Joint Structure Learning of Multiple Non-Exchangeable Networks

Several methods have recently been developed for joint structure learning of multiple (related) graphical models or networks. These methods treat individual networks as exchangeable, such that each pair of networks are equally encouraged to have similar structures. However, in many practical applications, exchangeability in this sense may not hold, as some pairs of networks may be more closely related than others, for example due to group and sub-group structure in the data. Here we present a novel Bayesian formulation that generalises joint structure learning beyond the exchangeable case. In addition to a general framework for joint learning, we (i) provide a novel default prior over the joint structure space that requires no user input; (ii) allow for latent networks; (iii) give an efficient, exact algorithm for the case of time series data and dynamic Bayesian networks. We present empirical results on non-exchangeable populations, including a real data example from biology, where cell-line-specific networks are related according to genomic features.Comment: To appear in Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics (AISTATS

Model selection in cosmology

Model selection aims to determine which theoretical models are most plausible given some data, without necessarily considering preferred values of model parameters. A common model selection question is to ask when new data require introduction of an additional parameter, describing a newly discovered physical effect. We review model selection statistics, then focus on the Bayesian evidence, which implements Bayesian analysis at the level of models rather than parameters. We describe our CosmoNest code, the first computationally efficient implementation of Bayesian model selection in a cosmological context. We apply it to recent WMAP satellite data, examining the need for a perturbation spectral index differing from the scaleinvariant (Harrison–Zel'dovich) case

Geometry of fully coordinated, two-dimensional percolation

We study the geometry of the critical clusters in fully coordinated percolation on the square lattice. By Monte Carlo simulations (static exponents) and normal mode analysis (dynamic exponents), we find that this problem is in the same universality class with ordinary percolation statically but not so dynamically. We show that there are large differences in the number and distribution of the interior sites between the two problems which may account for the different dynamic nature.Comment: ReVTeX, 5 pages, 6 figure

Electrostatic contribution to DNA condensation - application of 'energy minimization' in a simple model in strong Coulomb coupling regime

Bending of DNA from a straight rod to a circular form in presence of any of the mono-, di-, tri- or tetravalent counterions has been simulated in strong Coulomb coupling environment employing a previously developed energy minimization simulation technique. The inherent characteristics of the simulation technique allow monitoring the required electrostatic contribution to the bending. The curvature of the bending has been found to play crucial roles in facilitating electrostatic attractive potential energy. The total electrostatic potential energy has been found to decrease with bending which indicates that bending a straight DNA to a circular form or to a toroidal form in presence of neutralizing counterions is energetically favorable and practically is a spontaneous phenomenon

Doubly nonlocal system with Hardy-Littlewood-Sobolev critical nonlinearity

This article concerns about the existence and multiplicity of weak solutions for the following nonlinear doubly nonlocal problem with critical nonlinearity in the sense of Hardy-Littlewood-Sobolev inequality \begin{equation*} \left\{ \begin{split} (-\Delta)^su &= \lambda |u|^{q-2}u + \left(\int_{\Omega}\frac{|v(y)|^{2^*_\mu}}{|x-y|^\mu}~\mathrm{d}y\right) |u|^{2^*_\mu-2}u\; \text{in}\; \Omega (-\Delta)^sv &= \delta |v|^{q-2}v + \left(\int_{\Om}\frac{|u(y)|^{2^*_\mu}}{|x-y|^\mu}~\mathrm{d}y \right) |v|^{2^*_\mu-2}v \; \text{in}\; \Omega u &=v=0\; \text{in}\; \mb R^n\setminus\Omega, \end{split} \right. \end{equation*} where $\Omega$ is a smooth bounded domain in \mb R^n, $n >2s$, $s \in (0,1)$, $(-\Delta)^s$ is the well known fractional Laplacian, $\mu \in (0,n)$, $2^*_\mu = \displaystyle\frac{2n-\mu}{n-2s}$ is the upper critical exponent in the Hardy-Littlewood-Sobolev inequality, $1<q<2$ and $\lambda,\delta >0$ are real parameters. We study the fibering maps corresponding to the functional associated with $(P_{\lambda,\delta})$ and show that minimization over suitable subsets of Nehari manifold renders the existence of atleast two non trivial solutions of (P_{\la,\delta}) for suitable range of \la and $\delta$.Comment: 37 page