A Parallel Algorithm for Exact Bayesian Structure Discovery in Bayesian Networks

Exact Bayesian structure discovery in Bayesian networks requires exponential time and space. Using dynamic programming (DP), the fastest known sequential algorithm computes the exact posterior probabilities of structural features in $O(2(d+1)n2^n)$ time and space, if the number of nodes (variables) in the Bayesian network is $n$ and the in-degree (the number of parents) per node is bounded by a constant $d$. Here we present a parallel algorithm capable of computing the exact posterior probabilities for all $n(n-1)$ edges with optimal parallel space efficiency and nearly optimal parallel time efficiency. That is, if $p=2^k$ processors are used, the run-time reduces to $O(5(d+1)n2^{n-k}+k(n-k)^d)$ and the space usage becomes $O(n2^{n-k})$ per processor. Our algorithm is based the observation that the subproblems in the sequential DP algorithm constitute a $n$-$D$ hypercube. We take a delicate way to coordinate the computation of correlated DP procedures such that large amount of data exchange is suppressed. Further, we develop parallel techniques for two variants of the well-known \emph{zeta transform}, which have applications outside the context of Bayesian networks. We demonstrate the capability of our algorithm on datasets with up to 33 variables and its scalability on up to 2048 processors. We apply our algorithm to a biological data set for discovering the yeast pheromone response pathways.Comment: 32 pages, 12 figure

Greengard\u27s N-body Algorithm is not order N

Greengard\u27s N-body algorithm claims to compute the pairwise interactions in a system of N particles in O(N) time for a fixed precision. In this paper, we show that the choice of precision is not independent of N and has a lower bound of log N. We use this result to show that Greengard\u27s algorithm is not O(N)

Numerical study of solder joint failure under fast loading conditions

A numerical study was undertaken to investigate the solder joint failure under fast loading conditions. The finite element model assumes a lap-shear testing configuration, where the solder joint is bonded to two copper substrates. A progressive ductile damage model was incorporated into the rate-dependent constitutive response of the Sn (tin)-Ag (silver)-Cu (copper) solder alloy, resulting in the capability of simulating damage evolution leading to eventual failure through crack formation. Attention is devoted to deformation under relative high strain rates (1-100 s-1), mimicking those frequently encountered in drop and impact loading of the solder points. The effects of applied strain rate and loading mode on the overall ductility and failure pattern were specifically investigated. It was found that the solder joint can actually become more ductile as the applied strain rate increases, which is due to the alteration of the crack path. Failure of the solder is very sensitive to the deformation mode, with a superimposed tension/compression on shear easily changing the crack path and tending to reduce the solder joint ductility. In addition, cyclic shearing resulted in different failure patterns from those of monotonic loading. The two fatigue cracks, one at (or very close to) each interface, have both grown to a significant length with one responsible for final failure of the joint

Ferric Iron Nanoparticle Formation Mediated By Negatively Charged Polypeptides

The creation of magnetite particles by magnetotactic bacteria has been of great interest for a number of years. Previous studies have shown that magnetite nanocrystals have been synthesized in the presence of recombinant Mms6 protein. Mms6 plays a vital role in the biomineralization of bacterial magnetite nanocrystals. The objective of this research is to determine the effect of functional group type on size and shape of magnetic nanoparticles formed by biomineralization. Control over the size of nanoparticles is paramount. Use of nanoparticles as contrast agents in MRI is advantageous, as they are small enough to be localized in desired region by applying local magnetic fields. Sequences VA-Mms6, VA1, VA2, and VA3 were designed with modifications in the functional groups Mms6 sequence. Solutions of peptide were mixed with ferric and ferro salts and allowed to interact under inert atmosphere. The nanoparticles formed are examined under SEM and TEM and compared for differences. The SEM and TEM images of nanoparticles produced with the aid of the above peptides had similarity to those produced in the magnetotactic bacteria. However, discrete particles with a narrower size range were produced using the peptide VA2. XPS, AFM, DLS and MFM were also done on the synthesized nanoparticles. The results were in good agreement when compared to those with a standard control sample of magnetite nanoparticles. Use of peptides with different functional groups may provide a unique route to produce uniform magnetite nanocrystals with definite control of morphology