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PubMed2004

Propagating waves in one-dimensional discrete networks of coupled units.

We investigate the behavior of discrete systems on a one-dimensional lattice composed of localized units interacting with each other through nonlocal, nonlinear reactive dynamics. In the presence of second-order and third-order steps coupling two or three neighboring sites, respectively, we observe, for appropriate initial conditions, the propagation of waves which subsist in the absence of mass transfer by diffusion. For the case of the third-order (bistable) model, a counterintuitive effect is also observed, whereby the homogeneously less stable state invades the more stable one under certain conditions. In the limit of a continuous space the dynamics of these networks is described by a generic evolution equation, from which some analytical predictions can be extracted. The relevance of this mode of information transmission in spatially extended systems of interest in physical chemistry and biology is discussed.

Journal Article↗
PubMed2003

Sandpile on scale-free networks.

We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on scale-free (SF) networks, where the threshold height of each node is distributed heterogeneously, given as its own degree. We find that the avalanche size distribution follows a power law with an exponent tau. Applying the theory of the multiplicative branching process, we obtain the exponent tau and the dynamic exponent z as a function of the degree exponent gamma of SF networks as tau=gamma divided by (gamma-1) and z=(gamma-1) divided by (gamma-2) in the range 2 3, with a logarithmic correction at gamma=3. The analytic solution supports our numerical simulation results. We also consider the case of a uniform threshold, finding that the two exponents reduce to the mean-field ones.

Journal Article↗
PubMed1999

Collective behavior of networks with linear (VLSI) integrate-and-fire neurons.

We analyze in detail the statistical properties of the spike emission process of a canonical integrate-and-fire neuron, with a linear integrator and a lower bound for the depolarization, as often used in VLSI implementations (Mead, 1989). The spike statistics of such neurons appear to be qualitatively similar to conventional (exponential) integrate-and-fire neurons, which exhibit a wide variety of characteristics observed in cortical recordings. We also show that, contrary to current opinion, the dynamics of a network composed of such neurons has two stable fixed points, even in the purely excitatory network, corresponding to two different states of reverberating activity. The analytical results are compared with numerical simulations and are found to be in good agreement.

Afferent Pathways↗
PubMed2005

Entangled networks, synchronization, and optimal network topology.

A new family of graphs, entangled networks, with optimal properties in many respects, is introduced. By definition, their topology is such that it optimizes synchronizability for many dynamical processes. These networks are shown to have an extremely homogeneous structure: degree, node distance, betweenness, and loop distributions are all very narrow. Also, they are characterized by a very interwoven (entangled) structure with short average distances, large loops, and no well-defined community structure. This family of nets exhibits an excellent performance with respect to other flow properties such as robustness against errors and attacks, minimal first-passage time of random walks, efficient communication, etc. These remarkable features convert entangled networks in a useful concept, optimal or almost optimal in many senses, and with plenty of potential applications in computer science or neuroscience.

Animals↗
PubMed2007

The developmental nephrome: systems biology in the developing kidney.

PURPOSE OF REVIEW: A set of important genes and signaling pathways involved in kidney development is emerging from analyses of mutant mice, in-vitro models, and global gene expression patterns. Conversion of data into dynamic models or networks through the synthesis of information at multiple levels is crucial for a better understanding of kidney development. RECENT FINDINGS: Genetic and in-vitro evidence is beginning to provide a limited sense of the network topology in stages of kidney development. Intriguing data from other fields suggest how, with the aid of large-scale gene expression studies, these stages might be represented as dynamic attractor states. It is also suggested how branching morphogenesis of the epithelial ureteric bud may be sustained by an autocatalytic set of proteins whose interactions lead to repeated rounds of tip and stalk generation. Accumulating data in lower organisms suggest network topologies may be quite flexible, and the implications of these results for varieties of tubulogenesis and renal regeneration after acute injury are discussed. SUMMARY: Currently it may be feasible to build tentative dynamic multistage models of nephrogenesis that facilitate experimental thinking. As data accumulate, it may become possible to test their predictive value.

Animals↗
PubMed2003

Global stability of neural networks with distributed delays.

In this paper, a model describing the dynamics of recurrent neural networks with distributed delays is considered. Some sufficient criteria are derived ensuring the global asymptotic stability of distributed-delay recurrent neural networks with more general signal propagation functions by introducing real parameters p>1, q(ij)>0, and r(jj)>0, i,j=1, em leader,n, and applying the properties of the M matrix and inequality techniques. We do not assume that the signal propagation functions satisfy the Lipschitz condition and do not require them to be bounded, differentiable, or strictly increasing. Moreover, the symmetry of the connection matrix is also not necessary. These criteria are independent of the delays and possess infinitely adjustable real parameters, which is important in signal processing, especially in moving image treatment and the design of networks.

Biophysical Phenomena↗
PubMed1998

Neural network model of on-off units in the fly visual system: simulations of dynamic behavior.

We analyze the dynamic properties of a neural network model for on-off spiking neurons recorded in the first optic chiasm of the fly visual system. The model consists of two parallel pathways and three sequential processing stages. The first stage models photoreceptors. At the second stage, the signal is segregated into on- and off-pathways. These pathways are proposed to correspond to two populations of amacrine cells. At the third stage, the on- and off-pathways converge to on-off neurons. Furthermore, according to the model, on-off neurons interact via recurrent connections. This stage is proposed to correspond to lamina L4 neurons. In response to luminance increments and decrements, the model exhibits a three-component response and suggests pathways for each of the components. When stimulated by a train of pulses, the model exhibits fast adaptation for frequencies higher than about 5 Hz. Furthermore, adaptation to on- and off-pulses occurs independently. When the frequency of stimulation is reduced, the unit recovers rapidly from its adapted state. The temporal modulation transfer function has its peak around 7 Hz. The phase characteristics show a phase lead for low temporal frequencies changing to a phase lag for high frequencies. These model predictions are compared with data from Jansonius and van Hateren (1991).

Adaptation, Physiological↗
PubMed1994

Uncovering the synchronization dynamics from correlated neuronal activity quantifies assembly formation.

Synchronous network excitation is believed to play an outstanding role in neuronal information processing. Due to the stochastic nature of the contributing neurons, however, those synchronized states are difficult to detect in electrode recordings. We present a framework and a model for the identification of such network states and of their dynamics in a specific experimental situation. Our approach operationalizes the notion of neuronal groups forming assemblies via synchronization based on experimentally obtained spike trains. The dynamics of such groups is reflected in the sequence of synchronized states, which we describe as a renewal dynamics. We furthermore introduce a rate function which is dependent on the internal network phase that quantifies the activity of neurons contributing to the observed spike train. This constitutes a hidden state model which is formally equivalent to a hidden Markov model, and all its parameters can be accurately determined from the experimental time series using the Baum-Welch algorithm. We apply our method to recordings from the cat visual cortex which exhibit oscillations and synchronizations. The parameters obtained for the hidden state model uncover characteristic properties of the system including synchronization, oscillation, switching, background activity and correlations. In applications involving multielectrode recordings, the extracted models quantify the extent of assembly formation and can be used for a temporally precise localization of system states underlying a specific spike train.

Algorithms↗
PubMedDate not supplied

[Cyberspace and the negotiation of meaning: the social aspects of implementing digital communications networks in public health academic institutions].

This article analyzes social aspects in the incorporation of new information and communications technologies in public health academic institutions. To demarcate the study of these processes and demonstrate the close relationship between their social and technical aspects, the study employs concepts pertaining to "intellectual technologies" and a "critical theory of technology". Theoretical and methodological elements are identified to approach the implementation dynamics of electronic networks in public health institutions, through a discourse analysis of their social actors and the various meanings they attribute to such dynamics Considering discourse as an expression of the relations created during these implementation dynamics, the study seeks a proposal for the ways by which these relations might influence the social and technical dimensions of digital networks.

Computer Communication Networks↗
PubMed1999

Emergence of symmetric, modular, and reciprocal connections in recurrent networks with Hebbian learning.

While learning and development are well characterized in feedforward networks, these features are more difficult to analyze in recurrent networks due to the increased complexity of dual dynamics - the rapid dynamics arising from activation states and the slow dynamics arising from learning or developmental plasticity. We present analytical and numerical results that consider dual dynamics in a recurrent network undergoing Hebbian learning with either constant weight decay or weight normalization. Starting from initially random connections, the recurrent network develops symmetric or near-symmetric connections through Hebbian learning. Reciprocity and modularity arise naturally through correlations in the activation states. Additionally, weight normalization may be better than constant weight decay for the development of multiple attractor states that allow a diverse representation of the inputs. These results suggest a natural mechanism by which synaptic plasticity in recurrent networks such as cortical and brainstem premotor circuits could enhance neural computation and the generation of motor programs.

Animals↗
PubMed2001

Localist attractor networks.

Attractor networks, which map an input space to a discrete output space, are useful for pattern completion--cleaning up noisy or missing input features. However, designing a net to have a given set of attractors is notoriously tricky; training procedures are CPU intensive and often produce spurious attractors and ill-conditioned attractor basins. These difficulties occur because each connection in the network participates in the encoding of multiple attractors. We describe an alternative formulation of attractor networks in which the encoding of knowledge is local, not distributed. Although localist attractor networks have similar dynamics to their distributed counterparts, they are much easier to work with and interpret. We propose a statistical formulation of localist attractor net dynamics, which yields a convergence proof and a mathematical interpretation of model parameters. We present simulation experiments that explore the behavior of localist attractor networks, showing that they yield few spurious attractors, and they readily exhibit two desirable properties of psychological and neurobiological models: priming (faster convergence to an attractor if the attractor has been recently visited) and gang effects (in which the presence of an attractor enhances the attractor basins of neighboring attractors).

Animals↗
PubMed1990

[Cognitive processes and neuronal networks].

It is clear that computers are but a poor brain models: the nervous system has many "processors" (neurons) in parallel, whereas von Neuman's machines work sequentially on a single processor. In complex systems, emergent properties cannot be inferred from the behaviour of single elements. Anthills display collective "meaningful" moves, while each ant seems to obey local interactions only. Likewise, large parallel networks of processing elements elicit emergent properties. Like brains, some of them are self-organizing systems. In large parallel processing networks, each unit performs an elementary computation: adding inputs from other units. Large nets display surprising spontaneous computational abilities: associative memories, classes, generalizations may be seen as emergent properties of the network. Symbols are dynamical entities, whose handing is driven by local interactions of activation/inhibition of related representations. In such models, representations (memories) are distributed in the whole network, as stable configurations. Indeed, the basic properties of representation in connectionist models seem closer to human mental objects than the classic Artificial Intelligence concepts. Connectionist models have been used in many fields, namely simulations of real neural networks, pattern recognition and artificial vision, speech recognition, language understanding and knowledge representation, problem solving... Connectionist models have been thus used in neurobiology as well as cognition. One basic structure seems indeed able to account for a range of cognitive functions, from perception to problem solving and high level cognitive tasks. Nevertheless studies about "pathological" networks are yet rare, still an open field... We explore some of these fields.

Artificial Intelligence↗
PubMed1993

A modified neural network model of tumor cell interactions and subpopulation dynamics.

Tumors consist of phenotypically heterogeneous subpopulations of cells which are frequently affected by both autocrine and paracrine factors. Applying concepts from neural network theory, we have developed a computer model of chemical communication among hypothetical tumor cells, which simulates some of the complex epigenetic behavior of real tumors. Deletion of subpopulations often destabilized the whole population. The impact of deletion of specific subpopulations was affected by (a) which subpopulation was deleted, and (b) the timing of the deletion during tumor progression.

Cell Communication↗
PubMed2005

Costs and effects of chlamydial screening: dynamic versus static modeling.

OBJECTIVE: The objective of this study was to assess the impact of modeling type on the economic evaluation of screening programs for asymptomatic Chlamydia trachomatis infections. STUDY: We compared a stochastic network simulation model (dynamic model) with a decision analysis model (static model) for estimating the cost-effectiveness of an opportunistic screening program. The influence of the model type on the required data, the computed results, and the sensitivity of model parameters were investigated. RESULTS: When compared with static modeling, dynamic modeling yielded different cost-effectiveness ratios and identified other optimal screening strategies as it considers changes in the force of infection caused by screening. However, it is more complex, data- and time-demanding, and more sensitive to some parameters affecting the force of infection than static modeling. CONCLUSIONS: Dynamic models should be applied for the economic evaluation of prevention measures that have the potential to lower the force of infection such as large-scale chlamydial screening programs.

Adolescent↗
PubMed2003

Interface motion and pinning in small-world networks.

We show that the nonequilibrium dynamics of systems with many interacting elements located on a small-world network can be much slower than on regular networks. As an example, we study the phase ordering dynamics of the Ising model on a Watts-Strogatz network, after a quench in the ferromagnetic phase at zero temperature. In one and two dimensions, small-world features produce dynamically frozen configurations, disordered at large length scales, analogous to random field models. This picture differs from the common knowledge (supported by equilibrium results) that ferromagnetic shortcut connections favor order and uniformity. We briefly discuss some implications of these results regarding the dynamics of social changes.

Journal Article↗
PubMed2001

Pore network modelling of affinity chromatography: determination of the dynamic profiles of the pore diffusivity of beta-galactosidase and its effect on column performance as the loading of beta-galactosidase onto anti-beta-galactosidase varies with time.

A three-dimensional pore network model for diffusion in porous adsorbent particles was employed in a dynamic adsorption model that simulates the adsorption of a solute in porous particles packed in a chromatographic column. The solution of the combined model yielded the dynamic profiles of the pore diffusion coefficient of beta-galactosidase along the radius of porous adsorbent particles and along the length of the column as the loading of beta-galactosidase onto anti-beta-galactosidase immobilized on the surface of the pores of the particles occurred, and, the dynamic adsorptive capacity of the chromatographic column as a function of the design and operational parameters of the chromatographic system. It was found that for a given column length the dynamic profiles of the pore diffusion coefficient were influenced by (a) the superficial fluid velocity in the column, (b) the diameter of the adsorbent particles, and (c) the pore connectivity of the porous structure of the adsorbent particles. The effect of the magnitude of the pore connectivity on the dynamic profiles of the pore diffusion coefficient of beta-galactosidase increased as the diameter of the adsorbent particles and the superficial fluid velocity in the column increased. The dynamic adsorptive capacity of the column increased as (i) the particle diameter and the superficial fluid velocity in the column decreased, and (ii) the column length and the pore connectivity increased. In preparative affinity chromatography, it is desirable to obtain high throughputs within acceptable pressure gradients, and this may require the employment of larger diameter adsorbent particles. In such a case, longer column lengths satisfying acceptable pressure gradients with adsorbent particles having higher pore connectivity values could provide high dynamic adsorptive capacities. An alternative chromatographic system could be comprised of a long column packed with large particles which have fractal pores (fractal particles) that have high pore connectivities and which allow high intraparticle diffusional and convective flow mass transfer rates providing high throughputs and high dynamic adsorptive capacities. If large scale monoliths could be made to be reproducible and operationally stable, they could also offer an alternative mode of operation that could provide high throughputs and high dynamic adsorptive capacities.

Adsorption↗
PubMed2002

A computational perspective on the neural basis of multisensory spatial representations.

We argue that current theories of multisensory representations are inconsistent with the existence of a large proportion of multimodal neurons with gain fields and partially shifting receptive fields. Moreover, these theories do not fully resolve the recoding and statistical issues involved in multisensory integration. An alternative theory, which we have recently developed and review here, has important implications for the idea of 'frame of reference' in neural spatial representations. This theory is based on a neural architecture that combines basis functions and attractor dynamics. Basis function units are used to solve the recoding problem, whereas attractor dynamics are used for optimal statistical inferences. This architecture accounts for gain fields and partially shifting receptive fields, which emerge naturally as a result of the network connectivity and dynamics.

Animals↗