71 research outputs found
Rhythmogenic neuronal networks, pacemakers, and k-cores
Neuronal networks are controlled by a combination of the dynamics of
individual neurons and the connectivity of the network that links them
together. We study a minimal model of the preBotzinger complex, a small
neuronal network that controls the breathing rhythm of mammals through periodic
firing bursts. We show that the properties of a such a randomly connected
network of identical excitatory neurons are fundamentally different from those
of uniformly connected neuronal networks as described by mean-field theory. We
show that (i) the connectivity properties of the networks determines the
location of emergent pacemakers that trigger the firing bursts and (ii) that
the collective desensitization that terminates the firing bursts is determined
again by the network connectivity, through k-core clusters of neurons.Comment: 4+ pages, 4 figures, submitted to Phys. Rev. Let
Renormalized couplings and scaling correction amplitudes in the N-vector spin models on the sc and the bcc lattices
For the classical N-vector model, with arbitrary N, we have computed through
order \beta^{17} the high temperature expansions of the second field derivative
of the susceptibility \chi_4(N,\beta) on the simple cubic and on the body
centered cubic lattices. (The N-vector model is also known as the O(N)
symmetric classical spin Heisenberg model or, in quantum field theory, as the
lattice
O(N) nonlinear sigma model.) By analyzing the expansion of \chi_4(N,\beta) on
the two lattices, and by carefully allowing for the corrections to scaling, we
obtain updated estimates of the critical parameters and more accurate tests of
the hyperscaling relation d\nu(N) +\gamma(N) -2\Delta_4(N)=0 for a range of
values of the spin dimensionality N, including
N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model],
N=2 [the XY model], N=3 [the classical Heisenberg model]. Using the recently
extended series for the susceptibility and for the second correlation moment,
we also compute the dimensionless renormalized four point coupling constants
and some universal ratios of scaling correction amplitudes in fair agreement
with recent renormalization group estimates.Comment: 23 pages, latex, no figure
Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems
High-temperature series are computed for a generalized Ising model with
arbitrary potential. Two specific ``improved'' potentials (suppressing leading
scaling corrections) are selected by Monte Carlo computation. Critical
exponents are extracted from high-temperature series specialized to improved
potentials, achieving high accuracy; our best estimates are:
, , , ,
. By the same technique, the coefficients of the small-field
expansion for the effective potential (Helmholtz free energy) are computed.
These results are applied to the construction of parametric representations of
the critical equation of state. A systematic approximation scheme, based on a
global stationarity condition, is introduced (the lowest-order approximation
reproduces the linear parametric model). This scheme is used for an accurate
determination of universal ratios of amplitudes. A comparison with other
theoretical and experimental determinations of universal quantities is
presented.Comment: 65 pages, 1 figure, revtex. New Monte Carlo data by Hasenbusch
enabled us to improve the determination of the critical exponents and of the
equation of state. The discussion of several topics was improved and the
bibliography was update
Critical behavior of the three-dimensional XY universality class
We improve the theoretical estimates of the critical exponents for the
three-dimensional XY universality class. We find alpha=-0.0146(8),
gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and
delta=4.780(2). We observe a discrepancy with the most recent experimental
estimate of alpha; this discrepancy calls for further theoretical and
experimental investigations. Our results are obtained by combining Monte Carlo
simulations based on finite-size scaling methods, and high-temperature
expansions. Two improved models (with suppressed leading scaling corrections)
are selected by Monte Carlo computation. The critical exponents are computed
from high-temperature expansions specialized to these improved models. By the
same technique we determine the coefficients of the small-magnetization
expansion of the equation of state. This expansion is extended analytically by
means of approximate parametric representations, obtaining the equation of
state in the whole critical region. We also determine the specific-heat
amplitude ratio.Comment: 61 pages, 3 figures, RevTe
Thermodynamic characteristics of the classical n-vector magnetic model in three dimensions
The method of calculating the free energy and thermodynamic characteristics
of the classical n-vector three-dimensional (3D) magnetic model at the
microscopic level without any adjustable parameters is proposed. Mathematical
description is perfomed using the collective variables (CV) method in the
framework of the model approximation. The exponentially decreasing
function of the distance between the particles situated at the N sites of a
simple cubic lattice is used as the interaction potential. Explicit and
rigorous analytical expressions for entropy,internal energy, specific heat near
the phase transition point as functions of the temperature are obtained. The
dependence of the amplitudes of the thermodynamic characteristics of the system
for and on the microscopic parameters of the interaction
potential are studied for the cases and . The obtained
results provide the basis for accurate analysis of the critical behaviour in
three dimensions including the nonuniversal characteristics of the system.Comment: 25 pages, 5 figure
Critical structure factors of bilinear fields in O(N)-vector models
We compute the two-point correlation functions of general quadratic operators
in the high-temperature phase of the three-dimensional O(N) vector model by
using field-theoretical methods. In particular, we study the small- and
large-momentum behavior of the corresponding scaling functions, and give
general interpolation formulae based on a dispersive approach. Moreover, we
determine the crossover exponent associated with the traceless
tensorial quadratic field, by computing and analyzing its six-loop perturbative
expansion in fixed dimension. We find: ,
, and for respectively.Comment: 27 page
Crosstalk between HIV and hepatitis C virus during co-infection
An estimated one-third of individuals positive for HIV are also infected with hepatitis C virus (HCV). Chronic infection with HCV can lead to serious liver disease including cirrhosis and hepatocellular carcinoma. Liver-related disease is among the leading causes of death in patients with HIV, and individuals with HIV and HCV co-infection are found to progress more rapidly to serious liver disease than mono-infected individuals. The mechanism by which HIV affects HCV infection in the absence of immunosuppression by HIV is currently unknown. In a recent article published in BMC Immunology, Qu et al. demonstrated that HIV tat is capable of inducing IP-10 expression. Further, they were able to show that HIV tat, when added to cells, was able to enhance the replication of HCV. Importantly, the increase in HCV replication by tat was found to be dependent on IP-10. This work has important implications for understanding the effect HIV has on the outcome of HCV infection in co-infected individuals. The findings of Qu et al. may inform the design of intervention and treatment strategies for co-infected individuals
Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps
We study crossover phenomena in a model of self-avoiding walks with
medium-range jumps, that corresponds to the limit of an -vector
spin system with medium-range interactions. In particular, we consider the
critical crossover limit that interpolates between the Gaussian and the
Wilson-Fisher fixed point. The corresponding crossover functions are computed
using field-theoretical methods and an appropriate mean-field expansion. The
critical crossover limit is accurately studied by numerical Monte Carlo
simulations, which are much more efficient for walk models than for spin
systems. Monte Carlo data are compared with the field-theoretical predictions
concerning the critical crossover functions, finding a good agreement. We also
verify the predictions for the scaling behavior of the leading nonuniversal
corrections. We determine phenomenological parametrizations that are exact in
the critical crossover limit, have the correct scaling behavior for the leading
correction, and describe the nonuniversal lscrossover behavior of our data for
any finite range.Comment: 43 pages, revte
Dynamic clamp with StdpC software
Dynamic clamp is a powerful method that allows the introduction of artificial electrical components into target cells to simulate ionic conductances and synaptic inputs. This method is based on a fast cycle of measuring the membrane potential of a cell, calculating the current of a desired simulated component using an appropriate model and injecting this current into the cell. Here we present a dynamic clamp protocol using free, fully integrated, open-source software (StdpC, for spike timing-dependent plasticity clamp). Use of this protocol does not require specialist hardware, costly commercial software, experience in real-time operating systems or a strong programming background. The software enables the configuration and operation of a wide range of complex and fully automated dynamic clamp experiments through an intuitive and powerful interface with a minimal initial lead time of a few hours. After initial configuration, experimental results can be generated within minutes of establishing cell recording
On the Critical Exponents for the \Lambda-Transition in Liquid Helium
The use of a new method for summing divergent series makes it possible to
significantly increase the accuracy of determining the critical exponents from
the field theoretical renormalization group. The exponent value \nu=0.6700\pm
0.0006 for the \lambda-transition in liquid helium is in good agreement with
the experiment, but contradicts the last theoretical results based on using
high-temperature series, the Monte Carlo method, and their synthesis.Comment: PDF, 7 page
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