6,412 research outputs found
High Temperature Asymptotics of Orthogonal Mean-Field Spin Glasses
We evaluate the high temperature limit of the free energy of spin glasses on
the hypercube with Hamiltonian , where the
coupling matrix is drawn from certain symmetric orthogonally invariant
ensembles. Our derivation relates the annealed free energy of these models to a
spherical integral, and expresses the limit of the free energy in terms of the
limiting spectral measure of the coupling matrix . As an application, we
derive the limiting free energy of the Random Orthogonal Model (ROM) at high
temperatures, which confirms non-rigorous calculations of Marinari et al.
(1994). Our methods also apply to other well-known models of disordered
systems, including the SK and Gaussian Hopfield models.Comment: 15 pages, 1 figur
Combined study of time-series bifurcation and power spectral behaviour of a thalamo-cortico-thalamic neural mass model
A combined power spectral and time-series bifurcation analysis of a neural mass model is presented. Such 'multi-modal' analytical techniques are being used in several researches to understand Electroencephalograph (EEG) anomalies in brain disorders [1][2], in contrast to 'power spectra-only' analytical studies that were more common during the early days of EEG analysis. In a recent work, a combined analysis of a simple thalamo-cortical neural mass model in context to EEG abnormality in Alzheimer's disease (AD) is presented [3]. The study shows that 'unimodal' analytical techniques such as power spectra-only studies without a simultaneous observation of the time-series model output may lead to anomalous conclusions and hypotheses. Towards this, in this work, a 'multi-modal' analytical technique is applied on a thalamocorticothalamic (tct) model, which was earlier studied using power-spectra analysis only [4]. The tct model is an enhanced version of that used in [3] and is based on biological data available in current literature. Furthermore, it aims to mimic thalalmocortical oscillations such as observed in the EEG of both healthy and diseased brain.
Here, the power spectra of the tct model output is observed within the δ (1-3 Hz), θ (4-7 Hz), α (8-13 Hz), β (14-30 Hz) bands, along with a simultaneous analysis of the time series behaviour, the latter showing three behavioural modes: noisy point-attractor, spindle and limit-cycle. With all parameters at their basal values, the output time series is in a noisy point-attractor mode with maximum power within the alpha band (Figure 1). However the model shifts into a limit cycle oscillatory mode with a decrease in inhibitory connectivity parameters in the model (Figure 1); the corresponding power spectra show an increase in peak power within the θ and δ bands along with a simultaneous decrease in power within the α and β bands. The model behaviour is very much in agreement with in-vitro studies [5] which report an increased theta band power and a simultaneous decreased alpha band power during transition from wakefulness to sleep. Furthermore, the in-vitro time-series are qualitatively very similar to those obtained using the model. Thus, the model indicates a decreased inhibitory activity to be the neural correlate of the transitive state between wakefulness and sleep. On the other hand, increased mean firing activity of the extrinsic model inputs pushes the model, first into a spindling mode, and then into a limit cycle mode. In this state, the power within the delta band shows a significant increase compared to those within the other frequency bands. This behaviour is more similar to in-vivo studies of awake-to-sleep transition as reported in [5]
Quantum bound states for a derivative nonlinear Schrodinger model and number theory
A derivative nonlinear Schrodinger model is shown to support localized N-body
bound states for several ranges (called bands) of the coupling constant eta.
The ranges of eta within each band can be completely determined using number
theoretic concepts such as Farey sequences and continued fractions. For N > 2,
the N-body bound states can have both positive and negative momentum. For eta >
0, bound states with positive momentum have positive binding energy, while
states with negative momentum have negative binding energy.Comment: Revtex, 7 pages including 2 figures, to appear in Mod. Phys. Lett.
Studying the effects of thalamic interneurons in a thalamocortical neural mass model
Neural mass models of the thalamocortical circuitry are
often used to mimic brain activity during sleep and
wakefulness as observed in scalp electroencephalogram
(EEG) signals [1]. It is understood that alpha rhythms
(8-13 Hz) dominate the EEG power-spectra in the resting-state
[2] as well as the period immediately before
sleep [3]. Literature review shows that the thalamic
interneurons (IN) are often ignored in thalamocortical
population models; the emphasis is on the connections
between the thalamo cortical relay (TCR) and the thalamic
reticular nucleus (TRN). In this work, we look into
the effects of the IN cell population on the behaviour of
an existing thalamocortical model containing the TCR
and TRN cell populations [4]. A schematic of the
extended model used in this work is shown in Fig.1.
The model equations are solved in Matlab using the
Runge-Kutta method of the 4th/5th order. The model
shows high sensitivity to the forward and reverse rates
of reactions during synaptic transmission as well as on
the membrane conductance of the cell populations. The
input to the model is a white noise signal simulating
conditions of resting state with eyes closed, a condition
well known to be associated with dominant alpha band
oscillations in EEG e.g. [5]. Thus, the model parameters
are calibrated to obtain a set of basal parameter values
when the model oscillates with a dominant frequency
within the alpha band. The time series plots and the
power spectra of the model output are compared with
those when the IN cell population is disconnected from
the circuit (by setting the inhibitory connectivity parameter
from the IN to the TCR to zero). We observe
(Fig. 2 inset) a significant difference in time series output
of the TRN cell population with and without the IN
cell population in the model; this in spite of the IN
having no direct connectivity to and from the TRN cell
population (Fig. 1). A comparison of the power spectra
behaviour of the model output within the delta
(1-3.5Hz), theta (3.75-7.5Hz), alpha (7.75-13.5Hz) and
beta (13.75-30.5Hz) bands is shown in Fig. 2. Disconnecting
the IN cell population shows a significant drop in the
alpha band power and the dominant frequency of oscillation
now lies within the theta band. An overall ‘slowing’
(left-side shift) of the power spectra is observed with an
increase within the delta and theta bands and a decrease
in the alpha and beta bands. Such a slowing of EEG is a
signature of slow wave sleep in healthy individuals, and
this suggests that the IN cell population may be centrally
involved in the phase transition to slow wave sleep [6]. It
is also characteristic of the waking EEG in Alzheimer’s
disease, and may help us to understand the role of the IN
cell population in modulating TCR and TRN cell behaviour
in pathological brain conditions
Static, non-SUSY -branes in diverse dimensions
We give explicit constructions of static, non-supersymmetric -brane (for
, where is the space-time dimensionality and including
or D-instanton) solutions of type II supergravities in diverse dimensions. A
subclass of these are the static counterpart of the time dependent solutions
obtained in [hep-th/0309202]. Depending on the forms of the non-extremality
function defined in the text, we discuss various possible solutions and
their region of validity. We show how one class of these solutions interpolate
between the -brane--anti -brane solutions and the usual BPS -brane
solutions in , while the other class, although have BPS limits, do not
have such an interpretation. We point out how the time dependent solutions
mentioned above can be obtained by a Wick rotation of one class of these static
solutions. We also discuss another type of solutions which might seem
non-supersymmetric, but we show by a coordinate transformation that they are
nothing but the near horizon limits of the various BPS -branes already
known.Comment: 29 pages, typos corrected, references adde
Two early-stage inverse power-law dyamics in nonlinear complex systems far-from equilibrium
We consider the dynamics of the charge carriers in a tunneling-enhanced
percolation network, named as a Random Resistor cum Tunneling-bond Network
(RRTN), where we allow tunneling in the gap between two randomly thrown nearest
neighbour metallic bonds only. Our earlier studies involve the dc and the ac
nonlinear response, the percolative aspects, dielectric breakdown,
low-temperature variable range hopping (VRH) conduction, etc. in the RRTN. Here
we study the non-equilibrium dynamics of the carriers. With two far-from-
equilibrium, initial inverse power-law relaxations extending over several
decades, the dynamics has a lot of similarities with a wide variety of
naturally occuring avalance-like, run-away phenomena in driven, disordered
systems with statistically correlated randomness. In the power-law regime, the
RRTN violates the Boltzmann's (or Debye) relaxation time approximation
strongly. Beyond this regime, the response relaxes exponentially fast (acquires
one time-scale) to a steady-state, and thus the relaxation approximation
becomes exact.Comment: RevTex4, 6 pages, 4 figure
Building a Spiking Neural Network Model of the Basal Ganglia on SpiNNaker
We present a biologically-inspired and scalable model of the Basal Ganglia (BG) simulated on the SpiNNaker machine, a biologically-inspired low-power hardware platform allowing parallel, asynchronous computing. Our BG model consists of six cell populations, where the neuro-computational unit is a conductance-based Izhikevich spiking neuron; the number of neurons in each population is proportional to that reported in anatomical literature. This model is treated as a single-channel of action-selection in the BG, and is scaled-up to three channels with lateral cross-channel connections. When tested with two competing inputs, this three-channel model demonstrates action-selection behaviour. The SpiNNaker-based model is mapped exactly on to SpineML running on a conventional computer; both model responses show functional and qualitative similarity, thus validating the usability of SpiNNaker for simulating biologically-plausible networks. Furthermore, the SpiNNaker-based model simulates in real time for time-steps 1 ms; power dissipated during model execution is & #x2248;1.8 W
Brane Dynamics in the Randall-Sundrum model, Inflation and Graceful Exit
We study the averaged action of the Randall-Sundrum model with a time
dependent metric ansatz. It can be reformulated in terms of a Brans-Dicke
action with time dependent Newton's constant. We show that the physics of early
universe, particularly inflation, is governed by the Brans-Dicke theory. The
Brans-Dicke scalar, however, quickly settles to its equilibrium value and
decouples from the post-inflationary cosmology. The deceleration parameter is
negative to start with but changes sign before the Brans-Dicke scalar settles
to its equilibrium value. Consequently, the brane metric smoothly exits
inflation. We have also studied the slow-roll inflation in our model and
investigated the spectra of the density perturbation generated by the radion
field and find them consistent with the current observations.Comment: Revised version, Accepted in Class. Quant. Gravit
Novel multi-band quantum soliton states for a derivative nonlinear Schrodinger model
We show that localized N-body soliton states exist for a quantum integrable
derivative nonlinear Schrodinger model for several non-overlapping ranges
(called bands) of the coupling constant \eta. The number of such distinct bands
is given by Euler's \phi-function which appears in the context of number
theory. The ranges of \eta within each band can also be determined completely
using concepts from number theory such as Farey sequences and continued
fractions. We observe that N-body soliton states appearing within each band can
have both positive and negative momentum. Moreover, for all bands lying in the
region \eta > 0, soliton states with positive momentum have positive binding
energy (called bound states), while the states with negative momentum have
negative binding energy (anti-bound states).Comment: LaTeX, 20 pages including 2 figure
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