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PubMed1996

Networks with lateral connectivity. I. dynamic properties mediated by the balance of intrinsic excitation and inhibition.

1. We studied the rapid dynamic changes of neuron response properties in the somatosensory cortex by the use of computer simulations. The model consists of three feedforward layers of spiking neurons, corresponding to skin, subcortex, and cortex structures. Measurements and analysis of model activity throughout this work are similar to those used in neurophysiological experiments. 2. The effects of various parameters on response properties of model neurons were investigated. The most important parameters were the lateral excitation and inhibition in the simulated cortical network. 3. The balance between excitation and inhibition is a key factor in determining the stability of the network model. There is a large excitation-inhibition (E-I) parameter region within which the model can stably respond to inputs. 4. The input-output relations and receptive field (RF) sizes of simulated neurons are modifiable by the E-I balance. The shapes of RFs are determined by both feedforward projections and the spatial distribution of lateral connections. 5. We simulated changes in temporal and spatial properties of neurons in response to manipulations that mimic bicuculine methiodide or glutamate application to the cortex. Simulation results agreed well with experimental data, suggesting that cortical transmitter levels play an important role in the dynamic responses of the neural net through their effects on E-I balance. 6. With parameters of the model set to an inhibition-dominant scheme, the model was able to reproduce experimentally observed rapid RF expansions that follow cortical lesion or input denervation. Simulation results also suggested that spontaneous inputs to a sensory system can serve as a source of tonic inhibition in the cortex. 7. We conclude that lateral connections could produce and maintain a cortical network having dynamic properties without the need to invoke synaptic plasticity. Individual neuron properties could be modified by changing the balance of cortical layer excitation and inhibition. In a real brain, this could be achieved either by changing levels of cortical transmitter (gamma-aminobutyric acid. for example) or by changing tonic background input to the cortical network.

Afferent Pathways↗

PubMed1996

Dynamic behavior of a neural network model of locomotor control in the lamprey.

1. Experimental studies have shown that a central pattern generator in the spinal cord of the lamprey can produce the basic rhythm for locomotion. This pattern generator interacts with the reticular neurons forming a spinoreticulospinal loop. To better understand and investigate the mechanisms for locomotor pattern generation in the lamprey, we examine the dynamic behavior of a simplified neural network model representing a unit spinal pattern generator (uPG) and its interaction with the reticular system. We use the techniques of bifurcation analysis and specifically examine the effects on the dynamic behavior of the system of 1) changing tonic drives to the different neurons of the uPG; 2) altering inhibitory and excitatory interconnection strengths among the uPG neurons; and 3) feedforward-feedback interactions between the uPG and the reticular neurons. 2. The model analyzed is a qualitative left-right symmetric network based on proposed functional architecture with one class of phasic reticular neurons and three classes of uPG neurons: excitatory (E), lateral (L), and crossed (C) interneurons. In the model each class is represented by one left and one right neuron. Each neuron has basic passive properties akin to biophysical neurons and receives tonic synaptic drive and weighted synaptic input from other connecting neurons. The neuron's output as a function of voltage is given by a nonlinear function with a strict threshold and saturation. 3. With an appropriate set of parameter values, the voltage of each neuron can oscillate periodically with phase relationships among the different neurons that are qualitatively similar to those observed experimentally. The uPG alone can also oscillate, as observed experimentally in isolated lamprey spinal cords. Varying the parameters can, however, profoundly change the state of the system via different kinds of bifurcations. Change in a single parameter can move the system from nonoscillatory to oscillatory states via different kinds of bifurcations. For some parameter values the system can also exhibit multistable behavior (e.g., an oscillatory state and a nonoscillatory state). The analysis also shows us how the amplitudes of the oscillations vary and the periods of limit cycles change as different bifurcation points are approached. 4. Altering tonic drive to just one class of uPG neurons (without altering the interconnections) can change the state of the system by altering the stability of fixed points, converting fixed points to oscillations, single oscillations to two stable oscillations, etc. Two-parameter bifurcation diagrams show the critical regions in which a balance between the tonic drives is necessary to maintain stable oscillations. A minimum tonic drive is necessary to obtain stable oscillatory output. With appropriate changes in the tonic drives to the L and C neurons, stable oscillatory output can be obtained even after eliminating the E neurons. Indeed, the presence of active E neurons in the biological system does not prove they play a functional role in the system, because tonic drive from other sources can substitute for them. On the other hand, very high excitation of any one class of neurons can terminate oscillations. Appropriate balance of tonic drives to different neuron classes can help sustain stable oscillations for larger tonic drives. Published experimental results concerning changes in amplitude and swimming frequency with increased tonic drives are mimicked by the model's responses to increased tonic drive. 5. Interconnectivity among the neurons plays a crucial role. The analysis indicates that the C and L classes of neurons are essential components of the model network. Sufficient inhibition from the L to C neurons as well as mutual inhibition between the left and right halves is necessary to obtain stable oscillatory output. When the E neurons are present in the model network, they must receive appropriate tonic drive and provide appropriate excitation

Animals↗

PubMed2000

Collaborative activity between parietal and dorso-lateral prefrontal cortex in dynamic spatial working memory revealed by fMRI.

Functional MRI was used to determine how the constituents of the cortical network subserving dynamic spatial working memory respond to two types of increases in task complexity. Participants mentally maintained the most recent location of either one or three objects as the three objects moved discretely in either a two- or three-dimensional array. Cortical activation in the dorsolateral prefrontal (DLPFC) and the parietal cortex increased as a function of the number of object locations to be maintained and the dimensionality of the display. An analysis of the response characteristics of the individual voxels showed that a large proportion were activated only when both the variables imposed the higher level of demand. A smaller proportion were activated specifically in response to increases in task demand associated with each of the independent variables. A second experiment revealed the same effect of dimensionality in the parietal cortex when the movement of objects was signaled auditorily rather than visually, indicating that the additional representational demands induced by 3-D space are independent of input modality. The comodulation of activation in the prefrontal and parietal areas by the amount of computational demand suggests that the collaboration between areas is a basic feature underlying much of the functionality of spatial working memory.

Acoustic Stimulation↗

PubMed2001

Epidemic dynamics and endemic states in complex networks.

We study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks. In networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null. On the contrary, on a wide range of scale-free networks we observe the absence of an epidemic threshold and its associated critical behavior. This implies that scale-free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess. These results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks.

Journal Article↗

PubMed2005

General dynamics of topology and traffic on weighted technological networks.

For most technical networks, the interplay of dynamics, traffic, and topology is assumed crucial to their evolution. In this Letter, we propose a traffic-driven evolution model of weighted technological networks. By introducing a general strength-coupling mechanism under which the traffic and topology mutually interact, the model gives power-law distributions of degree, weight, and strength, as confirmed in many real networks. Particularly, depending on a parameter W that controls the total weight growth of the system, the nontrivial clustering coefficient C, degree assortativity coefficient r, and degree-strength correlation are all consistent with empirical evidence.

Journal Article↗

PubMed2004

Aggregation process on complex networks.

We study the dynamics of the aggregation of particles and the evolution of the mass distribution, on a complex network which is built following the Watts-Strogatz model. The particles perform random walks following the links on the network, and aggregate when they meet other particles. On disordered networks the density of particles decays as t(-1), while on regular networks it decays as t(-1/2). For intermediate levels of network disorder the dynamics follows that of regular networks at intermediate density, and for low density the disorder of the network becomes relevant and the density decays as t(-1). The crossover time between these two regimes scales with network disorder as t approximately p(-2). We study also an annealed model for the aggregation process, in which the quenched disorder of the network is replaced by stochastic long range jumps in the particle dynamics. The annealed model is found to obey a different scaling with network disorder, with a crossover time t approximately p(-1).

Biophysics↗

PubMed1994

Dynamic construction of a neural network from multiple pattern generators in the lobster stomatogastric nervous system.

In the stomatogastric nervous system (STNS) of the lobster Homarus gammarus, the rhythmic discharge of a pair of identified modulatory neurons (PS cells) is able to construct de novo a functional network from neurons otherwise belonging to other functional networks. The PS interneurons are electrically coupled and possess endogenous oscillatory properties that can be activated synaptically by stimulation of an identified sensory pathway. PS neurons themselves project synaptically onto the three major neural networks (esophageal, gastric mill, and pyloric) of the STNS. When a PS is rhythmically active in vitro, either spontaneously (rarely) or in response to direct stimulation, it dramatically restructures the otherwise independent activity patterns of all three target networks. This functional reconfiguration elicited by a single cell does not rely on changes in neuronal allegiance to pre-existing circuits, or on a simple merger of these different circuits. Rather, PS is responsible for the creation of an entirely new motor rhythm in that, via its widespread synaptic connections, the interneuron is able to subjugate the ongoing activity of the three STNS circuits and selectively appropriate individual elements to its own intrinsic rhythm. In addition, PS excites motor neurons that innervate dilator muscles of a valve situated between the esophagus and the stomach. The reorganization of the regional foregut motor rhythms by the interneuron is therefore coordinated to the opening of this valve, which itself carries sensory receptors that have been found to activate bursting in PS. Our data suggest that the role of PS in massively restructuring stomatogastric output is to generate a unique motor pattern appropriate for swallowing-like behavior. In a wider context, moreover, the results demonstrate that a neural network may not exist as a predefined entity within the CNS, but may be dynamically assembled according to changing behavioral circumstances.

Animals↗

PubMed2004

Inaccessibility in online learning of recurrent neural networks.

We apply nonlinear dynamical system techniques to recurrent neural networks. In particular, we numerically analyze the dynamical system characteristics of the online learning process. By introducing the notion of inaccessibility, we show that the learning process is well characterized by strong nonhyperbolicity and inaccessibility, which is a greater uncertainty than chaotic unpredictability. These results are clearly contrasted with a gradient descent dynamics, or ordinary chaos.

Artificial Intelligence↗

PubMed2001

Pore network modelling: determination of the dynamic profiles of the pore diffusivity and its effect on column performance as the loading of the solute in the adsorbed phase 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 ion-exchange particles and along the length of the column as the loading of the adsorbate molecules on the surface of the pores occurred, and, the dynamic adsorptive capacity of the chromatographic column as a function of the design and operational parameters of the chromatographic system. The pore size distribution of the porous adsorbent particles and the chemistry of the adsorption sites were unchanged in the simulations. It was found that for a given column length the dynamic profiles of the pore diffusion coefficient were influenced by: (i) the superficial fluid velocity in the column, (ii) the diameter of the adsorbent particles and (iii) 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 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: (a) the particle diameter and the superficial fluid velocity in the column decreased, and (b) the column length and the pore connectivity increased. In preparative 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↗

PubMed1998

Analysis of the signals generated by networks of neurons coupled to planar arrays of microtransducers in simulated experiments.

Planar microelectrode arrays can be used to characterize the dynamics of networks of neurons reconstituted in vitro. In this paper simulations related to experiments of the electrical activity recording by means of planar arrays of microtransducers coupled to networks of neurons are described. First a detailed model of single and synaptically connected neurons is given, appropriate to computer simulate the action potentials of neuronal populations. Then 'realistic' signals are generated. These signals are intended to reproduce, both in shape and intensity, those recorded by a microelectrode array. Typical experimental conditions are considered, and a detailed analysis given, of the bioelectronic coupling and of its influence on the shape of the recorded signals. Finally, simulated experiments dealing with dorsal root ganglia neurons are described and analysed in comparison with experimental results reported in the literature and obtained in our own laboratory. The effectiveness of the planar microelectrode technique is briefly discussed.

Animals↗

PubMed2005

A population-based model of the nonlinear dynamics of the thalamocortical feedback network displays intrinsic oscillations in the spindling (7-14 Hz) range.

The thalamocortical network is modelled using the Wilson-Cowan equations for neuronal population activity. We show that this population model with biologically derived parameters possesses intrinsic nonlinear oscillatory dynamics, and that the frequency of oscillation lies within the spindle range. Spindle oscillations are an early sleep oscillation characterized by high-frequency bursts of action potentials followed by a period of quiescence, at a frequency of 7-14 Hz. Spindles are generally regarded as being generated by intrathalamic circuitry, as decorticated thalamic slices and the isolated thalamic reticular nucleus exhibit spindles. However, the role of cortical feedback has been shown to regulate and synchronize the oscillation. Previous modelling studies have mainly used conductance-based models and hence the mechanism relied upon the inclusion of ionic currents, particularly the T-type calcium current. Here we demonstrate that spindle-frequency oscillatory activity can also arise from the nonlinear dynamics of the thalamocortical circuit, and we use bifurcation analysis to examine the robustness of this oscillation in terms of the functional range of the parameters used in the model. The results suggest that the thalamocortical circuit has intrinsic nonlinear population dynamics which are capable of providing robust support for oscillatory activity within the frequency range of spindle oscillations.

Animals↗

PubMed1992

Dynamic binding in a neural network for shape recognition.

Given a single view of an object, humans can readily recognize that object from other views that preserve the parts in the original view. Empirical evidence suggests that this capacity reflects the activation of a viewpoint-invariant structural description specifying the object's parts and the relations among them. This article presents a neural network that generates such a description. Structural description is made possible through a solution to the dynamic binding problem: Temporary conjunctions of attributes (parts and relations) are represented by synchronized oscillatory activity among independent units representing those attributes. Specifically, the model uses synchrony (a) to parse images into their constituent parts, (b) to bind together the attributes of a part, and (c) to bind the relations to the parts to which they apply. Because it conjoins independent units temporarily, dynamic binding allows tremendous economy of representation and permits the representation to reflect the attribute structure of the shapes represented.

Depth Perception↗

PubMed1990

Dynamics of small autocatalytic reaction networks--I. Bifurcations, permanence and exclusion.

Catalysis in replication networks has become an important issue in biophysics and other areas of biology. Examples are RNA catalysis, idiotype recognition in the immune response and dynamical models of Maynard-Smith games in sociobiology. Chemical reaction networks describing catalysed, template-induced reproduction of three species are analysed in full generality. The nine-dimensional parameter space is reduced to three relevant angular coordinates which determine completely the phase portraits (PPs) and the bifurcation patterns. All cases are classified and all generic as well as most of the non-generic transitions are listed and described.

Catalysis↗

PubMed1994

Flexible vowel recognition by the generation of dynamic coherence in oscillator neural networks: speaker-independent vowel recognition.

We propose a new model for speaker-independent vowel recognition which uses the flexibility of the dynamic linking that results from the synchronization of oscillating neural units. The system consists of an input layer and three neural layers, which are referred to as the A-, B- and C-centers. The input signals are a time series of linear prediction (LPC) spectrum envelopes of auditory signals. At each time-window within the series, the A-center receives input signals and extracts local peaks of the spectrum envelope, i.e., formants, and encodes them into local groups of independent oscillations. Speaker-independent vowel characteristics are embedded as a connection matrix in the B-center according to statistical data of Japanese vowels. The associative interaction in the B-center and reciprocal interaction between the A- and B-centers selectively activate a vowel as a global synchronized pattern over two centers. The C-center evaluates the synchronized activities among the three formant regions to give the selective output of the category among the five Japanese vowels. Thus, a flexible ability of dynamical linking among features is achieved over the three centers. The capability in the present system was investigated for speaker-independent recognition of Japanese vowels. The system demonstrated a remarkable ability for the recognition of vowels very similar to that of human listeners, including misleading vowels. In addition, it showed stable recognition for unsteady input signals and robustness against background noise. The optimum condition of the frequency of oscillation is discussed in comparison with stimulus-dependent synchronizations observed in neurophysiological experiments of the cortex.

Auditory Cortex↗

PubMed2003

Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell.

The physiological responses of cells to external and internal stimuli are governed by genes and proteins interacting in complex networks whose dynamical properties are impossible to understand by intuitive reasoning alone. Recent advances by theoretical biologists have demonstrated that molecular regulatory networks can be accurately modeled in mathematical terms. These models shed light on the design principles of biological control systems and make predictions that have been verified experimentally.

Animals↗

PubMed2004

Classification of equinus in ambulatory children with cerebral palsy-discrimination between dynamic tightness and fixed contracture.

In this study a generalised dynamic neural network (GDNN) was designed to process gait analysis parameters to evaluate equinus deformity in ambulatory children with cerebral palsy. The aim was to differentiate dynamic calf muscle tightness from fixed muscle contracture. Patients underwent clinical examination and had instrumented gait analysis before evaluating their equinus under anaesthesia and muscle relaxation at the time of surgery to improve gait. The performance of the clinical examination, the subjective interpretation of gait analysis results, and the application of the neural network to assess ankle function were compared to the examination under anaesthesia. Evaluation of equinus by a Neural Network showed high sensitivity and specificity values with a likelihood ratio of +14.63. The results indicate that dynamic calf muscle tightness can be differentiated from fixed calf muscle contracture with considerable precision that might facilitate clinical decision-making.

Algorithms↗

PubMed2003

Random vibrational networks and the renormalization group.

We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several real-space renormalization techniques which can be used to describe this dynamics on general networks, drawing on strong disorder techniques developed for regular lattices. The renormalization group is capable of elucidating the localization properties, and provides, even for specific network instances, a fast approximation technique for determining the spectra which compares well with exact results.

Journal Article↗

PubMed2006

Fifth-order two-dimensional Raman spectroscopy of liquid water, crystalline ice Ih and amorphous ices: sensitivity to anharmonic dynamics and local hydrogen bond network structure.

The theoretical study of off-resonant fifth-order two-dimensional (2D)-Raman spectroscopy is made to analyze the intermolecular dynamics of liquid and solid water. The 2D-Raman spectroscopy is susceptible to the nonlinear anharmonic dynamics and local hydrogen bond structure in water. It is found that the distinct 2D-Raman response appears as the negative signal near the t(2) axis. The origin of this negative signal for t(2)<15 fs is from the nonlinear polarizability in the librational motions, whereas that for 30 fs<t(2)<150 fs is attributed to the anharmonic translational motions. It is found that the mechanical anharmonicity and nonlinear polarizability couplings among modes clearly can be observed as the sum- and difference-frequency peaks in the 2D-Raman spectrum (i.e., Fourier transforms of the response). The 2D-Raman spectroscopies of ice Ih and amorphous ices, i.e., low density, high density, and very high density amorphous ices, are also investigated. It is found that the 2D-Raman spectroscopy is very sensitive to the anisotropy of the structure of ice Ih. The strong hydrogen bond stretching band is seen in the 2D-Raman spectroscopy of the polarization directions parallel to the c axis, whereas the contributions of the librational motion can be also seen in the spectrum with the polarization directions parallel to the a axis. The 2D-Raman spectroscopy is also found to be also very sensitive to the differences in local hydrogen bond network structures in various amorphous phases.

Journal Article↗