Coherence resonance induced by non-Gaussian noise in a deterministic Hodgkin-Huxley neuron

In this paper, we report a novel effect of a particular kind of non-Gaussian noise (NGN), especially its deviation from Gaussian noise, on the spiking activity in a deterministic Hodgkin-Huxley (HH) neuron. It is found via numerical simulations that the coefficient of variation (CV), characterizing the spiking regularity, nonlinearly changes with varying deviation and passes through a minimum at an optimal deviation value, representing the presence of the coherence resonance (CR). This phenomenon shows that, when the NGN is optimal, the neuron can exhibit the most regular firing behavior. This result provides a constructive role of the NGN in the timing precision of information processing and signal transduction in neural systems.     

Critical Exponents in Zero Dimensions

In the vicinity of the onset of an instability, we investigate the effect of colored multiplicative noise on the scaling of the moments of the unstable mode amplitude. We introduce a family of zero dimensional models for which we can calculate the exact value of the critical exponents ?? _m for all the moments. The results are obtained through asymptotic expansions that use the distance to onset as a small parameter. The examined family displays a variety of behaviors of the critical exponents that includes anomalous exponents: exponents that differ from the deterministic (mean-field) prediction, and multiscaling: non-linear dependence of the exponents on the order of the moment.     

Ground and excited state dipole moments of coumarin 337 laser dye

This paper reports that the effects of spectral properties of coumarin 337 laser dye have been investigated in different solvents considering solvent parameters like dielectric constant (?) and refractive index (n) of different solvent polarities. The ground state (μ_g) and excited state (μ_e) dipole moments are calculated using Lippert's, Bakhshiev's, and Kawski-Chamma-Viallet's equations. In all these three equations the variation of Stokes shift was used to calculate the excited state (μ_e) dipole moment. It is observed that the Bakhshiev method is comparatively better than the other two methods for ground state and excited state dipole moment calculations. The angle between the excited state and ground state dipole moments is also calculated.     

Vlasov moments, integrable systems and singular solutions

The Vlasov equation governs the evolution of the single-particle probability distribution function (PDF) for a system of particles interacting without dissipation. Its singular solutions correspond to the individual particle motions. The operation of taking the moments of the Vlasov equation is a Poisson map. The resulting Lie-Poisson Hamiltonian dynamics of the Vlasov moments is found to be integrable is several cases. For example, the dynamics for coasting beams in particle accelerators is associated by a hodograph transformation to the known integrable Benney shallow-water equation. After setting the context, the Letter focuses on geodesic Vlasov moment equations. Continuum closures of these equations at two different orders are found to be integrable systems whose singular solutions characterize the geodesic motion of the individual particles.     

Multiple coherence resonance induced by time-periodic coupling in stochastic Hodgkin-Huxley neuronal networks

In this paper, we study the effect of time-periodic coupling strength (TPCS) on the spiking coherence of Newman-Watts small-world networks of stochastic Hodgkin-Huxley (HH) neurons and investigate the relations between the coupling strength and channel noise when coherence resonance (CR) occurs. It is found that, when the amplitude of TPCS is varied, the spiking induced by channel noise can exhibit CR and coherence bi-resonance (CBR), and the CR moves to a smaller patch area (bigger channel noise) when the amplitude increases; when the frequency of TPCS is varied, the intrinsic spiking can exhibit CBR and multiple CR, and the CR always occurs when the frequency is equal to or multiple of the spiking period, manifesting as the locking between the frequencies of the intrinsic spiking and the coupling strength. These results show that TPCS can greatly enhance and optimize the intrinsic spiking coherence, and favors the spiking with bigger channel noise to exhibit CR. This implies that, compared to constant coupling strength, TPCS may play a more efficient role for improving the time precision of the information processing in stochastic neuronal networks.     

From the Perron-Frobenius equation to the Fokker-Planck equation

We show that for certain classes of deterministic dynamical systems the Perron-Frobenius equation reduces to the Fokker-Planck equation in an appropriate scaling limit. By perturbative expansion in a small time scale parameter, we also derive the equations that are obeyed by the first- and second-order correction terms to the Fokker-Planck limit case. In general, these equations describe non-Gaussian corrections to a Langevin dynamics due to an underlying deterministic chaotic dynamics. For double-symmetric maps, the first-order correction term turns out to satisfy a kind of inhomogeneous Fokker-Planck equation with a source term. For a special example, we are able solve the first- and second-order equations explicitly.     

Parameter dependence of stochastic resonance in the stochastic Hodgkin-Huxley neuron

Recently, the phenomena of stochastic resonance (SR) have attracted much attention in the studies of the excitable systems under inherent noise, in particular, nervous systems. We study SR in a stochastic Hodgkin-Huxley neuron under Ornstein-Uhlenbeck noise and periodic stimulus, focusing on the dependence of properties of SR on stimulus parameters. We find that the dependence of the critical forcing amplitude on the frequency of the periodic stimulus shows a bell-shaped structure with a minimum at the stimulus frequency, which is quite different from the monotonous dependence observed in the bistable system at a small frequency range. The frequency dependence of the critical forcing amplitude is explained in connection with the firing onset bifurcation curve of the Hodgkin-Huxley neuron in the deterministic situation. The optimal noise intensity for maximal amplification is also found to show a similar structure.     

Experimental Determination of Ground and Excited State Dipole Moments of N,N-Bis (2, 5-di-tert-butylphenyl)-3, 4:9, 10-perylenebis (dicarboximide) (DBPI) A Photostable Laser Dye

In the present work, the absorption, emission spectra and dipole moments(μ_g, μ_e) of N, N-bis (2, 5-di-tert-butylphenyl)-3, 4:9, 10- perylenebis (dicarboximide) (DBPI) have been studied in solvents of various polarities at room temperature. Using the methods of solvatochromism, the difference between the first excited singlet state (μ_e) and ground state (μ_g) dipole moments was estimated from Lippert – Mataga,, Bakhshiev, Kawski – Chamma – Viallet equations. The change in dipole moment (Δμ) was also calculated using the variation of the Stokes shift with microscopic solvent polarity parameter (E _T ^N ). It was observed that the value of excited singlet state dipole moment is higher (3.53 Debye) than the ground state one (1.92Debye), showing that the excited state of DBPI is more polar than the ground state.     

Magnetic structures of the rare earth orthotitanites RTiO3; R = Tb,Dy, Tm and Yb

The magnetic structures of the rare earth orthotitanites, RTiO₃, R = Tb, Dy, Tm and Yb, have been solved using neutron powder diffraction techniques.Two different types of magnetic structure have been found. One has the titanium and rare earth moments antiparallel along the c axis. The other structure has the rare earth moments in the ab plane with both ferromagnetic and antiferromagnetic components. In TbTiO₃, the terbium moment of (8.1 ± 0.4)μ_β has ferromagnetic and antiferromagnetic components along the [100] and [010] directions, respectively, with the moments lying at an angle of (36 ± 3)° to the [100] direction. In DyTiO₃, the dysprosium moment of (9.7 ± 0.7)μ_β has ferromagnetic and antiferromagnetic components along the [010] and [100] directions, respectively, with the moments making an angle of (31 ± 5)° to the [010] direction. TmTiO₃ has a thulium moment of (6.0 ± 0.4)μ_β in a ferromagnetic array along the [001] direction. The average titanium moment in the orthotitanites is (0.7 ± 0.3)μ_β in a direction antiparallel to the ferromagnetic component of the rare earth moment. The ytterbium moment in YbTiO₃ is quenched. It is found to be (1.7 ± 0.2)μ_β assuming a moment direction along [001]. The rare earth moment directions are found to be remarkably consistent in the series RMO₃, M = Ti, Cr, Fe and Al.     

Maximum entropy approach to the collisional Vlasov equation: Exact solutions

We show that the maximum entropy approach proposed by El-Wakil, Elhanbaly, and Abdou (from now on EEA) in [S.A. El-Wakil, A. Elhanbaly, M.A. Abdou, Physica A 323 (2003) 213] for solving approximately the collisional Vlasov equation actually can provide exact solutions if properly implemented. We consider here two alternative procedures for obtaining exact maximum entropy solutions of the aforementioned equation. On the one hand, after identifying an appropriate set of relevant mean values (moments), we show that there are exact maximum entropy solutions associated with that set of moments. These solutions can be studied focusing either on the equations of motion of the moments themselves, or on the equations of motion of the corresponding Lagrange multipliers. On the other hand, it is possible to find exact solutions of the reduced equation considered by EEA, if one takes explicitly into account the zeroth-order moment of the solutions.     

Stochastic bifurcation in FitzHugh-Nagumo ensembles subjected to additive and/or multiplicative noises

We have studied the dynamical properties of finite N-unit FitzHugh-Nagumo (FN) ensembles subjected to additive and/or multiplicative noises, reformulating the augmented moment method (AMM) with the Fokker-Planck equation (FPE) method [H. Hasegawa, J. Phys. Soc. Japan 75 (2006) 033001]. In the AMM, original 2N-dimensional stochastic equations are transformed to eight-dimensional deterministic ones, and the dynamics is described in terms of averages and fluctuations of local and global variables. The stochastic bifurcation is discussed by a linear stability analysis of the deterministic AMM equations. The bifurcation transition diagram of multiplicative noise is rather different from that of additive noise: the former has the wider oscillating region than the latter. The synchronization in globally-coupled FN ensembles is also investigated. Results of the AMM are in good agreement with those of direct simulations (DSs).     

Analysis of second-order conditional moment closure applied to an autoignitive lifted hydrogen jet flame

The timing and location of autoignition can be highly sensitive to turbulent fluctuations of composition. Second-order Conditional Moment Closure (CMC) provides transport equations for conditional (co)variances in turbulent reacting flows. CMC equations accounting for compressibility and differential diffusion are analyzed using data from direct numerical simulation of an autoignitive lifted turbulent hydrogen jet flame [C.S. Yoo, R. Sankaran, J.H. Chen, Three-dimensional direct numerical simulation of turbulent lifted hydrogen/air jet flame in a heated coflow. Part 1. J. Fluid. Mech., (2008)]. At the flame base, second-order moments were required to accurately model the conditional reaction rates. However, over 80% of the second-order reaction rate component was obtainable with a small subset (16%) of the species-temperature covariances. The balance of the second-order CMC equation showed that turbulent transport across spatial composition gradients initiates generation of conditional variances.     

Relaxation of probability characteristics of the brownian motion of a nonlinear oscillator

We consider an oscillator with nonlinear elasticity and nonlinear damping under the action of a Gaussian delta-correlated random force. The oscillator is treated as a Brownian particle in the corresponding potential profile. We analyze the problem using the analytical-numerical method based on solving the chain of differential equations for the statistical moments, which is broken in a certain manner. For the case of nonlinear elasticity, we find the dependence of the relaxation times of the mean values and variances of both the coordinates and velocities on the system parameters and noise intensity. By analogy, the relaxation of the probability characteristics of the oscillation amplitude is studied for a system with nonlinear damping. In both cases, the evolution of the Gaussian or Rayleigh probability distributions is described on the basis of the moment relaxation. Nizhny Novgorod Architectural and Construction University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 4, pp. 468–478, September, 2000.     

Variations on the deuteron theme

Several problems concerning the deuteron and having simple analytic solutions are considered. The relation between the electric quadrupole moment of the deuteron and the np scattering amplitude is established. The degree of the circular polarization of the photon emitted in the radiative capture of longitudinally polarized thermal neutrons is found. The anapole, electric dipole, and magnetic quadrupole moments of the deuteron are calculated.     

A moment approach to non-Gaussian colored noise

The Langevin system subjected to non-Gaussian colored noise has been discussed, by using the second-order moment approach with two kinds of models for generating the noise. We have derived the effective differential equation (DE) for a variable x, from which the stationary probability distribution P(x) has been calculated with the use of the Fokker-Planck equation. The result of P(x) calculated by the moment method is compared to several expressions obtained by different methods such as the universal colored noise approximation (UCNA) [Jung and Hänggi, Phys. Rev. A 35 (1987) 4464] and the functional-integral method. It has been shown that our P(x) is in good agreement with that of direct simulations (DSs). We have also discussed dynamical properties of the model with an external input, solving DEs in the moment method.     

Ru13原子簇基态的磁性

采用离散变分局域自旋密度泛函方法，研究了三种可能的高对称几何构型的由１３个钌原子组成的Ru₁₃原子簇的电子结构．结果表明，所有具有不同对称性的Ru₁₃原子簇在它们各自的平衡位置处都有两重磁性解，从能量上看，每一种构型的低自旋解都比高自旋解更为稳定．基态原子簇为Ｉ_hRu₁₃原子簇，具有４μ_B的磁矩，或每个原子具有０.３１μ_B的磁矩．这与实验测得的Ru₁₃原 关键词：     

Stochastic theory of nonlinear rate processes with multiple stationary states

A comparison has been made between the deterministic and stochastic (master equation) formulation of nonlinear chemical rate processes with multiple stationary states. We have shown, via two specific examples of chemical reaction schemes, that the master equations have quasi-stationary state solutions which agree with the various initial condition dependent equilibrium solutions of the deterministic equations. The presence of fluctuations in the stochastic formulation leads to true equilibrium solutions, i.e. solutions which are independent of initial conditions as t → ∞. We show that the stochastic formulation leads to two distinct time scales for relaxation. The mean time for the reaction system to reach the quasi-stationary states from any initial state is of $\text{O}$(N⁰) where N is a measure of the size of the reaction system. The mean time for relaxation from a quasi-stationary state to the true equilibrium state is $\text{O}$(e^N). The results obtained from the stochastic formulation as regards the number and location of the quasi-stationary states are in complete agreement with the deterministic results.     

Determination of electric dipole moment for the ν2 vibrational state of 15NH3 by infrared-infrared double resonances

An infrared-infrared double-resonance technique, employing the sidebands produced by electro-optic amplitude modulation of a single-frequency CO₂ laser, is used to observe the second-order Stark effect of the ν₂asR(2, 0) transition of ¹⁵NH₃. The technique enables the Stark shifts in ground and vibrationally excited states to be observed separately and yields the electric dipole moments: μ(v₂ = 1) = 1.253 ± 0.003 D, μ(v = 0) = 1.469 ± 0.004 D. The relative intensity distribution, linewidths, and line shapes of features in the double-resonance Stark spectra are also examined.     

A spatiotemporal master equation model of morphogen transport: Local accumulation times,noise measurement and diffusion force

Morphogen, a class of signaling molecules to direct and control pattern formation of cell and tissue, is first synthesized in a local region and then conveyed to other regions or degraded. In the previous studies, this transport process was modeled by deterministic models of ordinary differential equations. In microcosmic environments, however, the process is often affected by stochastic fluctuations (or the noise). It remains unclear how this noise affects morphogen gradients. Here, we build a spatiotemporal master equation model for the process of morphogen transport in a finite developmental field, from which we derive the first-order moment equations of this master equation. We derive the analytical expression of the local accumulation time that the morphogens reach a steady state, and find that this time is nonlinear with respect to the cell positions. We also derive the approximate expressions of the steady-state variances, the Fano factors and the local accumulation time of the variance. Interestingly, we find that the local accumulation time for the variance of the morphogen number is shorter than that of its corresponding second-order moment. Moreover, the noise in the morphogen number is almost not affected by the distance from the cellular position to morphogen source. In addition, we further study some quantities (e.g., potential energy and diffusion force) from the view of physical-chemical mechanisms, and uncover that the diffusion force is a key factor for the formation of the morphogen gradient. Our results provide insights on morphogen diffusion.     

Dynamic phase transitions and dynamic phase diagrams of the spin-2 Blume-Capel model under an oscillating magnetic field within the effective-field theory

The dynamic phase transitions are studied in the kinetic spin-2 Blume-Capel model under a time-dependent oscillating magnetic field using the effective-field theory with correlations. The effective-field dynamic equation for the average magnetization is derived by employing the Glauber transition rates and the phases in the system are obtained by solving this dynamic equation. The nature (first- or second-order) of the dynamic phase transition is characterized by investigating the thermal behavior of the dynamic magnetization and the dynamic phase transition temperatures are obtained. The dynamic phase diagrams are constructed in the reduced temperature and magnetic field amplitude plane and are of seven fundamental types. Phase diagrams contain the paramagnetic (P), ferromagnetic-2 (F₂) and three coexistence or mixed phase regions, namely the F₂+P, F₁+P and F₂+F₁+P, which strongly depend on the crystal-field interaction (D) parameter. The system also exhibits the dynamic tricritical behavior.