Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise

We extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise. The master equation formulation of stochastic neurodynamics represents the state of each population by the number of currently active neurons, and the state transitions are chosen so that deterministic Wilson-Cowan rate equations are recovered in the mean-field limit. We apply phase reduction and averaging methods to a corresponding Langevin approximation of the master equation in order to determine how intrinsic noise disrupts synchronization of the population oscillators driven by a common extrinsic noise source. We illustrate our analysis by considering one of the simplest networks known to generate limit cycle oscillations at the population level, namely, a pair of mutually coupled excitatory (E) and inhibitory (I) subpopulations. We show how the combination of intrinsic independent noise and extrinsic common noise can lead to clustering of the population oscillators due to the multiplicative nature of both noise sources under the Langevin approximation. Finally, we show how a similar analysis can be carried out for another simple population model that exhibits limit cycle oscillations in the deterministic limit, namely, a recurrent excitatory network with synaptic depression; inclusion of synaptic depression into the neural master equation now generates a stochastic hybrid system

Automatic shoe-pattern boundary extraction by image-processing techniques

[[abstract]]A footwear designer digitizes shoe patterns to extract their boundaries, once he finishes 3D shoe-model design, last-bottom flattening, and shoe-pattern making. Shoe-pattern boundaries are then imported to cutting machines to cut material into shoe-pattern shapes. In the shoe-pattern making process, a footwear designer may draw many arcs, lines and pigments on a shoe pattern. Therefore, a shoe pattern has smudges, stains, and marker pen drawings on its surface. It results in the difficulty of automatically digitizing and extracting a shoe-pattern boundary. This study aims to develop an effective image-processing method to automatically extract the boundary of a shoe pattern. In the study, we first use a histogram thresholding technique to segment out a shoe pattern from the scanned input image. Then boundary extraction is applied on the segmented image to detect and smooth the shoe-pattern boundary. Finally, the proposed method is tested and its performance is evaluated. Experimental results indicate that the proposed method is good for automatic shoe-pattern boundary extraction. © 2006 Elsevier Ltd. All rights reserved

Networks of piecewise linear neural mass models

Neural mass models are ubiquitous in large scale brain modelling. At the node level they are written in terms of a set of ordinary differential equations with a nonlinearity that is typically a sigmoidal shape. Using structural data from brain atlases they may be connected into a network to investigate the emergence of functional dynamic states, such as synchrony. With the simple restriction of the classic sigmoidal nonlinearity to a piecewise linear caricature we show that the famous Wilson-Cowan neural mass model can be explicitly analysed at both the node and network level. The construction of periodic orbits at the node level is achieved by patching together matrix exponential solutions, and stability is determined using Floquet theory. For networks with interactions described by circulant matrices, we show that the stability of the synchronous state can be determined in terms of a low-dimensional Floquet problem parameterised by the eigenvalues of the interaction matrix. Moreover, this network Floquet problem is readily solved using linear algebra, to predict the onset of spatio-temporal network patterns arising from a synchronous instability. We further consider the case of a discontinuous choice for the node nonlinearity, namely the replacement of the sigmoid by a Heaviside nonlinearity. This gives rise to a continuous-time switching network. At the node level this allows for the existence of unstable sliding periodic orbits, which we explicitly construct. The stability of a periodic orbit is now treated with a modification of Floquet theory to treat the evolution of small perturbations through switching manifolds via the use of saltation matrices. At the network level the stability analysis of the synchronous state is considerably more challenging. Here we report on the use of ideas originally developed for the study of Glass networks to treat the stability of periodic network states in neural mass models with discontinuous interactions

Central engine afterglow of Gamma-ray Bursts

Before 2004, nearly all GRB afterglow data could be understood in the context of the external shocks model. This situation has changed in the past two years, when it became clear that some afterglow components should be attributed to the activity of the central engine; i.e., the {\it central engine afterglow}. We review here the afterglow emission that is directly related to the GRB central engine. Such an interpretation proposed by Katz, Piran & Sari, peculiar in pre-{\it Swift} era, has become generally accepted now.Comment: 4 pages including 1 figure. Presented at the conference "Astrophysics of Compact Objects" (July 1-7, 2007; Huangshan, China

Synchrony in networks of Franklin bells

The Franklin bell is an electro-mechanical oscillator that can generate a repeating chime in the presence of an electric field. Benjamin Franklin famously used it as a lightning detector. The chime arises from the impact of a metal ball on a metal bell. Thus, a network of Franklin bells can be regarded as a network of impact oscillators. Although the number of techniques for analysing impacting systems has grown in recent years, this has typically focused on low dimensional systems and relatively little attention has been paid to networks. Here we redress this balance with a focus on synchronous oscillatory network states. We first study a single Franklin bell, showing how to construct periodic orbits and how to determine their linear stability and bifurcation. To cope with the non-smooth nature of the impacts we use saltation operators to develop the correct Floquet theory. We further introduce a new smoothing technique that circumvents the need for saltation and that recovers the saltation operators in some appropriate limit. We then consider the dynamics of a network of Franklin bells, showing how the master stability function approach can be adapted to treat the linear stability of the synchronous state for arbitrary network topolo-gies. We use this to determine conditions for network induced instabilities. Direct numerical simulations are shown to be in excellent agreement with theoretical results

Complex patterns of subcellular cardiac alternans

Cardiac alternans, in which the membrane potential and the intracellular calcium concentration exhibit alternating durations and peak amplitudes at consecutive beats, constitute a precursor to fatal cardiac arrhythmia such as sudden cardiac death. A crucial question therefore concerns the onset of cardiac alternans. Typically, alternans are only reported when they are fully developed. Here, we present a modelling approach to explore recently discovered microscopic alternans, which represent one of the earliest manifestations of cardiac alternans. In this case, the regular periodic dynamics of the local intracellular calcium concentration is already unstable, while the whole-cell behaviour suggests a healthy cell state. In particular, we use our model to investigate the impact of calcium diffusion in both the cytosol and the sarcoplasmic reticulum on the formation of microscopic calcium alternans. We find that for dominant cytosolic coupling, calcium alternans emerge via the traditional period doubling bifurcation. In contrast, dominant luminal coupling leads to a novel route to calcium alternans through a saddle-node bifurcation at the network level. Combining semi-analytical and computational approaches, we compute areas of stability in parameter space and find that as we cross from stable to unstable regions, the emergent patterns of the intracellular calcium concentration change abruptly in a fashion that is highly dependent upon position along the stability boundary. Our results demonstrate that microscopic calcium alternans may possess a much richer dynamical repertoire than previously thought and further strengthen the role of luminal calcium in shaping cardiac calcium dynamics

Energy saving evaluation of the ventilated BIPV walls."

ABSTRACT This study integrates photovoltaic (PV) system, building structure, and heat flow mechanism to propose the ventilated building-integrated photovoltaics (BIPV) walls. Energy-saving potential of the ventilated BIPV walls was investigated via engineering considerations and computational fluid dynamics (CFD) simulations. The results show that the heat removal rate and indoor heat gain of the proposed ventilated BIPV walls were dominantly affected by outdoor wind velocity and airflow channel width. Correlations for predicting the heat removal rate and indoor heat gain are introduced. After considering building construction practices, this prototype was transformed into a curtain wall structure that complemented the design of the overall construction

Nonlinear Waves in Disordered Diatomic Granular Chains

We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin", so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: In low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatio-temporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for such a transition. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.Comment: 10 pages, 8 figures (some with multiple parts), to appear in Physical Review E; summary of changes: new title, one new figure, additional discussion of several points (including both background and results