scholarly journals Characteristics of Single Encounters of Long-Periodic Comets With Jupiter

1979 ◽  
Vol 81 ◽  
pp. 299-301
Author(s):  
Tsuko Nakamura
Keyword(s):  
Random Walk ◽  
Probability Distributions ◽  
Numerical Integrations ◽  
Elliptic Orbits ◽  
Parabolic Orbits ◽  
Statistical Results

Original nearly parabolic orbits of comets are known to be evolved toward short-periodic elliptic orbits as statistical results of hundreds of encounters with Jupiter. There seems to be two methods to handle the process, namely, the method by exact numerical integrations for each orbit (Everhart, 1972) and random walk approach by using probability distributions of perturbations after single encounters (Lyttleton and Hammersley, 1963; Shteins, 1972). Since both methods need a great number of input parabolic comets to have only a few tens of short-periodic ones, the second method may save time compared with the first one, which is in turn more accurate. The purpose of this paper is to clarify the characteristics of single-encounter effects, in order to develope the second method more elaborately and extensively.

Stochastic Models and Fluctuations in Reversal Time of Ambiguous Figures

Perception ◽  
1977 ◽  
Vol 6 (6) ◽  
pp. 645-656 ◽  
Author(s):  
Angelo de Marco ◽  
Piero Penengo ◽  
Aurelia Trabucco ◽  
Antonio Borsellino ◽  
Franco Carlini ◽  
...  
Keyword(s):  
Random Walk ◽  
Gamma Distribution ◽  
Stochastic Models ◽  
Strong Correlation ◽  
Probability Distributions ◽  
Poisson Model ◽  
Ambiguous Figures ◽  
Underlying Process ◽  
Reversal Time ◽  
Low Efficiency

Five probability distributions for the description of temporal fluctuations in the perception of ambiguous figures were fitted to previously obtained experimental results and classified according to their efficiency in describing the data. The gamma, Wiener, and Capocelli-Ricciardi distributions showed the highest efficiency, while the χ2 and Taylor-Aldridge distributions showed a very low efficiency. Therefore the underlying process may be described either by a simple Poisson model or by a random-walk model. For the gamma distribution there was a strong correlation between the parameters, while for the Wiener distribution this correlation was lower.

scholarly journals Efficient circuits for quantum walks

2010 ◽  
Vol 10 (5&6) ◽  
pp. 420-434
Author(s):  
C.-F. Chiang ◽  
D. Nagaj ◽  
P. Wocjan
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Probability Distributions ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Problem Size ◽  
Integrable Probability ◽  
The Difference ◽  
General Method

We present an efficient general method for realizing a quantum walk operator corresponding to an arbitrary sparse classical random walk. Our approach is based on Grover and Rudolph's method for preparing coherent versions of efficiently integrable probability distributions \cite{GroverRudolph}. This method is intended for use in quantum walk algorithms with polynomial speedups, whose complexity is usually measured in terms of how many times we have to apply a step of a quantum walk \cite{Szegedy}, compared to the number of necessary classical Markov chain steps. We consider a finer notion of complexity including the number of elementary gates it takes to implement each step of the quantum walk with some desired accuracy. The difference in complexity for various implementation approaches is that our method scales linearly in the sparsity parameter and poly-logarithmically with the inverse of the desired precision. The best previously known general methods either scale quadratically in the sparsity parameter, or polynomially in the inverse precision. Our approach is especially relevant for implementing quantum walks corresponding to classical random walks like those used in the classical algorithms for approximating permanents \cite{Vigoda, Vazirani} and sampling from binary contingency tables \cite{Stefankovi}. In those algorithms, the sparsity parameter grows with the problem size, while maintaining high precision is required.

Fractional diffusion: probability distributions and random walk models

2002 ◽  
Vol 305 (1-2) ◽  
pp. 106-112 ◽  
Author(s):  
Rudolf Gorenflo ◽  
Francesco Mainardi ◽  
Daniele Moretti ◽  
Gianni Pagnini ◽  
Paolo Paradisi
Keyword(s):  
Random Walk ◽  
Probability Distributions ◽  
Fractional Diffusion

scholarly journals Verification of the Returns to Scale of Production Type for the Russian Federation Regions

2019 ◽  
Vol 224 ◽  
pp. 06011
Author(s):  
Igor Kirilyuk ◽  
Oleg Senko
Keyword(s):  
Time Series ◽  
Random Walk ◽  
Regression Model ◽  
Probability Distributions ◽  
Multivariate Time Series ◽  
Returns To Scale ◽  
Production Functions ◽  
Time Series Regression ◽  
Production Type ◽  
Statistical Validity

Monte-Carlo methods to asses a statistical validity of the relationship between coefficients of time series regression model were proposed. In economics such a relationship is present in the case when constant return to scale in production functions is assumed. The techniques being discussed here are virtually free from assumptions about underlying probability distributions and may be used in the case, when target variable or regressors are time series with random walk. This is achieved by comparing the regression model built on truly multivariate time series with those built on simulated time series with random walk. It has been shown that for the production functions of most Russian regions, the returns to scale significantly differs from a constant value at p<0.05.

Acomprehensive computer database for medical physics on-call program

2019 ◽  
Vol 19 (1) ◽  
pp. 10-14
Author(s):  
Mohamed Mohamed ◽  
James C. L. Chow
Keyword(s):  
Resource Allocation ◽  
Strategic Planning ◽  
Data Transfer ◽  
Probability Distributions ◽  
Medical Physics ◽  
Treatment Site ◽  
Emergency Radiotherapy ◽  
Statistical Results ◽  
Excel File

AbstractPurpose: A comprehensive and robust computer database was built to record and analyse the medical physics on-call data in emergency radiotherapy. The probability distributions of the on-call events varying with day and week were studied.Materials and methods: Variables of medical physics on-call events such as date and time of the event, number of event per day/week/month, treatment site of the event and identity of the on-call physicist were input to a programmed Excel file. The Excel file was linked to the MATLAB platform for data transfer and analysis. The total number of on-call events per day in a week and per month in a year were calculated based on the physics on-call data in 2010–18. In addition, probability distributions of on-call events varying with days in a week (Monday–Sunday) and months (January–December) in a year were determined.Results: For the total number of medical physics on-call events per week in 2010–18, it was found that the number was similar from Sundays to Thursdays but increased significantly on Fridays before the weekend. The total number of events in a year showed that the physics on-call events increased gradually from January up to March, then decreased in April and slowly increased until another peak in September. The number of events decreased in October from September, and increased again to reach another peak in December. It should be noted that March, September and December are months close to Easter, Labour Day and Christmas, when radiation staff usually take long holidays.Conclusions: A database to record and analyse the medical physics on-call data was created. Different variables such as the number of events per week and per year could be plotted. This roster could consider the statistical results to prepare a schedule with better balance of workload compared with scheduling it randomly. Moreover, the emergency radiotherapy team could use the analysed results to enhance their budget/resource allocation and strategic planning.

Moments based approximation for the stationary distribution of a random walk in Z+ with an application to the M/GI/1/n queueing system

2000 ◽  
Vol 37 (1) ◽  
pp. 290-299
Author(s):  
F. Simonot
Keyword(s):  
Random Walk ◽  
Convergence Rate ◽  
Stationary Distribution ◽  
Upper Bound ◽  
Queueing System ◽  
Probability Distributions

In this paper we consider an irreducible random walk in Z+ defined by X(m+1) = max(0, X(m) + A(m+1)) with E{A} < 0 and for an s ≥ 0 where a+ = max(0,a). Let π be the stationary distribution of X. We show that one can find probability distributions πn supported by {0,n} such that ||πn - π||1 ≤ Cn-s, where the constant C is computable in terms of the moments of A, and also that ||πn - π||1 = o(n-s). Moreover, this upper bound reveals exact for s ≥ 1, in the sense that, for any positive ε, we can find a random walk fulfilling the above assumptions and for which the relation ||πn - π||1 = o(n-s-ε) does not hold. This result is used to derive the exact convergence rate of the time stationary distribution of an M/GI/1/n queueing system to the time stationary distribution of the corresponding M/GI/1 queueing system when n tends to infinity.

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