Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies

In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of oscillators synchronizes for the static time-average of the topology, then the network will synchronize with the time-varying topology if the time-average is achieved sufficiently fast. Fast switching, fast on the time-scale of the coupled oscillators, overcomes the descychnronizing decoherence suggested by disconnected instantaneous networks. This result agrees in spirit with that of where empirical evidence suggested that a moving averaged graph Laplacian could be used in the master-stability function analysis. A new fast switching stability criterion here-in gives sufficiency of a fast-switching network leading to synchronization. Although this sufficient condition appears to be very conservative, it provides new insights about the requirements for synchronization when the network topology is time-varying. In particular, it can be shown that networks of oscillators can synchronize even if at every point in time the frozen-time network topology is insufficiently connected to achieve synchronization.Comment: Submitted to SIAD

Response of electrically coupled spiking neurons: a cellular automaton approach

Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate {\it vs.} stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. In order to assess the effect of electrical coupling in the sensory periphery, we calculate the response to a Poisson stimulus of a chain of excitable neurons modeled by $n$-state Greenberg-Hastings cellular automata in two approximation levels. The single-site mean field approximation is shown to give poor results, failing to predict the absorbing state of the lattice, while the results for the pair approximation are in good agreement with computer simulations in the whole stimulus range. In particular, the dynamic range is substantially enlarged due to the propagation of excitable waves, which suggests a functional role for lateral electrical coupling. For probabilistic spike propagation the Hill exponent of the response function is $\alpha=1$, while for deterministic spike propagation we obtain $\alpha=1/2$, which is close to the experimental values of the psychophysical Stevens exponents for odor and light intensities. Our calculations are in qualitative agreement with experimental response functions of ganglion cells in the mammalian retina.Comment: 11 pages, 8 figures, to appear in the Phys. Rev.

Dynamic clamp with StdpC software

Dynamic clamp is a powerful method that allows the introduction of artificial electrical components into target cells to simulate ionic conductances and synaptic inputs. This method is based on a fast cycle of measuring the membrane potential of a cell, calculating the current of a desired simulated component using an appropriate model and injecting this current into the cell. Here we present a dynamic clamp protocol using free, fully integrated, open-source software (StdpC, for spike timing-dependent plasticity clamp). Use of this protocol does not require specialist hardware, costly commercial software, experience in real-time operating systems or a strong programming background. The software enables the configuration and operation of a wide range of complex and fully automated dynamic clamp experiments through an intuitive and powerful interface with a minimal initial lead time of a few hours. After initial configuration, experimental results can be generated within minutes of establishing cell recording

Chaotic Desynchronization as the Therapeutic Mechanism of Deep Brain Stimulation

High frequency deep-brain stimulation of the subthalamic nucleus (deep brain stimulation, DBS) relieves many of the symptoms of Parkinson's disease in humans and animal models. Although the treatment has seen widespread use, its therapeutic mechanism remains paradoxical. The subthalamic nucleus is excitatory, so its stimulation at rates higher than its normal firing rate should worsen the disease by increasing subthalamic excitation of the globus pallidus. The therapeutic effectiveness of DBS is also frequency and intensity sensitive, and the stimulation must be periodic; aperiodic stimulation at the same mean rate is ineffective. These requirements are not adequately explained by existing models, whether based on firing rate changes or on reduced bursting. Here we report modeling studies suggesting that high frequency periodic excitation of the subthalamic nucleus may act by desynchronizing the firing of neurons in the globus pallidus, rather than by changing the firing rate or pattern of individual cells. Globus pallidus neurons are normally desynchronized, but their activity becomes correlated in Parkinson's disease. Periodic stimulation may induce chaotic desynchronization by interacting with the intrinsic oscillatory mechanism of globus pallidus neurons. Our modeling results suggest a mechanism of action of DBS and a pathophysiology of Parkinsonism in which synchrony, rather than firing rate, is the critical pathological feature

Synchronization from Second Order Network Connectivity Statistics

We investigate how network structure can influence the tendency for a neuronal network to synchronize, or its synchronizability, independent of the dynamical model for each neuron. The synchrony analysis takes advantage of the framework of second order networks, which defines four second order connectivity statistics based on the relative frequency of two-connection network motifs. The analysis identifies two of these statistics, convergent connections, and chain connections, as highly influencing the synchrony. Simulations verify that synchrony decreases with the frequency of convergent connections and increases with the frequency of chain connections. These trends persist with simulations of multiple models for the neuron dynamics and for different types of networks. Surprisingly, divergent connections, which determine the fraction of shared inputs, do not strongly influence the synchrony. The critical role of chains, rather than divergent connections, in influencing synchrony can be explained by their increasing the effective coupling strength. The decrease of synchrony with convergent connections is primarily due to the resulting heterogeneity in firing rates

Controversies in epilepsy: Debates held during the Fourth International Workshop on Seizure Prediction

Debates on six controversial topics were held during the Fourth International Workshop on Seizure Prediction (IWSP4) convened in Kansas City, KS, USA, July 4–7, 2009. The topics were (1) Ictogenesis: Focus versus Network? (2) Spikes and Seizures: Step-relatives or Siblings? (3) Ictogenesis: A Result of Hyposynchrony? (4) Can Focal Seizures Be Caused by Excessive Inhibition? (5) Do High-Frequency Oscillations Provide Relevant Independent Information? (6) Phase Synchronization: Is It Worthwhile as Measured? This article, written by the IWSP4 organizing committee and the debaters, summarizes the arguments presented during the debates