Convex Normalizations in Lift-and-Project Methods for 0–1 Programming

Branch-and-Cut algorithms for general 0–1 mixed integer programs can be successfully implemented by using Lift-and-Project (L&P) methods to generate cuts. L&P cuts are drawn from a cone of valid inequalities that is unbounded and, thus, needs to be truncated, or normalized. We consider general normalizations defined by arbitrary closed convex sets and derive dual problems for generating L&P cuts. This unified theoretical framework generalizes and covers a wide group of already known normalizations. We also give conditions for proving finite convergence of the cutting plane procedure that results from using such general L&P cuts.     

Cooperative origin of low-density domains in liquid water

We study clusters formed by water molecules possessing large enough tetrahedrality with respect to their nearest neighbors. Using Monte Carlo simulation of SPC/E water and Voronoi tessellation, we find that regions of lower density than the bulk are formed by accretion of molecules into clusters exceeding a minimum size. Clusters are predominantly linear objects and become less compact as they grow until they reach a size beyond which further accretion is not accompanied by a density decrease. The results suggest that the formation of "icelike" regions in liquid water is cooperative.     

Scanning tunneling microscopy and surface simulation of zinc-blende GaN(001) intrinsic 4x reconstruction: linear gallium tetramers?

Scanning tunneling microscopy images confirm electron diffraction studies that the zinc-blende GaN(001)-4x reconstruction consists of rows aligned along [110] with a spacing along [110] of 4a. Dual-bias imaging shows a 180 degree shift of the corrugation maximum position between the profiles of empty and occupied states, in agreement with surface simulations based on the 4 x 1 linear tetramer model of Neugebauer et al. [Phys. Rev. Lett. 80, 3097 (1998)]. Electronic structure calculations predict a surface band gap of 1.1 eV, close to the measured value of 1.14 eV and the previously predicted value (1.2 eV). Despite the successes of this model, high-resolution images reveal an unexpected 3x periodicity (not seen in diffraction) along the [110] row direction, indicating the need for a 4 x 3 model, and putting into question the existence of linear Ga tetramers.     

Investigation of transition States in bulk and freestanding film polymer glasses

We have performed transition state searches on the potential energy landscape for bulk and freestanding film polymer glasses and identified connected minima. An analysis of the displacements between minima shows that the sites that undergo the greatest displacement are highly localized in space for both the bulk and the thin-film systems studied. In the case of the thin film, the clusters originate at the surface and penetrate into the center of the film thereby coupling the relaxation in the center of the film to the mobile surface layer. Furthermore, the energy barriers between minima are lower in the thin film than in the bulk system. These findings can rationalize the experimentally observed depression of the glass transition temperature in freestanding polymer films.     

Photochemical preparation of highly functionalized 1-indanones

A series of o-alkylphenyl alkyl ketones 1 were synthesized by different methods. The presence of a leaving group X adjacent to the carbonyl group is the special peculiarity of these ketones. Upon irradiation the keto carbonyl group of these compounds undergoes an n-pi* excitation followed by a 1,5-hydrogen migration from the o-alkyl substituent to the carbonyl oxygen atom. The thus formed 1,4-diradicals are subject to a very rapid elimination of acid HX, giving 1,5-diradicals. We called this process spin center shift. After intersystem crossing these diradicals cyclize to 1-indanones 20 in good yields. Depending on the solvent and on substituents, o-alkoxyalkyl ketones 22 or benzo[c]furanes 21 are obtained as byproducts. The mechanism of the cyclization was elucidated by quantum chemical calculations and kinetic measurements.     

Numerical blow‐up for the porous medium equation with a source

We study numerical approximations of positive solutions of the porous medium equation with a nonlinear source, where m > 1, p > 0 and L > 0 are parameters. We describe in terms of p, m, and L when solutions of a semidiscretization in space exist globally in time and when they blow up in a finite time. We also find the blow‐up rates and the blow‐up sets, proving that there is no regional blow‐up for the numerical scheme. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004     

On the volume of unit vector fields on spaces of constant sectional curvature

A unit vector field X on a Riemannian manifold determines a submanifold in the unit tangent bundle. The volume of X is the volume of this submanifold for the induced Sasaki metric. It is known that the parallel fields are the trivial minima. In this paper, we obtain a lower bound for the volume in terms of the integrals of the 2i-symmetric functions of the second fundamental form of the orthogonal distribution to the field X. In the spheres ${\textbf {S}}^{2k+1}$, this lower bound is independent of X. Consequently, the volume of a unit vector field on an odd-sphere is always greater than the volume of the radial field. The main theorem on volumes is applied also to hyperbolic compact spaces, giving a non-trivial lower bound of the volume of unit fields.     

Molecular simulation of the reversible mechanical unfolding of proteins

In this work we have combined a Wang-Landau sampling scheme [F. Wang and D. Landau, Phys. Rev. Lett. 86, 2050 (2001)] with an expanded ensemble formalism to yield a simple and powerful method for computing potentials of mean force. The new method is implemented to investigate the mechanical deformation of proteins. Comparisons are made with analytical results for simple model systems such as harmonic springs and Rouse chains. The method is then illustrated on a model 15-residue alanine molecule in an implicit solvent. Results for mechanical unfolding of this oligopeptide are compared to those of steered molecular dynamics calculations.     

Aberro-polariscope for the human eye

We have developed an aberro-polariscope that simultaneously measures spatially resolved polarization properties and wave-front aberration in a living human eye. The setup consists of an infrared Hartmann-Shack sensor that incorporates a polariscope. A series of four Hartmann-Shack images corresponding to independent polarization states were recorded. The corresponding wave-front aberration was computed from each image. Moreover, from each set of four images spatially resolved (over the pupil plane) parameters of polarization were also determined. This instrument allows useful information on both the optical and the biomechanical properties of the eye to be obtained.