Multimodal transition and stochastic antiresonance in squid giant axons

The experimental data of N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, and G. Matsumoto, Physica D \textbf{43}, 318 (1990), on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the Hodgkin-Huxley model. The minimum of the firing rate as a function of the stimulus amplitude $I_0$ in the high-frequency regime is due to the multimodal transition. Below this singular point only odd multiples of the driving period remain and the system is highly sensitive to noise. The coefficient of variation has a maximum and the firing rate has a minimum as a function of the noise intensity which is an indication of the stochastic coherence antiresonance. The model calculations reproduce the frequency of occurrence of the most common modes in the vicinity of the transition. A linear relation of output frequency vs. $I_0$ for above the transition is also confirmed.Comment: 5 pages, 9 figure

An augmented moment method for stochastic ensembles with delayed couplings: I. Langevin model

By employing a semi-analytical dynamical mean-field approximation theory previously proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 041903 (2003)], we have developed an augmented moment method (AMM) in order to discuss dynamics of an $N$-unit ensemble described by linear and nonlinear Langevin equations with delays. In AMM, original $N$-dimensional {\it stochastic} delay differential equations (SDDEs) are transformed to infinite-dimensional {\it deterministic} DEs for means and correlations of local as well as global variables. Infinite-order DEs arising from the non-Markovian property of SDDE, are terminated at the finite level $m$ in the level-$m$ AMM (AMM$m$), which yields $(3+m)$-dimensional deterministic DEs. Model calculations have been made for linear and nonlinear Langevin models. The stationary solution of AMM for the linear Langevin model with N=1 is nicely compared to the exact result. The synchronization induced by an applied single spike is shown to be enhanced in the nonlinear Langevin ensemble with model parameters locating at the transition between oscillating and non-oscillating states. Results calculated by AMM6 are in good agreement with those obtained by direct simulations.Comment: 18 pages, 3 figures, changed the title with re-arranged figures, accepted in Phys. Rev. E with some change

Direct Detection of Galactic Halo Dark Matter

The Milky Way Galaxy contains a large, spherical component which is believed to harbor a substantial amount of unseen matter. Recent observations indirectly suggest that as much as half of this ``dark matter'' may be in the form of old, very cool white dwarfs, the remnants of an ancient population of stars as old as the Galaxy itself. We conducted a survey to find faint, cool white dwarfs with large space velocities, indicative of their membership in the Galaxy's spherical halo component. The survey reveals a substantial, directly observed population of old white dwarfs, too faint to be seen in previous surveys. This newly discovered population accounts for at least 2% of the halo dark matter. It provides a natural explanation for the indirect observations, and represents a direct detection of Galactic halo dark matter.Comment: 13 pages, 4 figures, 1 table. Note added after Science Express online publication: This text reflects the correction of a few typographical errors in the online version of the table. It also includes the new constraint on the calculation of d_max which accounts for the fact that the survey could not have detected stars with proper motions below 0.33 arcseconds per year. Published online at ScienceExpress www.sciencemag.org 22 March 2001; 10.1126/science.1059954; To appear in Science 27 April 200

Neuronal synchrony: peculiarity and generality

Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their “dynamical repertoire” includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neuronal networks with plastic synapses (synchronization with activity dependent coupling), (ii) synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks (partial synchronization of small composite structures), and (iv) coarse grained synchronization in larger systems (synchronization on a mesoscopic scale

Noise-assisted spike propagation in myelinated neurons

We consider noise-assisted spike propagation in myelinated axons within a multi-compartment stochastic Hodgkin-Huxley model. The noise originates from a finite number of ion channels in each node of Ranvier. For the subthreshold internodal electric coupling, we show that (i) intrinsic noise removes the sharply defined threshold for spike propagation from node to node, and (ii) there exists an optimum number of ion channels which allows for the most efficient signal propagation and it corresponds to the actual physiological values.Comment: 8 pages, 12 figures, accepted for publication in Phys. Rev.

An automated search for transiting exocomets

This paper discusses an algorithm for detecting single transits in photometric time-series data. Specifically, we aim to identify asymmetric transits with ingress that is more rapid than egress, as expected for cometary bodies with a significant tail. The algorithm is automated, so can be applied to large samples and only a relatively small number of events need to be manually vetted. We applied this algorithm to all long cadence light curves from the Kepler mission, finding 16 candidate transits with significant asymmetry, 11 of which were found to be artefacts or symmetric transits after manual inspection. Of the 5 remaining events, four are the 0.1% depth events previously identified for KIC 3542116 and 11084727. We identify HD 182952 (KIC 8027456) as a third system showing a potential comet transit. All three stars showing these events have H-R diagram locations consistent with $\sim$100Myr-old open cluster stars, as might be expected given that cometary source regions deplete with age, and giving credence to the comet hypothesis. If these events are part of the same population of events as seen for KIC 8462852, the small increase in detections at 0.1% depth compared to 10% depth suggests that future work should consider whether the distribution is naturally flat, or if comets with symmetric transits in this depth range remain undiscovered. Future searches relying on asymmetry should be more successful if they focus on larger samples and young stars, rather than digging further into the noise