28,979 research outputs found
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 is a smooth bounded domain in \mb R^n, , , is the well known fractional Laplacian, , is the upper critical
exponent in the Hardy-Littlewood-Sobolev inequality, and
are real parameters. We study the fibering maps
corresponding to the functional associated with 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 .Comment: 37 page
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