Stochastic mean field formulation of the dynamics of diluted neural networks

We consider pulse-coupled Leaky Integrate-and-Fire neural networks with randomly distributed synaptic couplings. This random dilution induces fluctuations in the evolution of the macroscopic variables and deterministic chaos at the microscopic level. Our main aim is to mimic the effect of the dilution as a noise source acting on the dynamics of a globally coupled non-chaotic system. Indeed, the evolution of a diluted neural network can be well approximated as a fully pulse coupled network, where each neuron is driven by a mean synaptic current plus additive noise. These terms represent the average and the fluctuations of the synaptic currents acting on the single neurons in the diluted system. The main microscopic and macroscopic dynamical features can be retrieved with this stochastic approximation. Furthermore, the microscopic stability of the diluted network can be also reproduced, as demonstrated from the almost coincidence of the measured Lyapunov exponents in the deterministic and stochastic cases for an ample range of system sizes. Our results strongly suggest that the fluctuations in the synaptic currents are responsible for the emergence of chaos in this class of pulse coupled networks.Comment: 12 Pages, 4 Figure

Cell assembly dynamics of sparsely-connected inhibitory networks: a simple model for the collective activity of striatal projection neurons

Striatal projection neurons form a sparsely-connected inhibitory network, and this arrangement may be essential for the appropriate temporal organization of behavior. Here we show that a simplified, sparse inhibitory network of Leaky-Integrate-and-Fire neurons can reproduce some key features of striatal population activity, as observed in brain slices [Carrillo-Reid et al., J. Neurophysiology 99 (2008) 1435{1450]. In particular we develop a new metric to determine the conditions under which sparse inhibitory networks form anti-correlated cell assemblies with time-varying activity of individual cells. We found that under these conditions the network displays an input-specific sequence of cell assembly switching, that effectively discriminates similar inputs. Our results support the proposal [Ponzi and Wickens, PLoS Comp Biol 9 (2013) e1002954] that GABAergic connections between striatal projection neurons allow stimulus-selective, temporally-extended sequential activation of cell assemblies. Furthermore, we help to show how altered intrastriatal GABAergic signaling may produce aberrant network-level information processing in disorders such as Parkinson's and Huntington's diseases.Comment: 22 pages, 9 figure

Exact firing time statistics of neurons driven by discrete inhibitory noise

Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre-synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post-synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Our results are not limited to stimulations of infinitesimal amplitude, but they apply as well to finite amplitude post-synaptic potentials, thus being able to capture the effect of rare and large spikes. The developed methods are able to reproduce also the average firing properties of heterogeneous neuronal populations.Comment: 20 pages, 8 Figures, submitted to Scientific Report

Death and rebirth of neural activity in sparse inhibitory networks

In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of the neural activity, as expected, but it can also promote neural reactivation. In particular, for globally coupled systems, the number of firing neurons monotonically reduces upon increasing the strength of inhibition (neurons' death). However, the random pruning of the connections is able to reverse the action of inhibition, i.e. in a sparse network a sufficiently strong synaptic strength can surprisingly promote, rather than depress, the activity of the neurons (neurons' rebirth). Thus the number of firing neurons reveals a minimum at some intermediate synaptic strength. We show that this minimum signals a transition from a regime dominated by the neurons with higher firing activity to a phase where all neurons are effectively sub-threshold and their irregular firing is driven by current fluctuations. We explain the origin of the transition by deriving an analytic mean field formulation of the problem able to provide the fraction of active neurons as well as the first two moments of their firing statistics. The introduction of a synaptic time scale does not modify the main aspects of the reported phenomenon. However, for sufficiently slow synapses the transition becomes dramatic, the system passes from a perfectly regular evolution to an irregular bursting dynamics. In this latter regime the model provides predictions consistent with experimental findings for a specific class of neurons, namely the medium spiny neurons in the striatum.Comment: 19 pages, 10 figures, submitted to NJ

Molino pendular de 8000 Kg/h

El objetivo de este proyecto es el de diseñar un molino para la trituración de arcillas y similares, que permita abarcar un importante sector de mercado en una industria de muy alta importancia en este país, como es la de la fabricación de productos cerámicos para la construcción. Se analizan diferentes tipos de molinos y entre ellos se opta por el pendular, por su mejor economía de molienda. El proyecto abarca el diseño completo de la máquina, en el cual se enfatizan aspectos de crucial importancia como son la reducción del nivel de desgaste de sus elementos a un valor mínimo, en vistas a reducir la necesidad de operaciones de mantenimiento, y la disminución del nivel de ruido y vibraciones transmitidos hasta un nivel mínimo comparado con las máquinas de características similares que se pueden encontrar en el mercado. También se consideran muy especialmente en la ejecución del diseño del molino las indicaciones de las normativas existentes a nivel de prevención de riesgos laborales y uso de la máquina por parte de los trabajadores. Se presentan planos, elaborados mediante Autocad® 2002, del conjunto montado de la máquina, así como despieces detallados que permitan la fabricación de sus principales componentes individuales. Asimismo, se elabora un plan de mantenimiento preventivo de la máquina para asegurar el correcto funcionamiento de la misma durante la vida prevista, que se estima de 10 años previa reposición tecnológica. También se incluye en el proyecto un estudio de viabilidad económica del mismo, que incluye el conjunto de la actividad explotadora que permite fabricar la serie prevista por los estudios de mercado durante los 10 años citados, y que muestra que el proyecto es plenamente rentable

Structural stability of the two-fold singularity

At a two-fold singularity, the velocity vector of a flow switches discontinuously across a codimension one switching manifold, between two directions that both lie tangent to the manifold. Particularly intricate dynamics arises when the local flow curves toward the switching manifold from both sides, a case referred to as the Teixeira singularity. The flow locally performs two different actions: it winds around the singularity by crossing repeatedly through, and passes through the singularity by sliding along, the switching manifold. The case when the number of rotations around the singularity is infinite has been analyzed in detail. Here we study the case when the flow makes a finite, but previously unknown, number of rotations around the singularity between incidents of sliding. We show that the solution is remarkably simple: the maximum and minimum numbers of rotations made anywhere in the flow differ only by one and increase incrementally with a single parameter -the angular jump in the flow direction across the switching manifold at the singularity

Detecting the Planform Changes Due to the Seasonal Flow Fluctuation and 2012 Severe Flood in the Amazon River near Iquitos City, Peru Based on Remote Sensing Image Analysis

The Upper Amazon River forms an anabranching planform, which has been found to have significant changes in migration rate and river morphology. Previous studies have elaborated long-term evolution of the anabranching systems; however, research on the influence of the water level on temporal changes in anabranching is absent. According to the theory of river hydraulics, fluvial scour usually occurs when the shear force possessed by the high flow exceeds the resistance of the streambank. In contrast, deposition occurs when the tractive force of the low flow is insufficient to overcome the forces of gravity and friction. This study investigated the Muyuy anabranching planform change of the Upper Peruvian Amazon River due to the seasonal flow fluctuations and a severe flood in 2012. The Muyuy anabranching area is located 20 km upstream of Iquitos City, Peru. Landsat images from the wet and dry seasons in 2008, 2009, 2012, and 2013 were collected. The images were classified into three land cover classes (water, bare soil, vegetation and others) based on NDVI analysis. Quantitative analysis of the erosion/deposition shows that deposition is more noticeable than erosion in the Muyuy anabranching area. Considerable deposition can be found on the island of the anabranching system, and the streambank erosion occurred in the outer (concave) side of the main channel. This phenomenon of river erosion and deposition consistently occurred in 2008 and 2009 because of the periodical variation among the wet and dry seasons. However, prominent erosion was observed in 2012 and it was recognized to be caused by the severe flood. Furthermore, the extensive island was formed in 2013, which means substantial depositions accumulated in the recession of the 2012 flood