BDD-based heuristics for binary optimization

In this paper we introduce a new method for generating heuristic solutions to binary optimization problems. We develop a technique based on binary decision diagrams. We use these structures to provide an under-approximation to the set of feasible solutions. We show that the proposed algorithm delivers comparable solutions to a state-of-the-art general-purpose optimization solver on randomly generated set covering and set packing problems.     

New Crystalline Lasers on the Base of Monoclinic KR(W04)2:Ln3+ Tungstates (R=Y and Ln)

Monoclinic KY(WO₄)₂:Pr₃₊, Tm₃₊:KY(WO₄)₂:Er₃₊, Yb₃₊ single crystals are grown by low-gradient Czochralski technique. Stimulated emission at 1.0223μm wavelength in the new lasing ¹D₂→³F₃ channel of Pr³⁺ ions in KY(WO₄)₂ at room temperature under Xe-flashlamp pumping is excited. Full sets of Stark-level energies for Pr₃₊ ions in KY(WO₄)2 and KGd(WO₄)₂ crystals at 77 K are determined. 4f²-4f² intensity-transitions for the KY(WO₄)₂:Pr³⁺ are analyzed preliminarily. All observed at present and earlier one-micron Pr³⁺-ion, induced transitions in the ¹D₂→³F₃ and ¹D₂→³F₄ channels are identified. In yttrium and gadolinium sensitized-tungstates a two-micron (³H₄→³H₆) low-threshold generation of Tm³⁺ ions at cryogenic temperatures is achieved.All authors cooperate with the Joint Open Laboratory for Laser Crystals and Precise Laser Systems at the Institute of Crystallography and Institute of Laser Physics, Russian Academy of Sciences.     

Additive global noise delays Turing bifurcations

We apply a stochastic center manifold method to the calculation of noise-induced phase transitions in the stochastic Swift-Hohenberg equation. This analysis is applied to the reduced mode equations that result from Fourier decomposition of the field variable and of the temporal noise. The method shows a pitchfork bifurcation at lower perturbation order, but reveals a novel additive-noise-induced postponement of the Turing bifurcation at higher order. Good agreement is found between the theory and the numerics for both the reduced and the full system. The results are generalizable to a broad class of nonlinear spatial systems.     

Self‐Pillared,Single‐Unit‐Cell Sn‐MFI Zeolite Nanosheets and Their Use for Glucose and Lactose Isomerization

Single‐unit‐cell Sn‐MFI, with the detectable Sn uniformly distributed and exclusively located at framework sites, is reported for the first time. The direct, single‐step, synthesis is based on repetitive branching caused by rotational intergrowths of single‐unit‐cell lamellae. The self‐pillared, meso‐ and microporous zeolite is an active and selective catalyst for sugar isomerization. High yields for the conversion of glucose into fructose and lactose to lactulose are demonstrated.     

3D Study of the Morphology and Dynamics of Zeolite Nucleation

The principle aspects and constraints of the dynamics and kinetics of zeolite nucleation in hydrogel systems are analyzed on the basis of a model Na‐rich aluminosilicate system. A detailed time‐series EMT‐type zeolite crystallization study in the model hydrogel system was performed to elucidate the topological and temporal aspects of zeolite nucleation. A comprehensive set of analytical tools and methods was employed to analyze the gel evolution and complement the primary methods of transmission electron microscopy (TEM) and nuclear magnetic resonance (NMR) spectroscopy. TEM tomography reveals that the initial gel particles exhibit a core–shell structure. Zeolite nucleation is topologically limited to this shell structure and the kinetics of nucleation is controlled by the shell integrity. The induction period extends to the moment when the shell is consumed and the bulk solution can react with the core of the gel particles. These new findings, in particular the importance of the gel particle shell in zeolite nucleation, can be used to control the growth process and properties of zeolites formed in hydrogels.     

Hohenberg–Kohn theorems in the presence of magnetic field

In this article, we examine Hohenberg–Kohn theorems for Current Density Functional Theory, that is, generalizations of the classical Hohenberg–Kohn theorem that includes both electric and magnetic fields. In the Vignale and Rasolt formulation (Vignale and Rasolt, Phys. Rev. Lett. 1987, 59, 2360), which uses the paramagnetic current density, we address the issue of degenerate ground states and prove that the ensemble‐representable particle and paramagnetic current density determine the degenerate ground states. For the formulation that uses the total current density, we note that the proof suggested by Diener (Diener, J. Phys.: Condens. Matter. 1991, 3, 9417) is unfortunately not correct. Furthermore, we give a proof that the magnetic field and the ensemble‐representable particle density determine the scalar and vector potentials up to a gauge transformation. This generalizes the result of Grayce and Harris (Grayce and Harris, Phys. Rev. A 1994, 50, 3089) to the case of degenerate ground states. We moreover prove the existence of a positive wavefunction that is the ground state of infinitely many different Hamiltonians. © 2014 Wiley Periodicals, Inc.     

Boojum and stripe textures in long-range orientationally ordered monolayers on solid substrates

Long-range organization of molecular tilt azimuth is a striking feature in monolayers at the air-water interface. We show that the boojum and stripe textures of pentadecanoic acid (PDA) with the continuous variations of molecular tilt azimuth formed at the air-water interface at temperatures lower than room temperature can be preserved after being transferred to glass substrates at low dipping speeds. The long-range tilt order in the transferred boojums and stripes is resolved by frictional force microscopy at room temperature, suggesting that the tilt order is "frozen" through the interaction of PDA molecules with the glass surface. The transferred stripe structure can be used as a unique alignment layer to induce a continuously azimuthal orientation of nematic liquid crystals.     

Correction factors for boundary diffusion in reaction-diffusion master equations

The reaction-diffusion master equation (RDME) has been widely used to model stochastic chemical kinetics in space and time. In recent years, RDME-based trajectorial approaches have become increasingly popular. They have been shown to capture spatial detail at moderate computational costs, as compared to fully resolved particle-based methods. However, finding an appropriate choice for the discretization length scale is essential for building a reasonable RDME model. Moreover, it has been recently shown [R. Erban and S. J. Chapman, Phys. Biol. 4, 16 (2007); R. Erban and S. J. Chapman, Phys. Biol. 6, 46001 (2009); D. Fange, O. G. Berg, P. Sjo?berg, and J. Elf, Proc. Natl. Acad. Sci. U.S.A. 107, 46 (2010)] that the reaction rates commonly used in RDMEs have to be carefully reassessed when considering reactive boundary conditions or binary reactions, in order to avoid inaccurate--and possibly unphysical--results. In this paper, we present an alternative approach for deriving correction factors in RDME models with reactive or semi-permeable boundaries. Such a correction factor is obtained by solving a closed set of equations based on the moments at steady state, as opposed to modifying probabilities for absorption or reflection. Lastly, we briefly discuss existing correction mechanisms for bimolecular reaction rates both in the limit of fast and slow diffusion, and argue why our method could also be applied for such purpose.     

Multivariate Analysis of Electron Detachment Dissociation and Infrared Multiphoton Dissociation Mass Spectra of Heparan Sulfate Tetrasaccharides Differing Only in Hexuronic acid Stereochemistry

The structural characterization of glycosaminoglycan (GAG) carbohydrates by mass spectrometry has been a long-standing analytical challenge due to the inherent heterogeneity of these biomolecules, specifically polydispersity, variability in sulfation, and hexuronic acid stereochemistry. Recent advances in tandem mass spectrometry methods employing threshold and electron-based ion activation have resulted in the ability to determine the location of the labile sulfate modification as well as assign the stereochemistry of hexuronic acid residues. To facilitate the analysis of complex electron detachment dissociation (EDD) spectra, principal component analysis (PCA) is employed to differentiate the hexuronic acid stereochemistry of four synthetic GAG epimers whose EDD spectra are nearly identical upon visual inspection. For comparison, PCA is also applied to infrared multiphoton dissociation spectra (IRMPD) of the examined epimers. To assess the applicability of multivariate methods in GAG mixture analysis, PCA is utilized to identify the relative content of two epimers in a binary mixture.     

Geodesic restrictions for the Casimir operator

We consider the hyperbolic Casimir operator C defined on the tangent sphere bundle SY of a compact hyperbolic Riemann surface Y. We prove a non-trivial bound on the L²-norm of the restriction of eigenfunctions of C to certain natural hypersurfaces in SY. The result that we obtain goes beyond known (sharp) local bounds of L. Hörmander.