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PubMed1987

Exact results for the average dynamic behavior of some non-linear neural networks.

We have studied the global dynamic behavior of neural-like networks of synchronous threshold elements by writing a master equation as a function of parameter values using statistical methods. Exact results for highly connected networks and no correlation are obtained, showing that in this case (contrary to previous results) the average activity can only display simple stable behaviour, the sole exception being special cases of a slow passage through a tangent bifurcation, and a limit cycle of length two. By introducing an appropriate probabilistic hypothesis, we also study the average activity and correlation for highly connected networks with the topology of a (Cayley) tree. In this case the dynamic is ruled by a pair of coupled equations linking activity and correlation, and the tendency is for the correlation to disappear over time. However, under reasonable biological conditions, this tendency will be extremely slow, giving rise to a region of pseudo-stability.

Animals↗
PubMed1992

Organizing for cancer control. The diffusion of a dynamic innovation in a community cancer network.

This paper examines the diffusion of a "dynamic" innovation--research on the prevention and control of cancer--in a community cancer network. By analyzing the social structures and communication strategies of network members, as well as the attributes of the innovation, the authors explain why this innovation is diffusing more slowly than its "formed" counterpart--research on the treatment of cancer.

Diffusion of Innovation↗
PubMed2005

Characterizing the network topology of the energy landscapes of atomic clusters.

By dividing potential energy landscapes into basins of attractions surrounding minima and linking those basins that are connected by transition state valleys, a network description of energy landscapes naturally arises. These networks are characterized in detail for a series of small Lennard-Jones clusters and show behavior characteristic of small-world and scale-free networks. However, unlike many such networks, this topology cannot reflect the rules governing the dynamics of network growth, because they are static spatial networks. Instead, the heterogeneity in the networks stems from differences in the potential energy of the minima, and hence the hyperareas of their associated basins of attraction. The low-energy minima with large basins of attraction act as hubs in the network. Comparisons to randomized networks with the same degree distribution reveals structuring in the networks that reflects their spatial embedding.

Journal Article↗
PubMed2005

Dynamic rewiring in small world networks.

We investigate equilibrium properties of small world networks, in which both connectivity and spin variables are dynamic, using replicated transfer matrices within the replica symmetric approximation. Population dynamics techniques allow us to examine the order parameters of our system at total equilibrium, probing both spin and graph statistics. Of these, interestingly, the degree distribution is found to acquire a Poisson-like form (both within and outside the ordered phase). Comparison with Glauber simulations confirms our results satisfactorily.

Journal Article↗
PubMed2003

Simulating market dynamics: interactions between consumer psychology and social networks.

Markets can show different types of dynamics, from quiet markets dominated by one or a few products, to markets with continual penetration of new and reintroduced products. In a previous article we explored the dynamics of markets from a psychological perspective using a multi-agent simulation model. The main results indicated that the behavioral rules dominating the artificial consumer's decision making determine the resulting market dynamics, such as fashions, lock-in, and unstable renewal. Results also show the importance of psychological variables like social networks, preferences, and the need for identity to explain the dynamics of markets. In this article we extend this work in two directions. First, we will focus on a more systematic investigation of the effects of different network structures. The previous article was based on Watts and Strogatz's approach, which describes the small-world and clustering characteristics in networks. More recent research demonstrated that many large networks display a scale-free power-law distribution for node connectivity. In terms of market dynamics this may imply that a small proportion of consumers may have an exceptional influence on the consumptive behavior of others (hubs, or early adapters). We show that market dynamics is a self-organized property depending on the interaction between the agents' decision-making process (heuristics), the product characteristics (degree of satisfaction of unit of consumption, visibility), and the structure of interactions between agents (size of network and hubs in a social network).

Computer Simulation↗
PubMed1997

Neural network model of short-term horizontal disparity vergence dynamics.

We present a neural network model of short-term dynamics of the human horizontal vergence system (HVS) and compare its predictions qualitatively and quantitatively with a large variety of horizontal disparity vergence data. The model consists of seven functional stages, namely: (1) computation of instantaneous disparity; (2) generation of a disparity map; (3) conversion of the disparity into a velocity signal; (4) push-pull integration of velocity to generate a position signal; (5) conversion of the position signal to motoneuron/plant activity for each eye; (6) gating of velocity overdrive signal to motoneuron/plant system; and finally (7) discharge path for position cells. Closed-loop (normal binocular viewing) symmetric step and staircase disparity vergence data were collected from three subjects and model parameters were determined to quantitatively match each subject's data. The simulated closed-loop as well as open-loop (disparity clamped viewing) symmetric step, sinusoidal, pulse, staircase, square and ramp wave responses closely resemble experimental results either recorded in our laboratory or reported in the literature. Where possible, the firing pattern of the neurons in the model have been compared to actual cellular recordings reported in the literature. The model provides insights into neural correlates underlying the dynamics of vergence eye movements. It also makes novel predictions about the human vergence system.

Convergence, Ocular↗
PubMed1998

Adapting a feedforward heteroassociative network to Hodgkin-Huxley dynamics.

Using the original McCulloch-Pitts notion of simple on and off spike coding in lieu of rate coding, an Anderson-Kohonen artificial neural network (ANN) associative memory model was ported to a neuronal network with Hodgkin-Huxley dynamics. In the ANN, the use of 0/1 (no-spike/spike) units introduced a cross-talk term that had to be compensated by introducing balanced feedforward inhibition. The resulting ANN showed good capacity and fair selectivity (rejection of unknown input vectors). Translation to the Hodgkin-Huxley model resulted in a network that was functional but not at all robust. Evaluation of the weaknesses of this network revealed that it functioned far better using spike timing, rather than spike occurrence, as the code. The algorithm requires a novel learning algorithm for feedforward inhibition that could be sought physiologically.

Action Potentials↗
PubMed2006

Speed of synchronization in complex networks of neural oscillators: analytic results based on Random Matrix Theory.

We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is determined by multiple operators, for which standard analysis is not suitable. We describe a general nonstandard solution to the multioperator problem. Subsequently, we derive a class of neuronal rise functions for which all stability operators become degenerate and standard eigenvalue analysis becomes a suitable tool. Interestingly, this class is found to consist of networks of leaky integrate-and-fire neurons. For random networks of inhibitory integrate-and-fire neurons, we then develop an analytical approach, based on the theory of random matrices, to precisely determine the eigenvalue distributions of the stability operators. This yields the asymptotic relaxation time for perturbations to the synchronous state which provides the characteristic time scale on which neurons can coordinate their activity in such networks. For networks with finite in-degree, i.e., finite number of presynaptic inputs per neuron, we find a speed limit to coordinating spiking activity. Even with arbitrarily strong interaction strengths neurons cannot synchronize faster than at a certain maximal speed determined by the typical in-degree.

Action Potentials↗
PubMed2006

Time-variant analysis of fast-fMRI and dynamic contrast agent MRI sequences as examples of 4-dimensional image analysis.

OBJECTIVES: Image sequences with time-varying information content need appropriate analysis strategies. The exploration of directed information transfer (interactions) between neuronal assemblies is one of the most important aims of current functional MRI (fMRI) analysis. Additionally, we examined perfusion maps in dynamic contrast agent MRI sequences of stroke patients. In this investigation, the focus centers on distinguishing between brain areas with normal and reduced perfusion on the basis of the dynamics of contrast agent inflow and washout. METHODS: Fast fMRI sequences were analyzed with time-variant Granger causality (tvGC). The tvGC is based on a time-variant autoregressive model and is used for the quantification of the directed information transfer between activated brain areas. Generalized Dynamic Neural Networks (GDNN) with time-variant weights were applied on dynamic contrast agent MRI sequences as a nonlinear operator in order to enhance differences in the signal courses of pixels of normal and injured tissues. RESULTS: A simple motor task (self-paced finger tapping) is used in an fMRI design to investigate directed interactions between defined brain areas. A significant information transfer can be determined for the direction primary motor cortex to supplementary motor area during a short time period of about five seconds after stimulus. The analysis of dynamic contrast agent MRI sequences demonstrates that the trained GDNN enables a reliable tissue classification. Three classes are of interest: normal tissue, tissue at risk for death, and dead tissue. CONCLUSIONS: The time-variant multivariate analysis of directed information transfer derived from fMRI sequences and the computation of perfusion maps by GDNN demonstrate that dynamic analysis methods are essential tools for 4D image analysis.

Cerebrovascular Circulation↗
PubMed2006

Biological network design strategies: discovery through dynamic optimization.

An important challenge in systems biology is the inherent complexity of biological network models, which complicates the task of relating network structure to function and of understanding the conceptual design principles by which a given network operates. Here we investigate an approach to analyze the relationship between a network structure and its function using the framework of optimization. A common feature found in a variety of biochemical networks involves the opposition of a pair of enzymatic chemical modification reactions such as phosphorylation-dephosphorylation or methylation-demethylation. The modification pair frequently adjusts biochemical properties of its target, such as activating and deactivating function. We applied optimization methodology to study a reversible modification network unit commonly found in signal transduction systems, and we explored the use of this methodology to discover design principles. The results demonstrate that different sets of rate constants used to parameterize the same network topology represent different compromises made in the resulting network operating characteristics. Moreover, the same topology can be used to encode different strategies for achieving performance goals. The ability to adopt multiple strategies may lead to significantly improved performance across a range of conditions through rate modulation or evolutionary processes. The optimization framework explored here is a practical approach to support the discovery of design principles in biological networks.

Computer Simulation↗
PubMed2000

Pipe network model for scaling of dynamic interfaces in porous media

We present a numerical study on the dynamics of imbibition fronts in porous media using a pipe network model. This model quantitatively reproduces the anomalous scaling behavior found in imbibition experiments [Phys. Rev. E 52, 5166 (1995)]. Using simple scaling arguments, we derive a new identity among the scaling exponents in agreement with the experimental results.

Journal Article↗
PubMed2006

Computational strategy for discovering druggable gene networks from genome-wide RNA expression profiles.

We propose a computational strategy for discovering gene networks affected by a chemical compound. Two kinds of DNA microarray data are assumed to be used: One dataset is short time-course data that measure responses of genes following an experimental treatment. The other dataset is obtained by several hundred single gene knock-downs. These two datasets provide three kinds of information; (i) A gene network is estimated from time-course data by the dynamic Bayesian network model, (ii) Relationships between the knocked-down genes and their regulatees are estimated directly from knock-down microarrays and (iii) A gene network can be estimated by gene knock-down data alone using the Bayesian network model. We propose a method that combines these three kinds of information to provide an accurate gene network that most strongly relates to the mode-of-action of the chemical compound in cells. This information plays an essential role in pharmacogenomics. We illustrate this method with an actual example where human endothelial cell gene networks were generated from a novel time course of gene expression following treatment with the drug fenofibrate, and from 270 novel gene knock-downs. Finally, we succeeded in inferring the gene network related to PPAR-alpha, which is a known target of fenofibrate.

Bayes Theorem↗
PubMed2002

Epidemic dynamics in finite size scale-free networks.

Many real networks present a bounded scale-free behavior with a connectivity cutoff due to physical constraints or a finite network size. We study epidemic dynamics in bounded scale-free networks with soft and hard connectivity cutoffs. The finite size effects introduced by the cutoff induce an epidemic threshold that approaches zero at increasing sizes. The induced epidemic threshold is very small even at a relatively small cutoff, showing that the neglection of connectivity fluctuations in bounded scale-free networks leads to a strong overestimation of the epidemic threshold. We provide the expression for the infection prevalence and discuss its finite size corrections. The present paper shows that the highly heterogeneous nature of scale-free networks does not allow the use of homogeneous approximations even for systems of a relatively small number of nodes.

Journal Article↗
PubMed2005

Target-specific short-term dynamics are important for the function of synapses in an oscillatory neural network.

Short-term dynamics such as facilitation and depression are present in most synapses and are often target-specific even for synapses from the same type of neuron. We examine the dynamics and possible functions of two synapses from the same presynaptic neuron in the rhythmically active pyloric network of the spiny lobster. Using simultaneous recordings, we show that the synapses from the lateral pyloric (LP) neuron to the pyloric dilator (PD; a member of the pyloric pacemaker ensemble) and the pyloric constrictor (PY) neurons both show short-term depression. However, the postsynaptic potentials produced by the LP-to-PD synapse are larger in amplitude, depress less, and recover faster than those produced by the LP-to-PY synapse. The main function of the LP-to-PD synapse is to slow down the pyloric rhythm. However, in some cases, it slows down the rhythm only when it is fast and has no effect or to speeds up when it is slow. In contrast, the LP-to-PY synapse functions to delay the activity of the PY neuron; this delay increases as the cycle period becomes longer. Using a computational model, we show that the short-term dynamics of synaptic depression observed for each of these synapses are tailored to their individual functions and that replacing the dynamics of either synapse with the other would disrupt these functions. Together, the experimental and modeling results suggest that the target-specific features of short-term synaptic depression are functionally important for synapses efferent from the same presynaptic neuron.

Animals↗
PubMed1999

Neuronal networks in the genetically epilepsy-prone rat.

It is now possible to develop a dynamic neuronal network model for generalized convulsive seizures because of in vivo data recently obtained in a naturally occurring epilepsy model--the genetically epilepsy-prone rats (GEPR-9s). GEPR-9s exhibit audiogenic seizures (AGS) that consist of a sequence of discrete behavioral phases (i.e., wild running, clonus-tonus, and post-ictal depression). The neuronal firing changes in most nuclei implicated in the network during each phase of AGS in behaving GEPR-9s have been examined. The inferior colliculus is critical in AGS initiation, because extensive firing increases in inferior colliculus are observed preceding seizure initiation. The deep layers of superior colliculus (DLSC) are crucial to wild running, based on the emergence of tonic firing of DLSC neurons just preceding this phase. The pontine reticular nucleus (PRF) and periaqueductal gray (PAG) are critical to the clonic-tonic phase, because tonic firing patterns appear in these neurons just prior to this phase. During post-ictal depression all areas except the PRF are quiescent. These temporal relationships suggest that each nucleus plays a specific hierarchic role in each discrete convulsive behavior. Generalized tonic-clonic seizure behavior observed in human epilepsy, in GEPR-9s, and in other seizure models is likely to involve similar neuronal network components. The neurotransmitter mechanisms subserving the abnormal neuronal responses in the GEPR-9 neuronal network involve an increased availability of glutamate and a decrease in the effectiveness of gamma-aminobutyric acid (GABA) in many brain regions. Focal modification of the effects of GABA, glutamate, norepinephrine, or serotonin also modulates the nuclei of the network differentially. Together, these data reveal the anatomic, neurotransmitter, and neurophysiologic mechanisms of the neuronal network hierarchy in GEPR-9s, which is currently the most completely developed of any generalized convulsive model. Differential effects of anticonvulsants on the AGS phases and concomitant differential modifications of neuronal firing are observed on neurons in these network nuclei. With nearly complete identification of the network nuclei, the differential effects of these anticonvulsant drugs on different aspects of neuronal firing in different brain sites indicate that this experimental approach can likely identify the most sensitive therapeutic target for these agents. This concept is potentially vital to developing the most selective treatment of different convulsive behaviors occurring in human epilepsy. The neuronal network for AGS does not require brain structures rostral to the midbrain for seizure expression. However, the forebrain is recruited into an expanded seizure network through AGS repetition ("kindling"), resulting in prolonged AGS, post-tonic clonus, and epileptiform electrographic cortical abnormalities. AGS kindling produces network expansion into medial geniculate body (MGB) and amygdala and involves neuronal firing increases in MGB.

Animals↗
PubMed2002

Decoding of a motor command vector from distributed activity in superior colliculus.

Several alternative methods for decoding the desired motor command vector from neural networks containing distributed, place-coded information have been suggested. The two most widely discussed candidate mechanisms are vector summation (VS) and a center-of-mass (CM) computation. The latter mechanism has also been called vector averaging. The present paper compares the operation of these two methods in a model of an experimentally well-studied neural structure, the superior colliculus (SC). The SC is one structure that has been shown to be responsible for generating saccadic command vectors in the form of distributed neural activity that is topologically arranged across its surface. It has been suggested that the pattern of eye-movement errors obtained following the placement of a collicular lesion can distinguish between these two mechanisms. As a result of this suggestion, the pattern of saccadic errors produced by lesions in the SC have been widely cited to support the CM hypothesis. In the present paper the placement of a discrete lesion is simulated in a recurrent (dynamic) neural network model of the SC. These dynamic connections in the model SC network produce a systematic shift of the locus of distributed activity away from the site of the lesion. The spatiotemporal shift in the location of SC activity then produces a pattern of saccadic errors that appear to support the CM hypothesis, even though ensemble activity in our model colliculus is decoded by VS. This result demonstrates that, when ensemble activity on the SC motor map is dynamically modulated over space and time by intrinsic collicular circuitry, an explicit CM computation is not needed to reproduce the pattern of physiological results that follow focal SC lesions.

Animals↗
PubMed2000

Static and dynamic properties of the backbone network for the irreversible kinetic gelation model

We study by Monte Carlo simulations the fractal nature of the backbone network for the irreversible kinetic gelation model in both two and three dimensions. The fractal dimension of the backbone network generated at the gel point is measured by various methods, and results are found to be consistent with that of the standard percolation backbone. Our observation is different from the previous work in three dimensions, where a distinctly larger value was observed. We also measure the spectral dimension d(B)(s) and the fractal dimension d(B)(w) of random walks on a backbone, defined by, respectively, the probability of random walks returning to the starting point and the rms displacements after t time steps. Results are also found to be consistent with the corresponding percolation values. We therefore conclude that the backbone network of the kinetic gelation model exhibits the same static and dynamic properties as those of the standard percolation backbone.

Journal Article↗
PubMed2005

Isobaric and isochoric fragilities and the influence of volume on the temperature dependence of local segmental relaxation in polyvinylethylene networks.

The ratio of the isochoric and isobaric activation enthalpies at T(g) is used to quantify the relative contributions of the specific volume and temperature to the local segmental dynamics of polyvinylethylene networks. The dynamics of the networks become more dominated by temperature with increasing cross-link density, consistent with an increasing isobaric fragility. We also find a correlation between the isochoric and isobaric fragilities for the polyvinylethylene networks, in accord with a previously reported relationship between these two quantities for polymers and molecular glass-forming liquids [R. Casalini and C. M. Roland, Phys. Rev. E 72, 031503 (2005)].

Journal Article↗