1,581 research outputs found
Scaling law for the transient behavior of type-II neuron models
We study the transient regime of type-II biophysical neuron models and
determine the scaling behavior of relaxation times near but below the
repetitive firing critical current, . For both
the Hodgkin-Huxley and Morris-Lecar models we find that the critical exponent
is independent of the numerical integration time step and that both systems
belong to the same universality class, with . For appropriately
chosen parameters, the FitzHugh-Nagumo model presents the same generic
transient behavior, but the critical region is significantly smaller. We
propose an experiment that may reveal nontrivial critical exponents in the
squid axon.Comment: 6 pages, 9 figures, accepted for publication in Phys. Rev.
Labyrinthine Turing Pattern Formation in the Cerebral Cortex
I propose that the labyrinthine patterns of the cortices of mammalian brains
may be formed by a Turing instability of interacting axonal guidance species
acting together with the mechanical strain imposed by the interconnecting
axons.Comment: See home page http://lec.ugr.es/~julya
Axon diameters and myelin content modulate microscopic fractional anisotropy at short diffusion times in fixed rat spinal cord
Mapping tissue microstructure accurately and noninvasively is one of the
frontiers of biomedical imaging. Diffusion Magnetic Resonance Imaging (MRI) is
at the forefront of such efforts, as it is capable of reporting on microscopic
structures orders of magnitude smaller than the voxel size by probing
restricted diffusion. Double Diffusion Encoding (DDE) and Double Oscillating
Diffusion Encoding (DODE) in particular, are highly promising for their ability
to report on microscopic fractional anisotropy ({\mu}FA), a measure of the pore
anisotropy in its own eigenframe, irrespective of orientation distribution.
However, the underlying correlates of {\mu}FA have insofar not been studied.
Here, we extract {\mu}FA from DDE and DODE measurements at ultrahigh magnetic
field of 16.4T in the aim to probe fixed rat spinal cord microstructure. We
further endeavor to correlate {\mu}FA with Myelin Water Fraction (MWF) derived
from multiexponential T2 relaxometry, as well as with literature-based
spatially varying axonal diameters. In addition, a simple new method is
presented for extracting unbiased {\mu}FA from three measurements at different
b-values. Our findings reveal strong anticorrelations between {\mu}FA (derived
from DODE) and axon diameter in the distinct spinal cord tracts; a moderate
correlation was also observed between {\mu}FA derived from DODE and MWF. These
findings suggest that axonal membranes strongly modulate {\mu}FA, which - owing
to its robustness towards orientation dispersion effects - reflects axon
diameter much better than its typical FA counterpart. The {\mu}FA exhibited
modulations when measured via oscillating or blocked gradients, suggesting
selective probing of different parallel path lengths and providing insight into
how those modulate {\mu}FA metrics. Our findings thus shed light into the
underlying microstructural correlates of {\mu}FA and are (...
Quantum Gauged Neural Network: U(1) Gauge Theory
A quantum model of neural network is introduced and its phase structure is
examined. The model is an extension of the classical Z(2) gauged neural network
of learning and recalling to a quantum model by replacing the Z(2) variables,
of neurons and of synaptic connections, to the U(1)
phase variables, and .
These U(1) variables describe the phase parts of the wave functions (local
order parameters) of neurons and synaptic connections. The model takes the form
similar to the U(1) Higgs lattice gauge theory, the continuum limit of which is
the well known Ginzburg-Landau theory of superconductivity. Its current may
describe the flow of electric voltage along axons and chemical materials
transfered via synaptic connections. The phase structure of the model at finite
temperatures is examined by the mean-field theory, and Coulomb, Higgs and
confinement phases are obtained. By comparing with the result of the Z(2)
model, the quantum effects is shown to weaken the ability of learning and
recalling.Comment: 8 pages, 4 figures: Revised with a new referenc
Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons
Networks of stochastic spiking neurons are interesting models in the area of
Theoretical Neuroscience, presenting both continuous and discontinuous phase
transitions. Here we study fully connected networks analytically, numerically
and by computational simulations. The neurons have dynamic gains that enable
the network to converge to a stationary slightly supercritical state
(self-organized supercriticality or SOSC) in the presence of the continuous
transition. We show that SOSC, which presents power laws for neuronal
avalanches plus some large events, is robust as a function of the main
parameter of the neuronal gain dynamics. We discuss the possible applications
of the idea of SOSC to biological phenomena like epilepsy and dragon king
avalanches. We also find that neuronal gains can produce collective
oscillations that coexists with neuronal avalanches, with frequencies
compatible with characteristic brain rhythms.Comment: 16 pages, 16 figures divided into 7 figures in the articl
- …