Parametric Inference for Biological Sequence Analysis

One of the major successes in computational biology has been the unification, using the graphical model formalism, of a multitude of algorithms for annotating and comparing biological sequences. Graphical models that have been applied towards these problems include hidden Markov models for annotation, tree models for phylogenetics, and pair hidden Markov models for alignment. A single algorithm, the sum-product algorithm, solves many of the inference problems associated with different statistical models. This paper introduces the \emph{polytope propagation algorithm} for computing the Newton polytope of an observation from a graphical model. This algorithm is a geometric version of the sum-product algorithm and is used to analyze the parametric behavior of maximum a posteriori inference calculations for graphical models.Comment: 15 pages, 4 figures. See also companion paper "Tropical Geometry of Statistical Models" (q-bio.QM/0311009

SIG-DB: leveraging homomorphic encryption to Securely Interrogate privately held Genomic DataBases

Genomic data are becoming increasingly valuable as we develop methods to utilize the information at scale and gain a greater understanding of how genetic information relates to biological function. Advances in synthetic biology and the decreased cost of sequencing are increasing the amount of privately held genomic data. As the quantity and value of private genomic data grows, so does the incentive to acquire and protect such data, which creates a need to store and process these data securely. We present an algorithm for the Secure Interrogation of Genomic DataBases (SIG-DB). The SIG-DB algorithm enables databases of genomic sequences to be searched with an encrypted query sequence without revealing the query sequence to the Database Owner or any of the database sequences to the Querier. SIG-DB is the first application of its kind to take advantage of locality-sensitive hashing and homomorphic encryption to allow generalized sequence-to-sequence comparisons of genomic data.Comment: 38 pages, 3 figures, 4 tables, 1 supplemental table, 7 supplemental figure