Liquid-crystalline polysiloxanes with fluoro-substituted side chains

Sixteen new side chain liquid polysiloxanes, either homopolymers derived from poly(hydrogenmethyl)siloxane or copolymers derived from poly(hydrogenmethyl-dimethylsiloxane), are reported with side chains carrying fluoro-substituents. The known effects of fluoro-substitution in low molar mass liquid crystals are strongly echoed in the polymeric analogues and interesting comparisons are made between homo- and co-polymers carrying the same fluorinated side chains.     

Pointwise Estimates and Regularity in Geometric Optics and Other Generated Jacobian Equations

The study of reflector surfaces in geometric optics necessitates the analysis of certain nonlinear equations of Monge‐Ampère type known as generated Jacobian equations. This class of equations, whose general existence theory has been recently developed by Trudinger, goes beyond the framework of optimal transport. We obtain pointwise estimates for weak solutions of such equations under minimal structural and regularity assumptions, covering situations analogous to those of costs satisfying the A3‐weak condition introduced by Ma, Trudinger, and Wang in optimal transport. These estimates are used to develop a C^1,α regularity theory for weak solutions of Aleksandrov type. The results are new even for all known near‐field reflector/refractor models, including the point source and parallel beam reflectors, and are applicable to problems in other areas of geometry, such as the generalized Minkowski problem.© 2017 Wiley Periodicals, Inc.     

Study of Blood Porphyrin Spectral Profile for Diagnosis of Tumor Progression

Renal cell carcinoma (RCC) accounts for approximately 3% of new cancer incidence and mortality in the United States. Unfortunately many RCC masses remain asymptomatic and nonpalpable until they are advanced. Diagnosis and localization of early carcinoma play an important role in the prevention and curative treatment of RCC. The autofluorescence of blood porphyrin of healthy and tumor induced in male SCID mice was analyzed using fluorescence and excitation spectroscopy. A significant contrast between normal and tumor blood could be established. Blood porphyrin fluorophore showed enhanced fluorescence band (around 630 nm) in function of the tumor growth. This indicates that either the autofluorescence intensity of the blood fluorescence may provide a good parameter for the “first approximation” characterization of the tumor stage.     

Design and scalable synthesis of new chiral selectors. Part 1: Synthesis and characterization of a new constrained cyclopeptide from unnatural bulky amino acids

We describe the conception, synthesis, and characterization of a novel cyclopeptide designed for chiral recognition. The asymmetric units are built from an unnatural amino acid in the series of α-aryl-α-methyl glycine. Modifications of standard methods of peptide synthesis are described in order to improve yields and purities when applied to hindered amino acids. First set of experiments about host-guest ability of the obtained cyclopeptide is disclosed.     

Temperature Integration: An efficient procedure for calculation of free energy differences

We propose a method, Temperature Integration, which allows an efficient calculation of free energy differences between two systems of interest, with the same degrees of freedom, which may have rough energy landscapes. The method is based on calculating, for each single system, the difference between the values of lnZ$lnZ$ at two temperatures, using a Parallel Tempering procedure. If our two systems of interest have the same phase space volume, they have the same values of lnZ$lnZ$ at high-T$T$, and we can obtain the free energy difference between them, using the two single-system calculations described above. If the phase space volume of a system is known, our method can be used to calculate its absolute (versus relative) free energy as well. We apply our method and demonstrate its efficiency on a “toy model” of hard rods on a 1-dimensional ring.     

Pseudo-atom phase shifts of liquid metals and alloys

Ziman pseudo-atom phase shifts have been evaluated, as functions of l and k _F, for monovalent ions, using a pseudo-potential technique. The results of their application to a number of physical problems suggest that our data are reasonably accurate.     

Setting targets for surrogate-based optimization

In the context of surrogate-based optimization (SBO), most designers have still very little guidance on when to stop and how to use infill measures with target requirements (e.g., one-stage approach for goal seeking and optimization); the reason: optimum estimates independent of the surrogate and optimization strategy are seldom available. Hence, optimization cycles are typically stopped when resources run out (e.g., number of objective function evaluations/time) or convergence is perceived, and targets are empirically set which may affect the effectiveness and efficiency of the SBO approach. This work presents an approach for estimating the minimum (target) of the objective function using concepts from extreme order statistics which relies only on the training data (sample) outputs. It is assumed that the sample inputs are randomly distributed so the outputs can be considered a random variable, whose density function is bounded (a, b), with the minimum (a) as its lower bound. Specifically, an estimate of the minimum (a) is obtained by: (i) computing the bounds (using training data and the moment matching method) of a selected set of analytical density functions (catalog), and (ii) identifying the density function in the catalog with the best match to the sample outputs distribution and corresponding minimum estimate (a). The proposed approach makes no assumption about the nature of the objective functions, and can be used with any surrogate, and optimization strategy even with high dimensional problems. The effectiveness of the proposed approach was evaluated using a compact catalog of Generalized Beta density functions and well-known analytical optimization test functions, i.e., F2, Hartmann 6D, and Griewangk 10D and in the optimization of a field scale alkali-surfactant-polymer enhanced oil recovery process. The results revealed that: (a) the density function (from a catalog) with the best match to a function outputs distribution, was the same for both large and reduced samples, (b) the true optimum value was always within a 95% confidence interval of the estimated minimum distribution, and (c) the estimated minimum represents a significant improvement over the present best solution and an excellent approximation of the true optimum value.     

On the equivalence of quadratic optimization problems commonly used in portfolio theory

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e., the Markowitz mean–variance problem as well as the problems based on the mean–variance utility function and the quadratic utility. Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean–variance optimal portfolios. It is shown that the solutions of the Markowitz optimization problem and the quadratic utility problem are not always mean–variance efficient.