This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and order...This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.展开更多
Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for ...Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,展开更多
The Markov chain random field(MCRF)model is a spatial statistical approach for modeling categorical spatial variables in multiple dimensions.However,this approach tends to be computationally costly when dealing with l...The Markov chain random field(MCRF)model is a spatial statistical approach for modeling categorical spatial variables in multiple dimensions.However,this approach tends to be computationally costly when dealing with large data sets because of its sequential simulation processes.Therefore,improving its computational efficiency is necessary in order to run this model on larger sizes of spatial data.In this study,we suggested four parallel computing solutions by using both central processing unit(CPU)and graphics processing unit(GPU)for executing the sequential simulation algorithm of the MCRF model,and compared them with the nonparallel computing solution on computation time spent for a land cover post-classification.The four parallel computing solutions are:(1)multicore processor parallel computing(MP),(2)parallel computing by GPU-accelerated nearest neighbor searching(GNNS),(3)MP with GPU-accelerated nearest neighbor searching(MPGNNS),and(4)parallel computing by GPU-accelerated approximation and GPU-accelerated nearest neighbor searching(GA-GNNS).Experimental results indicated that all of the four parallel computing solutions are at least 1.8×faster than the nonparallel solution.Particularly,the GA-GNNS solution with 512 threads per block is around 83×faster than the nonparallel solution when conducting a land cover post-classification with a remotely sensed image of 1000×1000 pixels.展开更多
文摘This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.
基金Supported by National Basic Research Program of China(973 Program No.2007CBS14903)National Science Foundation of China(70671069)
文摘Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,
基金supported in part by the U.S.National Science Foundation[grant number 1414108]Division of Behavioral and Cognitive Sciences.
文摘The Markov chain random field(MCRF)model is a spatial statistical approach for modeling categorical spatial variables in multiple dimensions.However,this approach tends to be computationally costly when dealing with large data sets because of its sequential simulation processes.Therefore,improving its computational efficiency is necessary in order to run this model on larger sizes of spatial data.In this study,we suggested four parallel computing solutions by using both central processing unit(CPU)and graphics processing unit(GPU)for executing the sequential simulation algorithm of the MCRF model,and compared them with the nonparallel computing solution on computation time spent for a land cover post-classification.The four parallel computing solutions are:(1)multicore processor parallel computing(MP),(2)parallel computing by GPU-accelerated nearest neighbor searching(GNNS),(3)MP with GPU-accelerated nearest neighbor searching(MPGNNS),and(4)parallel computing by GPU-accelerated approximation and GPU-accelerated nearest neighbor searching(GA-GNNS).Experimental results indicated that all of the four parallel computing solutions are at least 1.8×faster than the nonparallel solution.Particularly,the GA-GNNS solution with 512 threads per block is around 83×faster than the nonparallel solution when conducting a land cover post-classification with a remotely sensed image of 1000×1000 pixels.
