The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical

Let G be any n-vertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which

Pfam is a comprehensive collection of protein domains and families, represented as multiple sequence alignments and as profile hidden Markov models. The current release of Pfam (22.0) contains 9318 protein families. Pfam is now based not only on the UniProtKB sequence database, but also on NCBI Gen

This paper describes the Structure-Mapping Engine (SME), a program for studying analogical processing. SME has been built to explore Gentner's Structure-mapping theory of analogy, and provides a "tool kit" for constructing matching algorithms consistent with this theory. Its

Two kinds of contemporary developments in cryptography are examined. Widening applications of teleprocessing have given rise to a need for new types of cryptographic systems, which minimize the need for secure key distribution channels and supply the equivalent of a written signature. This paper

new combinatorial identity for unicellular maps, via a direct

as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, series-parallel digraphs, planar st-digraphs, and planar

Finding objective and effective thresholds for voxelwise statistics derived from neuroimaging data has been a long-standing problem. With at least one test performed for every voxel in an image, some correction of the thresholds is needed to control the error rates, but standard procedures

The increasing amount of genomic and molecular information is the basis for understanding higherorder biological systems, such as the cell and the 15 organism, and their interactions with the environment, as well as for medical, industrial and other practical applications. The KEGG resource

orientations on graphs, suitably adapted so as to operate only on the embeddings in a simple local way. In turn, Φ1,2 yield two new bijections F1,2 between families of (rooted) maps. (i) By identifying maps with specific constrained orientations, Φ2 ◦ Φ1 specialises to a bijection F1 between 2-connected maps