Entrainment range affected by the heterogeneity in the amplitude relaxation rate of suprachiasmatic nucleus neurons

Adaption of circadian rhythms in behavioral and physiological activities to the external light–dark cycle is achieved through the main clock, i.e., the suprachiasmatic nucleus(SCN) of the brain in mammals. It has been found that the SCN neurons differ in the amplitude relaxation rate, which represents the rigidity of the neurons to the external amplitude disturbance. Thus far, the appearance of that difference has not been explained. In the present study, an alternative explanation based on the Poincare′ model is given which takes into account the effect of the difference in the entrainment range of the SCN. Both our simulation results and theoretical analyses show that the largest entrainment range is obtained with suitable difference in the case that only a part of SCN neurons are sensitive to the light information. Our findings may give an alternative explanation for the appearance of that difference(heterogeneity) and shed light on the effects of the heterogeneity in the neuronal properties on the collective behaviors of the SCN neurons.

Patterns of cross-correlation in time series:A case study of gait trails

A complex system contains generally many elements that are networked by their couplings.The time series of output records of the system's dynamical process is subsequently a cooperative result of the couplings.Discovering the coupling structure stored in the time series is an essential task in time series analysis.However,in the currently used methods for time series analysis the structural information is merged completely by the procedure of statistical average.We propose a concept called mode network to preserve the structural information.Firstly,a time series is decomposed into intrinsic mode functions and residue by means of the empirical mode decomposition solution.The mode functions are employed to represent the contributions from different elements of the system.Each mode function is regarded as a mono-variate time series.All the mode functions form a multivariate time series.Secondly,the co-occurrences between all the mode functions are then used to construct a threshold network(mode network)to display the coupling structure.This method is illustrated by investigating gait time series.It is found that a walk trial can be separated into three stages.In the beginning stage,the residue component dominates the series,which is replaced by the mode function numbered M14 with peaks covering^680 strides(~12 min)in the second stage.In the final stage more and more mode functions join into the backbone.The changes of coupling structure are mainly induced by the co-occurrent strengths of the mode functions numbered as M11,M12,M13,and M14,with peaks covering 200-700 strides.Hence,the mode network can display the rich and dynamical patterns of the coupling structure.This approach can be extended to investigate other complex systems such as the oil price and the stock market price series.

Scale-Invariance Exists in the Series of Character Intervals in the Four Great Chinese Novels

The scale-invariance behavior has been widely observed in English or other phonetic language texts. In the present study, we examine whether the semantic language, Chinese can also show this behavior. Typically, the scale-invariance behavior is examined in the series of character intervals for the four great Chinese novels by a method of detrended fluctuation analysis. We observe that the scale-invariance behavior characterized by a scaling exponent around 0.60 exists in each novel. Moreover, we divide each novel into three parts with equal number of chapters, and we also observe the existence of scale-invariance in the interval series for each part. Interestingly, we find that there is evident difference in the scaling exponents between the first(or second) part and the third part in the novel of A dream of red mansions, and the difference between parts is not evident for the other three novels. Our observation suggests that there are two writing styles in A dream of red mansions, which are consistent with current prevailing view that the first 80 chapters and the last 40 chapters were accomplished by Xueqin Cao and E Gao, respectively. Our method may shed light on the identification of writing styles in written texts.

Ratio Between Sensitive Strength to Light Information and Coupling Strength Affects Entrainment Range of Suprachiasmatic Nucleus

The suprachiasmatic nucleus(SCN), an endogenous clock in the brain of the mammals, regulates the physiological and behavioral activities according to the natural 24 h light-darkness cycle. Animals can also entrain themselves to non 24 h light-darkness cycles. The range of the periods which the animal can entrain to is called entrainment range. Previous studies have found that the entrainment range depends on the coupling strength and the sensitive strength to the light for the SCN neurons. However, the effect of the interplay between these two strengths on the entrainment range has not been examined. In the present study, we examine the effect of the ratio of the sensitive strength to the coupling strength on the entrainment range. We find that there is a parabolic-like relationship between the entrainment range and the ratio, and the largest entrainment range is obtained with a suitable ratio. Interestingly,the value of this suitable ratio is related to the comparison in the intrinsic amplitudes between the light information sensitive neurons and the light information insensitive neurons. Our finding will shed light on the interplay between the sensitive strength to the light information and the coupling strength, and the understanding for the diversity of the entrainment range among various species.