Brain oscillations in a random neural network

[EN] It is well-known that rhythmic patterns of neural activity appear both in the normal and abnormal function of the brain. Apart from the standard bands of electric oscillations found in the electroencephalogram (EEG): from alpha (8-12 Hz) to delta waves (1-4 Hz), synchronized firing of neural populations characterize some complex cognitive functions such as memory, attention and consciousness. In the case of electrocardiogram (ECG) it is usually recognized that oscillations can be understood as the limit cycle of an underlying non-linear process in heart dynamics. However, the situation is not so clear for EEG and the origin and purpose of neural oscillations are still the subject of a heated debate. Our model is a version of the standard SIRS model from epidemiology in which susceptible, infected and recovered sites represent quiescent, firing and refractory neurons, respectively. Here we show that, in a SIRS random network epidemic model for neural activity, self-sustained oscillations appear in a restricted parameter region of the transition probabilities. This could explain the role of synchronized oscillations as a discriminant process for internal or external stimuli in brain dynamics. (C) 2011 Elsevier Ltd. All rights reserved.This work was supported by grant from the Universidad Politecnica de Valencia PAID-06-09 ref: 2588 and FIS Research Grant PI10/01433 from the Instituto de Salud Carlos III.Acedo Rodríguez, L.; Moraño Fernández, JA. (2013). Brain oscillations in a random neural network. Mathematical and Computer Modelling. 57(7-8):1768-1772. https://doi.org/10.1016/j.mcm.2011.11.02817681772577-

Random Network Models to Predict the Long-Term Impact of HPV Vaccination on Genital Warts

[EN] The Human papillomaviruses (HPV) vaccine induces a herd immunity effect in genital warts when a large number of the population is vaccinated. This aspect should be taken into account when devising new vaccine strategies, like vaccination at older ages or male vaccination. Therefore, it is important to develop mathematical models with good predictive capacities. We devised a sexual contact network that was calibrated to simulate the Spanish epidemiology of different HPV genotypes. Through this model, we simulated the scenario that occurred in Australia in 2007, where 12¿13 year-old girls were vaccinated with a three-dose schedule of a vaccine containing genotypes 6 and 11, which protect against genital warts, and also a catch-up program in women up to 26 years of age. Vaccine coverage were 73% in girls with three doses and with coverage rates decreasing with age until 52% for 20¿26 year-olds. A fast 59% reduction in the genital warts diagnoses occurred in the model in the first years after the start of the program, similar to what was described in the literature.We are grateful for the support from Sanofi Pasteur. The authors would also like to thank M. Diaz-Sanchis from the Institut Catala d'Oncologia (ICO) for her useful comments and the data provided on HPV prevalence. We would also like to thank the ICO for the HPV information centre at http://hpvcentre.net.Diez-Domingo, J.; Sánchez-Alonso, V.; Villanueva Micó, RJ.; Acedo Rodríguez, L.; Moraño Fernández, JA.; Villanueva-Oller, J. (2017). Random Network Models to Predict the Long-Term Impact of HPV Vaccination on Genital Warts. Viruses. 9(10). doi:10.3390/v9100300S91

Cellular automata and artificial brain dynamics

[EN] Brain dynamics, neuron activity, information transfer in brains, etc., are a vast field where a large number of questions remain unsolved. Nowadays, computer simulation is playing a key role in the study of such an immense variety of problems. In this work, we explored the possibility of studying brain dynamics using cellular automata, more precisely the famous Game of Life (GoL). The model has some important features (i.e., pseudo-criticality, 1/f noise, universal computing), which represent good reasons for its use in brain dynamics modelling. We have also considered that the model maintains sufficient flexibility. For instance, the timestep is arbitrary, as are the spatial dimensions. As first steps in our study, we used the GoL to simulate the evolution of several neurons (i.e., a statistically significant set, typically a million neurons) and their interactions with the surrounding ones, as well as signal transfer in some simple scenarios. 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Mathematical Modelling in Engineering & Human Behaviour 2018

This book includes papers in cross-disciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cutting-edge research, each chapter is focused on a different problem of modelling human behaviour or engineering problems at different levels. The reader would find this book to be a useful reference in identifying problems of interest in social, medicine and engineering sciences, and in developing mathematical models that could be used to successfully predict behaviours and obtain practical information for specialised practitioners. This book is a must-read for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods