Approximation Algorithms for the Asymmetric Traveling Salesman Problem : Describing two recent methods

The paper provides a description of the two recent approximation algorithms for the Asymmetric Traveling Salesman Problem, giving the intuitive description of the works of Feige-Singh[1] and Asadpour et.al\ [2].\newline [1] improves the previous $O(\log n)$ approximation algorithm, by improving the constant from 0.84 to 0.66 and modifying the work of Kaplan et. al\ [3] and also shows an efficient reduction from ATSPP to ATSP. Combining both the results, they finally establish an approximation ratio of $\left(\frac{4}{3}+\epsilon \right)\log n$ for ATSPP,\ considering a small $\epsilon>0$,\ improving the work of Chekuri and Pal.[4]\newline Asadpour et.al, in their seminal work\ [2], gives an $O\left(\frac{\log n}{\log \log n}\right)$ randomized algorithm for the ATSP, by symmetrizing and modifying the solution of the Held-Karp relaxation problem and then proving an exponential family distribution for probabilistically constructing a maximum entropy spanning tree from a spanning tree polytope and then finally defining the thin-ness property and transforming a thin spanning tree into an Eulerian walk.\ The optimization methods used in\ [2] are quite elegant and the approximation ratio could further be improved, by manipulating the thin-ness of the cuts.Comment: 12 page

Matrix Recipes for Hard Thresholding Methods

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for different configurations to achieve complexity vs. accuracy tradeoffs. Moreover, we study acceleration schemes via memory-based techniques and randomized, $\epsilon$-approximate matrix projections to decrease the computational costs in the recovery process. For most of the configurations, we present theoretical analysis that guarantees convergence under mild problem conditions. Simulation results demonstrate notable performance improvements as compared to state-of-the-art algorithms both in terms of reconstruction accuracy and computational complexity.Comment: 26 page

Quantifying precision and accuracy of measurements of dissolved inorganic carbon stable isotopic composition using continuous-flow isotope-ratio mass spectrometry

RATIONALE: We describe an analytical procedure that allows sample collection and measurement of carbon isotopic composition (δ13CV-PDB value) and dissolved inorganic carbon concentration, [DIC], in aqueous samples without further manipulation post field collection. By comparing outputs from two different mass spectrometers, we quantify with the statistical rigour uncertainty associated with the estimation of an unknown measurement. This is rarely undertaken, but it is needed to understand the significance of field data and to interpret quality assurance exercises.<p></p> METHODS: Immediate acidification of field samples during collection in evacuated, pre-acidified vials removed the need for toxic chemicals to inhibit continued bacterial activity that might compromise isotopic and concentration measurements. Aqueous standards mimicked the sample matrix and avoided headspace fractionation corrections. Samples were analysed using continuous-flow isotope-ratio mass spectrometry, but for low DIC concentration the mass spectrometer response could be non-linear. This had to be corrected for.<p></p> RESULTS: Mass spectrometer non-linearity exists. Rather than estimating precision as the repeat analysis of an internal standard, we have adopted inverse linear calibrations to quantify the precision and 95% confidence intervals (CI) of the δ13CDIC values. The response for [DIC] estimation was always linear. For 0.05–0.5 mM DIC internal standards, however, changes in mass spectrometer linearity resulted in estimations of the precision in the δ13CVPDB value of an unknown ranging from ± 0.44‰ to ± 1.33‰ (mean values) and a mean 95% CI half-width of ±1.1–3.1‰.<p></p> CONCLUSIONS: Mass spectrometer non-linearity should be considered in estimating uncertainty in measurement. Similarly, statistically robust estimates of precision and accuracy should also be adopted. Such estimations do not inhibit research advances: our consideration of small-scale spatial variability at two points on a small order river system demonstrates field data ranges larger than the precision and uncertainties. However, without such statistical quantification, exercises such as inter-lab calibrations are less meaningful.<p></p&gt

Uptake of systematic reviews and meta-analyses based on individual participant data in clinical practice guidelines: descriptive study.

To establish the extent to which systematic reviews and meta-analyses of individual participant data (IPD) are being used to inform the recommendations included in published clinical guidelines

Determination Methods of Food Fibers Characteristics in Milk Mixtures with the Modified Fat Composition

The article presents main determination methods of technological parameters of food fibers in milk mixtures of the modified fat composition.The methods of studying the ability of food fibers to water and fat-absorption are offered. The values that characterize swelling parameters of vegetable ingredients in experimental mixtures are obtained.The effectiveness of the method of IR-spectroscopy for indentifying and comparing water-binding forms in mixtures of food fibers with water and butterdish is proved.The indices of thermal stability and degree of liquid fat outflow for mixtures with the modified fat composition with the maximal replacement of cream butter by 25 % of oil are obtained. The research results indicate objective possibilities for the effective use of food fibers Vicetal for stabilizing the structure and preventing consistence defects of products with the modified fat composition

Biographical methods

The chapter reviews three different approaches to biographical methods, the biographical interpretive method, oral history and narrative analysis. Each is outlined in turn, looking at distinguishing characteristics. Each makes use of the interview to generate data and while each has unique strengths, the chapter concludes with a commitment to an oral history approach with its focus on the dynamics of the interview

Pricing Methods

In order to consider the range of pricing methods available, it is first necessary to choose a definition for road pricing. The term "road pricing" has been criticised as an inaccurate description of systems which is applied to (Thompson, 1990) and there is some inconsistency regarding the extent of charging policies which are considered to be included. A liberal definition could cover any fiscal form of traffic restraint, affecting the mode, time, route, destination of frequency of journeys. In this case road pricing already exists worldwide through taxes imposed upon the purchase and licensing of vehicles and through fuel taxation. The extension of conventional taxation arrangements has been used as part of road pricing strategies in both Hong Kong and Singapore (Dawson and Brown, 1985; LPAC, 1991). However, the essence of most road pricing work has been to replace and supplement these existing charges, which do not discriminate by time, location or amount of vehicle use, with charging structures which are directly related to these issues. For this reason the descriptions road-use pricing, congestion pricing and road user charging are sometimes preferred, and some recent texts have attempted to impose a narrower definition for road pricing, in which only charging systems relating directly to the time and distance travelled are included (CIT, 1992). For the purposes of this review it is best to retain the conventional term of road pricing and apply the broadest definition