Our motivating question was whether all traces on a U-ultrapower of a C*-algebra A, where U is a non-principal ultrafilter on N, are necessarily U-limits of traces on A. We show that this is false so long as A has infinitely many extremal traces, and even exhibit a 22 א0 size family of such traces on the ultrapower. For this to fail even when A has finitely many traces implies that A contains o...

Sipuncula is an ancient clade of unsegmented marine worms that develop through a conserved pattern of unequal quartet spiral cleavage. They exhibit putative character modifications, including conspicuously large first-quartet micromeres and prototroch cells, postoral metatroch with exclusive locomotory function, paired retractor muscles and terminal organ system, and a U-shaped digestive archit...

A versatile method, quartet puzzling, is introduced to reconstruct the topology (branching pattern) of a phylogenetic tree based on DNA or amino acid sequence data. This method applies maximum-likelihood tree reconstruction to all possible quartets that can be formed from n sequences. The quartet trees serve as starting points to reconstruct a set of optimal n-taxon trees. The majority rule con...

A fundamental problem in computational biology which has been widely studied in the last decades is the reconstruction of evolutionary trees from biological data. Unfortunately, almost all its known formulations are NPhard. The compelling need for having efficient computational tools to solve this biological problem has brought a lot of attention to the analysis of the quartet paradigm for infe...

We propose a fast algorithm for solving the Basis Pursuit problem, minu{|u|1, : Au = f}, which has application to compressed sensing. We design an efficient method for solving the related unconstrained problem minu E(u) = |u|1 +λ‖Au− f‖ 2 2 based on a greedy coordinate descent method. We claim that in combination with a Bregman iterative method, our algorithm will achieve a solution with speed ...

We consider abstract differential equations of the form u′(t) = Au(t)+f(t) or u′′(t)=Au(t)+f(t) in Banach spaces X, where f(·), R→X is almost-periodic, while A is a linear operator, (A)⊂X →X. If the solution u(·) is likewise almost-periodic, R→X, we establish connections between their Bohr-transforms, û(λ) and f̂ (λ). 2000 Mathematics Subject Classification. 34C27, 34G10.

Cauchy Problem, II. Here we consider the case in which the second operator is symmetric. Assume B : D V is a linear monotone operator with domain D V , where V is a Hilbert space, and that A : V V is a continuous linear symmetric monotone operator. Denote Ž .1 2 the space V with the seminorm A , by V . Then the injection a V V is continuous, and we have V V . V is a Hilbert space, for a a a whi...

Quartet-based phylogeny reconstruction methods, such as Quartet Puzzling, were introduced in the hope that they might be competitive with maximum likelihood methods, without being as computationally intensive. However, despite the numerous quartet-based methods that have been developed, their performance in simulation has been disappointing. In particular, Ranwez and Gascuel, the developers of ...