29,021 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
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
Microphysical, microchemical and adhesive properties of lunar material. 3: Gas interaction with lunar material
Knowledge of the reactivity of lunar material surfaces is important for understanding the effects of the lunar or space environment upon this material, particularly its nature, behavior and exposure history in comparison to terrestrial materials. Adsorptive properties are one of the important techniques for such studies. Gas adsorption measurements were made on an Apollo 12 ultrahigh vacuum-stored sample and Apollo 14 and 15 N2-stored samples. Surface area measurements were made on the latter two. Adsorbate gases used were N2, A, O2 and H2O. Krypton was used for the surface area determinations. Runs were made at room and liquid nitrogen temperature in volumetric and gravimetric systems. It was found that the adsorptive/desorptive behavior was in general significantly different from that of terrestrial materials of similar type and form. Specifically (1) the UHV-stored sample exhibited very high initial adsorption indicative of high surface reactivity, and (2) the N2-stored samples at room and liquid nitrogen temperatures showed that more gas was desorbed than introduced during adsorption, indicative of gas release from the samples. The high reactivity is a scribed cosmic ray track and solar wind damage
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
- …