Pseudo-orthogonality for graph 1-Laplacian eigenvectors and applications to higher Cheeger constants and data clustering

The data clustering problem consists in dividing a data set into prescribed groups of homogeneous data. This is an NP-hard problem that can be relaxed in the spectral graph theory, where the optimal cuts of a graph are related to the eigenvalues of graph 1-Laplacian. In this paper, we first give new notations to describe the paths, among critical eigenvectors of the graph 1-Laplacian, realizing sets with prescribed genus. We introduce the pseudo-orthogonality to characterize m₃(G), a special eigenvalue for the graph 1-Laplacian. Furthermore, we use it to give an upper bound for the third graph Cheeger constant h₃(G), that is, h₃(G) 6 m₃(G). This is a first step for proving that the k-th Cheeger constant is the minimum of the 1-Laplacian Raylegh quotient among vectors that are pseudo-orthogonal to the vectors realizing the previous k - 1 Cheeger constants. Eventually, we apply these results to give a method and a numerical algorithm to compute m₃(G), based on a generalized inverse power method.     

Human Y‐chromosome SNP characterization by multiplex amplified product‐length polymorphism analysis

We designed an allele‐specific amplification protocol to optimize Y‐chromosome SNP typing, which is an unavoidable step for defining the phylogenetic status of paternal lineages. It allows the simultaneous highly specific definition of up to six mutations in a single reaction by amplification fragment length polymorphism (AFLP) without the need of specialized equipment, at a considerably lower cost than that based on single‐base primer extension (SNaPshot?) technology or PCR‐RFLP systems, requiring as little as 0.5 ng DNA and compatible with the small fragments characteristic of low‐quality DNA. By designation of two primers recognizing the derived and ancestral state for each SNP, which can be differentiated by size by the addition of a noncomplementary nucleotide tail, we could define major Y clades E, F, K, R, Q, and subhaplogroups R1, R1a, R1b, R1b1b, R1b1c, J1, J2, G1, G2, I1, Q1a3, and Q1a3a1 through amplification fragments that ranged between 60 and 158bp.     

Pomeron vertices in perturbative QCD in diffractive scattering

We analyze the momentum space triple pomeron vertex in perturbative QCD. In addition to the standard form of this vertex which is used in the context of total cross sections at high energies and in the QCD reggeon field theory, there exists an alternative form which has to be used in the study of high-mass diffraction. We review and analyze the relation between these two versions. We discuss some implications for the BK equation. In the second part of our paper we extend this analysis to the pomeron-odderon-odderon vertex.Received: 11 January 2005, Revised: 24 January 2005, Published online: 3 March 2005     

Protection of flows under targeted attacks

We present a new robust optimization model for the problem of maximizing the amount of flow surviving the attack of an interdictor. Given some path flow, our model allows the interdictor to specify the amount of flow removed from each path individually. In contrast to previous models, for which no efficient algorithms are known, the most important basic variants of our model can be solved in poly-time. We also consider extensions where there is a budget to set the interdiction costs.     

A 3D QSAR approach to the search for geometrical similarity in a series of nonpeptide angiotensin II receptor antagonists

Summary A 3D QSAR methodology based on the combined use of conformational analysis and chemometrics was applied to perform a comparative analysis of the 3D conformational features of 13 nonpeptide angiotensin II receptor antagonists showing different levels of binding affinity. Conformational analysis by using a molecular mechanics MM2 method was carried out for each of these structures to obtain conformational minima. These minima were described by ten interatomic distances which define the relative spatial disposition of five significant atoms belonging to relevant functional groups present in all the 13 molecules. The structure-activity relationship between the interatomic distances and the biological activity was then assessed by using chemometric methods (cluster analysis, principal component analysis, classification methods). With our indirect approach based on the search for geometrical similarity it was possible, even though structural information on the receptor active site was lacking, to identify the 3D geometrical requirements for the binding affinity of nonpeptide angiotensin II receptor inhibitors.     

Ant colony optimization for the arc routing problem with intermediate facilities under capacity and length restrictions

The aim of this paper is to introduce a new ant colony optimization procedure for the Arc Routing Problem with Intermediate Facilities under Capacity and Length Restrictions (CLARPIF), a variant of the Capacitated Arc Routing Problem (CARP) and of the Capacitated Arc Routing Problem with Intermediate Facilities (CARPIF). Computational results show that this algorithm is capable of providing substantial improvements over other known heuristics.     

Separation routine and extended formulations for the stable set problem in claw-free graphs

Mathematical Programming - The maximum weighted stable set problem in claw-free graphs is a well-known generalization of the maximum weighted matching problem, and a classical problem in...     

A saturation phenomenon for a nonlinear nonlocal eigenvalue problem

Given \(1\le q \le 2\) and \(\alpha \in \mathbb {R}\), we study the properties of the solutions of the minimum problem

$$\begin{aligned} \lambda (\alpha ,q)=\min \left\{ \dfrac{\displaystyle \int _{-1}^{1}|u'|^{2}dx+\alpha \left| \int _{-1}^{1}|u|^{q-1}u\, dx\right| ^{\frac{2}{q}}}{\displaystyle \int _{-1}^{1}|u|^{2}dx}, u\in H_{0}^{1}(-1,1),\,u\not \equiv 0\right\} . \end{aligned}$$

In particular, depending on \(\alpha \) and q, we show that the minimizers have constant sign up to a critical value of \(\alpha =\alpha _{q}\), and when \(\alpha >\alpha _{q}\) the minimizers are odd.

     

Fatty acids by high-performance liquid chromatography and evaporative light-scattering detector

A high-performance liquid chromatographic (HPLC) separation method with an evaporative light-scattering detector (ELSD) has been developed for the separation and quantitative analysis of fatty acid methyl esters (FAME) in three different oils. Reverse-phased C18 HPLC separation of 13 FAME is achieved using a methanol/water eluent mixture. The retention times (RT) reflect the elution behavior of these compounds on C18 reversed-phase HPLC. The proposed method is tested on: soybean oil (Glycine max L.) as reference sample, rice bran oil (Oryza sativa L.), pumpkin seed oil (Cucurbita pepo L.) and algal oil (Arthrospira platensis Nordst.).