地震の時間間隔の分布, 及び之と地震動の最大振幅の分布との関係に関する統計的記述

A comprehensive temporal analysis has been performed on the 319 brightest GRBs with T90 > 2s from the BATSE current catalog. The GRBs were denoised using wavelets and subjected to an automatic pulse selection algorithm as an objective way of identifying pulses and quantifying the eects of neighbouring pulses. The number of statistically signicant pulses selected from the sample was greater than 3000. The rise times, fall times, full-widths at half-maximum (FWHM), pulse amplitudes and pulse areas were measured and the frequency distributions are presented here. All are consistent with lognormal distributions provided the pulses are well separated. The distribution of time intervals between pulses is not random but compatible with a lognormal distribution when allowance was made for the 64 ms time resolution and a small excess (5%) of long duration intervals that is often referred to as a Pareto-L evy tail. The time intervals between pulses are most important because they may be an almost direct measure of the activity in the central engine. Lognormal distributions of time intervals also occur in pulsars and SGR sources and therefore provide indirect evidence that the time intervals between pulses in GRBs are also generated by rotation powered systems with super-strong magnetic elds. A range of correlations are presented on pulse and burst properties. The rise and fall times, FWHM and area of the pulses are highly correlated with each other. The pulse amplitudes are anticorrelated with the FWHM. The time intervals between pulses and pulse amplitudes of neighbouring pulses are correlated with each other. It was also found that the number of pulses, N, in GRBs is strongly correlated with the fluence and duration and that can explain the well known correlation between duration and fluence. The GRBs were sorted into three categories based on N i.e. 3 N 12, 13 N 24 and N 25. The properties of pulses before and after the strongest pulse were compared for three categories of bursts. No major dierences were found between the distributions of the pulse properties before and after the strongest pulse in the GRB. However there is a strong trend for pulses to have slower rise times and faster fall times in the rst half of the burst and this pattern is strongest for category 3 N 12. This analysis revealed that the GRBs with large numbers of pulses have narrower and faster pulses and also larger fluences, longer durations and higher hardness ratios than the GRBs with smaller numbers of pulses. These results may be explained by either homogeneous or inhomogeneous jet models of GRBs. The GRBs with larger number of pulses are closer to the axis if varies with the opening angle of the jet and the imprint of the jet is preserved in the pulse structure of the burst. The distribution of the number of pulses per GRB broadly reflects the beaming by the jet.

Ships navigating in the Arctic and Antarctic regions frequently encounter the threat of ice. Floe ice exhibits various shapes and sizes, with significant variations in thickness and concentration across different ice fields. Estimating the number of ship-ice contact events accurately is crucial for strategic navigation and fatigue damage assessment. This paper focuses on the contact occurrence in floe ice fields which can be determined by the time intervals between contacts. The occurrence in level ice fields follows a Poisson distribution and the time intervals follow an exponential distribution which has been demonstrated in numerous studies. Based on the measurement data on Polar Supply and Research Vessel (PSRV) S.A. Agulhas II during 2018/19 Antarctic voyage which encountered extensive floe ice, this paper examines the applicability of previously proposed patterns in level ice fields to floe ice fields. A mixture exponential distribution model is proposed to fit the time intervals in floe ice fields and the statistical test is adopted to evaluate the goodness of fit. This paper then provides a procedure to obtain the contact occurrence by Monte Carlo method based on the distribution of time intervals. To further investigate the influence of contact occurrence on short term extreme distributions of local ice loads, three methods are employed and the distributions are found to be highly consistent.

We apply statistical analysis based on pairs of earthquakes to study spatial and temporal patterns of earthquake distribution in the aftershock zone of the 1984 Morgan Hill, California, earthquake (M = 6.2). We examine 6 years of preshock and 23 months of aftershock data, using frequency distributions of earthquake pairs. The nonrandomness in the observed spatial and temporal distribution of pairs is studied by comparison with simulated expected distributions. The significance of departures from the expected distributions is appraised by using tolerance limits that account for the scatter of the single trial expected frequencies. We find that the eathquake spatial distribution is nonuniform in two major ways. (1) Short‐distance clustering (distances less than 7 km) occurs in both the preshock and aftershock period. It is more pronounced and covers larger zones during the aftershock sequence. (2) A long‐distance nonuniformity is also observed (distances greater than 11 km) caused by concentration of events in two areas separated by a gap in earthquake activity. This feature is present in the preshock and early aftershock period but disappears in the late aftershock sequence. The distribution of time intervals between preshocks does not indicate any substantial nonrandom features. In contrast, the temporal distribution of aftershocks, although dominated by the classic power law decay in time, suggests the possible existence of characteristic time intervals that increase with magnitude and time after the mainshock.

The objective of this study was to compute reference SEMG values for normal subjects of 13 parameters extracted in the time, frequency and bispectrum domain, from the Biceps Brachii (BB) muscle generated under isometric voluntary contraction (IVC). SEMG signals were recorded from 94 subjects for 5 s at 10, 30, 50, 70 and 100% of maximum voluntary contraction (MVC). The Wilcoxon signed rank test was applied to detect significant differences or not at p < 0.05 between force levels for each of the 13 parameters. The main findings of this study can be summarized as follows: (i) The time domain parameters turns per second and number of zero crossings per second increase significantly with force level. (ii) The power spectrum median frequency parameter decreases significantly with force level, whereas maximum power and total power increase significantly with force level. (iii) The bispectrum parameter, maximum amplitude, increases significantly with force level with the exception the transition from 30% to 50% MVC. Although, the tests for Gaussianity and linearity show no significant difference with force level, the SEMG signal exhibits a more Gaussian distribution with increase of force up to 70% MVC. The SEMG linearity test, which is a measure of how constant the bicoherence index is in the bi-frequency domain, shows that the signal’s bicoherence index is less constant (hence, the signal is less linear) at 70% of MVC compared to 10, 30, 50 and 100% MVC. (iv) The time domain parameters have good correlation between them as well as, between each one of them and maximum and total power. The median frequency has a good (negative) correlation with the bispectrum peak amplitude. (v) No significant differences exist between values based on gender or age. The findings of this study can further be used for the assessment of subjects suffering with neuromuscular disorders, or in the rehabilitation laboratory for monitoring the elderly or the disabled, or in the occupational medicine laboratory.

A new physical model for earthquake time interval distribution

Three empirical distributions of the daily rainfall collected at the Fabra Observatory from 1917 to 1999 are fitted to different statistical models. The first two are designated as the distributions of cumulative amounts and cumulative times. The third distribution accounts for the time interval between two consecutive rainy days with rain amounts equalling or exceeding a threshold amount. Whereas the distribution of cumulative amounts follows an exponential model at monthly and annual scale, except for a few cases, the distribution of the cumulative times is well modelled by a Weibull function, whether monthly or annual scales are considered. The distribution of time intervals also follows a Weibull distribution for the different thresholds considered. In addition, the combination of the two first distributions leads to the normalised rainfall curve, NRC, which is also reproduced satisfactorily by a beta (type 1) distribution. It is worth mentioning that the NRCs follow the expected behaviour with respect to the coefficient of variation of daily rain amounts at monthly and annual scales. In addition, a better understanding of fluctuations and time trends affecting the daily pluviometric regime is achieved by analysing the annual NRCs. The impact of some features of this rain regime, developed for Barcelona, a crowded metropolitan area, on many human activities, may provides the focus of future interdisciplinary analyses.

Scaling laws of structure and fragmentation parameters of ZrO2 ceramics.

Certain correlations between characteristic events and smaller events are studied in the context of a spatially homogeneous, mechanical model for a fault. The model satisfies a one‐dimensional quasi‐linear wave equation in which the key nonlinearity is associated with the slipstick friction force at the interface between tectonic plates. We find that the model gives rise to slipping events of all sizes: the smaller events are consistent with the Gutenberg‐Richter statistical law, whereas the characteristic events have a separate statistical distribution. The crossover from smaller events to characteristic events coincides with a correlation length which sets the scale for clustering of smaller events before the characteristic rupture. Numerical results and scaling arguments relate the features of the distribution of characteristic events to the corresponding features of the distribution of smaller events as well as the length of the fault. The distribution of time intervals between characteristic events has the distinguishing features of asymmetry and a finite upper cutoff. The mean T and standard deviation σ of the time interval distribution are found to be related to features of the magnitude versus frequency distribution of smaller events, and the coefficient of variation σ/T is independent of the driving rate. Because this analysis relates properties of characteristic earthquakes to statistical features of smaller, more numerous events as well as geometric features of the fault, it may ultimately be useful for long‐term earthquake prediction.

Objective To investigate the effects of in vitro blood dilution with lactated ringer′s solution (RL), succinylated gelatin (GEL) and hydroxyethyl starch 130/0.4 (HES) on coagulopathy in the presence or absence of human fibrinogen (Fg) and human coagulation factor Ⅷ (FⅧ). Methods Blood collected from 18 patients scheduled for elective operations was diluted to 50%, followed by two different dose of Fg and FⅧ supplementation at 37 ℃. The influence was analyzed using TEG [The TEG variables of reaction time (R), coagulation time (K), growth angle (α) and maximum amplitude (MA) were determined]. Results TEG parameters changed significantly in all three groups after dilution. After dilution, the K values were increased and MA values were decreased in group RL compared to those values in whole blood (P 0.05). Conclusions Coagulation function was impaired by all three fluids with HES having the most profound impairment effect. Fg in vitro improved blood dilution induced coagulopathy. The effect of Fg supplementation depende on the kind of fluid. Coagulopathy induced by HES was completely correcterd only through high does Fg substation. Supplementation of FⅧ cannot improve blood dilution induced coagulopathy. Key words: In vitro; Hemodilution; Blood coagulation; Fibrinogen; Factor Ⅷ

In the modern society, each one is highly affected by the Internet from fundamentally living necessities to scientific developing. Surfing the Internet has become part of our life. Based on a database recording the timing of the Internet accessing for an educational institution, we present the distributions of the time intervals in Internet surfing and single website visiting. The time interval distributions follow a power law with different exponents from user to user, which is different from the universality class with characteristic exponent 1. Actually, both the single website accessing by the grouped users and the web browsing by a single use have power-law time interval distributions with exponents ranging from 2 to 3. The results in this paper give rise to a question to the mainstream hypothesis of universality classes. Whether the time interval of access Internet exist the universality class, if it exits, what is the exponential on earth? We believe this work could provide some insights of the latent mechanism of human dynamics.

When nuclear radiations or photons having a mean occurrence rate f/sub 0/ are detected by an ideal detector, the pulse train coming out of the detector also has a mean rate f/sub 0/. A method for deriving a probability density function f(s) for fluctuating dead time s in a real system is described. In the method, a time interval distribution (TID) is used. To obtain f(s), the true rate f/sub 0/ had to be determined from the TID result. Although f/sub 0/ was determined by an approximation and, therefore, the f(s) obtained was also an approximation, the method can be applied to various fields. An example of an application to a GM counter is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Knowledge about the statistical regularities of the world is essential for cognitive and sensorimotor function. In the domain of timing, prior statistics are crucial for optimal prediction, adaptation and planning. Where and how the nervous system encodes temporal statistics is, however, not known. Based on physiological and anatomical evidence for cerebellar learning, we develop a computational model that demonstrates how the cerebellum could learn prior distributions of time intervals and support Bayesian temporal estimation. The model shows that salient features observed in human Bayesian time interval estimates can be readily captured by learning in the cerebellar cortex and circuit level computations in the cerebellar deep nuclei. We test human behavior in two cerebellar timing tasks and find prior-dependent biases in timing that are consistent with the predictions of the cerebellar model.

In recent years, people have found the power law distribution appears in natural and human activities, even in the event of terrorism. However, In this paper we analyze the time interval distribution of terrorism events in several Asia countries, and find that not all of the time interval distributions are showing a power law distribution. The time interval distribution of terrorism events in China is exponential distribution. Through calculating burstiness parameter and memory parameter it is found that power-law distribution is origin from strong burst and the burst and memory are relatively weak corresponding to and the time interval exponent distribution of terrorism events in China.

A two-degree-of-freedom dynamical system has been analyzed to determine an optimum control sequence which will drive the dynamical system from an arbitrary initial position and velocity to one of a prescribed set of terminal position and velocity's in minimum time. The basic complexities are: (1) that the forcing function can change only at discrete intervals of time, and (2) that the prescribed terminal states allow a multiplicity of solutions to prevail. A novel but not unique force program which is dependent upon the initial state of the system has been determined. This program consists essentially of the continuous application of a force of the proper sense and maximum allowable amplitude followed by a time during which no force is applied. This is followed by a time interval in which the forcing function has a maximum amplitude but is of the opposite sign to that used in the first part of the program.

Introduction. When managing traffic at the packet level in modern telecommunication networks, it is proposed to use methods that transform a self-similar stochastic packet flow into a quasi-deterministic one. To do this, it is required to apply complex probabilistic laws of distribution of self-similar flows. From the literature, methods of balancing the network load are known, which, with the problem indicated above, contribute to increasing the efficiency of telecommunication systems. However, there is no strictly mathematical solution to find out the optimal probabilistic characteristics of the output flow, based on the input flow. The presented research is intended to fill this gap. Its objective is to create a method for determining the optimal probabilistic characteristics of the packet flow, using the minimum value of the proximity measure of the self-similar input and quasi-deterministic output flows.Materials and Methods. To solve the research problem, the parameters of the output flow distribution were selected so that the approximation function was close to 𝛿𝛿-function. The Kullback-Leibler divergence was used as a proximity measure of the input and output distributions of time intervals. Methods of set theory, metric spaces, multidimensional optimization, and teletraffic were used. The solution algorithm included minimization of the Kullback-Leibler divergence and the limit passage to 𝛿𝛿-function.Results. A probability distribution is shown — an approximation of 𝛿𝛿-function, which maintains the equality of time intervals of a quasi-deterministic output packet flow. A method for transforming a self-similar input flow into a quasideterministic output flow is presented. The Kullback–Leibler divergence was used as a measure of their proximity. The minimum of the Kullback-Leibler divergence between the input and output flows with a normal distribution was achieved in the case of equality of the mathematical expectations of these flows. Using the passage to the limit, it has been established that time interval T between packets of the quasi-deterministic output flow must be equal to the mathematical expectation of the time intervals between packets of the input self-similar flow. To obtain a quasi-deterministic flow, the passage to the limit is performed for the found value of the mathematical expectation at σ → 0.Discussion and Conclusion. The application of this method will reduce the negative impact of self-similarity of network traffic on the efficiency of the telecommunication network. The use of quasi-deterministic flows makes it possible to predict the load of network resources, which can be the basis for improving the quality of user service. Two difficulties associated with calculations and practical implementation of the solution are eliminated. Firstly, it is difficult to use the delta function as a function of the output flow distribution density. Secondly, there are no ideal deterministic flows in the operation of telecommunication networks. The proposed method has great potential in the design and optimization of communication networks.