Biomedical subjects

Theo Geisel

Publications and source records attributed to Theo Geisel.

16 recordsLinked to original sources

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↗

PubMed2005

Advancing the boundaries of high-connectivity network simulation with distributed computing.

The availability of efficient and reliable simulation tools is one of the mission-critical technologies in the fast-moving field of computational neuroscience. Research indicates that higher brain functions emerge from large and complex cortical networks and their interactions. The large number of elements (neurons) combined with the high connectivity (synapses) of the biological network and the specific type of interactions impose severe constraints on the explorable system size that previously have been hard to overcome. Here we present a collection of new techniques combined to a coherent simulation tool removing the fundamental obstacle in the computational study of biological neural networks: the enormous number of synaptic contacts per neuron. Distributing an individual simulation over multiple computers enables the investigation of networks orders of magnitude larger than previously possible. The software scales excellently on a wide range of tested hardware, so it can be used in an interactive and iterative fashion for the development of ideas, and results can be produced quickly even for very large networks. In contrast to earlier approaches, a wide class of neuron models and synaptic dynamics can be represented.

Action Potentials↗

PubMed2004

Long chaotic transients in complex networks.

We show that long chaotic transients dominate the dynamics of randomly diluted networks of pulse-coupled oscillators. This contrasts with the rapid convergence towards limit cycle attractors found in networks of globally coupled units. The lengths of the transients strongly depend on the network connectivity and vary by several orders of magnitude, with maximum transient lengths at intermediate connectivities. The dynamics of the transients exhibit a novel form of robust synchronization. An approximation to the largest Lyapunov exponent characterizing the chaotic nature of the transient dynamics is calculated analytically.

Models, Biological↗

PubMed2004

Topological speed limits to network synchronization.

We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in dependence on the dynamical and network parameters. Furthermore, we show that the speed of synchronization is limited by the network connectivity and remains finite, even if the coupling strength becomes infinite. In addition, our results indicate that synchrony is robust under structural perturbations of the network dynamics.

Models, Biological↗

PubMed2004

Breaking synchrony by heterogeneity in complex networks.

For networks of pulse-coupled oscillators with complex connectivity, we demonstrate that in the presence of coupling heterogeneity precisely timed periodic firing patterns replace the state of global synchrony that exists in homogenous networks only. With increasing disorder, these firing patterns persist until a critical temporal extent is reached that is of the order of the interaction delay. For stronger disorder the periodic firing patterns cease to exist and only asynchronous, aperiodic states are observed. We derive self-consistency equations to predict the precise temporal structure of a pattern from a network of given connectivity and heterogeneity. Moreover, we show how to design heterogeneous coupling architectures to create an arbitrary prescribed pattern.

Models, Biological↗

PubMed2004

Quantum reversibility: is there an echo?

We study the possibility to undo the quantum mechanical evolution in a time reversal experiment. The naive expectation, as reflected in the common terminology ("Loschmidt echo"), is that maximum compensation results if the reversed dynamics extends to the same time as the forward evolution. We challenge this belief and demonstrate that the time t(r) for maximum return probability is in general shorter. We find that t(r) depends on lambda=epsilon(evol)/epsilon(prep), being the ratio of the error in setting the parameters (fields) for the time-reversed evolution to the perturbation which is involved in the preparation process. Our results should be observable in spin-echo experiments where the dynamical irreversibility of quantum phases is measured.

Journal Article↗

PubMed2003

Signatures of classical diffusion in quantum fluctuations of two-dimensional chaotic systems.

We consider a two-dimensional (2D) generalization of the standard kicked rotor and show that it is an excellent model for the study of universal features of 2D quantum systems with underlying diffusive classical dynamics. First we analyze the distribution of wave-function intensities and compare them with the predictions derived in the framework of diffusive disordered samples. Next, we turn the closed system into an open one by constructing a scattering matrix. The distribution of the resonance widths P(Gamma) and Wigner delay times P(tau(W)) are investigated. The forms of these distributions are obtained for different symmetry classes and the traces of classical diffusive dynamics are identified. Our theoretical arguments are supported by extensive numerical calculations.

Journal Article↗

PubMed2003

Shot noise in chaotic cavities from action correlations.

We consider universal shot noise in ballistic chaotic cavities from a semiclassical point of view and show that it is due to action correlations within certain groups of classical trajectories. Using quantum graphs as a model system, we sum these trajectories analytically and find agreement with random-matrix theory. Unlike all action correlations which have been considered before, the correlations relevant for shot noise involve four trajectories and do not depend on the presence of any symmetry.

Journal Article↗

PubMed2003

Unstable attractors induce perpetual synchronization and desynchronization.

Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodic dynamics of the network. Under the influence of arbitrarily weak noise, this synchronization is followed by a desynchronization of clusters, a phenomenon induced by attractors that are unstable. Perpetual synchronization and desynchronization lead to a switching among attractors. This is explained by the geometrical fact, that these unstable attractors are surrounded by basins of attraction of other attractors, whereas the full measure of their own basin is located remote from the attractor. Unstable attractors do not only exist in these systems, but moreover dominate the dynamics for large networks and a wide range of parameters.

Models, Theoretical↗

PubMed2003

The pattern of ocular dominance columns in cat primary visual cortex: intra- and interindividual variability of column spacing and its dependence on genetic background.

We present a comprehensive analysis of the intrinsic variability of the periodicity of ocular dominance columns in cat primary visual cortex (area 17) and its relationship to genetic background and visual experience. We characterized the intra-areal and interindividual variability of column spacing in a large set (n = 49) of ocular dominance patterns adapting a recently developed technique for the two-dimensional analysis of orientation column patterns. Patterns were obtained from three different cat colonies (termed F, M and D), the cats having either normal visual experience or experimentally induced strabismus. Two-dimensional maps of local column spacing were calculated for every pattern. In individual cortices, local column spacings varied by > 50% with the majority of column spacings ranging between 0.6 and 1.5 mm in different animals. In animals from colonies F and M (n = 29), the mean column spacing ranged between 1.03 and 1.27 mm and exhibited no significant differences, either between the two breeds or between strabismic and normal animals. The mean spacing was moderately clustered in the left and right brain hemisphere of individual animals but not in littermates. In animals from colony D (n = 2), average column spacing ranged between 0.73 and 0.95 mm, and was thus significantly different from the distribution of spacings in animals from breeds F and M, suggesting an influence of genetic factors on the layout of ocular dominance columns. Local column spacing exhibited a considerable systematic intra-areal variation, with largest spacings along the representation of the horizontal meridian and smallest spacings along the peripheral representation of the vertical meridian. The total variability of ocular dominance column spacing comprised 24% systematic intra-areal variation, 18% interindividual differences of mean column spacing and 58% nonsystematic intra-areal variability.

Animals↗

PubMed2002

Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators.

For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is determined by a multitude of linear operators. We treat this multioperator problem exactly and show that for inhibitory interactions the synchronous state is stable, independent of the parameters and the network connectivity. In randomly connected networks with strong interactions this synchronous state, displaying regular dynamics, coexists with a balanced state exhibiting irregular dynamics. External signals may switch the network between qualitatively distinct states.

Biological Clocks↗

PubMed2002

Prevalence of unstable attractors in networks of pulse-coupled oscillators.

We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are unstable. These unstable attractors occur in networks of pulse-coupled oscillators, and become prevalent with increasing network size for a wide range of parameters. They are enclosed by basins of attraction of other attractors but are remote from their own basin volume such that arbitrarily small noise leads to a switching among attractors.

Journal Article↗

PubMed2002

Genetic influence on quantitative features of neocortical architecture.

The layout of functional cortical maps exhibits a high degree of interindividual variability that may account for individual differences in sensory and cognitive abilities. By quantitatively assessing the interindividual variability of orientation preference columns in the primary visual cortex, we demonstrate that column sizes and shapes as well as a measure of the homogeneity of column sizes across the visual cortex are significantly clustered in genetically related animals and in the two hemispheres of individual brains. Taking the developmental timetable of column formation into account, our data indicate a substantial genetic influence on the developmental specification of visual cortical architecture and suggest ways in which genetic information may influence an individual's visual abilities.

Animals↗

PubMed2002

Mesoscopic rectifiers based on ballistic transport.

Recent experiments on symmetry-broken mesoscopic semiconductor structures have exhibited an amazing rectifying effect in the transverse current-voltage characteristics with promising prospects for future applications. We present a simple microscopic model, which takes into account the energy dependence of current-carrying modes and explains the rectifying effect by an interplay of fully quantized and quasiclassical transport channels in the system. It also suggests the design of a ballistic rectifier with an optimized rectifying signal and predicts voltage oscillations which may provide an experimental test for the mechanism considered here.

Journal Article↗

PubMed2002

Pattern storage and processing in attractor networks with short-time synaptic dynamics.

Neurophysiological experiments show that the strength of synaptic connections can undergo substantial changes on a short time scale. These changes depend on the history of the presynaptic input. Using mean-field techniques, we study how short-time dynamics of synaptic connections influence the performance of attractor neural networks in terms of their memory capacity and capability to process external signals. For binary discrete-time as well as for firing rate continuous-time neural networks, the fixed points of the network dynamics are shown to be unaffected by synaptic dynamics. However, the stability of patterns changes considerably. Synaptic depression turns out to reduce the storage capacity. On the other hand, synaptic depression is shown to be advantageous for processing of pattern sequences. The analytical results on stability, size of the basins of attraction and on the switching between patterns are complemented by numerical simulations.

Algorithms↗

PubMedDate not supplied

Shaping of receptive fields in the visual cortex during retinal maturation.

We present a computational study of the formation of simple-cell receptive field patterns in the primary visual cortex. Based on the observation that the spatial frequency of the retinal filter increases postnatally, our results explain differences in the time course of the development of orientation selectivity in binocularly deprived and normally reared kittens. Development after eye-opening in normal animals is modelled by training with natural images, whereas in the case of binocular deprivation noise-like stimulation continues. Further, it is shown that different orientation selectivities are obtained for network models trained with natural images in contrast to random phase images of identical second order statistics. The latter finding suggests that higher-order statistics of the inputs influences development of primary visual cortex. Finally, we search for quantities that identify possible signatures of natural image statistics in order to specify the amount of constructiveness that visual experience has on the formation of receptive fields.

Aging↗