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ABSTRACT: Statistical properties of neuron firing are studied in the framework of a nonlinear leaky integrate-and-fire model that is driven by a slow periodic subthreshold signal. The firing events are characterized by first passage time densities. The experimentally better accessible interspike interval density generally depends on the sojourn times in a refractory state of the neuron. This aspect is not part of the integrate-and-fire model and must be modelled additionally. For a large class of refractory dynamics, a general expression for the interspike interval density is given and further evaluated for the two cases with an instantaneous resetting (i.e. no refractory state) and a refractory state possessing a deterministic lifetime. First passage time densities and interspike interval densities following from the proposed theory compare favorably with precise numerical simulations.
Mathematical Biosciences 07/2007; 207(2):302-11. · 1.54 Impact Factor
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ABSTRACT: The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a Fokker-Planck equation for the particle density. It is shown that in the limit of vanishing particle size a uniform particle distribution is always approached in the long time limit. For extended spherical particles, conditions are specified that lead to inhomogeneous densities and consequently to particle accumulation and depletion. Hereby the boundary conditions for the particle density play a decisive role: The centers of spherical particles must keep the minimal distance of their radius from the fluid boundaries. The normal components of the forces acting on the sphere then may assume finite values which are diffusively transported into the bulk of the fluid.
09/2006;
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ABSTRACT: Molecules that only differ by their chirality, so-called enantiomers, often possess different properties with respect to their biological function. Therefore, the separation of enantiomers presents a prominent challenge in molecular biology and has long been a main pursuit of organic chemistry. We suggest a new separation technique for chiral molecules that is based on the transport properties in a microfluidic flow with spatially variable vorticity. Because of their size the thermal fluctuating motion of the molecules must be taken into account. These fluctuations play a decisive role in the proposed separation mechanism.
Physical Review Letters 02/2006; 96(1):014502. · 7.37 Impact Factor
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ABSTRACT: The statistics of transitions between the metastable states of a periodically
driven bistable Brownian oscillator are investigated on the basis of a
two-state description by means of a master equation with time-dependent rates.
The results are compared with extensive numerical simulations of the Langevin
equation for a sinusoidal driving force. Very good agreement is achieved both
for the counting statistics of the number of transitions and the residence time
distribution of the process in either state. The counting statistics
corroborate in a consistent way the interpretation of stochastic resonance as a
synchronisation phenomenon for a properly defined generalized Rice phase.
09/2004;
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ABSTRACT: Analytical expressions are put forward to investigate the forced spiking activity of abstract neuron models such as the driven leaky integrate-and-fire model. The method is valid in a wide parameter regime beyond the restraining limits of weak driving (linear response) and/or weak noise. The novel approximation is based on a discrete state Markovian modeling of the full long-time dynamics with time-dependent rates. The scheme yields excellent agreement with numerical Langevin and Fokker-Planck simulations of the full nonstationary dynamics, not only for the first-passage time statistics, but also for the important interspike interval (residence time) distribution.
Physical Review Letters 08/2004; 93(4):048102. · 7.37 Impact Factor
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ABSTRACT: Analytical expressions are put forward to investigate the forced spiking activity of abstract neuron models such as the driven leaky integrate-and-fire (LIF) model. The method is valid in a wide parameter regime beyond the restraining limits of weak driving (linear response) and/or weak noise. The novel approximation is based on a discrete state Markovian modeling of the full dynamics with time-dependent rates. The scheme yields very good agreement with numerical Langevin and Fokker-Planck simulations of the full non-stationary dynamics for both, the first-passage time statistics and the interspike interval (residence time) distributions.
02/2004;
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ABSTRACT: The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a Fokker–Planck equation for the particle density. It is shown that for extended spherical particles the shape of the fluid domain gives rise to inhomogeneous particle densities, thereby leading to particle accumulation and corresponding depletion. For extended spherical particles, conditions are specified that lead to inhomogeneous densities and consequently to regions with particle accumulation and depletion.
Physica A: Statistical Mechanics and its Applications.
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ABSTRACT: We present an approximate analytical expression for escape rates of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrate-and-fire model for neural spiking. The novel approximation is based on a discrete state Markovian modeling of the full long-time dynamics with time-dependent rates. It is valid in a wide parameter regime beyond the restraining limits of weak driving (linear response) and/or weak noise. The scheme is carefully tested and yields excellent agreement with three different numerical methods based on the Langevin equation, the Fokker–Planck equation and an integral equation.
Physica A: Statistical Mechanics and its Applications.
