Fluctuation and Noise Letters

In this Letter, we study firing transitions induced by a particular kind of non-Gaussian noise (NGN) and coupling in Newman-Watts small-world neuronal networks. It is found that chaotic bursting can be tamed by the coupling and evolves to regular spiking or bursting behavior as the coupling increases. As the NGN's deviation from Gaussian noise changes, the neurons exhibit firing transitions from irregular spiking to regular bursting, and the number of spikes inside per burst varies with the change of the deviation. These results show that the NGN and the coupling play crucial roles in the firing activity of the neurons, and hence are of great importance to the information processing and transmission in the neuronal networks.

The number of permutations appearing in data series is used for detecting changes in the structure of such series. We show the influence of the permutations length (embedding dimension) in order to get good results. We use permutations to analyze real data from medical and biological origins. Some problems that appear in applying these techniques are pointed out.

We have studied the role of internal noise for intracellular calcium signaling in coupled biological cell system. It is found that internal noise can induce calcium oscillations and the performance of such oscillations shows two peaks with the variation of the cell size-Ω for any cell chain length-N, indicating the occurrence of system size bi-resonance or internal noise stochastic bi-resonance, which may be very relevant to the canard explosion. We also find that there exists an optimal cell chain length-N for the first peak at which the collective calcium oscillations show the best performance, it is also a phenomenon of "system size resonance". It is interesting to note that one of the optimal cell sizes is present at Ω ~ 10³ μm³, which is close to a real living cell size in vivo.

We examine the relationship between time-discrete nonlinear Markov processes defined in terms of nonlinear Markov chains and corresponding micro-dynamic models describing many-body systems composed of a finite number of units interacting with each other via a mean field. To this end, we consider a two-state model and examine appropriately defined measures for attractor strength and noise amplitude using variational calculus. We focus on a two-state model and demonstrate an application to free recall data from 8 participants.

Short-term traffic forecasting has played a key role in supporting the need of proactive and dynamic traffic control system. K-nearest neighbor (KNN) nonparametric regression models have been widely used in traffic prediction. KNN models give predictions based on the future state of traffic speed that is completely determined by the current state, but with no dependence on the past sequences of traffic speed that produced the current state. In fact, traffic speed is not completely random in nature, and some patterns repeat in the traffic stream. In this paper, we proposed a methodology called bi-pattern recognition KNN model (BKNN) which uses pattern recognition technique twice in the searching process to predict the future traffic state. Then the proposed BKNN model is applied to predict one day real traffic speed series of two sites, which are located near the North 2nd and 3rd Ring Road in Beijing, respectively. With the optimal neighbor and pattern size, the BKNN model provides good predictions. Moreover, in comparison with the KNN model, PKNN model (a modified model based on KNN), seasonal autoregressive integrated moving average (SARIMA) and the artificial neural networks (ANN), the BKNN model appears to be the most promising and robust of the five models to provide better short-term traffic prediction.

The paper devises a Parrondo's game model of biotic population with the network as its spatial carrier, trying to analyze individual's coopetition behavior and investigate the degree distribution of the heterogeneity on the impact of coopetition. The populational Parrondo's game model consists of a zero-sum game among individuals and a negative sum game between individuals and environment. In terms of relations of zero-sum game, four patterns are defined: cooperation, competition, harmony, and poor-competition-rich-cooperation. The simulation result shows that: (1) Cooperation and competition in any forms are adaptive behaviors. Cooperative and competitive behavior could convert the losing games combined into winning. The positive average fitness of the population represents the paradoxical feature that the Parrondo's game is counterintuitive. (2) BA Network is conducive to cooperation. (3) The relationships of individual fitness with node degree and with clustering coefficient are disclosed. As for cooperation and poor-competition-rich-cooperation pattern, the greater the node degree is, the greater the individual fitness is. (4) The heterogeneity has a positive impact on cooperation. (5) Population average fitness is the largest when the probability of playing zero-sum game is 1/3 in the Parrondo's game model.

The joint presence of heavy-tailed distribution and long memory in time series always leads to certain trouble in correctly obtaining the statistical characteristics for time series modeling. These two properties i.e., heavy-tailed distribution and long memory, cannot be neglected in time series analysis, because the tail thickness of the distribution and long memory property of the time series are critical in characterizing the essence of the resulting natural or man-made phenomenon of the time series. Meanwhile, the fluctuation of the varying local long memory parameter may be used to capture the internal changes which underlie the externally observed phenomenon. Therefore, in this paper, we proposed to use the variance trend, heavy-tailed distribution, long memory, and local long memory characteristics to analyze a time series recorded as in [1] from tracking the jumps of individual molecules on cell membranes. The tracked molecules are Class I major histocompatibility complex (MHCI) expressed on rat hepatoma cells. The analysis results show that the jump time series of molecular motion on the cell membrane obviously has both heavy-tailed distribution and local long memory characteristics. The tail heaviness parameters, long memory parameters, and the local long memory parameters of ten MHCI molecular jump time series are all summarized with tables and figures in the paper. These reported tables and figures are not only interesting but also important in terms of additional novel insights and characterization of the time series under investigation.

An analytical model of the high-frequency noise of frequency multipliers based on Schottky-barrier diodes (SBD) operating in series with a parallel resonant circuit under large-signal conditions is developed. Such a model, on one hand, takes into account the main intrinsic features of the SBD noise related to shot-noise, returning carriers, plasma resonance at n⁺n homojunctions, and, on the other hand, it incorporates the SBD noise spectrum modifications induced by the output resonant circuit. It is shown that the SBD embedding into an external circuit can produce the appearance of an extra noise due to up-down conversion of the fluctuations of the voltage drop between the SBD terminals originated by a periodic modulation of the varactor capacitance by the pumping signal.