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 $H_N(\sigma) = \sigma^T J \sigma$, where the coupling matrix $J$ 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 $J$. 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 pp-branes in diverse dimensions

We give explicit constructions of static, non-supersymmetric $p$-brane (for $p \leq d-4$, where $d$ is the space-time dimensionality and including $p=-1$ 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 $G(r)$ 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 $p$-brane--anti $p$-brane solutions and the usual BPS $p$-brane solutions in $d=10$, 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 $p$-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