Monte Carlo Tennis: A Stochastic Markov Chain Model

2009 ◽  
Vol 5 (3) ◽  
Author(s):  
Paul K Newton ◽  
Kamran Aslam
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Model ◽  
Chain Model ◽  
Stochastic Markov Chain

scholarly journals Uncertainty quantification on a spatial Markov-chain model for the progression of skin cancer

2019 ◽  
Vol 80 (3) ◽  
pp. 545-573 ◽  
Author(s):  
Fred Vermolen ◽  
Ilkka Pölönen
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Skin Cancer ◽  
Input Data ◽  
Markov Chain Model ◽  
Chain Model ◽  
Computational Domain ◽  
Spatial Markov Chain ◽  
Binary State ◽  
Probabilistic Nature

AbstractA spatial Markov-chain model is formulated for the progression of skin cancer. The model is based on the division of the computational domain into nodal points, that can be in a binary state: either in ‘cancer state’ or in ‘non-cancer state’. The model assigns probabilities for the non-reversible transition from ‘non-cancer’ state to the ‘cancer state’ that depend on the states of the neighbouring nodes. The likelihood of transition further depends on the life burden intensity of the UV-rays that the skin is exposed to. The probabilistic nature of the process and the uncertainty in the input data is assessed by the use of Monte Carlo simulations. A good fit between experiments on mice and our model has been obtained.

scholarly journals Study on Driving Cycle Synthesis Method for City Buses considering Random Passenger Load

2020 ◽  
Vol 2020 ◽  
pp. 1-21 ◽  
Author(s):  
Xiaodong Liu ◽  
Jian Ma ◽  
Xuan Zhao ◽  
Juan Du ◽  
Yanfeng Xiong
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Fuel Consumption ◽  
Real World ◽  
Markov Chain Model ◽  
Synthesis Method ◽  
Driving Cycle ◽  
Chain Model ◽  
Bus Stops ◽  
Road Slope

This paper proposes a novel driving cycle construction method in consideration of velocity, road slope, and passenger load, based on a real-world bus route with a plug-in hybrid electric bus (PHEB). The main purpose is to address the disadvantage that an inaccurate reflection of the real-world driving characteristics for city buses will be caused when ignoring the passenger load in the course of a driving cycle synthesis. Two contributions are supplemented to distinguish from the previous research. Firstly, a novel station-based method is proposed aiming at developing a driving cycle with high accuracy. The kinematic segments are partitioned according to the distance of adjacent bus stops, while a two-dimensional Markov chain Monte Carlo method is employed to synthesize driving cycle between each interval of adjacent bus stops. Secondly, the random passenger load for different bus stops is treated as a discrete Markov chain model, according to the correlation analysis of the measured passenger data which are distinguished for off-peak and peak hours. Meanwhile, Monte Carlo simulation and maximum likelihood estimation are utilized to determine the most likely number of passengers for each bus stop. At last, the fuel consumption of the PHEB is simulated with the best-synthesized driving cycle and contrasted to the mean fuel consumption of the later measured data which is composed of the velocity, road slope, and the passenger load. The results demonstrate that the synthesized driving cycle has a higher accuracy on fuel consumption estimation.

scholarly journals Aplicação do Modelo Estocástico Cadeia de Markov a Dados Diários de Precipitação dos Estados da Bahia e Sergipe (Application of Stochastic Markov Chain Model to Data Daily Rainfall of the States of Bahia and Sergipe)

2012 ◽  
Vol 5 (3) ◽  
pp. 509 ◽  
Author(s):  
Winicius Santos Araújo ◽  
Francisco De Assis Salviano de Sousa ◽  
José Ivaldo Barbosa de Brito ◽  
Lourivaldo Mota Lima
Keyword(s):  
Spatial Distribution ◽  
Markov Chain ◽  
Markov Chain Model ◽  
Winter Season ◽  
Coastal Region ◽  
Daily Rainfall ◽  
Summer Season ◽  
High Availability ◽  
Chain Model ◽  
Stochastic Markov Chain

O objetivo desta pesquisa foi fornecer uma distribuição espacial e computar as probabilidades incondicionais e condicionais de primeira ordem das precipitações dos Estados da Bahia e Sergipe. Para tanto, foram utilizados dados diários pluviais referentes a um período de 47 anos (1960-2006) de 75 postos e/ou estações meteorológicas fornecidos pela antiga rede de postos da SUDENE através do DCA. Os resultados mostram que a zona oeste da área pesquisada é a mais favorecida com a precipitação na estação verão, ocorrendo o oposto disto na estação inverno; o leste é o mais beneficiado no inverno, o sul na primavera, e o norte no outono. Foi obtido que a probabilidade incondicional, P(C), na região costeira, é influenciada pela alta disponibilidade de umidade do Atlântico e pela geração de sistemas que provocam precipitação devido ao contraste de temperatura da superfície oceano-continente, particularmente durante os meses de outono e primavera. No verão o efeito oceânico não é percebido devido à alta disponibilidade de umidade sobre a área pesquisada e a alta persistência observada da precipitação diária está associada com os núcleos de máximas precipitações que se destacam na estação verão, enquanto que no inverno a baixa persistência foi predominante.Palavras - chave: distribuição espacial, cadeia de markov, precipitação diária. Application of Stochastic Markov Chain Model to Data Daily Rainfall of the States of Bahia and Sergipe ABSTRACTThe objective of this research was to provide a spatial distribution and compute the probabilities conditional and unconditional first order of precipitation of the States of Bahia and Sergipe. It had been used daily rainfall data relating to a period of 47 years (1960-2006) of 75 stations and/or meteorological stations provided by the former station network SUDENE by DCA. The results show that the area west of the area searched is more favored with rainfall in the summer season, the opposite occurring in this winter season, the east is the most improved in the winter, spring in the south, and north in the autumn. It was obtained that the unconditional probability, P(C), the coastal region, is influenced by the high availability of moisture from the Atlantic and the generation of systems that cause precipitation due to the contrast of surface temperature of ocean-continent, particularly during the autumn months and Spring. In summer the ocean effect is not perceived due to the high availability of moisture over the area surveyed and observed high persistence of daily rainfall is associated with the nuclei of maximum precipitation that stand out in the summer season, while in winter the low persistence prevailed.Keywords: spatial distribution, markov chain, daily precipitation.

scholarly journals A Stochastic Markov Chain Model to Describe Lung Cancer Growth and Metastasis

PLoS ONE ◽  
2012 ◽  
Vol 7 (4) ◽  
pp. e34637 ◽  
Author(s):  
Paul K. Newton ◽  
Jeremy Mason ◽  
Kelly Bethel ◽  
Lyudmila A. Bazhenova ◽  
Jorge Nieva ◽  
...  
Keyword(s):  
Lung Cancer ◽  
Markov Chain ◽  
Markov Chain Model ◽  
Cancer Growth ◽  
Chain Model ◽  
Stochastic Markov Chain
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