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Fred Wolf

Publications and source records attributed to Fred Wolf.

12 recordsLinked to original sources

Unique features of action potential initiation in cortical neurons.

Neurons process and encode information by generating sequences of action potentials. For all spiking neurons, the encoding of single-neuron computations into sequences of spikes is biophysically determined by the cell's action-potential-generating mechanism. It has recently been discovered that apparently minor modifications of this mechanism can qualitatively change the nature of neuronal encoding. Here we quantitatively analyse the dynamics of action potential initiation in cortical neurons in vivo, in vitro and in computational models. Unexpectedly, key features of the initiation dynamics of cortical neuron action potentials--their rapid initiation and variable onset potential--are outside the range of behaviours described by the classical Hodgkin-Huxley theory. We propose a new model based on the cooperative activation of sodium channels that reproduces the observed dynamics of action potential initiation. This new model predicts that Hodgkin-Huxley-type dynamics of action potential initiation can be induced by artificially decreasing the effective density of sodium channels. In vitro experiments confirm this prediction, supporting the hypothesis that cooperative sodium channel activation underlies the dynamics of action potential initiation in cortical neurons.

Action Potentials↗

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↗

Symmetry, multistability, and long-range interactions in brain development.

An analytically tractable class of dynamical models for the pattern of contour detecting neurons in the visual cortex is introduced. A permutation symmetry of the model equations guarantees the emergence of contour detectors for all stimulus orientations. By this symmetry a large number of dynamically degenerate solutions exist that quantitatively reproduce the experimentally observed patterns. Long-range interactions are essential for the stability of these realistic solutions.

Animals↗

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↗

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↗

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↗

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↗

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↗

Diagnoses, syndromes, and diseases: a knowledge representation problem.

Despite their widespread use, the terms "syndrome", "disease" and "diagnosis" are sometimes utilized improperly and ambiguously, compounding the complexities of medical knowledge representation. The definitions and illustrative examples provided here will be useful for developers of diagnostic expert systems. Description of the Problem Representing medical knowledge is a highly complex endeavor. The improper use of the terms "syndrome", "disease" and their relations to "diagnosis" is one of the difficulties with which medical informaticians must deal, especially when developing expert systems to support diagnoses. Although ubiquitous in medical and lay discourse, the term "disease" has no unambiguous, generally accepted definition. How-ever, most of those using this term allow themselves the comfortable delusion that everyone knows what it means. Only sparse and fragmented literature could be found regarding this issue.

Diagnosis↗

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↗

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↗

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↗