One Kind of Multiple Dimensional Markovian BSDEs with Stochastic Linear Growth Generators

In this article, we deal with a multiple dimensional coupled Markovian BSDEs system with stochastic linear growth generators with respect to volatility processes. An existence result is provided by using approximation techniques.Comment: arXiv admin note: text overlap with arXiv:1412.121

Logic motif of combinatorial control in transcriptional networks

Combinatorial control is prevalent in transcriptional regulatory networks. However, whether there are specific logic patterns over- or under-represented in real networks remains uninvestigated. Using a theoretic model and _in-silico_ simulations, we systematically study how the relative abundance of distinct regulatory logic patterns influences the network’s global dynamics. We find that global dynamic characteristics are sensitive to several specific logic patterns regardless of the detailed network topology. We show it is possible to infer logic motifs based on the sensitivity profile and the biological interpretations of these global characteristics

Learning Loosely Connected Markov Random Fields

We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test based algorithm for learning the underlying graph structure. The novel maximization step in our algorithm ensures that the true edges are detected correctly even when there are short cycles in the graph. The number of samples required by our algorithm is C*log p, where p is the size of the graph and the constant C depends on the parameters of the model. We show that several previously studied models are examples of loosely connected Markov random fields, and our algorithm achieves the same or lower computational complexity than the previously designed algorithms for individual cases. We also get new results for more general graphical models, in particular, our algorithm learns general Ising models on the Erdos-Renyi random graph G(p, c/p) correctly with running time O(np^5).Comment: 45 pages, minor revisio