On the existence and uniqueness of minima and maxima on spheres of the integral functional of the calculus of variations

Given a bounded domain Ω⊂Rn, we prove that if is a C¹ function whose gradient is Lipschitzian in Rn+1 and non-zero at 0, then, for each r>0 small enough, the restriction of the integral functional to the sphere has a unique global minimum and a unique global maximum.     

On the asymptotic behavior of some algorithms

A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis techniques as it is usually done in this context. A new explicit representation of periodic functions involved is obtained at the same time. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Reconstruction of large phylogenetic trees: a parallel approach

Reconstruction of phylogenetic trees for very large datasets is a known example of a computationally hard problem. In this paper, we present a parallel computing model for the widely used Multiple Instruction Multiple Data (MIMD) architecture. Following the idea of divide-and-conquer, our model adapts the recursive-DCM3 decomposition method [Roshan, U., Moret, B.M.E., Williams, T.L., Warnow, T, 2004a. Performance of suptertree methods on various dataset decompositions. In: Binida-Emonds, O.R.P. (Eds.), Phylogenetic Supertrees: Combining Information to Reveal the Tree of Life, vol. 3 of Computational Biology, Kluwer Academics, pp. 301-328; Roshan, U., Moret, B.M.E., Williams, T.L., Warnow, T., 2004b. Rec-I-DCM3: A Fast Algorithmic Technique for reconstructing large phylogenetic trees, Proceedings of the IEEE Computational Systems Bioinformatics Conference (ICSB)] to divide datasets into smaller subproblems. It distributes computation load over multiple processors so that each processor constructs subtrees on each subproblem within a batch in parallel. It finally collects the resulting trees and merges them into a supertree. The proposed model is flexible as far as methods for dividing and merging datasets are concerned. We show that our method greatly reduces the computational time of the sequential version of the program. As a case study, our parallel approach only takes 22.1h on four processors to outperform the best score to date (Found at 123.7h by the Rec-I-DCM3 program [Roshan, U., Moret, B.M.E., Williams, T.L., Warnow, T, 2004a. Performance of suptertree methods on various dataset decompositions. In: Binida-Emonds, O.R.P. (Eds.), Phylogenetic Supertrees: Combining Information to Reveal the Tree of Life, vol. 3 of Computational Biology, Kluwer Academics, pp. 301-328; Roshan, U., Moret, B.M.E., Williams, T.L., Warnow, T., 2004b. Rec-I-DCM3: A Fast Algorithmic Technique for reconstructing large phylogenetic trees, Proceedings of the IEEE Computational Systems Bioinformatics Conference (ICSB)] on one dataset. Developed with the standard message-passing library, MPI, the program can be recompiled and run on any MIMD systems.     

The Ghost Cell Method and Its Applications for Inviscid Compressible Flow on Adaptive Tree Cartesian Grids

In this paper, an immersed boundary algorithm is developed by combining the ghost cell method with adaptive tree Cartesian grid method. Furthermore, the proposed method is successfully used to evaluate various inviscid compressible flow with immersed boundary. The extension to three dimensional cases is also achieved. Numerical examples demonstrate the proposed method is effective.     

On the “largeur d'arborescence”

Let la(G) be the invariant introduced by Colin de Verdière [J. Comb. Theory, Ser. B., 74:121–146, 1998], which is defined as the smallest integer n≥0 such that G is isomorphic to a minor of K_n×T, where K_n is a complete graph on n vertices and where T is an arbitrary tree. In this paper, we give an alternative definition of la(G), which is more in terms of the tree‐width of a graph. We give the collection of minimal forbidden minors for the class of graphs G with la(G)≤k, for k=2, 3. We show how this work on la(G) can be used to get a forbidden minor characterization of the graphs with (G)≤3. Here, (G) is another graph parameter introduced in the above cited paper. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 24–52, 2002     

LC-ESI/LTQ-Orbitrap-MS Based Metabolomics in Evaluation of Bitter Taste of Arbutus unedo Honey

Strawberry tree honey is a high-value honey from the Mediterranean area and it is characterised by a typical bitter taste. To possibly identify the secondary metabolites responsible for the bitter taste, the honey was fractionated on a C18 column and the individual fractions were subjected to sensory analysis and then analysed by liquid chromatography coupled with high-resolution tandem mass spectrometry in negative ion mode, using a mass spectrometer with an electrospray source coupled to a hybrid high resolution mass analyser (LC-ESI/LTQ-Orbitrap-MS). A chemometric model obtained by preliminary principal component analysis (PCA) of LC-ESI/LTQ-Orbitrap-MS data allowed the identification of the fractions that caused the perception of bitterness. Subsequently, a partial least squares (PLS) regression model was built. The studies carried out with multivariate analysis showed that unedone (2-(1,2-dihydroxypropyl)-4,4,8-trimethyl-1-oxaspiro [2.5] oct-7-en-6-one) can be considered responsible for the bitter taste of strawberry tree honey. Confirmation of the bitter taste of unedone was obtained by sensory evaluation of a pure standard, allowing it to be added to the list of natural compounds responsible for giving the sensation of bitterness to humans.     

On a class of degenerate and singular elliptic systems in bounded domains

This paper deals with the nonexistence and multiplicity of nonnegative, nontrivial solutions to a class of degenerate and singular elliptic systems of the form

where Ω is a bounded domain with smooth boundary ∂Ω in , N2, and , , h_i (i=1,2) are allowed to have “essential” zeroes at some points in Ω, (F_u,F_v)=F, and λ is a positive parameter. Our proofs rely essentially on the critical point theory tools combined with a variant of the Caffarelli–Kohn–Nirenberg inequality in [P. Caldiroli, R. Musina, On a variational degenerate elliptic problem, NoDEA Nonlinear Differential Equations Appl. 7 (2000) 189–199].     

Counting spanning trees in a small-world Farey graph

The problem of spanning trees is closely related to various interesting problems in the area of statistical physics, but determining the number of spanning trees in general networks is computationally intractable. In this paper, we perform a study on the enumeration of spanning trees in a specific small-world network with an exponential distribution of vertex degrees, which is called a Farey graph since it is associated with the famous Farey sequence. According to the particular network structure, we provide some recursive relations governing the Laplacian characteristic polynomials of a Farey graph and its subgraphs. Then, making use of these relations obtained here, we derive the exact number of spanning trees in the Farey graph, as well as an approximate numerical solution for the asymptotic growth constant characterizing the network. Finally, we compare our results with those of different types of networks previously investigated.