A perturbation analysis of spontaneous action potential initiation by stochastic ion channels

A stochastic interpretation of spontaneous action potential initiation is developed for the Morris- Lecar equations. Initiation of a spontaneous action potential can be interpreted as the escape from one of the wells of a double well potential, and we develop an asymptotic approximation of the mean exit time using a recently-developed quasi-stationary perturbation method. Using the fact that the activating ionic channel’s random openings and closings are fast relative to other processes, we derive an accurate estimate for the mean time to fire an action potential (MFT), which is valid for a below-threshold applied current. Previous studies have found that for above-threshold applied current, where there is only a single stable fixed point, a diffusion approximation can be used. We also explore why different diffusion approximation techniques fail to estimate the MFT

Flight evaluation of the x-15 ball-nose flow-direction sensor as an air-data system

Modification of ball-nose flow direction sensor for Mach number and air pressure altitude measurement

Instability and spatiotemporal rheochaos in a shear-thickening fluid model

We model a shear-thickening fluid that combines a tendency to form inhomogeneous, shear-banded flows with a slow relaxational dynamics for fluid microstructure. The interplay between these factors gives rich dynamics, with periodic regimes (oscillating bands, travelling bands, and more complex oscillations) and spatiotemporal rheochaos. These phenomena, arising from constitutive nonlinearity not inertia, can occur even when the steady-state flow curve is monotonic. Our model also shows rheochaos in a low-dimensional truncation where sharply defined shear bands cannot form

Avalanche of Bifurcations and Hysteresis in a Model of Cellular Differentiation

Cellular differentiation in a developping organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emenating from its environment. Depending on the form of the nonlinear reaction kinetics, this signal can trigger a series of bifurcations in the system. Differentiation starts at the surface where the signal is received, and cells change type up to a given distance, or under other conditions, the differentiation process propagates through the whole domain. When the signal diminishes hysteresis is observed

Noise-induced inhibitory suppression of malfunction neural oscillators

Motivated by the aim to find new medical strategies to suppress undesirable neural synchronization we study the control of oscillations in a system of inhibitory coupled noisy oscillators. Using dynamical properties of inhibition, we find regimes when the malfunction oscillations can be suppressed but the information signal of a certain frequency can be transmitted through the system. The mechanism of this phenomenon is a resonant interplay of noise and the transmission signal provided by certain value of inhibitory coupling. Analyzing a system of three or four oscillators representing neural clusters, we show that this suppression can be effectively controlled by coupling and noise amplitudes.Comment: 10 pages, 14 figure

SciRecSys: A Recommendation System for Scientific Publication by Discovering Keyword Relationships

In this work, we propose a new approach for discovering various relationships among keywords over the scientific publications based on a Markov Chain model. It is an important problem since keywords are the basic elements for representing abstract objects such as documents, user profiles, topics and many things else. Our model is very effective since it combines four important factors in scientific publications: content, publicity, impact and randomness. Particularly, a recommendation system (called SciRecSys) has been presented to support users to efficiently find out relevant articles

How the asymmetry of internal potential influences the shape of I-V characteristic of nanochannels

Ion transport in biological and synthetic nanochannels is characterized by such phenomena as ion current fluctuations, rectification, and pumping. Recently, it has been shown that the nanofabricated synthetic pores could be considered as analogous to biological channels with respect to their transport characteristics \cite{Apel, Siwy}. The ion current rectification is analyzed. Ion transport through cylindrical nanopores is described by the Smoluchowski equation. The model is considering the symmetric nanopore with asymmetric charge distribution. In this model, the current rectification in asymmetrically charged nanochannels shows a diode-like shape of $I-V$ characteristic. It is shown that this feature may be induced by the coupling between the degree of asymmetry and the depth of internal electric potential well. The role of concentration gradient is discussed

Universal behavior in populations composed of excitable and self-oscillatory elements

We study the robustness of self-sustained oscillatory activity in a globally coupled ensemble of excitable and oscillatory units. The critical balance to achieve collective self-sustained oscillations is analytically established. We also report a universal scaling function for the ensemble's mean frequency. Our results extend the framework of the `Aging Transition' [Phys. Rev. Lett. 93, 104101 (2004)] including a broad class of dynamical systems potentially relevant in biology.Comment: 4 pages; Changed titl

Photo-excited semiconductor superlattices as constrained excitable media: Motion of dipole domains and current self-oscillations

A model for charge transport in undoped, photo-excited semiconductor superlattices, which includes the dependence of the electron-hole recombination on the electric field and on the photo-excitation intensity through the field-dependent recombination coefficient, is proposed and analyzed. Under dc voltage bias and high photo-excitation intensities, there appear self-sustained oscillations of the current due to a repeated homogeneous nucleation of a number of charge dipole waves inside the superlattice. In contrast to the case of a constant recombination coefficient, nucleated dipole waves can split for a field-dependent recombination coefficient in two oppositely moving dipoles. The key for understanding these unusual properties is that these superlattices have a unique static electric-field domain. At the same time, their dynamical behavior is akin to the one of an extended excitable system: an appropriate finite disturbance of the unique stable fixed point may cause a large excursion in phase space before returning to the stable state and trigger pulses and wave trains. The voltage bias constraint causes new waves to be nucleated when old ones reach the contact.Comment: 19 pages, 8 figures, to appear in Phys. Rev.

A minimal model for chaotic shear banding in shear-thickening fluids

We present a minimal model for spatiotemporal oscillation and rheochaos in shear-thickening complex fluids at zero Reynolds number. In the model, a tendency towards inhomogeneous flows in the form of shear bands combines with a slow structural dynamics, modelled by delayed stress relaxation. Using Fourier-space numerics, we study the nonequilibrium `phase diagram' of the fluid as a function of a steady mean (spatially averaged) stress, and of the relaxation time for structural relaxation. We find several distinct regions of periodic behavior (oscillating bands, travelling bands, and more complex oscillations) and also regions of spatiotemporal rheochaos. A low-dimensional truncation of the model retains the important physical features of the full model (including rheochaos) despite the suppression of sharply defined interfaces between shear bands. Our model maps onto the FitzHugh-Nagumo model for neural network dynamics, with an unusual form of long-range coupling.Comment: Revised version (in particular, new section III.E. and Appendix A