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FN ISI Export Format VR 1.0 PT J AU Bass, RF Burdzy, K Chen, ZQ AF Bass, Richard F. Burdzy, Krzysztof Chen, Zhen-Qing TI On the Robin problem in fractal domains SO PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY AB We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum of the solution to the mixed Dirichlet-Robin boundary problem is greater than 0, and some other families of domains where it is equal to 0. We also give a new result on 'trap domains' defined in Burdzy, Chen and Marshall (Math. Z.), that is, domains where reflecting Brownian motion takes a long time to reach the center of the domain. C1 Univ Connecticut, Dept Math, Storrs, CT 06269 USA. Univ Washington, Dept Math, Seattle, WA 98195 USA. RP Bass, RF, Univ Connecticut, Dept Math, Storrs, CT 06269 USA. EM bass@math.uconn.edu burdzy@math.washington.edu zhen@math.washington.edu PD MAR PY 2008 VL 96 PN Part 2 BP 273 EP 311 UT ISI:000254148700001 ER PT J AU Rogalski, D Zhang, JJ AF Rogalski, D. Zhang, J. J. TI Canonical maps to twisted rings SO MATHEMATISCHE ZEITSCHRIFT AB If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism from A to a twisted homogeneous coordinate ring B(X, L, sigma), which is surjective in large degree. This result is a key step in the study of projectively simple rings. The proof relies on some results concerning the growth of graded rings which are of independent interest. C1 Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA. Univ Washington, Dept Math, Seattle, WA 98195 USA. RP Rogalski, D, Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA. EM drogalsk@math.ucsd.edu zhang@math.washington.edu PD JUN PY 2008 VL 259 IS 2 BP 433 EP 455 UT ISI:000254261200013 ER PT J AU Swanson, KR AF Swanson, Kristin R. TI Quantifying glioma cell growth and invasion in vitro SO MATHEMATICAL AND COMPUTER MODELLING AB A mathematical model has been developed to describe and quantify the growth and invasion of gliomas ( the most common type of primary brain tumors). The model has already been shown to agree well with in vivo imaging studies of gliomas. Here we demonstrate the model's agreement with in vitro experimental data. The analysis provided in this article demonstrates that the model agrees well with published observations of growth and invasion of gliomas cells in culture. These in vitro results support the model's utility in describing the behavior of glioma cells in experimental settings but also lends credence to the applications of the model to the in vivo setting. (c) 2007 Elsevier Ltd. All rights reserved. C1 Harborview Med Ctr, Neuropathol Lab, Dept Pathol, Seattle, WA 98104 USA. Univ Washington, Dept Appl Math, Seattle, WA 98105 USA. RP Swanson, KR, Harborview Med Ctr, Neuropathol Lab, Dept Pathol, Box 359791, Seattle, WA 98104 USA. EM swanson@amath.washington.edu PD MAR PY 2008 VL 47 IS 5-6 BP 638 EP 648 UT ISI:000254179800009 ER PT J AU Hunter, DR Goodreau, SM Handcock, MS AF Hunter, David R. Goodreau, Steven M. Handcock, Mark S. TI Goodness of fit of social network models SO JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION AB We present a systematic examination of a real network data set using maximum likelihood estimation for exponential random graph models as well as new procedures to evaluate how well the models fit the observed networks. These procedures compare structural statistics of the observed network with the corresponding statistics on networks simulated from the fitted model. We apply this approach to the study of friendship relations among high school students from the National Longitudinal Study of Adolescent Health (AddHealth). We focus primarily on one particular network of 205 nodes, although we also demonstrate that this method may be applied to the largest network in the AddHealth study, with 2,209 nodes. We argue that several well-studied models in the networks literature do not fit these data well and demonstrate that the fit improves dramatically when the models include the recently developed geometrically weighted edgewise shared partner, geometrically weighted dyadic shared partner, and geometrically weighted degree network statistics. We conclude that these models capture aspects of the social structure of adolescent friendship relations not represented by previous models. C1 Penn State Univ, Dept Stat, University Pk, PA 16802 USA. Univ Washington, Dept Anthropol, Seattle, WA 98195 USA. Univ Washington, Dept Stat & Social, Seattle, WA 98195 USA. RP Hunter, DR, Penn State Univ, Dept Stat, University Pk, PA 16802 USA. EM dhunter@stat.psu.edu goodreau@uwashington.edu handcock@uwashington.edu PD MAR PY 2008 VL 103 IS 481 BP 248 EP 258 UT ISI:000254311500029 ER PT J AU Nishimura, J Kutz, JN AF Nishimura, Joel Kutz, J. Nathan TI Stability and interactions of transverse field structures in optical parametric oscillators near resonance detuning SO JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS C1 Univ Washington, Dept Appl Math, Seattle, WA 98195 USA. RP Nishimura, J, Univ Washington, Dept Appl Math, Seattle, WA 98195 USA. PD MAR 28 PY 2008 VL 41 IS 6 AR 065401 DI ARTN 065401 UT ISI:000254153600009 ER PT J AU Tung, KK Camp, CD AF Tung, Ka Kit Camp, Charles D. TI Solar cycle warming at the Earth's surface in NCEP and ERA-40 data: A linear discriminant analysis SO JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES AB The total solar irradiance (TSI) has been measured by orbiting satellites since 1978 to vary on an 11-year cycle by about 0.08%. Because of previous controversies on the reality of solar cycle response at the surface, in this work we discuss the robustness of the solar response with respect to analysis methods, data sets and periods used. Furthermore we concentrate on the globally coherent signal. Two reanalysis data sets are used: one is from National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP for short) and the other is the European Centre for Medium-Range Weather Forecasts (ECMWF)'s most recent reanalysis denoted by ERA-40. Three analysis methods are considered, with increasing sophistication. Within each data set the analysis results are consistent with each other (i.e., each within the other's error bars), with the method of linear discriminant analysis (LDA) yielding the smallest error bar and the unfiltered global mean data yielding the largest error bar in the temperature amplitude. All three methods and both data sets are able to demonstrate that the 11-year signal is statistically significant and attributable (i.e., related) to the solar cycle. We deduce the spatial surface pattern over the globe which best distinguishes the solar maximum years from the solar minimum years using the LDA method. The resulting warming pattern shows clearly the polar amplification of warming and the preference for continents over oceans. We propose that the magnitude of the surface warming is consistent with direct solar radiative forcing if positive feedback processes such as ice albedo, water vapor/lapse rate and cloud feedbacks, similar to some of those studied for the greenhouse warming problem, are incorporated. It does not appear to be necessary to invoke some previously proposed exotic indirect mechanisms for an explanation of the observed solar signal. C1 Univ Washington, Dept Appl Math, Seattle, WA 98195 USA. Calif Polytech State Univ San Luis Obispo, Dept Math, San Luis Obispo, CA 93407 USA. RP Tung, KK, Univ Washington, Dept Appl Math, Seattle, WA 98195 USA. EM tung@amath.washington.edu PD MAR 13 PY 2008 VL 113 IS D5 AR D05114 DI ARTN D05114 UT ISI:000254165900005 ER PT J AU Langmore, I AF Langmore, Ian TI The stationary transport problem with angularly averaged measurements SO INVERSE PROBLEMS AB We consider an inverse problem for the stationary linear (Boltzmann) transport equation on a bounded domain X. R-n, with n >= 2. In our measurement scheme we inject X with L-1 integrable flux having both positional and directional dependence. We then measure a weighted average of the outgoing flux. Taking measurements at every point on. partial derivative X, we are able to reconstruct the total extinction coefficient, sigma. Once s is known, measurements made at one point allow recovery of the scattering kernel under some additional assumptions. In particular, we assume that scattering is supported inside of X, the scattering phase function is known, and that the scattering kernel is small. The required smallness depends upon s. We also require that s and the phase function are 'close to' real analytic. Stability estimates are then obtained. C1 Univ Washington, Dept Math, Seattle, WA 98195 USA. RP Langmore, I, Univ Washington, Dept Math, Seattle, WA 98195 USA. EM ilangmor@math.washington.edu PD FEB PY 2008 VL 24 IS 1 AR 015024 DI ARTN 015024 UT ISI:000254150900026 ER EF
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