New variants of the Schroder method for finding zeros of nonlinear equations having unknown multiplicity

There are two aims of this paper, firstly, we define new variants of the Schroder method for finding zeros of nonlinear equations having unknown multiplicity and secondly, we introduce a new formula for approximating multiplicity m. Using the new formula, the five particular well-established methods are identical to the classical Schroder method. In terms of computational cost the new iterative method requires three evaluations of functions per iteration. It is proved that the each of the methods has a convergence of order two. Numerical examples are given to demonstrate the performance of the methods with and without multiplicity m

A class of optimal eighth-order derivative-free methods for solving the Danchick-Gauss problem

A derivative-free optimal eighth-order family of iterative methods for solving nonlinear equations is constructed using weight functions approach with divided first order differences. Its performance, along with several other derivative-free methods, is studied on the specific problem of Danchick's reformulation of Gauss' method of preliminary orbit determination. Numerical experiments show that such derivative-free, high-order methods offer significant advantages over both, the classical and Danchick's Newton approach. (C) 2014 Elsevier Inc. All rights reserved.This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02.Andreu Estellés, C.; Cambil Teba, N.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2014). A class of optimal eighth-order derivative-free methods for solving the Danchick-Gauss problem. Applied Mathematics and Computation. 232:237-246. https://doi.org/10.1016/j.amc.2014.01.056S23724623

Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation

In this work we show a general procedure to obtain optimal derivative free iterative methods for nonlinear equations f (x) = 0, applying polynomial interpolation to a generic optimal derivative free iterative method of lower order. Let us consider an optimal method of order q = 2(n-1), v = phi(n)(x), that uses n functional evaluations. Performing a Newton step w = v - f(v)/f'(v) one obtains a method of order 2(n), that is not optimal because it introduces two new functional evaluations. Instead, we approximate the derivative by using a polynomial of degree n that interpolates n+1 already known functional values and keeps the order 2(n). We have applied this idea to Steffensen's method, obtaining a family of optimal derivative free iterative methods of arbitrary high order. We provide different numerical tests, that confirm the theoretical results and compare the new family with other well known family of similar characteristics. (C) 2012 Elsevier Ltd. All rights reserved.This research was supported by Ministerio de Ciencia e Innovacion MTM2011-28636-C02-02 and by Vicerrectorado de Investigacion. Universitat Politecnica de Valencia PAID-06-2010-2285.Cordero Barbero, A.; Hueso Pagoaga, JL.; Martínez Molada, E.; Torregrosa Sánchez, JR. (2013). Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation. Mathematical and Computer Modelling. 57(7-8):1950-1956. https://doi.org/10.1016/j.mcm.2012.01.012S19501956577-

An Ill Wind? Climate Change, Migration, and Health

Background: Climate change is projected to cause substantial increases in population movement in coming decades. Previous research has considered the likely causal influences and magnitude of such movements and the risks to national and international security. There has been little research on the consequences of climate-related migration and the health of people who move

Inflammatory breast cancer: dynamic contrast-enhanced MR in patients receiving bevacizumab. Initial experience

To retrospectively compare three dynamic contrast material-enhanced magnetic resonance (MR) imaging (dynamic MR imaging) analytic methods to determine the parameter or combination of parameters most strongly associated with changes in tumor microvasculature during treatment with bevacizumab alone and bevacizumab plus chemotherapy in patients with inflammatory or locally advanced breast cancer. MATERIALS AND METHODS: This study was conducted in accordance with the institutional review board of the National Cancer Institute and was compliant with the Privacy Act of 1974. Informed consent was obtained from all patients. Patients with inflammatory or locally advanced breast cancer were treated with one cycle of bevacizumab alone (cycle 1) followed by six cycles of combination bevacizumab and chemotherapy (cycles 2-7). Serial dynamic MR images were obtained, and the kinetic parameters measured by using three dynamic analytic MR methods (heuristic, Brix, and general kinetic models) and two region-of-interest strategies were compared by using two-sided statistical tests. A P value of .01 was required for significance. RESULTS: In 19 patients, with use of a whole-tumor region of interest, the authors observed a significant decrease in the median values of three parameters measured from baseline to cycle 1: forward transfer rate constant (Ktrans) (-34% relative change, P=.003), backflow compartmental rate constant extravascular and extracellular to plasma (Kep) (-15% relative change, P<.001), and integrated area under the gadolinium concentration curve (IAUGC) at 180 seconds (-23% relative change, P=.009). A trend toward differences in the heuristic slope of the washout curve between responders and nonresponders to therapy was observed after cycle 1 (bevacizumab alone, P=.02). The median relative change in slope of the wash-in curve from baseline to cycle 4 was significantly different between responders and nonresponders (P=.009). CONCLUSION: The dynamic contrast-enhanced MR parameters Ktrans, Kep, and IAUGC at 180 seconds appear to have the strongest association with early physiologic response to bevacizumab. Clinical trial registration no. NCT0001654

LSST: from Science Drivers to Reference Design and Anticipated Data Products

(Abridged) We describe here the most ambitious survey currently planned in the optical, the Large Synoptic Survey Telescope (LSST). A vast array of science will be enabled by a single wide-deep-fast sky survey, and LSST will have unique survey capability in the faint time domain. The LSST design is driven by four main science themes: probing dark energy and dark matter, taking an inventory of the Solar System, exploring the transient optical sky, and mapping the Milky Way. LSST will be a wide-field ground-based system sited at Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m effective) primary mirror, a 9.6 deg$^2$ field of view, and a 3.2 Gigapixel camera. The standard observing sequence will consist of pairs of 15-second exposures in a given field, with two such visits in each pointing in a given night. With these repeats, the LSST system is capable of imaging about 10,000 square degrees of sky in a single filter in three nights. The typical 5$\sigma$ point-source depth in a single visit in $r$ will be $\sim 24.5$ (AB). The project is in the construction phase and will begin regular survey operations by 2022. The survey area will be contained within 30,000 deg$^2$ with $\delta<+34.5^\circ$, and will be imaged multiple times in six bands, $ugrizy$, covering the wavelength range 320--1050 nm. About 90\% of the observing time will be devoted to a deep-wide-fast survey mode which will uniformly observe a 18,000 deg$^2$ region about 800 times (summed over all six bands) during the anticipated 10 years of operations, and yield a coadded map to $r\sim27.5$. The remaining 10\% of the observing time will be allocated to projects such as a Very Deep and Fast time domain survey. The goal is to make LSST data products, including a relational database of about 32 trillion observations of 40 billion objects, available to the public and scientists around the world.Comment: 57 pages, 32 color figures, version with high-resolution figures available from https://www.lsst.org/overvie

DISPARE: DIScriminative PAttern REfinement for Position Weight Matrices

<p>Abstract</p> <p>Background</p> <p>The accurate determination of transcription factor binding affinities is an important problem in biology and key to understanding the gene regulation process. Position weight matrices are commonly used to represent the binding properties of transcription factor binding sites but suffer from low information content and a large number of false matches in the genome. We describe a novel algorithm for the refinement of position weight matrices representing transcription factor binding sites based on experimental data, including ChIP-chip analyses. We present an iterative weight matrix optimization method that is more accurate in distinguishing true transcription factor binding sites from a negative control set. The initial position weight matrix comes from JASPAR, TRANSFAC or other sources. The main new features are the discriminative nature of the method and matrix width and length optimization.</p> <p>Results</p> <p>The algorithm was applied to the increasing collection of known transcription factor binding sites obtained from ChIP-chip experiments. The results show that our algorithm significantly improves the sensitivity and specificity of matrix models for identifying transcription factor binding sites.</p> <p>Conclusion</p> <p>When the transcription factor is known, it is more appropriate to use a discriminative approach such as the one presented here to derive its transcription factor-DNA binding properties starting with a matrix, as opposed to performing <it>de novo </it>motif discovery. Generating more accurate position weight matrices will ultimately contribute to a better understanding of eukaryotic transcriptional regulation, and could potentially offer a better alternative to <it>ab initio </it>motif discovery.</p