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.     

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...     

Mass and heat transfer modeling of bio-substrates during packaging

Perishable bio-substrate behavior can be modeled during packaged storage. Local mass and heattransfer have been coupled to respiration rate and microbial growth. Validating measurements have also been performed, and a multi-objective optimization was employed to tune the model. The model is able to simulate gas composition history and local bacteria spoilage in storage modes commonly adopted by the food industry, depending on product features and temperature. Exploitation of this mathematical tool would allow for informed technical and management decisions.     

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.     

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.     

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     

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.

     

RESEARCH NOTE

Abstract— The endogenous levels of indole-3-acetic acid (IAA), abscisic acid (ABA) and gibberellins (GA) were examined by gas chromatography-mass spectrometry in Prunus cerasus plantlets grown under different light conditions in relation to previous work on the photocontrol of stem elongation. The endogenous levels of free and conjugated IAA in the apical sections of red-grown shoots were about two-fold higher than those in the blue-treated plants, and these corresponded with maximum shoot elongation. By contrast, greater concentrations of ABA and GA were found in blue-grown plants compared to red with intermediate shoot growth. When blue was combined with red or far red, lower levels of IAA, ABA and GA correlated with less growth. These results suggest that the regulation of stem elongation by phytochrome and a blue-absorbing pigment may, at least in part, occur through a modulation of hormone levels.