Responses of a Hodgkin-Huxley neuron to various types of spike-train inputs

Numerical investigations have been made of responses of a Hodgkin-Huxley (HH) neuron to spike-train inputs whose interspike interval (ISI) is modulated by deterministic, semi-deterministic (chaotic), and stochastic signals. As deterministic one, we adopt inputs with the time-independent ISI and with time-dependent ISI modulated by sinusoidal signal. The R?ssler and Lorentz models are adopted for chaotic modulations of ISI. Stochastic ISI inputs with the gamma distribution are employed. It is shown that distribution of output ISI data depends not only on the mean of ISIs of spike-train inputs but also on their fluctuations. The distinction of responses to the three kinds of inputs can be made by return maps of input and output ISIs, but not by their histograms. The relation between the variations of input and output ISIs is shown to be different from that of the integrate and fire (IF) model because of the refractory period in the HH neuron.     

Models of the temporal dynamics of visual processing

Single unit recordings of neurons in primary visual cortex have demonstrated complex temporal patterns in the interspike interval return maps when presented with periodic input. Two models are tested to account for these patterns. An integrate-and-fire model is only able to replicate thein vivo data if its synaptic input is a chaotic function of time (such as a time series derived from the sinusoidally driven Duffing equation). Simpler purely periodic inputs are insufficient to replicate the experimental data. A Hodgkin-Huxley ionic model with a periodic input can replicate some of the features of the neural data, however it seems to be lacking as a complete model. These results indicate that thein vivo dynamics are not a result of the intrinsic properties of the neuron, but arise from a chaotic input to the neuron.     

Markov analysis of stochastic resonance in a periodically driven integrate-and-fire neuron

We model the dynamics of the leaky integrate-and-fire neuron under periodic stimulation as a Markov process with respect to the stimulus phase. This avoids the unrealistic assumption of a stimulus reset after each spike made in earlier papers and thus solves the long-standing reset problem. The neuron exhibits stochastic resonance, both with respect to input noise intensity and stimulus frequency. The latter resonance arises by matching the stimulus frequency to the refractory time of the neuron. The Markov approach can be generalized to other periodically driven stochastic processes containing a reset mechanism.     

Physical grounds and models of pattern representation and recognition in a neuron cytoskeleton microtubule

The physics of the dipole system of a neuron cytoskeleton microtubule is put forward, and a Hamiltonian of the dipole system is constructed. The previously developed microscopic model of the cytoskeleton microtubule dipole system is extended for the case of dipole-dipole bonds when the bonds are not fully ordered and are constrained (exhibit the memory property). Molecular field expressions are derived for a random polarization function and its two moments: mean polarization and rms polarization. An evolutionary equation for a random order parameter is of a relaxation character and describes the pattern recognition process. It is shown that the phase transition nonlinearly transforms (projects) one (nodal) space of higher dimension pattern features to another space of lower dimension attributes (order parameters), this transformation greatly cutting the body of data to be processed.     

Two kinds of upper hybrid soliton bistability

The basic model employed to describe nonlinear upper hybrid wave structures is the generalized nonlinear Schrödinger equation including second and fourth order dispersive effects as well as local and nonlocal nonlinearity. For two kinds of such an equation the existence of two stable solitons with the same plasmon number but with different spatial scales and amplitudes is shown as two qualitatively different kinds of upper hybrid soliton bistability. An integral relation for an arbitrary nonlinear upper hybrid wave packet evolution is derived taking into account higher order dispersive effects. Necessary conditions for soliton formation from arbitrary wave packets and the impossibility of wave packet collapse are demonstrated taking into account higher order dispersive effects.     

Setting boundary conditions on the Khokhlov–Zabolotskaya equation for modeling ultrasound fields generated by strongly focused transducers

An equivalent source model is developed for setting boundary conditions on the parabolic diffraction equation in order to simulate ultrasound fields radiated by strongly focused medical transducers. The equivalent source is defined in a plane; corresponding boundary conditions for pressure amplitude, aperture, and focal distance are chosen so that the axial solution to the parabolic model in the focal region of the beam matches the solution to the full diffraction model (Rayleigh integral) for a spherically curved uniformly vibrating source. It is shown that the proposed approach to transferring the boundary condition from a spherical surface to a plane makes it possible to match the solutions over an interval of several diffraction maxima around the focus even for focused sources with F-numbers less than unity. This method can be used to accurately simulate nonlinear effects in the fields of strongly focused therapeutic transducers using the parabolic Khokhlov–Zabolotskaya equation.     

Theoretical model for thin ferroelectric films and the multilayer structures based on them

A modified Weiss mean-field theory is used to study the dependence of the properties of a thin ferroelectric film on its thickness. The possibility of introducing gradient terms into the thermodynamic potential is analyzed using the calculus of variations. An integral equation is introduced to generalize the well-known Langevin equation to the case of the boundaries of a ferroelectric. An analysis of this equation leads to the existence of a transition layer at the interface between ferroelectrics or a ferroelectric and a dielectric. The permittivity of this layer is shown to depend on the electric field direction even if the ferroelectrics in contact are homogeneous. The results obtained in terms of the Weiss model are compared with the results of the models based on the correlation effect and the presence of a dielectric layer at the boundary of a ferroelectric and with experimental data.     

On time-dependent radiative transfer

An integral equation is developed for application to time-dependent laboratory experiments in which partial redistribution effects are important. The equation of transport with the Heasley-Kneer emission coefficient and the equation of statistical equilibrium lead to a time-dependent redistribution function containing an absorption—re-emission term which decays exponentially in time and a scattering term which is instantaneous. This integral equation does not agree with an equation written by Payne et al. [Phys. Rev. A 9, 1050 (1974)] that has been used to compare theory with experiments. The difference between the Payne equation and the equation developed here needs to be examined in detail, since it might under some circumstances be on the same order as the difference between partial and complete redistribution.     

Mass operator for wave scattering from a slightly random surface

This paper deals with the mass operator representing multiple-scattering effects in the theory of wave scattering from a slightly random surface. By means of the stochastic-functional approach, a recurrence equation for the mass operator is obtained in the form of an iterative integral. However, its solution oscillates in a non-physical manner against the number of iterations. Next, the recurrence equation may be regarded as a nonlinear integral equation, when the number of iterations goes to infinity. An analytical solution of the nonlinear integral equation is presented for a special case in which the roughness spectrum is the Dirac delta function. Then, the nonlinear integral equation is solved numerically for the Gaussian roughness spectrum by iteration, starting from such an analytical solution. It is shown that only a few iterations are required to obtain the mass operator, even when the correlation distance is small. Effects of the mass operators on the coherent reflection coefficient and the incoherent scattering cross section are calculated and shown in figures.     

Analysis and comparison of four anhysteretic polarization models for lead magnesium niobate

Four anhysteretic polarization models that have been used in the literature to evaluate data acquired from lead magnesium niobate (PMN) are analyzed and compared. Derivations of two of the models from assumed spatial distributions of dipole energy states, using first physical principles, are presented. A third model is derived from a suitable integral averaging calculation. These derivations are used as the basis for developing an integral equation for determining an energy-state distribution that produces a fourth model, which was not originally formulated in terms of an assumed distribution. A new polarization function is also presented. Excellent approximations to each of the four polarization functions of interest can be deduced from this new polarization function by adjusting the numerical value of just a single parameter. An application of two of the models to data is presented. It is shown that it can be necessary to consider a sample to be an admixture of two distinct species of poles, in the sense that two polarization functions must be added together in order to accommodate the data.     

Zur Reversibilität der Vlasov-Gleichung

The difference between Landaus decaying solutions of the linearized Vlasov equation and the damped solutions of a loaded electrical circuit is shown. An integral equation for the field acting in the plasma is investigated and the Laplace transforms of its solutions are considered. Some simple initial value problems for the Cauchy distribution for a perturbation by external fields too, are solved. It is demonstrated that the time arrow in the behaviour of measurable quantities of the Vlasov plasma stems from the accentuation of a non-probable initial state.     

Nonlocal corrections to the Boltzmann equation for dense Fermi systems

A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider's equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second-order quantum virial corrections. The medium effects on binary collisions are shown to mediate the latent heat, i.e. an energy conversion between correlation and thermal energy. An implementation to heavy ion collisions is discussed.     

Travelling waves in a model of quasi-active dendrites with active spines

Dendrites, the major components of neurons, have many different types of branching structures and are involved in receiving and integrating thousands of synaptic inputs from other neurons. Dendritic spines with excitable channels can be present in large densities on the dendrites of many cells. The recently proposed Spike-Diffuse-Spike (SDS) model that is described by a system of point hot-spots (with an integrate-and-fire process) embedded throughout a passive tree has been shown to provide a reasonable caricature of a dendritic tree with supra-threshold dynamics. Interestingly, real dendrites equipped with voltage-gated ion channels can exhibit not only supra-threshold responses, but also sub-threshold dynamics. This sub-threshold resonant-like oscillatory behaviour has already been shown to be adequately described by a quasi-active membrane. In this paper we introduce a mathematical model of a branched dendritic tree based upon a generalisation of the SDS model where the active spines are assumed to be distributed along a quasi-active dendritic structure. We demonstrate how solitary and periodic travelling wave solutions can be constructed for both continuous and discrete spine distributions. In both cases the speed of such waves is calculated as a function of system parameters. We also illustrate that the model can be naturally generalised to an arbitrary branched dendritic geometry whilst remaining computationally simple. The spatio-temporal patterns of neuronal activity are shown to be significantly influenced by the properties of the quasi-active membrane. Active (sub- and supra-threshold) properties of dendrites are known to vary considerably among cell types and animal species, and this theoretical framework can be used in studying the combined role of complex dendritic morphologies and active conductances in rich neuronal dynamics.     

A finite element approach for predicting nozzle admittances

A finite element method is used to predict the admittances of axisymmetric nozzles. It is assumed that the flow in the nozzle is isentropic and irrotational, and the disturbances are small so that linear analyses apply. An approximate, two dimensional compressible model is used to describe the steady flow in the nozzle. The propagation of acoustic disturbances is governed by the complete linear wave equation. The differential form of the acoustic equation is transformed to an integral equation by using Galerkin's method, and Green's theorem is applied so that the acoustic boundary conditions can be introduced through the boundary residuals. The boundary conditions are described for both straight and curved sonic lines. A two dimensional FEM with linear elements is used to solve the acoustic equation. A one dimensional FEM is also used to solve the reduced equation of Crocco, and the solution verifies the sufficiency of the boundary residual formulation. Comparison between computed admittances and experimental data is shown to be quite good.     

Mean discharge frequency locking in the response of a noisy neuron model to subthreshold periodic stimulation

Leaky integrate-and-fire neuron models display stochastic resonance-like behavior when stimulated by subthreshold periodic signal and noise. Previous works have shown that matching between the time scales of the noise induced discharges and the modulation period can account for this phenomenon at low modulation amplitudes, but not large subthreshold modulation amplitude. In order to examine the discharge patterns of the model in this regime, we introduce a method for the computation of the power spectral density of the discharge train. Using this method, we clarify the role of the distribution of the input phase at discharge times. Finally, we argue that for large subthreshold inputs, mean discharge frequency locking accounts for the enhanced response.     

Wave propagation in 1D elastic solids in presence of long-range central interactions

In this paper wave propagation in non-local elastic solids is examined in the framework of the mechanically based non-local elasticity theory established by the author in previous papers. It is shown that such a model coincides with the well-known Kröner-Eringen integral model of non-local elasticity in unbounded domains. The appeal of the proposed model is that the mechanical boundary conditions may easily be imposed because the applied pressure at the boundaries of the solid must be equilibrated by the Cauchy stress. In fact, the long-range forces between different volume elements are modelled, in the body domain, as central body forces applied to the interacting elements. It is shown that the shape change of travelling disturbances coalesces with those predicted by the non-local integral theory of elasticity in unbounded domains, but several differences arise in the case of bounded domains. The wave propagation problem has been formulated by means of the Hamiltonian functional of the proposed mechanically based model of non-local elasticity, introducing an additional term to the elastic potential energy that accounts for elastic long-range interactions. In this way, the wave equation may be obtained in a weak formulation and be further used to provide approximate analytical solutions to the governing equation in the context of standing wave analysis. An equivalent discrete point-spring model, similar to lattice-type networks, has also been introduced to show the mechanical equivalence of the non-local elastic model as well as to provide a mechanical scheme suitable for the numerical treatment of pressure waves travelling in non-local bounded domains.     

Darboux transformations in integral and differential forms for generalized Schrödinger equations

The Darboux transformation operator technique is applied to the generalized Schrödinger equation with a position-dependent effective mass and with linearly energy-dependent potentials. Intertwining operators are obtained in an explicit form and used for constructing generalized Darboux transformations. An interrelation is established between the differential and integral transformation operators. It is shown how to construct the quantum well potentials in nanoelectronic with a given spectrum.     

最小神经元模型放电起始动态控制与分析

本文采用最小神经元模型,从生理学角度设计wash-out滤波器,实现了不同放电起始动态机理之间的转换,并证明wash-out滤波器控制通过影响阈下电流的竞争结果改变了神经元的放电起始动态机理. 关键词： 放电起始动态机理 阈下电流竞争 最小神经元模型 wash-out滤波器     

Extended Wronskian Determinant Approach and Iterative Solutions of One-Dimensional Dirac Equation

An approximation method, namely, the Extended Wronskian Determinant Approach, is suggested to study the one-dimensional Dirac equation. An integral equation, which can be solved by iterative procedure to find the wave functions, is established. We employ this approach to study the one-dimensional Dirac equation with one-well potential, and give the energy levels and wave functions up to the first order iterative approximation. For double-well potential, the energy levels up to the first order approximation are given.     

微波电热推进器中等离子体的吸收特性

提出了一个谐振腔内微波与等离子体相互作用的简化模型。通过对格林函数并矢的渐进展开,用Fredholm矢量积分方程计算了等离子体散射区的电场分布和等离子体的吸收效率。对非均匀性,等离子体密度等素对吸收效率的影响进行了分析。