A scaling technique for finding the weighted analytic center of a polytope

Let a bounded full dimensional polytope be defined by the systemAx b whereA is anm × n matrix. Leta _i denote theith row of the matrixA, and define theweighted analytic center of the polytope to be the point that minimizes the strictly convex barrier function – _i=1 ^m w _i ln(a _i ^T x –b _i ). The proper selection of weightsw _i can make any desired point in the interior of the polytope become the weighted analytic center. As a result, the weighted analytic center has applications in both linear and general convex programming. For simplicity we assume that the weights are positive integers.If some of thew _i 's are much larger than others, then Newton's method for minimizing the resulting barrier function is very unstable and can be very slow. Previous methods for finding the weighted analytic center relied upon a rather direct application of Newton's method potentially resulting in very slow global convergence. We present a method for finding the weighted analytic center that is based on the scaling technique of Edmonds and Karp and is an enhancement of Newton's method. The scaling algorithm runs in iterations, wherem is the number of constraints defining the polytope andW is the largest weight given on any constraint. Each iteration involves taking a step in the Newton direction and its complexity is dominated by the time needed to solve a system of linear equations.Supported by the Campus Research Board, University of Illinois at Urbana-Champaign.Supported by the National Science Foundation under Grants CCR-9057481 and CCR-9007195.     

AnO(n logn) algorithm for the all-nearest-neighbors Problem

Given a setV ofn points ink-dimensional space, and anL _q -metric (Minkowski metric), the all-nearest-neighbors problem is defined as follows: for each pointp inV, find all those points inV–{p} that are closest top under the distance metricL _q . We give anO(n logn) algorithm for the all-nearest-neighbors problem, for fixed dimensionk and fixed metricL _q . Since there is an (n logn) lower bound, in the algebraic decision-tree model of computation, on the time complexity of any algorithm that solves the all-nearest-neighbors problem (fork=1), the running time of our algorithm is optimal up to a constant factor.This research was supported by a fellowship from the Shell Foundation. The author is currently at AT&T Bell Laboratories, Murray Hill, New Jersey, USA.     

Medium energy,heavy and inert ion irradiation of metallic thin films: studies of surface nano‐structuring and metal burrowing

In context to the ion induced surface nanostructuring of metals and their burrowing in the substrates, we report the influence of Xe and Kr ion‐irradiation on Pt:Si and Ag:Si thin films of ~5‐nm thickness. For the irradiation of thin films, several ion energies (275 and 350 keV of Kr; 450 and 700 keV of Xe) were chosen to maintain a constant ratio of the nuclear energy loss to the electronic energy loss (S_n/S_e) in Pt and Ag films (five in present studies). The ion‐fluence was varied from 1.0 × 10¹⁵ to 1.0 × 10¹⁷ ions/cm². The irradiated films were characterized using Rutherford backscattering spectroscopy (RBS), atomic force microscopy (AFM) and scanning electron microscopy (SEM). The AFM and SEM images show ion beam induced systematic surface nano‐structuring of thin films. The surface nano‐structures evolve with the ion fluence. The RBS spectra show fluence dependent burrowing of Pt and Ag in Si upon the irradiation of both ion beams. At highest fluence, the depth of metal burrowing in Si for all irradiation conditions remains almost constant confirming the synergistic effect of energy losses by the ion beams. The RBS analysis also shows quite large sputtering of thin films bombarded with ion beams. The sputtering yield varied from 54% to 62% by irradiating the thin films with Xe and Kr ions of chosen energies at highest ion fluence. In the paper, we present the experimental results and discuss the ion induced surface nano‐structuring of Pt and Ag and their burrowing in Si. Copyright © 2016 John Wiley & Sons, Ltd.     

Fate of CS2 in viscose process: a chemistry perspective

Cellulose dissolution in the viscose process has been facilitated through derivatization by carbon disulphide (CS₂) at xanthation stage by converting alkali cellulose (AC) to cellulose xanthate (CX). CX formation has been always accompanied with sulphur based byproducts formation as dictated by the mechanism published in earlier study (Gondhalekar et al. (Cellulose 26 3 1595–1604, 2019)). The sulphur byproducts formed during viscose synthesis are sodium sulphide (Na₂S), sodium trithiocarbonate (Na₂CS₃: TTC) and other minor sulphur compounds. These byproducts continue to form during ripening process as dictated by time and temperature coupled with concentration of free caustic and CS₂ present in the system. These byproducts get converted into sodium sulphate (Na₂SO₄), hydrogen sulphide (H₂S), CS₂ and other sulphurous compounds during spinning. Overall, uncontrolled ripening without parametric optimization adversely impacts raw material (RM) consumption and creates sustainability challenges. Overall optimization based on viscose process fundamental insights presented in this study will effectively help in achieving operational excellence by reducing rate of undesired reactions to improve RM specific consumption and will compliment overall sustainability efforts in viscose industry.

     

A new combination of cyclohexylhydrazine and IBX for oxidative generation of cyclohexyl free radical and related synthesis of parvaquone

The present paper demonstrates a single-step and straightforward synthesis of parvaquone through intermediacy of cyclohexyl radical generated from novel combination of cyclohexylhydrazine and o-iodoxybenzoic acid and subsequently trapped by 2-hydroxy-1,4-naphthoquinone. Formation of cyclohexyl free radical using this new combination was reaffirmed by cyclohexylation of readily available 2-amino-1,4-naphthoquinone.     

Simple efficient synthesis of 4‐aminoquinazoline via amidine of N‐arylamidoxime

Preparation of 4‐amino‐2‐aryl quinazolines by reduction of N‐(2‐cyanoaryl) amidoximes via amidines using SnCl₂ in ethanol. J. Heterocyclic Chem., (2011).     

Diffraction characteristics of optical vortex passing through an aperture-iris diaphragm

The diffraction of an optical vortex through an iris diaphragm which is a close approximation to a circular aperture has been investigated. The results are compared with those obtained from the diffraction of a Gaussian beam through the same aperture. In our findings the diffraction of an optical vortex and a Gaussian beam produce ball bearing sort of structure of darkness and brightness. The singularity of the vortex beam is found to be consistent even after the diffraction through the aperture. The presence of singularity at the centre of diffraction pattern of an optical vortex has been confirmed by interferometry. There is a good agreement between the experimental and numerical results. We propose that these results may find various applications in optical trapping experiments.     

Dissociation constants of some derivatives of 5-amino isophthalic acid in mixed solvents

The dissociation constants of some derivatives of 5-amino isophthalic acid have been measured by Calvin Bjerrum pH titration method in DMF-water and DMSO-water (60: 40 v/v) systems at 308.15 K. It is observed that dissociation constant depends on the solvent and substituents group present in the compound.     

Dietary agents in cancer prevention: an immunological perspective(†)

Skin cancer is the most common form of cancer diagnosed in the United States. Exposure to solar ultraviolet (UV) radiations is believed to be the primary cause for skin cancer. Excessive UV radiation can lead to genetic mutations and damage in the skin's cellular DNA that in turn can lead to skin cancer. Lately, chemoprevention by administering naturally occurring non-toxic dietary compounds has proven to be a potential strategy to prevent the occurrence of tumors. Attention has been drawn toward several natural dietary agents such as resveratrol, one of the major components found in grapes, red wines, berries and peanuts, proanthocyanidins from grape seeds, (-)-epigallocatechin-3-gallate from green tea, etc. However, the effect these dietary agents have on the immune system and the immunological mechanisms involved therein are still being explored. In this review, we shall focus on the role of key chemopreventive agents on various immune cells and discuss their potential as antitumor agents with an immunological perspective.