Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a mean-field treatment with a Gaussian approximation allows us to find examples where the infinite-dimensional system is reduced to a few ordinary differential equations. Our focus lies in the cooperative behavior in a population consisting of two parts, where one is composed of excitable elements, while the other one contains only self-oscillatory units. Surprisingly, excitable behavior in the whole system sets in only if the excitable elements have a smaller coupling strength than the self-oscillating units. In this way positive local correlations between natural frequencies and couplings shape the global behavior of mixed populations of excitable and oscillatory elements.     

Stern-Brocot trees in cascades of mixed-mode oscillations and canards in the extended Bonhoeffer-van der Pol and the FitzHugh-Nagumo models of excitable systems

We report a systematic two-parameter study of the organization of mixed-mode oscillations and period-adding sequences observed in an extended Bonhoeffer-van der Pol and in a FitzHugh-Nagumo oscillator. For both systems, we construct isospike diagrams and show that the number of spikes of their periodic oscillations are organized in a remarkable hierarchical way, forming a Stern-Brocot tree. The Stern-Brocot tree is more general than the Farey tree. We conjecture the Stern-Brocot tree to also underlie the hierarchical structure of periodic oscillations of other systems supporting mixed-mode oscillations.     

分数阶FitzHugh-Nagumo模型神经元的动力学特性及其同步

通过对分数阶FitzHugh-Nagumo模型神经元的研究,当外加电流强度作为分岔参数时,发现这种模型神经元从静息态到周期放电态所经历的Hopf分岔点不同于相应的整数阶模型神经元的分岔点;而且分数阶FitzHugh-Nagumo模型神经元呈现周期放电的外加电流强度的范围比相应的整数阶模型神经元的范围小,然而放电频率却比相应的整数阶模型神经元的放电频率高.同时还揭示在周期放电的情况下分数阶FitzHugh-Nagumo模型神经元之间的同步速率比相应的整数阶模型神经元之间的同步速率快.在数值模拟分数阶微分方程 关键词： 分数阶 Hopf分岔 FitzHugh-Nagumo模型 同步     

Stochastic resonance in the FitzHugh-Nagumo model from a dynamic mutual information point of view

Stochastic resonance(SR) in a FitzHugh-Nagumo neuron model is investigated based on a dynamic mutual information (DMI) between the input and the corresponding output signals. The DMI is expressed in terms of the (cross)power spectra of the input and output time series. Both stochastic-periodic and aperiodic SR are treated based on the DMI and our results are in good accord with the SR measured by the signal to noise ratio(SNR) for the case of the stochastic-periodic input and the power norm for the case of the aperiodic input.     

非高斯噪声激励下含周期信号FitzHugh-Nagumo系统的响应特征

研究了非高斯噪声激励下含周期信号的FHN模型的动力学行为. 通过计算神经元的平均响应时间、观察神经元的共振活化和噪声增强稳定现象,分析了非高斯噪声对神经元动力学行为的影响. 发现通过改变非高斯噪声的相关时间可以有效地改变共振活化和噪声增强稳定现象. 观察到在强相关噪声下不同强度的非高斯噪声抑制了神经元的噪声增强稳定现象而共振活化现象几乎不变,也就是非高斯噪声有效地增强了神经响应的效率. 观察了平均响应时间与非高斯噪声参数q之间的关系,当q为一个有限的小于1的值时,平均响应时间取得最小值. 最后表明在一定条件下,非高斯噪声出现重尺度现象,即非高斯噪声产生的效果可以由高斯白噪声来估计. 关键词： FHN神经系统 非高斯噪声 平均响应时间 共振活化现象     

A model of a neuron with oscillatory activity below the excitation threshold

We propose a dynamic model of a neuron with spontaneous periodic oscillations below the excitation threshold. Such neurons, in particular, play an important role in the problem of coordination of motions by the brain specifying the universal rhythm of muscular contractions. The model is constructed on the basis of the known model dynamic systems and is described by a system of fourth-order differential equations. A good qualitative agreement between the model dynamics and experimental data for the actual neurons is obtained. This work was presented at the Summer Workshop “Dynamic Days” (Nizhny Novgorod, June 30–July 2, 1998). Lobachevsky State University of Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 12, pp. 1623–1635, December, 1998.     

Spinor-unit field representation of electromagnetism applied to a model inflationary cosmology

The new spinor-unit field representation of the electromagnetism (Nash in J Math Phys 51:042501-1–042501-27, 2010) (with quark and lepton sources) is integrated via minimal coupling with standard Einstein gravitation, to formulate a Lagrangian model of the very early universe. A completely new solution to the coupled Einstein–Maxwell equations, with sources, is derived. These equations are generalized somewhat, but not in a way that violates any physical principles. The solution of the coupled Euler–Lagrange field equations yields a scale factor a(t) (comoving coordinates) that initially exponentially increases N e-folds from a(0) ≈ 0 to a ₁ =? a(0) e ^N (N = 60 is illustrated), then exponentially decreases, then exponentially increases to a ₁, and so on almost periodically. (Oscillatory cosmological models are not knew, and have been derived from string theory and loop quantum gravity.) It is not known if the scale factor escapes this periodic trap. This model is noteworthy in several respects: 1. All fundamental fields other than gravity are realized by spinor fields. 2. A plausible connection between the unit field u and the generalization of the photon wave function with a form of Dark Energy is described, and a simple natural scenario is outlined that allocates a fraction of the total energy of the Universe to this form of Dark Energy. 3. A solution of an analog of the pure Einstein–Maxwell equations is found using an approach that is in marked contrast with the method followed to obtain a solution of the well known Friedmann model of a radiation-dominated universe.     

Effect of auditory stimulation on the pulsatile echo, blood pressure, and electroencephalogram

Results of studies made during auditory stimulation of human subjects by pencil-tapping are presented. Details of the equipment used in making the ultrasonic intercranial measurements are featured, together with a discussion of the latest results.     

An analytical model for a dodecahedron loudspeaker applied to the design of omni-directional loudspeaker arrays

The dodecahedron (12 sided) loudspeaker is used extensively for acoustic measurements as an approximation to an omni-directional sound source, for example in building acoustics and automotive applications. In many instances its use is favoured above other omni-directional source approximations e.g. open pipe because of its greater power. However, analysis by other authors has shown that the radiation deviates from omni-directional above a certain frequency. In this paper an analytical model of the sound pressure field generated by a dodecahedron loudspeaker is constructed. The sound pressure field generated by the model is then compared with measured data and good agreement is demonstrated. Having established and validated the model, it is adapted to form alternative spherical loudspeaker arrays based on Platonic and Archimedean solid geometry and also a number of spherical packing routines. The aim of the analysis is to determine the optimal geometry for an omni-directional source using pistonic loudspeakers.The analysis shows that constructive interference of the pressure field across the spherical baffle surface and not individual loudspeaker pistonic radiation characteristics is the most significant factor with respect to deviations from omni-directional radiation for a complete spherical array. Consequently, loudspeaker elements which physically occupy the spherical baffle surface to their maximum extent provide the most extended frequency range of omni-directional operation. The most optimal spherical array distribution is shown to be the dodecahedron.     

The FBCS model and the inverse gap equations applied to the tin isotopes

The FBCS model for odd nuclei and the inverse gap equations are applied to a whole sequence of tin isotopes,viz.^111–125Sn. From spectroscopic data on the odd isotopes, the single-particle energies and interaction strengths are obtained. With these parameters the lowest states of the even isotopes are calculated by a number-projected two-quasiparticle diagonalization and by the usual BCS one. This is done with two Gaussian interactions and the SDI. In the case of the Gaussian forces the experimental energies are well reproduced by the number-projected treatment. Effective charges for Eλ transitions, which are required to reproduce the experimental transition rates, are rather constant for the whole series of isotopes, in case of the number-projected treatment. In addition a number of spectroscopic factors for one-nucleon transfer reactions are calculated and good agreement with experiments is observed.     

A theoretical model of the pressure field arising from asymmetric intraglottal flows applied to a two-mass model of the vocal folds

A theoretical flow solution is presented for predicting the pressure distribution along the vocal fold walls arising from asymmetric flow that forms during the closing phases of speech. The resultant wall jet was analyzed using boundary layer methods in a non-inertial reference frame attached to the moving wall. A solution for the near-wall velocity profiles on the flow wall was developed based on a Falkner-Skan similarity solution and it was demonstrated that the pressure distribution along the flow wall is imposed by the velocity in the inviscid core of the wall jet. The method was validated with experimental velocity data from 7.5 times life-size vocal fold models, acquired for varying flow rates and glottal divergence angles. The solution for the asymmetric pressures was incorporated into a widely used two-mass model of vocal fold oscillation with a coupled acoustical model of sound propagation. Asymmetric pressure loading was found to facilitate glottal closure, which yielded only slightly higher values of maximum flow declination rate and radiated sound, and a small decrease in the slope of the spectral tilt. While the impact on symmetrically tensioned vocal folds was small, results indicate the effect becomes more significant for asymmetrically tensioned vocal folds.     

Analytical properties of theS-matrix applied to the resonance model of transition metals

Summary A method to construct ionic potentials for transition metals from the knowledge of the resonantd-band phase shiftη ₂=tg^-21/2W/(E-E_d) is developed. This is based on an inversescattering approach using the analytic properties of theS-matrix and Jost functions to reconstruct the interparticle potential in the spirit of the Marchenko and Gel'fand-Levitan formalisms. A specific form of the solution of the resulting integral equation is discussed and possible applications to a host of transition metal properties are outlined.

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Riassunto Si mette a punto un metodo per costruire potenziali ionici per metalli di transieione partendo dalla conoscenza dello sfasamento risonante della bandad,η ₂=tg^-21/2W/(E-E_d). Questo è basato su un approccio allo scattering inverso che tiene conto delle proprietà analitiche della matriceS e delle funzioni di Jost per ricostruire il potenziale tra particelle nell'ambito dei formalismi di Marchenko e Gel'fand. Si discute una forma specifica dell'equazione integrale risultante e si sottolineano le possibili applicazioni ad una grande quantità di proprietà dei metalli di transizione.

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Резюме Развивается метод для конструирования ионных потенциалов для переходных металлов, исходя из знания резонансного фазового сдвигаd-зоны,η ₂=tg^-21/2W/(E-E_d). Этот метод основан на обратной задаче рассеяния с использованием аналитических свойствS-матрицы и функций Йоста для конструирования междучастичного потенциала в духе формализма Марченко и Гельфанда-Левитана. Обсуждается специальная форма решения полученного интегрального уравнения. Указываются возможные применения для описания свойств переходных металлов.

     

Further evaluation of a model of loudness perception applied to cochlear hearing loss.

This paper describes further tests of a model for loudness perception in people with cochlear hearing loss. It is assumed that the hearing loss (the elevation in absolute threshold) at each audiometric frequency can be partitioned into a loss due to damage to outer hair cells (OHCs) and a loss due to damage to inner hair cells (IHCs) and/or neurons. The former affects primarily the active mechanism that amplifies the basilar membrane (BM) response to weak sounds. It is modeled by increasing the excitation level required for threshold, which results in a steeper growth of specific loudness with increasing excitation level. Loss of frequency selectivity, which results in broader excitation patterns, is also assumed to be directly related to the OHC loss. IHC damage is modeled by an attenuation of the calculated excitation level at each frequency. The model also allows for the possibility of complete loss of IHCs or functional neurons at certain places within the cochlea ("dead" regions). The parameters of the model (OHC loss at each audiometric frequency, plus frequency limits of the dead regions) were determined for three subjects with unilateral cochlear hearing loss, using data on loudness matches between sinusoids presented alternately to their two ears. Further experiments used bands of noise that were either 1-equivalent rectangular bandwidth (ERB) wide or 6-ERBs wide, centered at 1 kHz. Subjects made loudness matches for these bands of noise both within ears and across ears. The model was reasonably accurate in predicting the results of these matches without any further adjustment of the parameters.     

The angular overlap model applied to the calculation of nuclear quadrupole interactions

By the application of the angular overlap model to the calculation of nuclear quadrupole interactions (NQI), it is shown that it is possible to predict the NQI for the¹¹¹Cd nucleus in a cadmium complex with known coordination geometry. This fact makes it relevant to apply such calculations to nuclear quadrupole interaction data for¹¹¹Cd substituted zinc enzymes. It is demonstrated that with an approximate knowledge about the geometry and type of protein ligands from X-ray diffractions, it is possible to extract knowledge about type and geometry of nonprotein ligands in zinc enzymes, such as coordination of water, anions, or substrate molecules.     

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.     

A time series analysis and a non-homogeneous Poisson model with multiple change-points applied to acoustic data

High levels of the so-called community noise may produce hazardous effect on the health of a population exposed to them for large periods of time. Hence, the study of the behaviour of those noise measurements is very important. In this work we analyse that in terms of the probability of exceeding a given threshold level a certain number of times in a time interval of interest. Since the datasets considered contain missing measurements, we use a time series model to estimate the missing values and complete the datasets. Once the data is complete, we use a non-homogeneous Poisson model with multiple change-points to estimate the probability of interest. Estimation of the parameters of the models are made using the usual time series methodology as well as the Bayesian point of view via Markov chain Monte Carlo algorithms. The models are applied to data obtained from two measuring sites in Messina, Italy.     

Gauge independent theory applied to a model of atomic ionization by an intense laser pulse

An explicitly gauge invariant strong field theory is introduced and tested using a model laser-atom interaction. The theory relies on a power series in the target potential. Transitions amplitudes are obtained by using a corresponding series in the momentum space wave function. We demonstrate that this approach is explicitly gauge invariant to all orders. A well know 1D delta function potential model is used to test the convergence of the series in the evaluation of total ionization probabilities and ionization spectra. Actually, the convergence is verified when both, the perturbation as well as the order of the expansion, are increased.     

Two-amplitude model of pion DCX applied to the 18O angular distribution and excitation function

An earlier model developed to fit the DCX excitation function of ¹⁸O has been extended to account for the $\text{T}{}_{\mathrm{\pi }}\text{= 164}\text{MeV}{}^{18}\text{O DCX}$ angular distribution in terms of that for ¹⁶O and a double-isobaric-analog transition.     

随机相位扰动抑制激发介质中漂移的螺旋波

研究了一类二维变量描述的激发系统中漂移螺旋波的抑制问题.通过在整个系统中局部注入带随机相位的电信号，如在系统256×256格点的边界或中心区域中选取4×4或者5×5格点区域施加一个带随机相位的外部激励电信号，在系统内部产生一个持续的靶波信号，实现靶波对螺旋波的动态竞争.数值计算表明：该方法对于Barkley模型中螺旋波有很强的抑制作用，与简单的局部周期信号驱动比较，具有暂态过程比较短的特点，而且对于时空噪声具有一定的抗干扰性.在一定的噪声范围内，即使系统出现不均匀性，也可以观测到靶波，新出现的靶波对螺旋波有抑制作用. 关键词： 螺旋波 靶波 Barkley模型 随机相位