Fast and reliable reconstruction of phylogenetic trees with indistinguishable edges

Phylogenetic reconstruction methods attempt to reconstruct a tree describing the evolution of a given set of species using sequences of characters (e.g. DNA) extracted from these species as input. A central goal in this area is to design algorithms which guarantee reliable reconstruction of the tree from short input sequences, assuming common stochastic models of evolution. The fast converging reconstruction algorithms introduced in the last decade dramatically reduced the sequence length required to guarantee accurate reconstruction of the entire tree. However, if the tree in question contains even few edges which cannot be reliably reconstructed from the input sequences, then known fast converging algorithms may fail to reliably reconstruct all or most of the other edges. This calls for an adaptive approach suggested in this paper, called adaptive fast convergence, in which the set of edges which can be reliably reconstructed gradually increases with the amount of information (length of input sequences) available to the algorithm. This paper presents an adaptive fast converging algorithm which returns a partially resolved topology containing no false edges: edges that cannot be reliably reconstructed are contracted into high degree vertices. We also present an upper bound on the weights of those contracted edges, which is determined by the length of input sequences and the depth of the tree. As such, the reconstruction guarantee provided by our algorithm for individual edges is significantly stronger than any previously published edge reconstruction guarantee. This fact, together with the optimal complexity of our algorithm (linear space and quadratic‐time), makes it appealing for practical use. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 350–384, 2011     

Reliable Solution of Bidiagonal Systems with Applications

We show that the stability of Gaussian elimination with partial pivoting relates to the well definition of the reduced triangular systems. We develop refined perturbation bounds that generalize Skeel bounds to the case of ill conditioned systems. We finally develop reliable algorithms for solving general bidiagonal systems of linear equations with applications to the fast and stable solution of tridiagonal systems.     

Deterministic Percolation

This paper examines percolation questions in a deterministic setting. In particular, I consider , the set of elements of Z ² with greatest common divisor equal to 1, where two sites are connected if they are at distance 1. The main result of the paper proves that the infinite component has an asymptotic density. An “almost everywhere” sieve of J. Friedlander is used to obtain the result. Received: 1 November 1998 / Accepted: 1 April 1999     

Tetrazole Diversification of Amino Acids and Peptides via Silver-Catalyzed Intermolecular Cycloaddition with Aryldiazonium Salts

Selective structural modification of amino acids and peptides is a central strategy in organic chemistry, chemical biology but also in pharmacology and material science. In this context, the formation of tetrazole rings, known to possess significant therapeutic properties, would expand the chemical space of unnatural amino acids but has received less attention. In this study, we demonstrated that the classic unimolecular Wolff rearrangement of α-amino acid-derived diazoketones could be replaced by a faster intermolecular cycloaddition reaction with aryldiazonium salts under identical practical conditions. This strategy provides an efficient synthetic platform that could transform proteinogenic α-amino acids into a plethora of unprecedented tetrazole-decorated amino acid derivatives with preservation of the stereocenters. Density functional theory studies shed some light on the reaction mechanism and provided information regarding the origins of the chemo- and regioselectivity. Furthermore, this diazo-cycloaddition protocol was applied to construct tetrazole-modified peptidomimetics and drug-like amino acid derivatives.     

Selective Terminal Functionalization of Linear Alkanes**

A two-step sequential strategy involving a biocatalytic dehydrogenation/remote hydrofunctionalization, as a unified and versatile approach to selectively convert linear alkanes into a large array of valuable functionalized aliphatic derivatives is reported. The dehydrogenation is carried out by a mutant strain of a bacteria Rhodococcus and the produced alkenes are subsequently engaged in a remote functionalization through a metal-catalyzed hydrometalation/migration sequence that subsequently react with a large variety of electrophiles. The judicious implementation of this combined biocatalytic and organometallic approach enabled us to develop a high-yielding protocol to site-selectively functionalize unreactive primary C−H bonds.