The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-F...The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-Flipper operation preserves the regularity and weak connectivity of multi-digraphs.The generalized 1-Flipper operation is proved to be symmetric.Moreover,it is presented that a series of random generalized 1-Flipper operations eventually lead to a uniform probability distribution over all connected d-regular multi-digraphs without loops.展开更多
Some dynamical properties were discussed for additive cellular automata(CA)over finite abelian groups.These properties include surjection,ergodicity,sensitivity to initial conditions and positive expansivity.Some nece...Some dynamical properties were discussed for additive cellular automata(CA)over finite abelian groups.These properties include surjection,ergodicity,sensitivity to initial conditions and positive expansivity.Some necessary and sufficient conditions of determining ergodicity and sensitivity of the above additive CA were presented,respectively.A necessary condition for the positive expansivity of the above additive CA was given.The positive expansivity was proved to be preserved under the shift mappings for the general CA.The discussion was mainly based on the structure theorem of the finite abelian groups and the matrix associated with the global rule of the additive CA over the finite abelian p-groups.展开更多
基金National Natural Science Foundation of China(No.11671258)。
文摘The properties of generalized flip Markov chains on connected regular digraphs are discussed.The 1-Flipper operation on Markov chains for undirected graphs is generalized to that for multi-digraphs.The generalized 1-Flipper operation preserves the regularity and weak connectivity of multi-digraphs.The generalized 1-Flipper operation is proved to be symmetric.Moreover,it is presented that a series of random generalized 1-Flipper operations eventually lead to a uniform probability distribution over all connected d-regular multi-digraphs without loops.
基金National Natural Science Foundation of China(No.11671258)。
文摘Some dynamical properties were discussed for additive cellular automata(CA)over finite abelian groups.These properties include surjection,ergodicity,sensitivity to initial conditions and positive expansivity.Some necessary and sufficient conditions of determining ergodicity and sensitivity of the above additive CA were presented,respectively.A necessary condition for the positive expansivity of the above additive CA was given.The positive expansivity was proved to be preserved under the shift mappings for the general CA.The discussion was mainly based on the structure theorem of the finite abelian groups and the matrix associated with the global rule of the additive CA over the finite abelian p-groups.
