Neural networks with dynamical synapses: from mixed-mode oscillations and spindles to chaos

Understanding of short-term synaptic depression (STSD) and other forms of synaptic plasticity is a topical problem in neuroscience. Here we study the role of STSD in the formation of complex patterns of brain rhythms. We use a cortical circuit model of neural networks composed of irregular spiking excitatory and inhibitory neurons having type 1 and 2 excitability and stochastic dynamics. In the model, neurons form a sparsely connected network and their spontaneous activity is driven by random spikes representing synaptic noise. Using simulations and analytical calculations, we found that if the STSD is absent, the neural network shows either asynchronous behavior or regular network oscillations depending on the noise level. In networks with STSD, changing parameters of synaptic plasticity and the noise level, we observed transitions to complex patters of collective activity: mixed-mode and spindle oscillations, bursts of collective activity, and chaotic behaviour. Interestingly, these patterns are stable in a certain range of the parameters and separated by critical boundaries. Thus, the parameters of synaptic plasticity can play a role of control parameters or switchers between different network states. However, changes of the parameters caused by a disease may lead to dramatic impairment of ongoing neural activity. We analyze the chaotic neural activity by use of the 0-1 test for chaos (Gottwald, G. & Melbourne, I., 2004) and show that it has a collective nature.Comment: 7 pages, Proceedings of 12th Granada Seminar, September 17-21, 201

Critical and resonance phenomena in neural networks

Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural networks with stochastic neurons in the presence of noise, we show that spontaneous appearance of network oscillations occurs as a dynamical (non-equilibrium) phase transition at a critical point determined by the noise level, network structure, the balance between excitatory and inhibitory neurons, and other parameters. We find that the relaxation time of neural activity to a steady state, response to periodic stimuli at the frequency of the oscillations, amplitude of damped oscillations, and stochastic fluctuations of neural activity are dramatically increased when approaching the critical point of the transition.Comment: 8 pages, Proceedings of 12th Granada Seminar, September 17-21, 201

Voyager cartography

The Jovian and Saturnian satellites are being mapped at several scales from Voyager 1 and 2 data. The maps are especially formatted color mosaics, controlled photomosaics, and airbrush maps. At 1:5,000,000 scale, mapping of Io, Europa, and Ganymede is complete. At 1:15,000,000 scale, mapping of Io and Europa is complete, and mapping of Ganymede is approximately complete. A controlled mosaic of Rhea has been compiled as a Digital Image Model (DIM) in the same format as is being used for Mars. The mosaic is being formatted for publication as a two-sheet set (Lambert Azimuthal Equal Area, Mercator, and Polar Stereographic projections). Magnetic tape copies of the DIM have been distributed to regional Planetary Image Facilities and other interested users. The DIM has a scale of 1/16 degree/pixel, corresponding to approximately 833 m/pixel on Rhea. Details of the status of the various map series are reported quarterly to Planetary Geology Principal Investigators

Diagnostics of accelerating plasma Semiannual progress report, 1 Mar. - 31 Aug. 1968

Plasma diagnostics in electromagnetically driven shock tubes using laser scattering methods as compared to spectroscopic technique

Dyons in N=4 Supersymmetric Theories and Three-Pronged Strings

We construct and explore BPS states that preserve 1/4 of supersymmetry in N=4 Yang-Mills theories. Such states are also realized as three-pronged strings ending on D3-branes. We correct the electric part of the BPS equation and relate its solutions to the unbroken abelian gauge group generators. Generic 1/4-BPS solitons are not spherically symmetric, but consist of two or more dyonic components held apart by a delicate balance between static electromagnetic force and scalar Higgs force. The instability previously found in three-pronged string configurations is due to excessive repulsion by one of these static forces. We also present an alternate construction of these 1/4-BPS states from quantum excitations around a magnetic monopole, and build up the supermultiplet for arbitrary (quantized) electric charge. The degeneracy and the highest spin of the supermultiplet increase linearly with a relative electric charge. We conclude with comments.Comment: 33 pages, two figures, LaTex, a footnote added, the figure caption of Fig.2 expanded, one more referenc

Critical dynamics of the k-core pruning process

We present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure, and solve them numerically and, in the critical regime of the process, analytically. We show that the pruning process exhibits three different behaviors depending on whether the mean degree of the initial network is above, equal to, or below the threshold _c corresponding to the emergence of the giant k-core. We find that above the threshold the network relaxes exponentially to the k-core. The system manifests the phenomenon known as "critical slowing down", as the relaxation time diverges when tends to _c. At the threshold, the dynamics become critical characterized by a power-law relaxation (1/t^2). Below the threshold, a long-lasting transient process (a "plateau" stage) occurs. This transient process ends with a collapse in which the entire network disappears completely. The duration of the process diverges when tends to _c. We show that the critical dynamics of the pruning are determined by branching processes of spreading damage. Clusters of nodes of degree exactly k are the evolving substrate for these branching processes. Our theory completely describes this branching cascade of damage in uncorrelated networks by providing the time dependent distribution function of branching. These theoretical results are supported by our simulations of the $k$-core pruning in Erdos-Renyi graphs.Comment: 12 pages, 10 figure

Ensemble of Vortex Loops in the Abelian-Projected SU(3)-Gluodynamics

Grand canonical ensemble of small vortex loops emerging in the London limit of the effective Abelian-projected theory of the SU(3)-gluodynamics is investigated in the dilute gas approximation. An essential difference of this system from the SU(2)-case is the presence of two interacting gases of vortex loops. Two alternative representations for the partition function of such a grand canonical ensemble are derived, and one of them, which is a representation in terms of the integrals over vortex loops, is employed for the evaluation of the correlators of both kinds of loops in the low-energy limit.Comment: 10 pages, LaTeX2e, no figures, minor corrections, to appear in Mod. Phys. Lett.

Critical behavior of charmonia across the phase transition: A QCD sum rule approach

We investigate medium-induced change of mass and width of J/psi and eta_c across the phase transition in hot gluonic matter using QCD sum rules. In the QCD sum rule approach, the medium effect on heavy quarkonia is induced by the change of both scalar and twist-2 gluon condensates, whose temperature dependences are extracted from the lattice calculations of energy density and pressure. Although the stability of the operator product expansion side seems to break down at T > 1.06Tc for the vector channel and T>1.04Tc for the pseudoscalar channel, we find a sudden change of the spectral property across the critical temperature Tc, which originates from an equally rapid change of the scalar gluon condensate characterized by e-3p. By parameterizing the ground state of the spectral density by the Breit-Wigner form, we find that for both J/psi and eta_c, the masses suddenly decrease maximally by a few hundreds of MeV and the widths broaden to ~100 MeV slightly above Tc. Implications for recent and future heavy ion experiments are discussed. We also carry out a similar analysis for charmonia in nuclear matter, which could serve as a testing ground for observing the precursor phenomena of the QCD phase transition. We finally discuss the possibility of observing the mass shift at nuclear matter at the FAIR project at GSI.Comment: 18 pages, 21 figures, 2 figures are added and discussion on effect of dynamical quarks is extended. version to appear in Phys.Rev.