A GRASP algorithm for the multi-criteria minimum spanning tree problem

This paper proposes a GRASP (Greedy Randomized Adaptive Search Procedure) algorithm for the multi-criteria minimum spanning tree problem, which is NP-hard. In this problem a vector of costs is defined for each edge of the graph and the problem is to find all Pareto optimal or efficient spanning trees (solutions). The algorithm is based on the optimization of different weighted utility functions. In each iteration, a weight vector is defined and a solution is built using a greedy randomized constructive procedure. The found solution is submitted to a local search trying to improve the value of the weighted utility function. We use a drop-and-add neighborhood where the spanning trees are represented by Prufer numbers. In order to find a variety of efficient solutions, we use different weight vectors, which are distributed uniformly on the Pareto frontier. The proposed algorithm is tested on problems with r=2 and 3 criteria. For non-complete graphs with n=10, 20 and 30 nodes, the performance of the algorithm is tested against a complete enumeration. For complete graphs with n=20, 30 and 50 nodes the performance of the algorithm is tested using two types of weighted utility functions. The algorithm is also compared with the multi-criteria version of the Kruskal’s algorithm, which generates supported efficient solutions. This work was funded by the Municipal Town Hall of Campos dos Goytacazes city. The used computer was acquired with resource of CNPq.     

Goal programming model for grocery shelf space allocation

The highly competitive grocery retail industry has annual sales of roughly half a trillion dollars in the US. While gross margins average about 28% of sales, net profits after taxes are only 1% industry-wide, causing retailers to continually search for operational improvements that increase profitability and improve customer service. One important decision that affects both of these goals is how to allocate shelf space to different products.     

The shape of extremal functions for Poincaré-Sobolev-type inequalities in a ball

We study extremal functions for a family of Poincaré-Sobolev-type inequalities. These functions minimize, for subcritical or critical p?2, the quotient ‖∇u_‖2/‖up_‖ among all u∈H¹(B)?{0} with B_∫u=0. Here B is the unit ball in RN. We show that the minimizers are axially symmetric with respect to a line passing through the origin. We also show that they are strictly monotone in the direction of this line. In particular, they take their maximum and minimum precisely at two antipodal points on the boundary of B. We also prove that, for p close to 2, minimizers are antisymmetric with respect to the hyperplane through the origin perpendicular to the symmetry axis, and that, once the symmetry axis is fixed, they are unique (up to multiplication by a constant). In space dimension two, we prove that minimizers are not antisymmetric for large p.     

New saponins from Sechium mexicanum

The chemical study of Sechium mexicanum roots led to the isolation of the two new saponins {3‐O‐β‐D ‐glucopyranosyl (1 → 3)‐β‐D ‐glucopyranosyl‐2β,3β,16α,23‐tetrahydroxyolean‐12‐en‐28‐oic acid 28‐O‐α‐L ‐rhamnopyranosyl‐(1 → 3)‐β‐D ‐xylopyranosyl‐(1 → 4)‐α‐L ‐rhamnopyranosyl‐(1 → 2)‐α‐L ‐arabinopyranoside} (1) and {3‐O‐β‐D ‐glucopyranosyl (1 → 3)‐β‐D ‐glucopyranosyl‐2β,3β,16α,23‐tetrahydroxyolean‐12‐en‐28‐oic acid 28‐O‐α‐L ‐rhamnopyranosyl‐(1 → 3)‐β‐D ‐xylopyranosyl‐(1 → 4)‐[β‐D ‐apiosyl‐(1 → 3)]‐α‐L ‐rhamnopyranosyl‐(1 → 2)‐α‐L ‐arabinopyranoside} (2), together with the known compounds {3‐O‐β‐D ‐glucopyranosyl‐(1 → 3)‐β‐D ‐glucopyranosyl‐2β,3β,6β,16α,23‐pentahydroxyolean‐12‐en‐28‐oic acid 28‐O‐α‐L ‐rhamnopyranosyl‐(1 → 3)‐β‐D ‐xylopyranosyl‐(1 → 4)‐α‐L ‐rhamnopyranosyl‐(1 → 2)‐α‐L ‐arabinopyranoside} (3), tacacosides A₁ (4) and B₃ (5). The structures of saponins 1 and 2 were elucidated using a combination of ¹H and ¹³C 1D‐NMR, COSY, TOCSY, gHMBC and gHSQC 2D‐NMR, and FABMS of the natural compounds and their peracetylated derivates, as well as by chemical degradation. Compounds 1–3 are the first examples of saponins containing polygalacic and 16‐hydroxyprotobasic acids found in the genus Sechium, while 4 and 5, which had been characterized partially by NMR, are now characterized in detail. Copyright © 2009 John Wiley & Sons, Ltd.     

NMR assignments and histone specificity of the ING2 PHD finger

The ING2 plant homeodomain (PHD) finger is recruited to the nucleosome through specific binding to histone H3 trimethylated at lysine 4 (H3K4me3). Here, we describe backbone and side chain assignments of the ING2 PHD finger, analyze its binding to the unmodified and modified histone and p53 peptides, and map the histone H3 and H3K4me3 binding sites based on chemical shift perturbation analysis. Copyright © 2009 John Wiley & Sons, Ltd.     

The Assembly of Macrocyclic Bis‐ and Tetra‐β‐lactams with Embedded Platinum or Palladium Square‐Planar Centers

The synthesis, isolation, and full characterization of different types of stable, metal‐assembled macrocyclic β‐lactams are reported. By using adequately functionalized bis‐β‐lactams with defined stereochemistry as building blocks, a series of mono‐ and bimetallic Pd and Pt macrocycles has been prepared in good to quantitative yields. These novel structures combine the β‐lactam moiety with transition‐metal fragments with cis‐square‐planar geometry and constitute a new class of metal‐assembled cavities involving molecules with biological relevance as building blocks. By combining the adequate ligands, metallic fragments, and tuning the reaction conditions, different mono‐ and bimetallic macrocyclic β‐lactam cavities can be selectively obtained. Macrocycles with Pt–ethynyl groups are suitable to form host–silver triflate guest complexes in a tweezer fashion.     

Modeling slow deformation of polygonal particles using DEM

We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach improves efficiency and accuracy of the Discrete Element Method （DEM） when modeling the dynamics of the granular packing. We determine the proper upper limit for the integration step in the standard numerical scheme using a wide range of material parameters. To this end, we study the kinetic energy decay in a stress controlled test between two particles. Second, we show that the usual way of defining the contact plane between two polygonal particles is, in general, not unique which leads to discontinuities in the direction of the contact plane while particles move. To solve this drawback, we introduce an accurate definition for the contact plane based on the shape of the overlap area between touching particles, which evolves continuously in time.