Neural networks with dynamical synapses: from mixed-mode oscillations and spindles to chaos

Understanding of short-term synaptic depression (STSD) and other forms of synaptic plasticity is a topical problem in neuroscience. Here we study the role of STSD in the formation of complex patterns of brain rhythms. We use a cortical circuit model of neural networks composed of irregular spiking excitatory and inhibitory neurons having type 1 and 2 excitability and stochastic dynamics. In the model, neurons form a sparsely connected network and their spontaneous activity is driven by random spikes representing synaptic noise. Using simulations and analytical calculations, we found that if the STSD is absent, the neural network shows either asynchronous behavior or regular network oscillations depending on the noise level. In networks with STSD, changing parameters of synaptic plasticity and the noise level, we observed transitions to complex patters of collective activity: mixed-mode and spindle oscillations, bursts of collective activity, and chaotic behaviour. Interestingly, these patterns are stable in a certain range of the parameters and separated by critical boundaries. Thus, the parameters of synaptic plasticity can play a role of control parameters or switchers between different network states. However, changes of the parameters caused by a disease may lead to dramatic impairment of ongoing neural activity. We analyze the chaotic neural activity by use of the 0-1 test for chaos (Gottwald, G. & Melbourne, I., 2004) and show that it has a collective nature.Comment: 7 pages, Proceedings of 12th Granada Seminar, September 17-21, 201

Critical and resonance phenomena in neural networks

Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural networks with stochastic neurons in the presence of noise, we show that spontaneous appearance of network oscillations occurs as a dynamical (non-equilibrium) phase transition at a critical point determined by the noise level, network structure, the balance between excitatory and inhibitory neurons, and other parameters. We find that the relaxation time of neural activity to a steady state, response to periodic stimuli at the frequency of the oscillations, amplitude of damped oscillations, and stochastic fluctuations of neural activity are dramatically increased when approaching the critical point of the transition.Comment: 8 pages, Proceedings of 12th Granada Seminar, September 17-21, 201

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data

On the canonical map of surfaces with q>=6

We carry out an analysis of the canonical system of a minimal complex surface of general type with irregularity q>0. Using this analysis we are able to sharpen in the case q>0 the well known Castelnuovo inequality K^2>=3p_g+q-7. Then we turn to the study of surfaces with p_g=2q-3 and no fibration onto a curve of genus >1. We prove that for q>=6 the canonical map is birational. Combining this result with the analysis of the canonical system, we also prove the inequality: K^2>=7\chi+2. This improves an earlier result of the first and second author [M.Mendes Lopes and R.Pardini, On surfaces with p_g=2q-3, Adv. in Geom. 10 (3) (2010), 549-555].Comment: Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in the special issue of Science of China Ser.A: Mathematics dedicated to him. V2:some typos have been correcte

The atrial resting potential distribution within a fibrotic zone and its effects on the conduction on non-fibrotic zones: A simulation study

Atrial fibrillation (AF) is a heart condition commonly diagnosed within the clinical praxis. During an AF episode, rapid and irregular heartbeats are present and they underly a complex electrical activity. It is known that the atrial structural alterations play a role in establishing the fibrillatory propagation patterns. However, the specific mechanisms are not fully understood. Fibrosis is a hallmark of AF and it represents structural abnormalities that disturbs the atrial electrical conduction. In this work, the behavior of the cardiomyocytes resting action potential in a fibrotic tissue, under distinct textures, is studied. A computational model of atrial electrophysiology is implemented. For the fibrosis model, spatial complex-order derivatives are used. Several values for the derivative order are tested in order to generate different degrees of structural complexity. The fibrosis model also includes cellular heterogeneity through the presence of fibroblasts coupled to cardiomyocytes. Diffuse, interstitial and compact fibrosis textures are implemented in a 2D domain and the amount of fibrosis is varied. The distribution of the resting potential is assessed using the Shannon entropy and the tissue is stimulated in order to evaluate the conduction velocity. The results indicate that, the distinct fibrosis structural conditions generate a wide range of resting potential distributions: from normal to heavy-tailed. The entropy values indicate the changes in the resting potential distribution when the structural complexity varies. Such analysis evinced that the amount of fibrosis generates specific entropy curves respect the derivative order. Moreover, the conduction velocity outside the fibrotic area is affected by the fibrotic configuration, which evinces the long-range effect of the fractional derivative operator and agrees with experimental observations. These results suggest that the proposed complex-order model can be useful for modeling fibrosis during atrial fibrillation and the entropy approach allows characterizing the wide range of fibrillatory scenarios under distinct fibrosis configurations.info:eu-repo/semantics/publishedVersio

Testing demand responsive shared transport services via agent-based simulations

Demand Responsive Shared Transport DRST services take advantage of Information and Communication Technologies ICT, to provide on demand transport services booking in real time a ride on a shared vehicle. In this paper, an agent-based model ABM is presented to test different the feasibility of different service configurations in a real context. First results show the impact of route choice strategy on the system performance

Exploiting Template Metaprogramming to customize an object-oriented operating system

Nowadays, the growing complexity of embedded systems demands for configurability, variability and reuse. Conditional compilation and object-orientation are two of the most applied approaches in the management of system variability. While the former increases the code management complexity, the latter leverages the needed modularity and adaptability to simplify the development of reusable and customizable software at the expense of performance and memory penalty. This paper shows how C++ TMP (Template Metaprogramming) can be applied to manage the variability of an object-oriented operating system and at the same time get ride out of the performance and memory footprint overhead. In doing so, it will be statically generated only the desired functionalities, thus ensuring that code is optimized and adjusted to application requirements and hardware resources.Fundação para a Ciência e a Tecnologia (FCT