Sequential Desynchronization in Networks of Spiking Neurons with Partial Reset

The response of a neuron to synaptic input strongly depends on whether or not it has just emitted a spike. We propose a neuron model that after spike emission exhibits a partial response to residual input charges and study its collective network dynamics analytically. We uncover a novel desynchronization mechanism that causes a sequential desynchronization transition: In globally coupled neurons an increase in the strength of the partial response induces a sequence of bifurcations from states with large clusters of synchronously firing neurons, through states with smaller clusters to completely asynchronous spiking. We briefly discuss key consequences of this mechanism for more general networks of biophysical neurons

Wiretapping a hidden network

We consider the problem of maximizing the probability of hitting a strategically chosen hidden virtual network by placing a wiretap on a single link of a communication network. This can be seen as a two-player win-lose (zero-sum) game that we call the wiretap game. The value of this game is the greatest probability that the wiretapper can secure for hitting the virtual network. The value is shown to equal the reciprocal of the strength of the underlying graph. We efficiently compute a unique partition of the edges of the graph, called the prime-partition, and find the set of pure strategies of the hider that are best responses against every maxmin strategy of the wiretapper. Using these special pure strategies of the hider, which we call omni-connected-spanning-subgraphs, we define a partial order on the elements of the prime-partition. From the partial order, we obtain a linear number of simple two-variable inequalities that define the maxmin-polytope, and a characterization of its extreme points. Our definition of the partial order allows us to find all equilibrium strategies of the wiretapper that minimize the number of pure best responses of the hider. Among these strategies, we efficiently compute the unique strategy that maximizes the least punishment that the hider incurs for playing a pure strategy that is not a best response. Finally, we show that this unique strategy is the nucleolus of the recently studied simple cooperative spanning connectivity game

Scale-Free topologies and Activatory-Inhibitory interactions

A simple model of activatory-inhibitory interactions controlling the activity of agents (substrates) through a "saturated response" dynamical rule in a scale-free network is thoroughly studied. After discussing the most remarkable dynamical features of the model, namely fragmentation and multistability, we present a characterization of the temporal (periodic and chaotic) fluctuations of the quasi-stasis asymptotic states of network activity. The double (both structural and dynamical) source of entangled complexity of the system temporal fluctuations, as an important partial aspect of the Correlation Structure-Function problem, is further discussed to the light of the numerical results, with a view on potential applications of these general results.Comment: Revtex style, 12 pages and 12 figures. Enlarged manuscript with major revision and new results incorporated. To appear in Chaos (2006

The Glial Regenerative Response to Central Nervous System Injury Is Enabled by Pros-Notch and Pros-NFκB Feedback

Organisms are structurally robust, as cells accommodate changes preserving structural integrity and function. The molecular mechanisms underlying structural robustness and plasticity are poorly understood, but can be investigated by probing how cells respond to injury. Injury to the CNS induces proliferation of enwrapping glia, leading to axonal re-enwrapment and partial functional recovery. This glial regenerative response is found across species, and may reflect a common underlying genetic mechanism. Here, we show that injury to the Drosophila larval CNS induces glial proliferation, and we uncover a gene network controlling this response. It consists of the mutual maintenance between the cell cycle inhibitor Prospero (Pros) and the cell cycle activators Notch and NFκB. Together they maintain glia in the brink of dividing, they enable glial proliferation following injury, and subsequently they exert negative feedback on cell division restoring cell cycle arrest. Pros also promotes glial differentiation, resolving vacuolization, enabling debris clearance and axonal enwrapment. Disruption of this gene network prevents repair and induces tumourigenesis. Using wound area measurements across genotypes and time-lapse recordings we show that when glial proliferation and glial differentiation are abolished, both the size of the glial wound and neuropile vacuolization increase. When glial proliferation and differentiation are enabled, glial wound size decreases and injury-induced apoptosis and vacuolization are prevented. The uncovered gene network promotes regeneration of the glial lesion and neuropile repair. In the unharmed animal, it is most likely a homeostatic mechanism for structural robustness. This gene network may be of relevance to mammalian glia to promote repair upon CNS injury or disease

On the equivalence of phase-oscillator and integrate-and-fire models

A quantitative comparison of various classes of oscillators (integrate-and-fire, Winfree, and Kuramoto-Daido type) is performed in the weak-coupling limit for a fully connected network of identical units. An almost perfect agreement is found, with only tiny differences among the models. We also show that the regime of self-consistent partial synchronization [SCPS] is rather general and can be observed for arbitrarily small coupling strength in any model class. As a by-product of our study, we are able to show that an integrate-and-fire model with a generic pulse shape can be always transformed into a similar model with $\delta$-pulses and a suitable phase response curve.Comment: 28 pages; 8 figures - accepted in PR

A Spectral Network Model of Pitch Perception

A model of pitch perception, called the Spatial Pitch Network or SPINET model, is developed and analyzed. The model neurally instantiates ideas front the spectral pitch modeling literature and joins them to basic neural network signal processing designs to simulate a broader range of perceptual pitch data than previous spectral models. The components of the model arc interpreted as peripheral mechanical and neural processing stages, which arc capable of being incorporated into a larger network architecture for separating multiple sound sources in the environment. The core of the new model transforms a spectral representation of an acoustic source into a spatial distribution of pitch strengths. The SPINET model uses a weighted "harmonic sieve" whereby the strength of activation of a given pitch depends upon a weighted sum of narrow regions around the harmonics of the nominal pitch value, and higher harmonics contribute less to a pitch than lower ones. Suitably chosen harmonic weighting functions enable computer simulations of pitch perception data involving mistuned components, shifted harmonics, and various types of continuous spectra including rippled noise. It is shown how the weighting functions produce the dominance region, how they lead to octave shifts of pitch in response to ambiguous stimuli, and how they lead to a pitch region in response to the octave-spaced Shepard tone complexes and Deutsch tritones without the use of attentional mechanisms to limit pitch choices. An on-center off-surround network in the model helps to produce noise suppression, partial masking and edge pitch. Finally, it is shown how peripheral filtering and short term energy measurements produce a model pitch estimate that is sensitive to certain component phase relationships.Air Force Office of Scientific Research (F49620-92-J-0225); American Society for Engineering Educatio