On the decomposition of stochastic cellular automata

In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over the state set of a stochastic cellular automaton, i.e. images that show the average state of each cell during the evolution of the stochastic cellular automaton. The second property shows that stochastic cellular automata are equivalent to so-called stochastic mixtures of deterministic cellular automata. Based on this property, any stochastic cellular automaton can be decomposed into a set of deterministic cellular automata, each of which contributes to the behavior of the stochastic cellular automaton.Comment: Submitted to Journal of Computation Science, Special Issue on Cellular Automata Application

An evolutionary approach to the identification of Cellular Automata based on partial observations

In this paper we consider the identification problem of Cellular Automata (CAs). The problem is defined and solved in the context of partial observations with time gaps of unknown length, i.e. pre-recorded, partial configurations of the system at certain, unknown time steps. A solution method based on a modified variant of a Genetic Algorithm (GA) is proposed and illustrated with brief experimental results.Comment: IEEE CEC 201

Number-conserving cellular automata with a von Neumann neighborhood of range one

We present necessary and sufficient conditions for a cellular automaton with a von Neumann neighborhood of range one to be number-conserving. The conditions are formulated for any dimension and for any set of states containing zero. The use of the geometric structure of the von Neumann neighborhood allows for computationally tractable conditions even in higher dimensions.Comment: 15 pages, 3 figure

A split-and-perturb decomposition of number-conserving cellular automata

This paper concerns $d$-dimensional cellular automata with the von Neumann neighborhood that conserve the sum of the states of all their cells. These automata, called number-conserving or density-conserving cellular automata, are of particular interest to mathematicians, computer scientists and physicists, as they can serve as models of physical phenomena obeying some conservation law. We propose a new approach to study such cellular automata that works in any dimension $d$ and for any set of states $Q$. Essentially, the local rule of a cellular automaton is decomposed into two parts: a split function and a perturbation. This decomposition is unique and, moreover, the set of all possible split functions has a very simple structure, while the set of all perturbations forms a linear space and is therefore very easy to describe in terms of its basis. We show how this approach allows to find all number-conserving cellular automata in many cases of $d$ and $Q$. In particular, we find all three-dimensional number-conserving CAs with three states, which until now was beyond the capabilities of computers

A dynamical systems approach to the discrimination of the modes of operation of cryptographic systems

Evidence of signatures associated with cryptographic modes of operation is established. Motivated by some analogies between cryptographic and dynamical systems, in particular with chaos theory, we propose an algorithm based on Lyapunov exponents of discrete dynamical systems to estimate the divergence among ciphertexts as the encryption algorithm is applied iteratively. The results allow to distinguish among six modes of operation, namely ECB, CBC, OFB, CFB, CTR and PCBC using DES, IDEA, TEA and XTEA block ciphers of 64 bits, as well as AES, RC6, Twofish, Seed, Serpent and Camellia block ciphers of 128 bits. Furthermore, the proposed methodology enables a classification of modes of operation of cryptographic systems according to their strength.Comment: 14 pages, 10 figure

pySODM: Simulating and Optimizing Dynamical Models in Python 3

In this work we present our generic framework to construct, simulate and calibrate dynamical systems in Python 3. Its goal is to reduce the time it takes to implement a dynamical system with n-dimensional states represented by coupled ordinary differential equations (ODEs), simulate the system deterministically or stochastically, and, calibrate the system using n-dimensional data. We demonstrate our code's capabilities by building three models in the context of two case studies. First, we forecast the yields of the enzymatic esterification reaction of D-glucose and Lauric acid, performed in a continuous-flow, packed-bed reactor. The model yields satisfactory predictions under different flow rates and can be applied to design a viable process. Second, we build a stochastic, age-stratified model to make forecasts on the evolution of influenza in Belgium during the 2017-2018 season. By presenting real-world case studies from two scientific disciplines, we demonstrate our code's applicability across domains

The Impact of Hurricanes on the Oceanographic Conditions in the Exclusive Economic Zone of Cuba

In this work, we analysed the satellite-based responses of sea surface temperature (SST) and chlorophyll-a (chl-a) concentration in the waters of the Exclusive Economic Zone (EEZ) of Cuba to hurricanes that crossed the EEZ between 1998 and 2016. We considered two spatial scales to capture the spatially heterogeneous nature of the effects of hurricanes. A first more fine-grained one where we considered 120 km radius disks centered at every consecutive hurricane position within the EEZ (scale 1) and a second more coarse grained one enclosing the entire EEZ (scale 2). We conclude that the hurricanes induced a weak cooling since 75 and 85% of the SST anomalies at scale 1 and 2, respectively, were smaller than -1{\deg}C. The cooling was mainly caused by the wind, inducing mixing and/or upwelling of subsurface cool waters. The maximum chl-a responses were recorded in the first and second post-storm weeks, with 60% ranging between -0.01 and 0.04 mg m$^{-3}$ at scale 1, and between -0.07 and 0.02 mg m$^{-3}$ at scale 2. During those post-storm weeks SST and chl-a anomalies were 18 and 44% higher at scale 1 than at scale 2, respectively. We argue that the transport of chl-a from the deep chlorophyll maximum and/or the rich coastal waters are the dominant mechanisms determining the post-storm chl-a response in the EEZ. We also found that the magnitude of the Island Mass Effect in the EEZ after the passage of the hurricanes was 89% higher than before its passage.Comment: 33 pages, 14 figures. Submitted to Remote Sensing of Environmen

Real-time prediction of influenza outbreaks in Belgium

Seasonal influenza is a worldwide public health concern. Forecasting its dynamics can improve the management of public health regulations, resources and infrastructure, and eventually reduce mortality and the costs induced by influenza-related absenteism. In Belgium, a network of Sentinel General Practitioners (SGPs) is in place for the early detection of the seasonal influenza epidemic. This surveillance network reports the weekly incidence of influenza-like illness (ILI) cases, which makes it possible to detect the epidemic onset, as well as other characteristics of the epidemic season. In this paper, we present an approach for predicting the weekly ILI incidence in real-time by resorting to a dynamically calibrated compartmental model, which furthermore takes into account the dynamics of other influenza seasons. In order to validate the proposed approach, we used data collected by the Belgian SGPs for the influenza seasons 2010–2016. In spite of the great variability among different epidemic seasons, providing weekly predictions makes it possible to capture variations in the ILI incidence. The confidence region becomes more representative of the epidemic behavior as ILI data from more seasons become available. Since the SIR model is then calibrated dynamically every week, the predicted ILI curve gets rapidly tuned to the dynamics of the ongoing season. The results show that the proposed method can be used to characterize the overall behavior of an epidemic

The impact of resource dependence of the mechanisms of life on the spatial population dynamics of an in silico microbial community

Biodiversity has a critical impact on ecosystem functionality and stability, and thus the current biodiversity crisis has motivated many studies of the mechanisms that sustain biodiversity, a notable example being non-transitive or cyclic competition. We therefore extend existing microscopic models of communities with cyclic competition by incorporating resource dependence in demographic processes, characteristics of natural systems often oversimplified or overlooked by modellers. The spatially explicit nature of our individual-based model of three interacting species results in the formation of stable spatial structures, which have significant effects on community functioning, in agreement with experimental observations of pattern formation in microbial communities. Published by AIP Publishing