scholarly journals Return time statistics of extreme events in discrete nonlinear lattices

2017 ◽  
Vol 15 (1) ◽  
pp. 35-44
Author(s):  
Ana Mancic ◽  
Aleksandra Maluckov
Keyword(s):  
Probability Distribution ◽  
Extreme Events ◽  
Distribution Curve ◽  
Return Time ◽  
One Dimensional ◽  
Statistical Measures ◽  
Nonlinear Lattices ◽  
Dynamical Regimes ◽  
The Mean ◽  
Statistics Of Extreme Events

Time statistics of extreme events (EEs) in one-dimensional discrete Salerno lattices is investigated numerically. We show that the dependence of the mean return time of EEs on the amplitude threshold can be used as a criterion to differentiate between various dynamical regimes of the extreme events. Also, we found that dispersion of points on the time probability distribution curve can be an indicator of the appearance of EEs in the system, but it has to be complemented with other statistical measures. The results obtained here can be used to distinguish between different dynamical regimes and as identifiers of the EEs existence in the lattice system.

Global Predictability of Chaotic Epidemiological Dynamics in Coupled Populations

2003 ◽  
Vol 10 (04) ◽  
pp. 311-320
Author(s):  
Matt Davison ◽  
C. Essex ◽  
J. S. Shiner
Keyword(s):  
Standard Deviation ◽  
Probability Distribution ◽  
Coupling Strength ◽  
Chaotic Dynamics ◽  
Statistical Measures ◽  
Sensitive Dependence ◽  
Strength Dependence ◽  
The Mean ◽  
Long Term Prediction

When the dynamics of an epidemic are chaotic, detailed prediction is effectively impossible, except perhaps in the short term. However, a probability distribution underlying the motion does allow for the long term prediction of statistical measures such as the mean or the standard deviation. Even this weaker long term predictability might be lost if distinct populations with chaotic dynamics are coupled. We show that such coupling can result in a phenomenon we call “sensitive dependence on neglected dynamics”. In light of this phenomenon, it is somewhat surprising that when two logistic maps are coupled, the long term predictability of the mean and standard deviation is maintained. This is true even though the probability distribution describing the time series depends on the coupling strength. The coupling-strength dependence does reveal itself in the loss of predictability of higher order moments such as skewness and kurtosis.

scholarly journals Return Time Probability Distribution of a Finite Markov Chain

2019 ◽  
Vol 9 (1) ◽  
pp. 2520-2522
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Time Distribution ◽  
Return Time ◽  
Vital Role ◽  
Recurrence Time ◽  
Finite Markov Chain ◽  
The Mean ◽  
Discrete Markov Chain

In this paper we have considered a finite discrete Markov chain and derived a recurrence relation for the calculating the return time probability distribution. The mean recurrence time is also calculated. Return time distribution helps to identify the most frequently visited states. Return time distribution plays a vital role in the classification of Markov chain. These concepts are illustrated through an example.

SCALING OF RETURN TIMES FOR A HIGH-RESOLUTION RAINFALL TIME SERIES

Fractals ◽  
2002 ◽  
Vol 10 (03) ◽  
pp. 285-290 ◽  
Author(s):  
F. SCHMITT ◽  
C. NICOLIS
Keyword(s):  
Time Series ◽  
High Resolution ◽  
Probability Density ◽  
Extreme Events ◽  
Return Time ◽  
Rainfall Time Series ◽  
Large Intensity ◽  
Return Times ◽  
Wide Range ◽  
The Mean

Rainfall is a highly intermittent field over a wide range of time and space scales. We study a high resolution rainfall time series exhibiting large intensity fluctuations and localized events. We consider the return times of a given intensity, and show that the time series composed of these return times is itself also very intermittent, obeying to a hyperbolic probability density, entailing that the mean return time diverges. This is an unexpected property since mean return times are often introduced in meteorology, especially for the study of risk associated to extreme events. It suggests that the intermittency of first return times of extreme events should be taken into account when making statistical predictions.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

scholarly journals Probability Characteristics, Area Reduction, and Wind Directionality Effects of Extreme Pressure Coefficients of High-Rise Buildings

2021 ◽  
Vol 11 (15) ◽  
pp. 7121
Author(s):  
Shouke Li ◽  
Feipeng Xiao ◽  
Yunfeng Zou ◽  
Shouying Li ◽  
Shucheng Yang ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Pressure Coefficient ◽  
Wind Pressure ◽  
Extreme Pressure ◽  
Distribution Law ◽  
Distribution Fitting ◽  
Pressure Coefficients ◽  
High Rise ◽  
Area Reduction ◽  
The Mean

Wind tunnel tests are carried out for the Commonwealth Advisory Aeronautical Research Council (CAARC) high-rise building with a scale of 1:400 in exposure categories D. The distribution law of extreme pressure coefficients under different conditions is studied. Probability distribution fitting is performed on the measured area-averaged extreme pressure coefficients. The general extreme value (GEV) distribution is preferred for probability distribution fitting of extreme pressure coefficients. From the comparison between the area-averaged coefficients and the value from GB50009-2012, it is indicated that the wind load coefficients from GB50009-2012 may be non-conservative for the CAARC building. The area reduction effect on the extreme wind pressure is smaller than that on the mean wind pressure from the code. The recommended formula of the area reduction factor for the extreme pressure coefficient is proposed in this study. It is found that the mean and the coefficient of variation (COV) for the directionality factors are 0.85 and 0.04, respectively, when the orientation of the building is given. If the uniform distribution is given for the building’s orientation, the mean value of the directionality factors is 0.88, which is close to the directionality factor of 0.90 given in the Chinese specifications.

scholarly journals Discrete-time quantum walks generated by aperiodic fractal sequence of space coin operators

2018 ◽  
Vol 29 (10) ◽  
pp. 1850098 ◽  
Author(s):  
R. F. S. Andrade ◽  
A. M. C. Souza
Keyword(s):  
Wave Function ◽  
Probability Distribution ◽  
Discrete Time ◽  
Numerical Study ◽  
Entanglement Entropy ◽  
Quantum Effects ◽  
Quantum Walks ◽  
Cantor Set ◽  
One Dimensional ◽  
Time Quantum

Properties of one-dimensional discrete-time quantum walks (DTQWs) are sensitive to the presence of inhomogeneities in the substrate, which can be generated by defining position-dependent coin operators. Deterministic aperiodic sequences of two or more symbols provide ideal environments where these properties can be explored in a controlled way. Based on an exhaustive numerical study, this work discusses a two-coin model resulting from the construction rules that lead to the usual fractal Cantor set. Although the fraction of the less frequent coin [Formula: see text] as the size of the chain is increased, it leaves peculiar properties in the walker dynamics. They are characterized by the wave function, from which results for the probability distribution and its variance, as well as the entanglement entropy, were obtained. A number of results for different choices of the two coins are presented. The entanglement entropy has shown to be very sensitive to uncovering subtle quantum effects present in the model.

scholarly journals Distribution-Free Model for Ambulance Location Problem with Ambiguous Demand

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Feng Chu ◽  
Lu Wang ◽  
Xin Liu ◽  
Chengbin Chu ◽  
Yang Sui
Keyword(s):  
Probability Distribution ◽  
Location Problem ◽  
Service Level ◽  
Mixed Integer ◽  
Distribution Free ◽  
Demand Information ◽  
The Mean ◽  
Constrained Model ◽  
Short Time ◽  
Ambulance Location

Ambulance location problem is a key issue in Emergency Medical Service (EMS) system, which is to determine where to locate ambulances such that the emergency calls can be responded efficiently. Most related researches focus on deterministic problems or assume that the probability distribution of demand can be estimated. In practice, however, it is difficult to obtain perfect information on probability distribution. This paper investigates the ambulance location problem with partial demand information; i.e., only the mean and covariance matrix of the demands are known. The problem consists of determining base locations and the employment of ambulances, to minimize the total cost. A new distribution-free chance constrained model is proposed. Then two approximated mixed integer programming (MIP) formulations are developed to solve it. Finally, numerical experiments on benchmarks (Nickel et al., 2016) and 120 randomly generated instances are conducted, and computational results show that our proposed two formulations can ensure a high service level in a short time. Specifically, the second formulation takes less cost while guaranteeing an appropriate service level.

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