method is shown to be secure against the most important cryptanalytic attacks.