Successive Standardization of Rectangular Arrays

In this note we illustrate and develop further with mathematics and examples, the work on successive standardization (or normalization) that is studied earlier by the same authors in Olshen and Rajaratnam (2010) and Olshen and Rajaratnam (2011). Thus, we deal with successive iterations applied to rectangular arrays of numbers, where to avoid technical difficulties an array has at least three rows and at least three columns. Without loss, an iteration begins with operations on columns: first subtract the mean of each column; then divide by its standard deviation. The iteration continues with the same two operations done successively for rows. These four operations applied in sequence completes one iteration. One then iterates again, and again, and again,.... In Olshen and Rajaratnam (2010) it was argued that if arrays are made up of real numbers, then the set for which convergence of these successive iterations fails has Lebesgue measure 0. The limiting array has row and column means 0, row and column standard deviations 1. A basic result on convergence given in Olshen and Rajaratnam (2010) is true, though the argument in Olshen and Rajaratnam (2010) is faulty. The result is stated in the form of a theorem here, and the argument for the theorem is correct. Moreover, many graphics given in Olshen and Rajaratnam (2010) suggest that but for a set of entries of any array with Lebesgue measure 0, convergence is very rapid, eventually exponentially fast in the number of iterations. Because we learned this set of rules from Bradley Efron, we call it "Efron's algorithm". More importantly, the rapidity of convergence is illustrated by numerical examples

Successive normalization of rectangular arrays

Standard statistical techniques often require transforming data to have mean $0$ and standard deviation $1$. Typically, this process of "standardization" or "normalization" is applied across subjects when each subject produces a single number. High throughput genomic and financial data often come as rectangular arrays where each coordinate in one direction concerns subjects who might have different status (case or control, say), and each coordinate in the other designates "outcome" for a specific feature, for example, "gene," "polymorphic site" or some aspect of financial profile. It may happen, when analyzing data that arrive as a rectangular array, that one requires BOTH the subjects and the features to be "on the same footing." Thus there may be a need to standardize across rows and columns of the rectangular matrix. There arises the question as to how to achieve this double normalization. We propose and investigate the convergence of what seems to us a natural approach to successive normalization which we learned from our colleague Bradley Efron. We also study the implementation of the method on simulated data and also on data that arose from scientific experimentation.Comment: Published in at http://dx.doi.org/10.1214/09-AOS743 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org). With Correction

Second post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies

Starting from the recently obtained 2PN accurate forms of the energy and angular momentum fluxes from inspiralling compact binaries, we deduce the gravitational radiation reaction to 2PN order beyond the quadrupole approximation - 4.5PN terms in the equation of motion - using the refined balance method proposed by Iyer and Will. We explore critically the features of their construction and illustrate them by contrast to other possible variants. The equations of motion are valid for general binary orbits and for a class of coordinate gauges. The limiting cases of circular orbits and radial infall are also discussed.Comment: 38 pages, REVTeX, no figures, to appear in Phys. Rev.

Localization and Fluctuations in Quantum Kicked Rotors

We address the issue of fluctuations, about an exponential lineshape, in a pair of one-dimensional kicked quantum systems exhibiting dynamical localization. An exact renormalization scheme establishes the fractal character of the fluctuations and provides a new method to compute the localization length in terms of the fluctuations. In the case of a linear rotor, the fluctuations are independent of the kicking parameter $k$ and exhibit self-similarity for certain values of the quasienergy. For given $k$, the asymptotic localization length is a good characteristic of the localized lineshapes for all quasienergies. This is in stark contrast to the quadratic rotor, where the fluctuations depend upon the strength of the kicking and exhibit local "resonances". These resonances result in strong deviations of the localization length from the asymptotic value. The consequences are particularly pronounced when considering the time evolution of a packet made up of several quasienergy states.Comment: REVTEV Document. 9 pages, 4 figures submitted to PR

FDM preparation of bio-compatible UHMWPE polymer for artificial implant

Due to its properties of high wear, creep resistance, high stiffness and strength, Ultra-High Molecular Weight Polyethylene (UHMWPE) was developed to eliminate most metallic wear in artificial implant, which conventionally found in stainless steel, Cobalt Chromium (Co-Cr) and Titanium (Ti) alloys. UHMWPE has an ultra-high viscosity that renders continuous melt-state processes including one of the additive manufacturing processes, Fused Deposition Modeling (FDM) ineffective for making UHMWPE implant. Attempt to overcome this problem and adapting this material to FDM is by blending UHMWPE with other polyethylene including High Density Polyethylene (HDPE) and Polyethylene-Glycol (PEG) which provide adequate mechanical properties for biomedical application along with the improvement in extrudability. It was demonstrated that the inclusion of 60% HDPE fraction has improved the flowability of UHMWPE in MFI test and showing adequate thermal stability in TGA

Thaan Vuzha Nilam Tharisu: the land without a farmer becomes barren

This report forms a part of the international research project on policy and sustainable agriculture, Policies that Work for Sustainable Agriculture and Regenerated Rural Economies. The report details the findings of one of the constituent studies, undertaken by an Indian NGO, the Society for People's Education and Economic Change (SPEECH). The Importance of this project is that it concentrated on rainfed rather than irrigated agriculture - i.e. the sharp end of rural development in India, and that the focus was very much on the micro-level, looking at policy as seen from the ground. One of the recurring themes throughout the research was the importance of appreciating people as individuals, and in this spirit some of the personal qualities of the research team are shared. The research covers events in sites in the Virudhunagar district of Tamilnadu: Tiruchuli Panchayat Union and the Villur chain of tanks. This is an essentially rural area, where the need for sustainable forms of agriculture and rural livelihoods is clear. The political landscape is fractured and complex (§2.3), and the officials with the responsibility of implementing policy face significant obstacles and disincentives in doing so in response to the needs of local communities

High magnetoresistance at room temperature in p-i-n graphene nanoribbons due to band-to-band tunneling effects

A large magnetoresistance effect is obtained at room-temperature by using p-i-n armchair-graphene-nanoribbon (GNR) heterostructures. The key advantage is the virtual elimination of thermal currents due to the presence of band gaps in the contacts. The current at B=0T is greatly decreased while the current at B>0T is relatively large due to the band-to-band tunneling effects, resulting in a high magnetoresistance ratio, even at room-temperature. Moreover, we explore the effects of edge-roughness, length, and width of GNR channels on device performance. An increase in edge-roughness and channel length enhances the magnetoresistance ratio while increased channel width can reduce the operating bias.Comment: http://dx.doi.org/10.1063/1.362445