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At least 1,261 records · Page 70Linked to original sources
PubMed2005

Clustering and the synchronization of oscillator networks.

By manipulating the clustering coefficient of a network without changing its degree distribution, we examine the effect of clustering on the synchronization of phase oscillators on networks with Poisson and scale-free degree distributions. For both types of networks, increased clustering hinders global synchronization as the network splits into dynamical clusters that oscillate at different frequencies. Surprisingly, in scale-free networks, clustering promotes the synchronization of the most connected nodes (hubs) even though it inhibits global synchronization. As a result, they show an additional, advanced transition instead of a single synchronization threshold. This cluster-enhanced synchronization of hubs may be relevant to the brain that is scale-free and highly clustered.

Journal Article↗
PubMed2005

Epidemic spreading and cooperation dynamics on homogeneous small-world networks.

We introduce a class of small-world networks--homogeneous small-worlds--which, in contrast with the well-known Watts-Strogatz small-worlds, exhibit a homogeneous connectivity distribution, in the sense that all nodes have the same number of connections. This feature allows the investigation of pure small-world effects, detached from any associated heterogeneity. Furthermore, we use at profit the remarkable similarity between the properties of homogeneous small worlds and the heterogeneous small-worlds of Watts-Strogatz to assess the separate roles of heterogeneity and small-world effects. We investigate the dependence on these two mechanisms of the threshold for epidemic outbreaks and also of the coevolution of cooperators and defectors under natural selection. With respect to the well-studied regular homogeneous limits, we find a subtle interplay between these mechanisms. While they both contribute to reduce the threshold for an epidemic outburst, they exhibit opposite behavior in the evolution of cooperation, such that the overall results mask the true nature of their individual contribution to this process.

Journal Article↗
PubMed2006

Aging dynamics and the topology of inhomogenous networks.

We study phase ordering on networks and we establish a relation between the exponent a(x) of the aging part of the integrated auto-response function and the topology of the underlying structures. We show that a(x) > 0 in full generality on networks which are above the lower critical dimension d(L), i.e., where the corresponding statistical model has a phase transition at finite temperature. For discrete symmetry models on finite ramified structures with T(c) = 0, which are at the lower critical dimension d(L), we show that a(x) is expected to vanish. We provide numerical results for the physically interesting case of the 2 - d percolation cluster at or above the percolation threshold, i.e., at or above d(L), and for other networks, showing that the value of a(x) changes according to our hypothesis. For O(N) models we find that the same picture holds in the large-N limit and that a(x) only depends on the spectral dimension of the network.

Journal Article↗
PubMed2001

Dynamical stability conditions for recurrent neural networks with unsaturating piecewise linear transfer functions.

We establish two conditions that ensure the nondivergence of additive recurrent networks with unsaturating piecewise linear transfer functions, also called linear threshold or semilinear transfer functions. As Hahnloser, Sarpeshkar, Mahowald, Douglas, and Seung (2000) showed, networks of this type can be efficiently built in silicon and exhibit the coexistence of digital selection and analog amplification in a single circuit. To obtain this behavior, the network must be multistable and nondivergent, and our conditions allow determining the regimes where this can be achieved with maximal recurrent amplification. The first condition can be applied to nonsymmetric networks and has a simple interpretation of requiring that the strength of local inhibition match the sum over excitatory weights converging onto a neuron. The second condition is restricted to symmetric networks, but can also take into account the stabilizing effect of nonlocal inhibitory interactions. We demonstrate the application of the conditions on a simple example and the orientation-selectivity model of Ben-Yishai, Lev Bar-Or, and Sompolinsky (1995). We show that the conditions can be used to identify in their model regions of maximal orientation-selective amplification and symmetry breaking.

Animals↗
PubMed1997

A model for clinical learning experiences in integrated health care networks.

Clinical learning experiences in nursing education are an essential part of the curriculum. In the changing health care environment, there is a need to evaluate the organization of these experiences. In this article, a model for clinical learning experiences in integrated health care networks is presented. A new approach to clinical instruction is proposed in which students move into integrated health care networks for their entire clinical learning experience (vertical pathway), guided by a clinical teaching team of faculty and clinical experts from the network. The focus of student learning is nurse case management and the provision of coordinated care as individuals and families move into and out of organizations within the network. A horizontal curricular pathway establishes opportunities for students to study the dynamics of multiple networks and their relationship to the broader community.

Case Management↗
PubMed2002

Module dynamics of the GnRH signal transduction network.

We analyse computational modules of a frequency decoding signal transduction network. The gonadotropin releasing hormone (GnRH) signal transduction network mediates the biosynthesis and release of the gonadotropins, luteinizing hormone (LH) and follicle stimulating hormone (FSH). The pulsatile pattern of GnRH production by the hypothalamus has a critical influence on the release and synthesis of gonadotropins in the pituitary. In humans, slower pulses lead to the expression of the beta-subunit of the LH protein and cause anovulation and amenorrhea. Higher frequency pulses lead to expression of the alpha subunit and a hypogonadal state. The frequency sensitivity is a consequence of the structure of the GnRH signal transduction network. We analyse individual components of this network, organized into three network architectures, and describe the frequency-decoding capabilities of each of these modules. We find that these modules are comparable to simple circuit elements, some of which integrate and others which perform as frequency sensitive filters. We propose that the cell computes by exploiting variation in the time scales of protein activation (phosphorylation) and gene expression.

Animals↗
PubMed1990

Complex dynamics and noise in simple neural networks with delayed mixed feedback.

This paper briefly reviews the role of mixed feedback, neural delays, and neural noise in the genesis of complex oscillations in neurological feedback systems. The results are concretely discussed within the context of recurrent inhibition in the mammalian hippocampus, and a hybrid version of the pupil light reflex with externally imposed electronic feedback.

Animals↗
PubMed1997

A stochastic model for interconnected neurons.

A model is proposed to describe the collective behavior of a biologically plausible neural network, composed of interconnected spiking neurons which separately receive external stationary stimulations. The spiking dynamics of each neuron is represented by an hourglass metaphor. This network model was first studied in a special case where the connections are only inhibitory (Cottrell, 1988, 1992). We study the network dynamics as a function of the parameters which quantify the strengths of both inhibitory and excitatory connections. We show that the model exhibits two kinds of limit states. In the first states (convergent case), the system is ergodic and all neurons have a positive mean firing rate. In the other states (divergent case), some neurons become definitively inactive while the sub-network of the active neurons is ergodic. The patterns which result from these divergent states can be seen as a neural coding of the external stimulation by the network. This property is applied to the olfactory system to produce a code for an odor. The role of inhibitory connections in odor discrimination is studied.

Action Potentials↗
PubMed2006

Dynamics and effective topology underlying synchronization in networks of cortical neurons.

Cognitive processes depend on synchronization and propagation of electrical activity within and between neuronal assemblies. In vivo measurements show that the size of individual assemblies depends on their function and varies considerably, but the timescale of assembly activation is in the range of 0.1-0.2 s and is primarily independent of assembly size. Here we use an in vitro experimental model of cortical assemblies to characterize the process underlying the timescale of synchronization, its relationship to the effective topology of connectivity within an assembly, and its impact on propagation of activity within and between assemblies. We show that the basic mode of assembly activation, "network spike," is a threshold-governed, synchronized population event of 0.1-0.2 s duration and follows the logistics of neuronal recruitment in an effectively scale-free connected network. Accordingly, the sequence of neuronal activation within a network spike is nonrandom and hierarchical; a small subset of neurons is consistently recruited tens of milliseconds before others. Theory predicts that scale-free topology allows for synchronization time that does not increase markedly with network size; our experiments with networks of different densities support this prediction. The activity of early-to-fire neurons reliably forecasts an upcoming network spike and provides means for expedited propagation between assemblies. We demonstrate this capacity by observing the dynamics of two artificially coupled assemblies in vitro, using neuronal activity of one as a trigger for electrical stimulation of the other.

Action Potentials↗
PubMed2004

Emergence of complex dynamics in a simple model of signaling networks.

Various physical, social, and biological systems generate complex fluctuations with correlations across multiple time scales. In physiologic systems, these long-range correlations are altered with disease and aging. Such correlated fluctuations in living systems have been attributed to the interaction of multiple control systems; however, the mechanisms underlying this behavior remain unknown. Here, we show that a number of distinct classes of dynamical behaviors, including correlated fluctuations characterized by 1/f scaling of their power spectra, can emerge in networks of simple signaling units. We found that, under general conditions, complex dynamics can be generated by systems fulfilling the following two requirements, (i) a "small-world" topology and (ii) the presence of noise. Our findings support two notable conclusions. First, complex physiologic-like signals can be modeled with a minimal set of components; and second, systems fulfilling conditions i and ii are robust to some degree of degradation (i.e., they will still be able to generate 1/f dynamics).

Mathematics↗
PubMed2006

Spontaneous dynamics of asymmetric random recurrent spiking neural networks.

In this letter, we study the effect of a unique initial stimulation on random recurrent networks of leaky integrate-and-fire neurons. Indeed, given a stochastic connectivity, this so-called spontaneous mode exhibits various nontrivial dynamics. This study is based on a mathematical formalism that allows us to examine the variability of the afterward dynamics according to the parameters of the weight distribution. Under the independence hypothesis (e.g., in the case of very large networks), we are able to compute the average number of neurons that fire at a given time-the spiking activity. In accordance with numerical simulations, we prove that this spiking activity reaches a steady state. We characterize this steady state and explore the transients.

Action Potentials↗
PubMed2003

What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance.

When the local field potential of a cortical network displays coherent fast oscillations ( approximately 40-Hz gamma or approximately 200-Hz sharp-wave ripples), the spike trains of constituent neurons are typically irregular and sparse. The dichotomy between rhythmic local field and stochastic spike trains presents a challenge to the theory of brain rhythms in the framework of coupled oscillators. Previous studies have shown that when noise is large and recurrent inhibition is strong, a coherent network rhythm can be generated while single neurons fire intermittently at low rates compared to the frequency of the oscillation. However, these studies used too simplified synaptic kinetics to allow quantitative predictions of the population rhythmic frequency. Here we show how to derive quantitatively the coherent oscillation frequency for a randomly connected network of leaky integrate-and-fire neurons with realistic synaptic parameters. In a noise-dominated interneuronal network, the oscillation frequency depends much more on the shortest synaptic time constants (delay and rise time) than on the longer synaptic decay time, and approximately 200-Hz frequency can be realized with synaptic time constants taken from slice data. In a network composed of both interneurons and excitatory cells, the rhythmogenesis is a compromise between two scenarios: the fast purely interneuronal mechanism, and the slower feedback mechanism (relying on the excitatory-inhibitory loop). The properties of the rhythm are determined essentially by the ratio of time scales of excitatory and inhibitory currents and by the balance between the mean recurrent excitation and inhibition. Faster excitation than inhibition, or a higher excitation/inhibition ratio, favors the feedback loop and a much slower oscillation (typically in the gamma range).

Action Potentials↗
PubMed1999

Correlation dimension maps of EEG from epileptic absences.

PURPOSE: The understanding of brain activity, and in particular events such as epileptic seizures, lies on the characterisation of the dynamics of the neural networks. The theory of non-linear dynamics provides signal analysis techniques which may give new information on the behaviour of such networks. METHODS: We calculated correlation dimension maps for 19-channel EEG data from 3 patients with a total of 7 absence seizures. The signals were analysed before, during and after the seizures. Phase randomised surrogate data was used to test chaos. RESULTS: In the seizures of two patients we could distinguish two dynamical regions on the cerebral cortex, one that seemed to exhibit chaos whereas the other seemed to exhibit noise. The pattern shown is essentially the same for seizures triggered by hyperventilation, but differ for seizures triggered by light flashes. The chaotic dynamics that one seems to observe is determined by a small number of variables and has low complexity. On the other hand, in the seizures of another patient no chaotic region was found. Before and during the seizures no chaos was found either, in all cases. CONCLUSIONS: The application of non-linear signal analysis revealed the existence of differences in the spatial dynamics associated to absence seizures. This may contribute to the understanding of those seizures and be of assistance in clinical diagnosis.

Adolescent↗
PubMed2001

Diluted neural networks with adapting and correlated synapses.

We consider the dynamics of diluted neural networks with clipped and adapting synapses. Unlike previous studies, the learning rate is kept constant as the connectivity tends to infinity: the synapses evolve on a time scale intermediate between the quenched and annealing limits and all orders of synaptic correlations must be taken into account. The dynamics is solved by mean-field theory, the order parameter for synapses being a function. We describe the effects, in the double dynamics, due to synaptic correlations.

Biophysical Phenomena↗