5,976 research outputs found
Two distinct desynchronization processes caused by lesions in globally coupled neurons
To accomplish a task, the brain works like a synchronized neuronal network
where all the involved neurons work together. When a lesion spreads in the
brain, depending on its evolution, it can reach a significant portion of
relevant area. As a consequence, a phase transition might occur: the neurons
desynchronize and cannot perform a certain task anymore. Lesions are
responsible for either disrupting the neuronal connections or, in some cases,
for killing the neuron. In this work, we will use a simplified model of
neuronal network to show that these two types of lesions cause different types
of desynchronization.Comment: 5 pages, 3 figure
Some Observations for Mean-Field Spin Glass Models
We obtain bounds to show that the pressure of a two-body, mean-field spin
glass is a Lipschitz function of the underlying distribution of the random
coupling constants, with respect to a particular semi-norm. This allows us to
re-derive a result of Carmona and Hu, on the universality of the SK model, by a
different proof, and to generalize this result to the Viana-Bray model. We also
prove another bound, suitable when the coupling constants are not independent,
which is what is necessary if one wants to consider ``canonical'' instead of
``grand canonical'' versions of the SK and Viana-Bray models. Finally, we
review Viana-Bray type models, using the language of L\'evy processes, which is
natural in this context.Comment: 15 pages, minor revision
Effective transport barriers in nontwist systems
In fluids and plasmas with zonal flow reversed shear, a peculiar kind of transport barrier appears in the shearless region, one that is associated with a proper route of transition to chaos. These barriers have been identified in symplectic nontwist maps that model such zonal flows. We use the so-called standard nontwist map, a paradigmatic example of nontwist systems, to analyze the parameter dependence of the transport through a broken shearless barrier. On varying a proper control parameter, we identify the onset of structures with high stickiness that give rise to an effective barrier near the broken shearless curve. Moreover, we show how these stickiness structures, and the concomitant transport reduction in the shearless region, are determined by a homoclinic tangle of the remaining dominant twin island chains. We use the finite-time rotation number, a recently proposed diagnostic, to identify transport barriers that separate different regions of stickiness. The identified barriers are comparable to those obtained by using finite-time Lyapunov exponents.FAPESPCNPqCAPESMCT/CNEN (Rede Nacional de Fusao)Fundacao AraucariaUS Department of Energy DE-FG05-80ET-53088Physic
Phase synchronization of coupled bursting neurons and the generalized Kuramoto model
Bursting neurons fire rapid sequences of action potential spikes followed by
a quiescent period. The basic dynamical mechanism of bursting is the slow
currents that modulate a fast spiking activity caused by rapid ionic currents.
Minimal models of bursting neurons must include both effects. We considered one
of these models and its relation with a generalized Kuramoto model, thanks to
the definition of a geometrical phase for bursting and a corresponding
frequency. We considered neuronal networks with different connection topologies
and investigated the transition from a non-synchronized to a partially
phase-synchronized state as the coupling strength is varied. The numerically
determined critical coupling strength value for this transition to occur is
compared with theoretical results valid for the generalized Kuramoto model.Comment: 31 pages, 5 figure
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