Based on a model of network encoding and dynamics called the artificial genome, we propose a segmental duplication and divergence model for evolving artificial regulatory networks. We find that this class of networks ...Based on a model of network encoding and dynamics called the artificial genome, we propose a segmental duplication and divergence model for evolving artificial regulatory networks. We find that this class of networks share structural properties with natural transcriptional regulatory networks. Specifically, these networks can display scale-free and small-world structures. We also find that these networks have a higher probability to operate in the ordered regimen, and a lower probability to operate in the chaotic regimen. That is, the dynamics of these networks is similar to that of natural networks. The results show that the structure and dynamics inherent in natural networks may be in part due to their method of generation rather than being exclusively shaped by subsequent evolution under natural selection.展开更多
The objective of this paper is to attempt to apply the theoretical techniques of probabilistic functional analysis to answer the question of existence and Uniqueness of a Random Solution to It? Stochastic Integral Equ...The objective of this paper is to attempt to apply the theoretical techniques of probabilistic functional analysis to answer the question of existence and Uniqueness of a Random Solution to It? Stochastic Integral Equation. Another type of stochastic integral equation which has been of considerable importance to applied mathematicians and engineers is that involving the It? or It?-Doob form of stochastic integrals.展开更多
A family of closed subalgebras, indexed by R (the set of real numbers), of the Wick algebra is constructed. Fundamental properties of the family are shown including the increasing property and the right–continuity. T...A family of closed subalgebras, indexed by R (the set of real numbers), of the Wick algebra is constructed. Fundamental properties of the family are shown including the increasing property and the right–continuity. The notion of adaptedness to the family is defined for quantum stochastic processes in terms of generalized operators. The existence and uniqueness of solutions adapted to the family is established for quantum stochastic differential equations in terms of generalized operators.展开更多
Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theor...Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals.展开更多
In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator...In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism.展开更多
文摘Based on a model of network encoding and dynamics called the artificial genome, we propose a segmental duplication and divergence model for evolving artificial regulatory networks. We find that this class of networks share structural properties with natural transcriptional regulatory networks. Specifically, these networks can display scale-free and small-world structures. We also find that these networks have a higher probability to operate in the ordered regimen, and a lower probability to operate in the chaotic regimen. That is, the dynamics of these networks is similar to that of natural networks. The results show that the structure and dynamics inherent in natural networks may be in part due to their method of generation rather than being exclusively shaped by subsequent evolution under natural selection.
文摘The objective of this paper is to attempt to apply the theoretical techniques of probabilistic functional analysis to answer the question of existence and Uniqueness of a Random Solution to It? Stochastic Integral Equation. Another type of stochastic integral equation which has been of considerable importance to applied mathematicians and engineers is that involving the It? or It?-Doob form of stochastic integrals.
基金Supported by National Natural Science Foundation of China(10171035)Natural Science Foundation of Gansu Province and NWNU-KJCXGC-212
文摘A family of closed subalgebras, indexed by R (the set of real numbers), of the Wick algebra is constructed. Fundamental properties of the family are shown including the increasing property and the right–continuity. The notion of adaptedness to the family is defined for quantum stochastic processes in terms of generalized operators. The existence and uniqueness of solutions adapted to the family is established for quantum stochastic differential equations in terms of generalized operators.
文摘Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals.
基金Supported by National Natural Science Foundation of China(10171035)Natural Science Foundation of Gansu Province(ZS021-A25-004-Z) NWNU-KJCXGC-212
文摘In this paper we first introduce and investigate some special classes of nonlinear maps and get several useful results. Then, by using these results, we obtain analytic criteria for checking whether or not an operator defined only on the exponential vectors of a symmetric Fock space becomes a Hilbert-Schmidt operator on the whole space. Additionally, as an application, we also get an analytic criterion for Hilbert-Schmidt operators on a Gaussian probability space through the Wiener-Ito-Segal isomorphism.
