Embracing the giant component

Consider a game in which edges of a graph are provided a pair at a time, and the player selects one edge from each pair, attempting to construct a graph with a component as large as possible. This game is in the spirit of recent papers on avoiding a giant component, but here we embrace it. We analyze this game in the offline and online setting, for arbitrary and random instances, which provides for interesting comparisons. For arbitrary instances, we find that the competitive ratio (the best possible solution value divided by best possible online solution value) is large. For “sparse” random instances the competitive ratio is also large, with high probability (whp); If the instance has ¼(1 + ε)n random edge pairs, with 0 < ε ≤ 0.003, then any online algorithm generates a component of size O((log n)^3/2) whp , while the optimal offline solution contains a component of size Ω(n) whp . For “dense” random instances, the average‐case competitive ratio is much smaller. If the instance has ½(1 ? ε)n random edge pairs, with 0 < ε ≤ 0.015, we give an online algorithm which finds a component of size Ω(n) whp . © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

A Web-Based Molecular-Level Inquiry Laboratory Activity

This paper presents a new computer-based atomic level simulation of an ideal gas. The simulation is written in Java and is accessed by students through a Web browser. This software is used in conjunction with a written laboratory experiment developed within the framework of an inquiry instructional strategy. This molecular-level laboratory experiment is used in combination with a parallel macroscopic laboratory experiment. We hypothesize that students exposed to these kinds of parallel activities will be better able to link the macroscopic, microscopic, and symbolic understanding of chemical concepts.Presented at the ACS Division of Chemical Education sponsored symposium on web-assisted learning in chemistry at its 221st national meeting in San Diego, CA April 1–5, 2001.     

Summability and estimates for polynomials and multilinear mappings

In this paper we extend and generalize several known estimates for homogeneous polynomials and multilinear mappings on Banach spaces. Applying the theory of absolutely summing nonlinear mappings, we prove that estimates which are known for mappings on ?_p spaces in fact hold true for mappings on arbitrary Banach spaces.     

Abraham Model Expressions for Describing Water-to-Diethylene Glycol and Gas-to-Diethylene Glycol Solute Transfer Processes at 298.15 K

A gas chromatographic headspace analysis method was used to experimentally determine gas-to-liquid partition coefficients and infinite dilution activity dilution for 14 different aliphatic and cyclic hydrocarbons (alkanes, cycloalkanes, alkenes, alkynes), eight different aromatic compounds (benzene, alkylbenzenes, halobenzenes), five different chloroalkanes (dichloromethane, trichloromethane, 1-chlorobutane, 1,2-dichloropropane, isopropylbromide), tetrahydrofuran, butyl acetate, and acetonitrile dissolved in diethylene glycol at 298.15 K. Solubilities were also measured at 298.15 K for 31 crystalline nonelectrolyte organic solutes including several polycyclic aromatic hydrocarbons and substituted benzoic acid derivatives. The experimental results of the headspace chromatographic and spectroscopic solubility measurements were converted to gas-to-diethylene glycol and water-to-diethylene glycol partition coefficients, and molar solubility ratios using standard thermodynamic relationships. Expressions were derived for solute transfer into diethylene glycol from the calculated partition coefficients and solubility ratios. Mathematical correlations based on the Abraham model describe the observed partition coefficient and solubility data to within 0.14 log₁₀ units (or less).     

ChemInform Abstract: From 1∞ [(UO2)2O(MoO4)4]6‐ to 1∞ [(UO2)2(MoO4)3(MoO5)] 6‐ Infinite Chains in A6U2Mo4O21 (A: Na,K, Rb,Cs) Compounds: Synthesis and Crystal Structure of Cs6 [(UO2)2(MoO4)3(MoO5)] .

Single crystals of the title compound are obtained from a melt of U₃O₈, MoO₃, and excess Cs₂CO₃ (Pt crucible, 950 °C, 12 h, cooling rate 5 °C/h).     

Flat-on lamellae in spin-coated, stable films of poly(propylene azelate)

Thin films (5-500 nm thick) of the linear aliphatic polyester (3,7) poly(propylene azelate) (PPAz) were prepared by spin-coating of CHCl(3) polymer solutions with different polymer concentrations. The morphology and structure of the spin-coated thin films were investigated by atomic force microscopy (AFM) and by grazing incidence wide-angle X-ray scattering (GIWAXS) techniques. AFM revealed the continuous nature of the flat, spherulitic films which are stable against dewetting even for polymer coatings as thin as 15 nm. GIWAXS patterns revealed a high crystal orientation of the films. A sharp reflection on the meridian whose spacing is related to the polymer chain unit length (c-axis) supports the presence of flat-on lamellae morphology in the whole range of film thicknesses investigated. The flat-on lamellae morphology is also supported by AFM images. A triclinic unit cell with the c*-axis perpendicular to the substrate is proposed for PPAz. The repulsion of the long aliphatic spacer by the Si-substrate is invoked as the main reason for the flat-on morphology observed.     

Three-dimensional key in a modified joint transform correlator encryption scheme

We propose a modified encryption joint transform correlator scheme that introduces an additional random phase mask. The positions of both the conventional and the new mask are crucial for successful recovery of the original data. Although the two random phase masks are 2D, variation of their relative distance constitutes an additional dimension. Consequently by including this notion, both random phase masks act as a 3-dimensional (3D) key code increasing thereby the security with respect to the conventional JTC encryption scheme. We employ this scheme to multiplex encrypted data, displacing the encoding masks. During decryption of the multiplexed information, we only reconstruct the object that matches the correct predetermined 3D key code, i.e. that matches the random masks positions in the encryption step. We present actual experimental results, by using BSO crystal as recording medium, as well as their respective analysis.     

Experimental opto-digital synthesis of encrypted sub-samples of an image to improve its decoded quality

We develop an experimental protocol to visualize decrypted images that otherwise would have been barely recognizable, while keeping the standard security levels. This image deterioration is partly due to the natural speckle noise as well as the practical limitations arising from the optical elements composing the setup. This protocol is based on an optical image synthesis with digital holography using enlarged sub-samples of an entire image together with a multiplexing technique. We implement the process using a Mach-Zehnder interferometer with a joint transform correlator encrypting architecture. As a result, we get smaller speckle patterns on the final assembled image and a spatial frequency enhancement with respect to the decoded image obtained with the conventional procedures.