Exact Algorithms for Maximum Independent Set

We show that the maximum independent set problem (MIS) on an $n$-vertex graph can be solved in $1.1996^nn^{O(1)}$ time and polynomial space, which even is faster than Robson's $1.2109^{n}n^{O(1)}$-time exponential-space algorithm published in 1986. We also obtain improved algorithms for MIS in graphs with maximum degree 6 and 7, which run in time of $1.1893^nn^{O(1)}$ and $1.1970^nn^{O(1)}$, respectively. Our algorithms are obtained by using fast algorithms for MIS in low-degree graphs in a hierarchical way and making a careful analyses on the structure of bounded-degree graphs

Improvements in the reconstruction of time-varying gene regulatory networks: dynamic programming and regularization by information sharing among genes

<b>Method:</b> Dynamic Bayesian networks (DBNs) have been applied widely to reconstruct the structure of regulatory processes from time series data, and they have established themselves as a standard modelling tool in computational systems biology. The conventional approach is based on the assumption of a homogeneous Markov chain, and many recent research efforts have focused on relaxing this restriction. An approach that enjoys particular popularity is based on a combination of a DBN with a multiple changepoint process, and the application of a Bayesian inference scheme via reversible jump Markov chain Monte Carlo (RJMCMC). In the present article, we expand this approach in two ways. First, we show that a dynamic programming scheme allows the changepoints to be sampled from the correct conditional distribution, which results in improved convergence over RJMCMC. Second, we introduce a novel Bayesian clustering and information sharing scheme among nodes, which provides a mechanism for automatic model complexity tuning. <b>Results:</b> We evaluate the dynamic programming scheme on expression time series for Arabidopsis thaliana genes involved in circadian regulation. In a simulation study we demonstrate that the regularization scheme improves the network reconstruction accuracy over that obtained with recently proposed inhomogeneous DBNs. For gene expression profiles from a synthetically designed Saccharomyces cerevisiae strain under switching carbon metabolism we show that the combination of both: dynamic programming and regularization yields an inference procedure that outperforms two alternative established network reconstruction methods from the biology literature

X(1812) in Quarkonia-Glueball-Hybrid Mixing Scheme

Recently a $J^{PC}=0^{++}$ (X(1812)) state with a mass near the threshold of $\omega$ and $\phi$ has been observed by the BES collaboration in $J/\psi \to \gamma \omega \phi$ decay. It has been suggested that it is a $I^G = 0^+$ state. If it is true, this state fits in a mixing scheme based on quarkonia, glueball and hybrid (QGH) very nicely where five physical states are predicted. Together with the known $f_0(1370)$, $f_0(1500)$, $f_0(1710)$, and $f_0(1790)$ states, X(1812) completes the five members in this family. Using known experimental data on these particles we determine the ranges of the mixing parameters and predict decay properties for X(1812). We also discuss some features which may be able to distinguish between four-quark and hybrid mixing schemes.Comment: 15 pages, 2 figures, 3 table

Constraining supersymmetry from the satellite experiments

In this paper we study the detectability of $\gamma$-rays from dark matter annihilation in the subhalos of the Milky Way by the satellite-based experiments, EGRET and GLAST. We work in the frame of supersymmetric extension of the standard model and assume the lightest neutralino being the dark matter particles. Based on the N-body simulation of the evolution of dark matter subhalos we first calculate the average intensity distribution of this new class of $\gamma$-ray sources by neutralino annihilation. It is possible to detect these $\gamma$-ray sources by EGRET and GLAST. Conversely, if these sources are not detected the nature of the dark matter particls will be constrained by these experiments, which, however, depending on the uncertainties of the subhalo profile.Comment: 19 pages, 5 gigures; references added, more discussions adde