Growth-driven percolations: the dynamics of connectivity in neuronal systems

The quintessential property of neuronal systems is their intensive patterns of selective synaptic connections. The current work describes a physics-based approach to neuronal shape modeling and synthesis and its consideration for the simulation of neuronal development and the formation of neuronal communities. Starting from images of real neurons, geometrical measurements are obtained and used to construct probabilistic models which can be subsequently sampled in order to produce morphologically realistic neuronal cells. Such cells are progressively grown while monitoring their connections along time, which are analysed in terms of percolation concepts. However, unlike traditional percolation, the critical point is verified along the growth stages, not the density of cells, which remains constant throughout the neuronal growth dynamics. It is shown, through simulations, that growing beta cells tend to reach percolation sooner than the alpha counterparts with the same diameter. Also, the percolation becomes more abrupt for higher densities of cells, being markedly sharper for the beta cells. In the addition to the importance of the reported concepts and methods to computational neuroscience, the possibility of reaching percolation through morphological growth of a fixed number of objects represents in itself a novel paradigm of great theoretical and practical interest for the areas of statistical physics and critical phenomena.     

Neuronal devices: understanding neuronal cultures through percolation helps prepare for the next step

Cultures of dissociated neurons are an invaluable experimental tool in studying neuronal networks at an intermediate scale in an in vitro controlled physico-chemical environment. Moreover, current micro-fabrication techniques allow the design of a custom connectivity between subpopulations, which could make it possible to carry out computations with devices involving living cells. The quorum percolation (QP) model has been designed in the context of neurobiology to describe bursts of activity occurring in neuronal cultures from the point of view of collective phenomena rather than from a dynamical synchronization approach. Such a model is well suited to describe triggered activity in neuronal devices, and its generic character points at the necessity of heavily structured devices to go beyond collective bursting. We derive a continuous extension of the QP model, seen as information propagation on a non-metric directed graph, and discuss how its critical behavior might give insight on the connectivity of neuronal networks. The link with metric graphs, embedded in a two-dimensional space, is tackled by the introduction of a geometrical model based upon a random walk, where axon growth is constrained by obstacles such as walls and channels. This provides a starting point for the construction of neuronal devices in vitro capable of more complex behaviors. Lastly, we show how simulations of bursts with a dynamical adaptive integrate-and-fire model can be interpreted in terms of QP, confirming the robustness of this synchronized behavior.     

Symbolic recurrence plots: A new quantitative framework for performance analysis of manufacturing networks

During the last years, the concept of recurrence plots has received considerable interest as a tool for analysing nonlinear and non-stationary time series. However, in the case of discrete-valued observables or variations on very different time scales, problems may occur in direct interpretations of the results of recurrence quantification analysis (RQA). As a potential solution, we suggest combining this approach with ideas from symbolic time series analysis, which allows an arbitrary static or dynamic coarse-graining of the dynamics that goes beyond recent recurrence plot based methods. As an illustrative application, we discuss how the resulting symbolic recurrence plots may be used for a quantitative investigation of the dynamics of discrete-valued inventory levels of cooperating firms in a manufacturing network. Based on discrete-event simulations, measures from traditional RQA are used to evaluate the performance of the individual firms under different production strategies as well as order policies. The results of our investigations are an important step towards an anticipative knowledge about the performance of manufacturing systems under different conditions, which is of major importance for the planning and control of both production and logistics.     

Numerical characteristics of recurrence plots as applied to the evaluation of mechanical damage in materials

The response of a material with a random uniform distribution of pores to a sound impulse was studied. The behavior of the numerical characteristics of the recurrence plots (RP) of the normal displacement vector component depending on the degree of damage was investigated. It was shown that the recurrence quantification analysis (RQA) parameters could be very informative for sonic fault detection.     

Analyzing convergence and synchronicity of business and growth cycles in the euro area using cross recurrence plots

Convergence and synchronisation of business and growth cycles are important issues in the efficient formulation of euro area monetary policy by the European Central Bank (ECB). Although several studies in the economics literature address the issue of synchronicity of growth within the euro area, this is the first study to address this issue using cross recurrence analysis. The main findings are that member state growth rates have largely converged since the introduction of the euro, but there is a wide degree of different synchronisation behaviours which appear to be non-linear in nature. These differences could cause problems in future implementation of a single (ECB-determined)monetary policy in the euro area.     

Interaction of solitons through radiation in optical fibers with randomly varying birefringence

Propagation of solitons in optical fibers is studied taking into account the polarization mode dispersion (PMD) effect. We show that the soliton interaction caused by the radiation emitted by solitons due to the PMD disorder leads to soliton jitter, and we find its statistical properties. The theoretical predictions are justified by direct numerical simulations.     

The influence of connectivity on the firing rate in a neuronal network with electrical and chemical synapses

We study the firing rate properties of a cellular automaton model for a neuronal network with chemical synapses. We propose a simple mechanism in which the nonlocal connections are included, through electrical and chemical synapses. In the latter case, we introduce a time delay which produces self-sustained activity. Nonlocal connections, or shortcuts, are randomly introduced according to a specified connection probability. There is a range of connection probabilities for which neuron firing occurs, as well as a critical probability for which the firing ceases in the absence of time delay. The critical probability for nonlocal shortcuts depends on the network size according to a power-law. We also compute the firing rate amplification factor by varying both the connection probability and the time delay for different network sizes.     

An assessment of coherent coupling through radiation fields in time varying slab waveguides

This paper presents an analytical methodology for analysing two-dimensional, dielectric slab waveguides where the guiding region is subject to abrupt and arbitrary temporal changes in permittivity. The methodology solves Maxwell’s equations in the frequency domain and recovers the solutions for the guided and radiation fields in the time domain using the Laplace transformation (LT). Explicit separation of the complete field solution into a set of guided modes and a radiation field continuum provides a clearer insight into the transient effects present in time-varying dielectric waveguides. In particular, the method is used to assess and quantify the impact of coherent radiation field coupling for arbitrary time variation of the waveguide permittivity.     

Increased phase synchronization of spontaneous calcium oscillations in epileptic human versus normal rat astrocyte cultures

Stochastic synchronization analysis is applied to intracellular calcium oscillations in astrocyte cultures prepared from epileptic human temporal lobe. The same methods are applied to astrocyte cultures prepared from normal rat hippocampus. Our results indicate that phase-repulsive coupling in epileptic human astrocyte cultures is stronger, leading to an increased synchronization in epileptic human compared to normal rat astrocyte cultures.     

Role of spontaneous emission through operating transition in probe-field spectroscopy of two-level systems

Analytical and numerical investigations are carried out of the effect of spontaneous decay through operating transition on the shape of a resonance in the work of a probe field under a strong field applied to the transition. A narrow nonlinear resonance arising on transitions with long-living lower level in the work of a probe field can manifest itself in the form of a traditional minimum and a peak as a function of the first Einstein coefficient for the operating transition. The transformation of the resonance from a minimum to a peak is attributed to the specific character of relaxation of lower-level population beatings on a closed or almost closed transition (the decay of the upper level occurs completely or almost completely through the operating transition).     

Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks

We study the effect of delays on the dynamics of large networks of neurons. We show that delays give rise to a wealth of bifurcations and to a rich phase diagram, which includes oscillatory bumps, traveling waves, lurching waves, standing waves arising via a period-doubling bifurcation, aperiodic regimes, and regimes of multistability. We study the existence and the stability of the various dynamical patterns analytically and numerically in a simplified rate model as a function of the interaction parameters. The results derived in that framework allow us to understand the origin of the diversity of dynamical states observed in large networks of spiking neurons.     

Generation of photon pairs in dispersion shift fibers through spontaneous four wave mixing: Influence of self-phase modulation

Correlated signal and idler photon pairs with small detuning in the telecom band can be generated through spontaneous four-wave mixing in dispersion shift fibers. However, photons originated from other nonlinear processes in optical fibers, such as Raman scattering and self-phase modulation, may contaminate the photon pairs. It has been proved that photons produced by Raman scattering are the background noise of photon pairs. Here we show that photons induced by self-phase modulation of pump pulses are another origin of background noise. After studying the dependence of self-phase modulation induced photons in signal and idler bands, we demonstrate that the quantum correlation of photon pairs can be degraded by the self-phase modulation effect. The investigations are useful for characterizing and optimizing an all fiber source of photon pairs.     

Sub region-specific modulation of synchronous neuronal burst firing after a kainic acid insult in organotypic hippocampal cultures

Background  

Excitotoxicity occurs in a number of pathogenic states including stroke and epilepsy. The adaptations of neuronal circuits in response to such insults may be expected to play an underlying role in pathogenesis. Synchronous neuronal firing can be induced in isolated hippocampal slices and involves all regions of this structure, thereby providing a measure of circuit activity. The effect of an excitotoxic insult (kainic acid, KA) on Mg²⁺-free-induced synchronized neuronal firing was tested in organotypic hippocampal culture by measuring extracellular field activity in CA1 and CA3.     

PtPb nanoparticle electrocatalysts: control of activity through synthetic methods

Solution phase synthesis of intermetallic nanoparticles without using surfactants (for catalytic applications) and subsequent control of size distribution remains a challenge: of growing interest, but not widely explored yet. To understand the questions in the syntheses of Pt containing intermetallic nanoparticles (as electrocatalysts for direct fuel cells) by using sodium naphthalide as the reducing agent, the effects of the Pt precursors’ organic ligands were investigated. PtPb syntheses were studied as the model case. In particular, methods that lead to nanoparticles that are independent single crystals are desirable. Platinum acetylacetonate, which is soluble in many organic solvents, has ligands that may interfere less with nanoparticle growth and ordering. Interesting trends, contrary to expectations, were observed when precursors were injected into a reducing agent solution at high temperatures. The presence of acetylacetonate, from the precursor, on the nanoparticles was confirmed by ATR, while SEM imaging showed evidence of morphological changes in the nanoparticles with increasing reaction temperature. A definite relationship between domain size and extent of observed residue (organic material and sodium) present on the particles could be established. By varying post-reaction solvent removal techniques, room temperature crystallization of PtPb nanoparticles was also achieved. Electrochemical activity of the nanoparticles was also much higher than that of nanoparticles synthesized by previous reaction schemes using sodium naphthalide as the reducing agent. Along with the above mentioned techniques, BET, TEM, CBED, SAED, and XRD were used as characterization tools for the prepared nanoparticles.     

Analysis of the connectivity and robustness of inter-satellite links in a constellation

In the design of new constellation configurations or research of existing constellation performance,the connectivity and robustness of inter-satellite links (ISL) are needed for analysis.In this paper,graph theory is used to analyze the connectivity and robustness of the ISL in constellations,which are measured under the requirements of a short average distance and a small range of ISL azimuth angles,elevation angles and distances.The method to determine ISL connectivity by using the adjacency matrix of gra...     

A serial functional connectivity MRI study in healthy individuals assessing the variability of connectivity measures: reduced interhemispheric connectivity in the motor network during continuous performance

To date, little data is available on the reproducibility of functional connectivity MRI (fcMRI) studies. Here, we tested the variability and reproducibility of both the functional connectivity itself and different statistical methods to analyze this phenomenon. In the main part of our study, we repeatedly examined two healthy subjects in 10 sessions over 6 months with fcMRI. Cortical areas involved in motor function were examined under two different cognitive states: during continuous performance (CP) of a flexion/extension task of the fingers of the right hand and while subjects were at rest. Connectivity to left primary motor cortex (lSM1) was calculated by correlation analysis. The resulting correlation coefficients were transformed to z-scores of the standard normal distribution. For each subject, multisession statistical analyses were carried out with the z-score maps of the resting state (RS) and the CP experiments. First, voxel based t tests between the two groups of fcMRI experiments were performed. Second, ROI analyses were carried out for contralateral right SM1 and for supplementary motor area (SMA). For both ROI, mean and maximum z-score were calculated for each experiment. Also, the fraction of significantly (P<.05) correlated voxels (FCV) in each ROI was calculated. To evaluate the differences between the RS and the CP condition, paired t tests were performed for the mean and maximum z-scores, and Wilcoxon signed ranks tests for matched pairs were carried out for the FCV. All statistical methods and connectivity measures under investigation yielded a distinct loss in left–right SM1 connectivity under the CP condition. For SMA, interindividual differences were apparent. We therefore repeated the fcMRI experiments and the ROI analyses in a group of seven healthy subjects (including the two subjects of the main study). In this substudy, we were able to verify the reduction of left–right SM1 connectivity during unilateral performance. Still, the direction of SMA to lSM1 connectivity change during the CP condition remained undefined as four subjects showed a connectivity increase and three showed a decrease. In summary, we were able to demonstrate a distinct reduction in left–right SM1 synchrony in the CP condition compared to the RS both in the longitudinal and in the multisubject study. This effect was reproducible with all statistical methods and all measures of connectivity under investigation. We conclude that despite intra- and interindividual variability, serial and cross-sectional assessment of functional connectivity reveals stable and reliable results.     

Direct detection of neuronal activity with MRI: Fantasy, possibility, or reality?

Hemodynamic-based functional magnetic resonance imaging (fMRI) techniques have proven to be extremely robust and sensitive methods for noninvasive detection and mapping of human brain activation. Nevertheless, limitations in temporal and spatial resolution as well as interpretation remain because hemodynamic changes accompanying brain activation are relatively sluggish and variable and therefore imprecise measures of neuronal activity. A hope among brain imagers would be to possess a technique that would allow direct mapping of brain activity with spatial resolution on the order of a cortical column and temporal resolution on the order of an action potential or at least a postsynaptic potential. Recent efforts in understanding the direct effects of neuronal activity on MRI signal have provided some degree of hope for those who want a more precise noninvasive brain activation mapping technique than fMRI as we know it now. While the manner in which electrical currents influence MRI signal is well understood, the manner in which neuronal firing spatially and temporally integrates on the spatial scale of an MRI voxel to produce a magnetic field shift and subsequently an NMR phase and/or magnitude change is not well understood. It is also not established that this field shift would be large or long enough in duration to be detected. The objective of this paper is to provide a perspective of the work that has been performed towards the direction of achieving direct neuronal current imaging with MRI. A specific goal is to further clarify what is understood about the theoretical and practical possibilities of neuronal current imaging. Specifically discussed are modeling efforts, phantom studies, in vitro studies, and human studies.     

On-off intermittency in time series of spontaneous paroxysmal activity in rats with genetic absence epilepsy

In the present paper we consider the on-off intermittency phenomena observed in time series of spontaneous paroxysmal activity in rats with genetic absence epilepsy. The method to register and analyze the electroencephalogram with the help of continuous wavelet transform is also suggested.