December 5, 2012

Record 1 of 7.

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Title:

On a vegetation pattern formation model governed by a nonlinear parabolic system

Author Full Names:

Marinov, Kaloyan; Wang, Tianze; Yang, Yisong

Source:

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 14 (1):507-525; 10.1016/j.nonrwa.2012.07.012 FEB 2013

Abstract:

A fundamental subject in ecology is to understand how an ecosystem responds to its environmental changes. The purpose of this paper is to study the desertification and vegetation pattern formation phenomena and understand the dependence of the biomass density B of vegetation on the level of available environmental water resources, controlled by a water supply rate parameter R, which is governed by a coupled system of nonlinear parabolic equations in a mathematical model proposed recently by Shnerb, Sarah, Lavee, and Solomon. It is shown that, when R is below the death rate mu of the vegetation in the absence of water, the solution evolving from any initial state approaches exponentially fast the desert state characterized by B = 0; when R is above mu, the solution evolves into a green vegetation state characterized by B negated right arrow 0 as time t -> infinity. In the flower-pot limit where the system becomes a system of ordinary differential equations, it is shown tha! t nontrivial periodic vegetation states exist provided that the water supply rate R is a periodic function and maintains a suitable average level. Furthermore, some conservation laws relating the asymptotic values of the vegetation biomass B and available water density W are also obtained. (C) 2012 Elsevier Ltd. All rights reserved.

Record 2 of 7.

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Title:

Prospective Study of Particulate Air Pollution Exposures, Subclinical Atherosclerosis, and Clinical Cardiovascular Disease The Multi-Ethnic Study of Atherosclerosis and AIr Pollution (MESA Air)

Author Full Names:

Kaufman, Joel D.; Adar, Sara D.; Allen, Ryan W.; Barr, R. Graham; Budoff, Matthew J.; Burke, Gregory L.; Casillas, Adrian M.; Cohen, Martin A.; Curl, Cynthia L.; Daviglus, Martha L.; Roux, Ana V. Diez; Jacobs, David R., Jr.; Kronmal, Richard A.; Larson, Timothy V.; Liu, Sally Lee-Jane; Lumley, Thomas; Navas-Acien, Ana; O'Leary, Daniel H.; Rotter, Jerome I.; Sampson, Paul D.; Sheppard, Lianne; Siscovick, David S.; Stein, James H.; Szpiro, Adam A.; Tracy, Russell P.

Source:

AMERICAN JOURNAL OF EPIDEMIOLOGY, 176 (9):825-837; 10.1093/aje/kws169 NOV 1 2012

Abstract:

The Multi-Ethnic Study of Atherosclerosis and Air Pollution (MESA Air) was initiated in 2004 to investigate the relation between individual-level estimates of long-term air pollution exposure and the progression of subclinical atherosclerosis and the incidence of cardiovascular disease (CVD). MESA Air builds on a multicenter, community-based US study of CVD, supplementing that study with additional participants, outcome measurements, and state-of-the-art air pollution exposure assessments of fine particulate matter, oxides of nitrogen, and black carbon. More than 7,000 participants aged 4584 years are being followed for over 10 years for the identification and characterization of CVD events, including acute myocardial infarction and other coronary artery disease, stroke, peripheral artery disease, and congestive heart failure; cardiac procedures; and mortality. Subcohorts undergo baseline and follow-up measurements of coronary artery calcium using computed tomography and car! otid artery intima-medial wall thickness using ultrasonography. This cohort provides vast exposure heterogeneity in ranges currently experienced and permitted in most developed nations, and the air monitoring and modeling methods employed will provide individual estimates of exposure that incorporate residence-specific infiltration characteristics and participant-specific time-activity patterns. The overarching study aim is to understand and reduce uncertainty in health effect estimation regarding long-term exposure to air pollution and CVD.

Record 3 of 7.

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Title:

The attenuated ray transform for connections and Higgs fields

Author Full Names:

Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther

Source:

GEOMETRIC AND FUNCTIONAL ANALYSIS, 22 (5):1460-1489; 10.1007/s00039-012-0183-6 OCT 2012

Abstract:

We show that for a simple surface with boundary the attenuated ray transform in the presence of a unitary connection and a skew-Hermitian Higgs field is injective modulo the natural obstruction for functions and vector fields. We also show that the connection and the Higgs field are uniquely determined by the scattering relation modulo a gauge transformation. The proofs involve a Pestov type energy identity for connections together with holomorphic gauge transformations which arrange the curvature of the connection to have definite sign.

Record 4 of 7.

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Title:

Hard Sard: Quantitative Implicit Function and Extension Theorems for Lipschitz Maps

Author Full Names:

Azzam, Jonas; Schul, Raanan

Source:

GEOMETRIC AND FUNCTIONAL ANALYSIS, 22 (5):1062-1123; 10.1007/s00039-012-0189-0 OCT 2012

Abstract:

We prove a global implicit function theorem. In particular we show that any Lipschitz map (with n-dim. image) can be precomposed with a bi-Lipschitz map such that will satisfy, when we restrict to a large portion of the domain , that is bi-Lipschitz in the first coordinate, and constant in the second coordinate. Geometrically speaking, the map distorts in a controlled manner so that the fibers of f are straightened out. Furthermore, our results stay valid when the target space is replaced by any metric space. A main point is that our results are quantitative: the size of the set E on which behavior is good is a significant part of the discussion. Our estimates are motivated by examples such as Kaufman's 1979 construction of a C (1) map from [0, 1](3) onto [0, 1](2) with rank a parts per thousand currency sign 1 everywhere. On route we prove an extension theorem which is of independent interest. We show that for any D a parts per thousand yen n, any Lipschitz function gives r! ise to a large (in an appropriate sense) subset such that is bi-Lipschitz and may be extended to a bi-Lipschitz function defined on all of . This extends results of Jones and David, from 1988. As a simple corollary, we show that n-dimensional Ahlfors-David regular spaces lying in having big pieces of bi-Lipschitz images also have big pieces of big pieces of Lipschitz graphs in . This was previously known only for D a parts per thousand yen 2n + 1 by a result of David and Semmes.

Record 5 of 7. )

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Title:

Integrating external biological knowledge in the construction of regulatory networks from time-series expression data

Author Full Names:

Lo, Kenneth; Raftery, Adrian E.; Dombek, Kenneth M.; Zhu, Jun; Schadt, Eric E.; Bumgarner, Roger E.; Yeung, Ka Yee

Source:

BMC SYSTEMS BIOLOGY, 6 10.1186/1752-0509-6-101 AUG 16 2012

Abstract:

Background: Inference about regulatory networks from high-throughput genomics data is of great interest in systems biology. We present a Bayesian approach to infer gene regulatory networks from time series expression data by integrating various types of biological knowledge.
Results: We formulate network construction as a series of variable selection problems and use linear regression to model the data. Our method summarizes additional data sources with an informative prior probability distribution over candidate regression models. We extend the Bayesian model averaging (BMA) variable selection method to select regulators in the regression framework. We summarize the external biological knowledge by an informative prior probability distribution over the candidate regression models.
Conclusions: We demonstrate our method on simulated data and a set of time-series microarray experiments measuring the effect of a drug perturbation on gene expression levels, and show that it outperforms leading regression-based methods in the literature.

Record 6 of 7.

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Title:

Is Napoleon's Theorem Really Napoleon's Theorem?

Author Full Names:

Gruenbaum, Branko

Source:

AMERICAN MATHEMATICAL MONTHLY, 119 (6):495-501; 10.4169/amer.math.monthly.119.06.495 JUN-JUL 2012

Abstract:

A result frequently attributed to Napoleon Bonaparte is the topic of this note; it has an interesting history, and there are a considerable number of papers devoted to it. Several relevant articles have appeared in this MONTHLY. Here we present additional information about the history of the result, supplementing and correcting some of the earlier publications.

Record 7 of 7.

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Title:

SECOND-ORDER SUBDIFFERENTIAL CALCULUS WITH APPLICATIONS TO TILT STABILITY IN OPTIMIZATION

Author Full Names:

Mordukhovich, B. S.; Rockafellar, R. T.

Source:

SIAM JOURNAL ON OPTIMIZATION, 22 (3):953-986; 10.1137/110852528 2012

Abstract:

This paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finite-dimensional spaces. The main focus is the so-called (full and partial) second-order subdifferentials of extended-real-valued functions, which are dual-type constructions generated by coderivatives of first-order subdifferential mappings. We develop an extended second-order subdifferential calculus and analyze the basic second-order qualification condition ensuring the fulfillment of the principal second-order chain rule for strongly and fully amenable compositions. We also calculate the second-order subdifferentials for some major classes of piecewise linear-quadratic functions. These results are applied to the study of tilt stability of local minimizers for important classes of problems in constrained optimization that include, in particular, problems of nonlinear programming and certain cl! asses of extended nonlinear programs described in composite terms.