Narrow Results

In this paper, we propose a novel ensemble gene selection method to obtain a gene subset. Then we provide a reverse construction method of gene network derived from expression profile data of the gene subset. The uncertainty coefficient based on information entropy are used to define the existence of logical relations among these genes. If the uncertainty coefficient between some genes exceeds predefined thresholds, the gene nodes will be connected by directed edges. Thus, a gene network is generated, which we define as gene logical network. This method is applied to the breast cancer data including control group and experimental group, with comparisons of the 2nd-order logic type distribution, average degree as well as average path length of the networks. It is found that these structures with different networks are quite distinct. By the comparison of the degree difference between control group and experimental group, the key genes are picked up. By defining the dynamics evolution rules of state transition based on the logical regulation among the key genes in the network, the dynamic behaviors for normal breast cells and cells with cancer of different stages are simulated numerically. Some of them are highly related to the development of breast cancer through literature inquiry. The study may provide a useful revelation to the biological mechanism in the formation and development of cancer.

This paper presents results on the dynamics of asynchronous irregular cellular automata (as representations of natural information-processing systems). It is an approach to explaining global dynamics from local dynamics without the use of unrealistic intermediate structure (i.e., without synchronization or regular communication). The unrealistic intermediate structure is replaced by the the realistic assumption that local behavior is entropy reducing (an idea of E. Schrödinger).

It has been shown that, for systems composed of cells programmed as cyclic finite-state automata, the observed global oscillation can be explained in terms of the structure of attractors in the global state space. The degree of local connectivity (i.e., of communication between cells) is shown here to determine the size of global attractors, and in turn the sharpness of global behavior. However, the primary result here is the extension of these results to systems whose cells are programmed as arbitrary strongly connected automata. Finally, these phenomena are demonstrated by the simulations.

Non-autonomous dynamical systems generate cocycles w.r.t. a flow. We give conditions for the existence of attractors for cocycles based on the so-called pull back convergence. These conditions will be applied to the non-autonomous Navier Stokes equation. In particular. we do not need compactness assumption for the time dependent coefficients of this equation.