Transitions in Active Rotator Systems: Invariant Hyperbolic Manifold Approach

The statistics of the condensed polaritons is described in terms of the Wigner function. In the framework of the truncated Wigner method, the Wigner function obeys a Fokker- Planck equation, which is solved analytically. The second order correlations in the stationary state are in excellent agreement with those obtained from the numerical solution of the master equation and show a qualitative and, well above threshold, also quantitative agreement with recent experiments. Furthermore, the contributions of the different noise effects that influence the polariton ground state statistics are explicitly defined. Exploiting the equivalence between Fokker-Planck and Langevin descriptions of stochastic processes, the time dependent correlations of the polaritons close to the stationary state are derived. Explicit expressions for the linewidth and for the relaxation rate of the polariton intensity are obtained, whose values are of the same order of magnitude of the experimental data. Finally, the limit of validity of the truncated Wigner method in the present model is discussed.

Non-linear time series and linear models were not designed to detect probabilistic process that are depict by velocity and drift associated to returns the way Ornstein-Uhlenbeck stochastic process describes diffusion and velocity associated to series or waves influenced by Brownian motion or Lévy process. In this research, Brownian motion and Lévy process were conflated as driving force for Ornstein-Uhlenbeck process with its solution applied to Naira-Dollar exchange rates from 2009-2019.The drift and diffusion estimates for the Ornstein-Uhlenbeck process driven by Brownian motion and Lévy process are realization of AR (1) with 2.991 and 0.1672 respectively. The AR(1) realization for the Ornstein-Uhlenbeck process was stationary with estimate that lies outside the unit circle. The AIC, BIC, RMSE, and MSE for the Ornstein-Uhlenbeck process were estimated to be 483.7572, 483.4782, 0.00101, and 8.395 respectively, compare to estimates of the same indexes for AR (1) of 767.5, 634.09, 0.3819, and 23.48. The criterion via the residuals from the Ornstein-Uhlenbeck process was smaller, which connotes that the errors approximated in using drift, Brownian motion and to estimate is relatively small via the Ornstein-Uhlenbeck process. Keywords: Brownian motion; Drift; Diffusion; Lévy process; Ornstein-Uhlenbeck Process DOI: 10.7176/MTM/11-3-02 Publication date: May 31 st 2021

The frequency-dependent effects of mechanical vibration on human comfort and working efficiency are now clearly recognized, as are the effects of airborne noise on hearing. But vibration and intense noise at very low frequencies can also provoke disturbing non-auditory symptoms which are as yet ill understood. Moreover, the establishment of frequency-and time-dependence of these effects calls for further research. The author reviews current problems in this field and mentions the work of the International Organization for Standardization aimed at defining limits of acceptable human exposure to vibration and intense noise.

Given the increasing number of citizen complaints about port noise and the lack of relevant studies assessing resident exposure, the effects of port noise are gaining increasing public attention. It is especially significant in ports near residential areas, where excessive noise emissions can seriously impact the urban environment. This paper aimed to investigate the perceptions and attitudes of the population living near the cargo terminals in the Port of Split regarding the impact of port noise in the urban area, focusing on their health and standards of living. The research methodology included a questionnaire distributed in the areas where the residents are most affected by noise. In addition to conventional descriptive survey analysis, the authors used regression analysis and two-way ANOVA with the Tukey post hoc test as a parametric data analysis tool. The survey results showed the harmful effects of port noise on most set parameters, and perceived noise intensity for three different times of the day caused a high level of concern for the urban environment. In addition, the regression analysis results showed a weak and reverse dependency between the distance of the selected residences from the noise sources and the perceived noise intensity. These findings support the validity of the respondents’ perceptions and the credibility of the obtained results. The application of parametric data analysis revealed a lack of formal knowledge of residents about the effects of noise and a strong differentiation between groups based on the variables that determine the level of education of residents and their assessments of the noise intensity of the cargo terminal. However, the subjective impressions and the psycho-physical and emotional states of the residents need also to be included in the validation of the results. The obtained results will facilitate the adoption of noise management policies and implementation of noise abatement programs in the Port of Split.

The mixed problem for the telegraph equation well-known in electrical engineering and electronics, provided that the line is free from distortions, is reduced to a similar problem for one-dimensional inhomogeneous wave equation. An effective way to solve this problem is based on the use of special functions – polylogarithms, which are complex power series with power coefficients, converging in the unit circle. The exact solution of the problem is expressed in integral form in terms of the imaginary part of the first-order polylogarithm on the unit circle, and the approximate one – in the form of a finite sum in terms of the real part of the dilogarithm and the imaginary part of the third-order polylogarithm. All the indicated parts of the polylogarithms are periodic functions that have polynomial expressions of the corresponding degrees on an interval of length in the period, which makes it possible to obtain a solution to the problem in elementary functions. In the paper, we study a mixed problem for the telegrapher’s equation which is well-known in applications. This problem of linear substitution of the desired function witha time-exponential coefficient is reduced to a similar problem for the Klein – Gordon equation. The solution of the latter can be found by dividing the variables in the form of a series of trigonometric functions of a line point with time-dependent coefficients. Such a solution is of little use for practical application, since it requires the calculation of a large number of coefficients-integrals and it is difficult to estimate the error of calculations. In the present paper, we propose another way to solve this problem, based on the use of special He-functions, which are complex power series of a certain type that converge in the unit circle. The exact solution of the problem is presented in integral form in terms of second-order He-functions on the unit circle. The approximate solution is expressed in the final form in terms of third-order He-functions. The paper also proposes a simple and effective estimate of the error of the approximate solution of the problem. It is linear in relation to the line splitting step with a time-exponential coefficient. An example of solving the problem for the Klein – Gordon equation in the way that has been developed is given, and the graphs of exact and approximate solutions are constructed.

A common method for analyzing the effects of molecular noise in chemical reaction networks is to approximate the underlying chemical master equation by a Fokker--Planck equation and to study the st...

10 male and 10 female undergraduates were asked to estimate 5-, 10-, 15-, and 30-sec. intervals under five intensities of ambient noise (50, 60, 70, 80, and 90 dB). Interval estimates became shorter as the intensity of noise increased from 50 to 80 dB but became longer at 90 dB. The effects of intensity of noise were most prominant in the two longest intervals. These results are interpreted in terms of CNS arousal theory.

The synchronization transition in coupled piecewise map lattices is studied. The average order parameter is calculated to diagnose synchronization of coupled piecewise maps. As a result, it shows that coexistence of a period cluster and synchronization states in the synchronization transition process. A detailed research shows that the period clusters consist of two coexisting period attractors, and their period orbit is an unstable periodic orbit of the isolate map. The unstable periodic orbit is stabilized again by the mutual interactions of the local nonlinearity and the spatial coupling. The influence of noise on the complete synchronization (CS) in coupled piecewise map systems is also studied in this work. Synchronization probability densities and average order parameters as a function of the coupling strength with various noise intensities are calculated. When the noise intensity is small, the noise can postpone synchronization transition processes. However, if the noise intensity is larger, the noise can destroy the period clusters states, shorten the synchronization transition and enhance the CS in coupled piecewise maps.

In this paper, (supra-threshold) stochastic resonance phenomenon of noise-enhanced information transmission is studied in detail through the numerical calculation and the computer simulation in a non-linear multilevel threshold neural networks system, which is affected by both additive noise and multiplicative noise, then the mutual information is used to characterize the phenomenon. The mutual information as a function of additive noise intensity or multiplicative noise intensity brings on convex changes under a suitable system threshold and a fixed multiplicative noise intensity or additive noise intensity, which shows that the (supra-threshold) stochastic resonance phenomenon occurs. The increases in the number of the system threshold units can enhance the effectiveness of information transmission; the increase of the system threshold can increase the signal components that are under the threshold, and thus the supra-threshold stochastic resonance takes place more easily. In addition, by changing the additive noise intensity the supra-threshold stochastic resonance occurs more easily than by changing the multiplicative noise intensity. The above results show that both the existence of the supra-threshold stochastic resonance and the effectiveness of noise-improved the signal transmission are closely related to multiplicative or additive noise intensity, the number of threshold units, and the system threshold level.

In this chapter we introduce shift-invariant algebras, the main objects of this book. These are uniform algebras on a compact connected group G, consisting of continuous functions on G, whose spectrum is contained in a semigroup S of the dual group Ĝ. If Ĝ is a subgroup of ℝ, and S ⊂ ℝ+, then the maximal ideal space of the corresponding shift-invariant algebra is the G-disc, or, big disc over G. In this chapter we describe two important models of shift-invariant algebras, namely, by the means of almost periodic functions on ℝ, and by the means of H∞-functions on the unit circle. The set of automorphisms, and the peak groups of shift-invariant algebras are also characterized. Extensions on G-discs and groups of several classical theorems of Complex Analysis, such as Radó’s theorem for null-sets and the Riemann theorem for removable singularities of analytic functions, are stated and proved. It is shown that these extensions hold for some semigroups, while in general they fail. In principle we state all results for general shift-invariant algebras AS, though they apply automatically to the particular cases of algebras APS of almost periodic functions, and of H S ∞ -algebras. Asymptotically almost periodic functions combine the properties of classical almost periodic functions on ℝ, and of continuous functions on ℝ that vanish at infinity.

Effects of noise on the collective dynamic phenomena such as patterns and firing synchronization are studied in a square-lattice FitzHugh–Nagumo neural network with gap junctions. It is shown that as the noise intensity is above a critical value, typical patterns can emerge and propagate through the network in the form of coexisting circular waves and parallel ones with spatially periodic structure. Circular waves can change from a single-array to double-array as the noise increases. Furthermore, we can observe that spatial evolutions of patterns can exhibit different styles as the noise is changed. In addition, we study noise-induced firing synchronization of neurons. In particular, firing synchronization can be enhanced, and then can reach a saturated value as the noise is large enough. More interestingly, it is found that the stronger the coupling strength is, the larger the noise intensity is needed to make neurons fire. Finally, the critical relation between the noise intensity and the coupling strength is given to investigate the occurrence of firing synchronization in the network.

The laser is an important component of the resonator fiber-optic gyroscope (RFOG) and the optical noise of the laser severely limits the performance of the RFOG system. The mathematical model which presents the effect of the intensity noise on the RFOG is established. In order to verify the correctness of the model, an acousto-optic modulator is innovatively used to generate the intensity noise of the laser, through which the intensity noise could be quantitatively changed without introducing unexpected noises of the laser. The experimental results indicate the intensity noise results in the deterioration of the scale factor nonlinearity and the increase of detected rotation rate error. In addition, a scheme based on the second harmonic demodulation of the intensity-modulated signal is proposed to compensate the light intensity fluctuation of the laser in the RFOG. The test results show the drift of the gyro introduced by the light intensity fluctuation could be reduced >8 dB through this method.

We investigate the modular transformation properties of observable (light) fields in heterotic orbifolds, in the light of recent calculations of CP-violating quantities. Measurable quantities must be modular invariant functions of string moduli, even if the light fields are noninvariant. We show that physical invariance may arise by patching smooth functions that are separately noninvariant. CP violation for <T> on the unit circle, which requires light and heavy states to mix under transformation, is allowed in principle, although the Jarlskog parameter J_CP(T) must be amended relative to previous results. However, a toy model of modular invariant mass terms indicates that the assumption underlying these results is unrealistic. In general the mass eigenstate basis is manifestly modular invariant and coupling constants are smooth invariant functions of T, thus CP is unbroken on the unit circle. We also discuss the status of CP-odd quantities when CP is a discrete gauge symmetry, and point out a link with baryogenesis.

We study the effects of different coupling strengths and network topologies on signal detection in small-world neuronal networks. Research has previously revealed that the ability of detecting subthreshold signals could be significantly enhanced by appropriately fine-tuning the noise intensity. Here we show that the coupling strength and the structure of the underlying network can also lead toward enhanced signal detection. In particular, we show that there are two levels of the coupling strength at which the subthreshold signal can be detected at an appropriate noise intensity and network structure. We also show that the network structure has little impact on signal detection if the coupling is weak. On the other hand, for intermediate coupling strengths, we show that the shorter the average path length, the better the signal detection. Finally, if the coupling is strong, we show that there exists an intermediate average path length at which signal detection becomes optimal.

The effects of industrial noise on resting heart rate and blood pressure were studied in 3,105 blue-collar workers. Heart rate and blood pressure were measured in different workers at various times during the workday. After controlling for several possible confounders, we found that resting heart rate in females was associated positively with noise intensity (p = .036) and with time of day (p = .054). In males, resting heart rate was associated with noise intensity; however, such association was related to time of day (p = .046). No such associations were found for blood pressure in either sex. We plotted the mean resting heart rate by time of day for workers exposed to high [ > or = 80 db(A)] and low noise, and no difference was evident with respect to morning heart rate in either sex. After 4 h of noise exposure for males (and less time for females), individuals who were exposed to high noise had higher heart rates; however, in females this was not observed at the end of the workday. Thus, recurrent daily exposure to high noise at work has an acute, though not residual, effect on resting heart rate.