A Scalable Parallel Interior Point Algorithm for Stochastic Linear Programming and Robust Optimization

We present a computationally efficient implementation of an interior point algorithm for solving large-scale problems arising in stochastic linear programming and robust optimization. A matrix factorization procedure is employed that exploits the structure of the constraint matrix, and it is implemented on parallel computers. The implementation is perfectly scalable. Extensive computational results are reported for a library of standard test problems from stochastic linear programming, and also for robust optimization formulations.The results show that the codes are efficient and stable for problems with thousands of scenarios. Test problems with 130 thousand scenarios, and a deterministic equivalent linear programming formulation with 2.6 million constraints and 18.2 million variables, are solved successfully.     

String tension in the three-dimensional Abelian Higgs model

We measure the expectation values of the Wilson loops for the radially active Abelian Higgs Model in three dimensions with Higgs chargeq=1 andq=2. We observe a drastic fall-off of the area term as we pass to the Higgs phase, as well as a peak of the perimetric term at the phase transition. Implications of our results for other Higgs models are also discussed.     

Consecutive k-out-of-n systems with maintenance

A consective k-out-of-n system consists of n linearly or cycliccally ordered components such that the system fails if and only if at least k consecutive components fail. In this paper we consider a maintained system where each component is repaired independently of the others according to an exponential distribution. Assuming general lifetime distributions for system's components we prove a limit theorem for the time to first failure of both linear and circular systems.     

Decay of the transient Cu(B)-CO complex is accompanied by formation of the heme Fe-CO complex of cytochrome cbb(3)-CO at ambient temperature: evidence from time-resolved Fourier transform infrared spectroscopy

Time-resolved step-scan Fourier infrared spectroscopy has been used to study the CO-bound cbb(3)-type cytochrome c oxidase from Pseudomonas stutzeri at room temperature. We observe a single band in the FTIR spectrum at 1956 cm(-1) (beta-form). The time-resolved data indicate that upon photolysis, CO is transferred from heme b(3) (nu(CO) = 1956 cm(-1)) to CuB (nu(CO) = 2064 cm(-1)). The decay of the 2065 cm(-1) peak (t(1/2) = 120 +/- 16 ms) and the development of the 1956 cm(-1) peak (t(1/2) = 144 +/- 8 ms ) suggest that formation of the Fe-CO complex is concurrent with the decay of the CuB-CO complex. The intensity ratio of the Fe-CO/CuB-CO (2.15) remains constant for all data points, and thus we conclude that no fraction of CO escapes the binuclear center at 293 K.     

Exponentially divergent trajectories and RRKM behaviour of Ar3 clusters

The rate of exponential divergence of two initially adjacent trajectories has been studied for Ar₂ clusters at low and high energies. It is found that at the dissociation limit energy randomization occurs during two typical vibrational periods. Lifetime distributions for energies not far above the dissociation limit have a random lifetime pattern but highly energized clusters show non-RRKM behaviour     

Water clusters: the (H2O)64 case

Minimum energy structures and dynamics of (H₂O)₆₄ cluster are investigated by molecular dynamics techniques and an empirical potential energy surface. Using plots of the cluster, the oxygen-oxygen distance distribution function, and power spectra, we show the existence of minima with deformed cubic arrangement. These results together with previous calculations on smaller clusters support the conclusion that the cubic type geometries are common among water aggregates.     

Universal frames

For a class of frames we define the notion of a universal element and prove that in the class of all frames of weight less than or equal to a fixed infinite cardinal number τ there are such elements.     

Universality and asymptotics of graph counting problems in non-orientable surfaces

Bender-Canfield showed that a plethora of graph counting problems in orientable/non-orientable surfaces involve two constants tg and pg for the orientable and the non-orientable case, respectively. T.T.Q. Le and the authors recently discovered a hidden relation between the sequence tg and a formal power series solution u(z) of the Painlevé I equation which, among other things, allows to give exact asymptotic expansion of tg to all orders in 1/g for large g. The paper introduces a formal power series solution v(z) of a Riccati equation, gives a non-linear recursion for its coefficients and an exact asymptotic expansion to all orders in g for large g, using the theory of Borel transforms. In addition, we conjecture a precise relation between the sequence pg and v(z). Our conjecture is motivated by the enumerative aspects of a quartic matrix model for real symmetric matrices, and the analytic properties of its double scaling limit. In particular, the matrix model provides a computation of the number of rooted quadrangulations in the 2-dimensional projective plane. Our conjecture implies analyticity of the O(N)- and Sp(N)-types of free energy of an arbitrary closed 3-manifold in a neighborhood of zero. Finally, we give a matrix model calculation of the Stokes constants, pose several problems that can be answered by the Riemann-Hilbert approach, and provide ample numerical evidence for our results.     

Ablated gratings on borosilicate glass by 193-nm excimer laser radiation

Relief gratings of 500-nm period have been fabricated on Er/Yb-doped borosilicate glass substrates by laser ablation through the use of an excimer laser, at a wavelength of 193-nm, and a modified Mach-Zehnder interferometer. The grating fabrication process has been quantified by the use of diffraction efficiency measurements and atomic force microscope microscans and is related to the incident energy density.