Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the rob...Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the robust range for a certain optimal policy and to obtain value intervals of exact transition probabilities.Our research yields powerful contributions for Markov decision processes(MDPs)with uncertain transition probabilities.We first propose a method for estimating unknown transition probabilities based on maximum likelihood.Since the estimation may be far from accurate,and the highest expected total reward of the MDP may be sensitive to these transition probabilities,we analyze the robustness of an optimal policy and propose an approach for robust analysis.After giving the definition of a robust optimal policy with uncertain transition probabilities represented as sets of numbers,we formulate a model to obtain the optimal policy.Finally,we define the value intervals of the exact transition probabilities and construct models to determine the lower and upper bounds.Numerical examples are given to show the practicability of our methods.展开更多
Background:Patients with type 2 diabetes are at high risk for developing multiple chronic complications.However,there is a lack of studies of the cumulative number of diabetic complications in China.Methods:A retrospe...Background:Patients with type 2 diabetes are at high risk for developing multiple chronic complications.However,there is a lack of studies of the cumulative number of diabetic complications in China.Methods:A retrospective cohort study was performed from 2009 to 2021.Type 2 diabetes patients who were first diagnosed after the age of 35 years between January 1,2009,and December 31,2017,were included.Five states were defined according to the number of chronic complications:no(S0),one(S1),two(S2),three(S3),and four or more complications(S4).A multi-state Markov model was constructed to estimate transition probability,transition intensity,mean sojourn time,and the possible factors for each state.Results:The study included 32653 type 2 diabetes patients(mean age,59.59 years;15929(48.8%)male),and mean follow-up time of 7.75 years.In all,4375 transitions were observed.The 12-year transition probability of from state S0 to S1 was the lowest at 16.4%,while that from S2 to S3 was the highest,at 45.6%.Higher fasting blood glucose,lower high-density lipoprotein cholesterol,higher total cholesterol,and an unhealthy diet were associated with higher risk of progression from S0 to S1.Being female,less than 60 years old,weekly physical activity,and vegetarian diet decreased this risk.Being female and less than 60 years old reduced the likelihood of transition from S1 to S2,whereas lower high-density lipoprotein cholesterol increased this likelihood.Conclusions:Following the occurrence of two complications in type 2 diabetes patients,the risk for accumulating a third complication within a short time is significantly increased.It is important to take advantage of the stable window period when patients have fewer than two complications,strengthen the monitoring of blood glucose and blood lipids,and encourage patients to maintain good living habits to prevent further deterioration.展开更多
Significant land-use changes in North Dakota have been reported and are widespread over the entire state. Such changing patterns may portend localized impairment to agricultural watersheds. In this study, Land-use Lan...Significant land-use changes in North Dakota have been reported and are widespread over the entire state. Such changing patterns may portend localized impairment to agricultural watersheds. In this study, Land-use Land-cover (LULC) change was modeled using geostatistics. The study area was within the Pipestem Creek watershed, a part of the Missouri Watershed James Subregion of North Dakota, USA. Landsat Thematic mapper images from the years 2007, 2011 and 2015 were used as preliminary data. LULC information for these datasets was acquired from the Global Land-cover facility and Landsat Program. Data analysis, spectral classification and post classification techniques were applied on the datasets. A transition matrix was derived using a Markov chain Monte Carlo (MCMC) model. This study demonstrates that the integration of satellite remote sensing, GIS and statistics may be an effective approach for analyzing the direction, rate, and spatial pattern of land-use change.展开更多
1 引言迭代函数系IFS(Iterated Function Systems),是混沌分形理论研究的一个重要部分,其理论与方法是分形自然景观模拟及分形图像压缩的理论基础。1985年,Williams和Hutchinson开创了分形几何中IFS的研究,建立了IFS的一般基础理论;M.F....1 引言迭代函数系IFS(Iterated Function Systems),是混沌分形理论研究的一个重要部分,其理论与方法是分形自然景观模拟及分形图像压缩的理论基础。1985年,Williams和Hutchinson开创了分形几何中IFS的研究,建立了IFS的一般基础理论;M.F.Barnsley和S.Demko的进一步工作使得这一方法成为构造任意维数分形集方便、有效的方法,并将之应用到图像的压缩与处理,使得该方法引起人们的关注。展开更多
基金Supported by the National Natural Science Foundation of China(71571019).
文摘Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the robust range for a certain optimal policy and to obtain value intervals of exact transition probabilities.Our research yields powerful contributions for Markov decision processes(MDPs)with uncertain transition probabilities.We first propose a method for estimating unknown transition probabilities based on maximum likelihood.Since the estimation may be far from accurate,and the highest expected total reward of the MDP may be sensitive to these transition probabilities,we analyze the robustness of an optimal policy and propose an approach for robust analysis.After giving the definition of a robust optimal policy with uncertain transition probabilities represented as sets of numbers,we formulate a model to obtain the optimal policy.Finally,we define the value intervals of the exact transition probabilities and construct models to determine the lower and upper bounds.Numerical examples are given to show the practicability of our methods.
基金supported by the National Natural Science Foundation of China(grant No.72074011)the Real World Study Project of Hainan Boao Lecheng Pilot Zone(Real World Study Base of NMPA)(HNLC2022RWS012)+1 种基金the fundamental research funds for central public welfare research institutes(2023CZ-11)National Natural Science Foundation of China(No.82003536).
文摘Background:Patients with type 2 diabetes are at high risk for developing multiple chronic complications.However,there is a lack of studies of the cumulative number of diabetic complications in China.Methods:A retrospective cohort study was performed from 2009 to 2021.Type 2 diabetes patients who were first diagnosed after the age of 35 years between January 1,2009,and December 31,2017,were included.Five states were defined according to the number of chronic complications:no(S0),one(S1),two(S2),three(S3),and four or more complications(S4).A multi-state Markov model was constructed to estimate transition probability,transition intensity,mean sojourn time,and the possible factors for each state.Results:The study included 32653 type 2 diabetes patients(mean age,59.59 years;15929(48.8%)male),and mean follow-up time of 7.75 years.In all,4375 transitions were observed.The 12-year transition probability of from state S0 to S1 was the lowest at 16.4%,while that from S2 to S3 was the highest,at 45.6%.Higher fasting blood glucose,lower high-density lipoprotein cholesterol,higher total cholesterol,and an unhealthy diet were associated with higher risk of progression from S0 to S1.Being female,less than 60 years old,weekly physical activity,and vegetarian diet decreased this risk.Being female and less than 60 years old reduced the likelihood of transition from S1 to S2,whereas lower high-density lipoprotein cholesterol increased this likelihood.Conclusions:Following the occurrence of two complications in type 2 diabetes patients,the risk for accumulating a third complication within a short time is significantly increased.It is important to take advantage of the stable window period when patients have fewer than two complications,strengthen the monitoring of blood glucose and blood lipids,and encourage patients to maintain good living habits to prevent further deterioration.
文摘Significant land-use changes in North Dakota have been reported and are widespread over the entire state. Such changing patterns may portend localized impairment to agricultural watersheds. In this study, Land-use Land-cover (LULC) change was modeled using geostatistics. The study area was within the Pipestem Creek watershed, a part of the Missouri Watershed James Subregion of North Dakota, USA. Landsat Thematic mapper images from the years 2007, 2011 and 2015 were used as preliminary data. LULC information for these datasets was acquired from the Global Land-cover facility and Landsat Program. Data analysis, spectral classification and post classification techniques were applied on the datasets. A transition matrix was derived using a Markov chain Monte Carlo (MCMC) model. This study demonstrates that the integration of satellite remote sensing, GIS and statistics may be an effective approach for analyzing the direction, rate, and spatial pattern of land-use change.
文摘1 引言迭代函数系IFS(Iterated Function Systems),是混沌分形理论研究的一个重要部分,其理论与方法是分形自然景观模拟及分形图像压缩的理论基础。1985年,Williams和Hutchinson开创了分形几何中IFS的研究,建立了IFS的一般基础理论;M.F.Barnsley和S.Demko的进一步工作使得这一方法成为构造任意维数分形集方便、有效的方法,并将之应用到图像的压缩与处理,使得该方法引起人们的关注。
