{0, 1/2}-Chvátal-Gomory cuts

Given the integer polyhedronP _t := conv{x ∈ℤ ⁿ :Ax⩽b}, whereA ∈ℤ ^{m × n} andb ∈ℤ ^m , aChvátal-Gomory (CG)cut is a valid inequality forP ₁ of the type λτAx⩽⌊λτb⌋ for some λ∈ℝ ₊ ^m such that λτA∈ℤ ⁿ . In this paper we study {0, 1/2}-CG cuts, arising for λ∈{0, 1/2} ^m . We show that the associated separation problem, {0, 1/2}-SEP, is equivalent to finding a minimum-weight member of a binary clutter. This implies that {0, 1/2}-SEP is NP-complete in the general case, but polynomially solvable whenA is related to the edge-path incidence matrix of a tree. We show that {0, 1/2}-SEP can be solved in polynomial time for a convenient relaxation of the systemAx<-b. This leads to an efficient separation algorithm for a subclass of {0, 1/2}-CG cuts, which often contains wide families of strong inequalities forP ₁. Applications to the clique partitioning, asymmetric traveling salesman, plant location, acyclic subgraph and linear ordering polytopes are briefly discussed.     

Functionalized azabicycloalkane amino acids by nitrone 1,3-dipolar intramolecular cycloaddition

[reaction: see text] An efficient and operationally simple method for the synthesis of functionalized azaoxobicyclo[X.3.0]alkane amino acids has been devised. The key step is an intramolecular nitrone cycloaddition on 5-allyl- or 5-homoallylproline that was found to be completely regio- and stereoselective.     

Synthesis of α-trifluoromethyl-α-amino-β-sulfone hydroxamates: novel nanomolar inhibitors of matrix metalloproteinases

The racemic α-trifluoromethyl-α-amino-β-sulfone hydroxamates 1 were synthesized by means of a nucleophilic addition of sulfur-stabilized carbanions to a N-Cbz imine of trifluoropyruvate (4). The free amino derivative 1a was the most potent inhibitor of both MMP-3 (stromelysin-1) and MMP-9 (gelatinase-B), showing an IC₅₀ = 14 nM and 1 nM, respectively, and excellent selectivity versus MMP-1 (>5000-fold difference in inhibitory capacity). The N-Me derivative 1b was the most selective for MMP-3 with respect to MMP-9 (62-fold difference).     

Second-order conditions in C 1,1 constrained vector optimization

We consider the constrained vector optimization problem min _C f(x), g(x) ∈ ?K, where f:? ⁿ →? ^m and g:? ⁿ →? ^p are C ^1,1 functions, and C ? ^m and K ? ^p are closed convex cones with nonempty interiors. Two type of solutions are important for our considerations, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers). We formulate and prove in terms of the Dini directional derivative second-order necessary conditions for a point x ⁰ to be a w-minimizer and second-order sufficient conditions for x ⁰ to be an i-minimizer of order two. We discuss the reversal of the sufficient conditions under suitable constraint qualifications of Kuhn-Tucker type. The obtained results improve the ones in Liu, Neittaanmäki, K?í?ek [21].     

The feasibility pump

In this paper we consider the NP-hard problem of finding a feasible solution (if any exists) for a generic MIP problem of the form min{c^Tx:Ax≥b,x_j integer ∀j ∈ }. Trivially, a feasible solution can be defined as a point x* ∈ P:={x:Ax≥b} that is equal to its rounding , where the rounded point is defined by := x*_j if j ∈ and := x*_j otherwise, and [·] represents scalar rounding to the nearest integer. Replacing “equal” with “as close as possible” relative to a suitable distance function Δ(x*, ), suggests the following Feasibility Pump (FP) heuristic for finding a feasible solution of a given MIP.We start from any x* ∈ P, and define its rounding . At each FP iteration we look for a point x* ∈ P that is as close as possible to the current by solving the problem min {Δ(x, ): x ∈ P}. Assuming Δ(x, ) is chosen appropriately, this is an easily solvable LP problem. If Δ(x*, )=0, then x* is a feasible MIP solution and we are done. Otherwise, we replace by the rounding of x*, and repeat.We report computational results on a set of 83 difficult 0-1 MIPs, using the commercial software ILOG-Cplex 8.1 as a benchmark. The outcome is that FP, in spite of its simple foundation, proves competitive with ILOG-Cplex both in terms of speed and quality of the first solution delivered. Interestingly, ILOG-Cplex could not find any feasible solution at the root node for 19 problems in our test-bed, whereas FP was unsuccessful in just 3 cases.     

The use of dynamical networks to detect the hierarchical organization of financial market sectors

Two kinds of filtered networks: minimum spanning trees (MSTs) and planar maximally filtered graphs (PMFGs) are constructed from dynamical correlations computed over a moving window. We study the evolution over time of both hierarchical and topological properties of these graphs in relation to market fluctuations. We verify that the dynamical PMFG preserves the same hierarchical structure as the dynamical MST, providing in addition a more significant and richer structure, a stronger robustness and dynamical stability. Central and peripheral stocks are differentiated by using a combination of different topological measures. We find stocks well connected and central; stocks well connected but peripheral; stocks poorly connected but central; stocks poorly connected and peripheral. It results that the Financial sector plays a central role in the entire system. The robustness, stability and persistence of these findings are verified by changing the time window and by performing the computations on different time periods. We discuss these results and the economic meaning of this hierarchical positioning.     

Stable control of pulse speed in parametric three-wave solitons

We analyze the control of the propagation speed of three wave packets interacting in a medium with quadratic nonlinearity and dispersion. We find analytical expressions for mutually trapped pulses with a common velocity in the form of a three-parameter family of solutions of the three-wave resonant interaction. The stability of these novel parametric solitons is simply related to the value of their common group velocity.     

In situ extended X-ray absorption fine structure study during selective alcohol oxidation over Pd/Al2O3 in supercritical carbon dioxide

High-pressure in situ X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) data are reported during the selective oxidation of benzyl alcohol to benzaldehyde in supercritical carbon dioxide over a Pd/Al(2)O(3) catalyst (shell impregnated). For this purpose, a continuous-flow system with a spectroscopic cell suitable for in situ X-ray absorption studies on heterogeneous catalysts up to 200 degrees C and 200 bar has been developed. Due to the high contribution of the dense fluid to the overall X-ray absorption, high stability of the process pressure is mandatory, particularly when recording EXAFS spectra. According to EXAFS and XANES results, the palladium particles were fully reduced after exposure to benzyl alcohol in scCO(2). In contrast to Pd-catalyzed liquid-phase oxidation, a higher oxygen tolerance of the catalyst was observed. Palladium was partially oxidized on the surface under typical reaction conditions (0.9 mol % benzyl alcohol/0.5 mol % O(2) in carbon dioxide), which gradually increased when the concentration of oxygen in the feed was raised. Both XANES and EXAFS data uncovered that palladium is mainly oxidized on the surface or within the outermost layers. These results are in accordance with simulations of the XANES data using the FEFF8.20 code (program for ab initio calculations on multiple scattering XAS) and EXAFS data fitting/simulation.     

Functionally relevant electric-field induced perturbations of the prosthetic group of yeast ferrocytochrome c mutants obtained from a vibronic analysis of low-temperature absorption spectra

We have measured the low temperature (T = 20 K) absorption spectra of the N52A, N52V, N52I, Y67F, and N52AY67F mutants of ferrous Saccharomyces cerevisiae (baker's yeast) cytochrome c. All the bands in the Q0- and Q(v)-band region are split, and the intensity distributions among the split bands are highly asymmetric. The spectra were analyzed by a decomposition into Voigtian profiles. The spectral parameters thus obtained were further analyzed in terms of the vibronic coupling model of Schweitzer-Stenner and Bigman (Schweitzer-Stenner, R.; Bigman, D. J. Phys. Chem. B 2001, 7064-7073) to identify parameters related to electronic and vibronic perturbations of the heme macrocycle. We report that the electronic perturbation is of B(1g) symmetry and reflects the heterogeneity of the electric field at the heme, that is, the difference between the gradients along the perpendicular N-Fe-N axis of the heme core. We found that all the investigated mutations substantially increase this electronic perturbation, so that the spectral properties become similar to those of horse heart cytochrome c. Moreover, the electronic perturbation was found to correlate nonlinearly with the enthalpy changes associated with the reduction of the heme iron. Group theoretical arguments are invoked to propose a simple model which explains how a perturbation of the obtained symmetry can stabilize the reduced state of the heme iron. Finally, vibronic coupling parameters obtained from the analysis of the Q(v)-band region suggest that the investigated mutations decrease the nonplanar deformations of the heme group. This finding was reproduced by a normal mode structural decomposition (NSD) analysis of the N52V and N52VY67F heme conformations obtained from a 1 ns molecular dynamics simulation. We argue that the reduced nonplanarity contributes to the stabilization of the reduced state.