A Parallel Interior Point Method and Its Application to Facility Location Problems

We present a parallel interior point algorithm to solve block structured linear programs. This algorithm can solve block diagonal linear programs with both side constraints (common rows) and side variables (common columns). The performance of the algorithm is investigated on uncapacitated, capacitated and stochastic facility location problems. The facility location problems are formulated as mixed integer linear programs. Each subproblem of the branch and bound phase of the MIP is solved using the parallel interior point method. We compare the total time taken by the parallel interior point method with the simplex method to solve the complete problems, as well as the various costs of reoptimisation of the non-root nodes of the branch and bound. Computational results on two parallel computers (Fujitsu AP1000 and IBM SP2) are also presented in this paper.     

Modular invariant partition functions in the quantum Hall effect

We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard form of rational conformal field theories. In particular, it is invariant under modular transformations of the toroidal geometry made by the angular variable and the compact Euclidean time. The Jain series of plateaus have been described by two types of edge theories: the minimal models of the W_1+∞ algebra of quantum area-preserving diffeomorphisms, and their non-minimal version, the theories with affine algebra. We find modular invariant partition functions for the latter models. Moreover, we relate the Wen topological order to the modular transformations and the Verlinde fusion algebra. We find new, non-diagonal modular invariants which describe edge theories with extended symmetry algebra; their Hall conductivities match the experimental values beyond the Jain series.     

DETERMINATION OF EFFICIENT RANGE OF TARGET LEVELS IN MULTIPLE OBJECTIVE PLANNING

This paper describes a nonlinear programming model combined with a binary search technique that systematically searches for the minimum value of a given objective within the nondominated solution set. The procedure provides a way of determining the range of efficient target levels for any multiobjective planning problem using information contained in the pay-off table. The method is illustrated using a numerical example.     

Conformational flexibility of a synthetic glycosylaminoglycan bound to a fibroblast growth factor. FGF-1 recognizes both the (1)C(4) and (2)S(O) conformations of a bioactive heparin-like hexasaccharide

The first direct NMR determination of the conformation of a conformationally flexible heparin-like hexasaccharide bound to a key receptor, FGF-1, is described. The determination has been based on the use of a 13C-labeled protein and a regular 12C sugar. FGF-1 recognizes several conformations of the iduronic moieties of the hexasaccharide. Therefore, this case is different than that described for the controversial recognition of heparin-like saccharides by AT-III, which seems to recognize just one conformation of the iduronic acid residues.     

Water dynamics in ionomer membranes by field-cycling NMR relaxometry

The dynamic behavior of water within two types of ionomer membranes, Nafion and sulfonated polyimide, has been investigated by field-cycling nuclear magnetic relaxation. This technique, applied to materials prepared at different hydration levels, allows the proton motion on a time scale of microseconds to be probed. The NMR longitudinal relaxation rate R(1) measured over three decades of Larmor angular frequencies omega is particularly sensitive to the host-water interactions and thus well-suited to study fluid dynamics in restricted geometries. In the polyimide membranes, we have observed a strong dispersion of R(1)(omega) following closely a 1/square root omega law in a low-frequency range (correlation times from 0.1 to 10 micros). This is indicative of a strong interaction of water with "interfacial" hydrophilic groups of the polymeric matrix (wetting situation). Variations of the relaxation rates with water uptake reveal a two-step hydration process: solvation and formation of disconnected aqueous clusters near polar groups, followed by the formation of a continuous hydrogen bond network. On the contrary, in the Nafion we observed weak variations of R(1)(omega) at low frequencies. This is typical of a nonwetting behavior. At early hydration stages, R(1)(omega) evolves logarithmically, suggesting a confined bidimensional diffusion of protons in the microsecond time range. Such an evolution is lost at higher swelling where a plateau related to three-dimensional diffusion is observed.     

Sulfated zirconia-catalyzed synthesis of 3,4-dihydropyrimidin-2(1H)-ones (DHPMs) under solventless conditions: competitive multicomponent Biginelli vs. Hantzsch reactions

The catalytic ability of ZrO(2)/SO(4)(2-) to promote solventless three-component condensation reactions of a diversity of aromatic aldehydes, urea or thoiurea and ethyl acetoacetate was studied. Products resulting from Hantzsch and/or Biginelli multi-component reactions are obtained in the presence of solid acid catalysts using the same reactants but different temperature conditions. The sulfated zirconia catalyst can be recovered and recycled in subsequent reactions with a gradual decrease of activity.     

Algorithms for clique-independent sets on subclasses of circular-arc graphs

A circular-arc graph is the intersection graph of arcs on a circle. A Helly circular-arc graph is a circular-arc graph admitting a model whose arcs satisfy the Helly property. A clique-independent set of a graph is a set of pairwise disjoint cliques of the graph. It is NP-hard to compute the maximum cardinality of a clique-independent set for a general graph. In the present paper, we propose polynomial time algorithms for finding the maximum cardinality and weight of a clique-independent set of a -free CA graph. Also, we apply the algorithms to the special case of an HCA graph. The complexity of the proposed algorithm for the cardinality problem in HCA graphs is O(n). This represents an improvement over the existing algorithm by Guruswami and Pandu Rangan, whose complexity is O(n²). These algorithms suppose that an HCA model of the graph is given.