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Title:

Explicit Constructions of Centrally Symmetric k-Neighborly Polytopes and Large Strictly Antipodal Sets

Author Full Names:

Barvinok, Alexander; Lee, Seung Jin; Novik, Isabella

Source:

DISCRETE & COMPUTATIONAL GEOMETRY, 49 (3):429-443; 10.1007/s00454-013-9495-z APR 2013

Abstract:

We present explicit constructions of centrally symmetric -neighborly -dimensional polytopes with about vertices and of centrally symmetric -neighborly -polytopes with about vertices. Using this result, we construct for a fixed and arbitrarily large and , a centrally symmetric -polytope with vertices that has at least faces of dimension , where and for . Another application is a construction of a set of points in every two of which are strictly antipodal as well as a construction of an -point set (for an arbitrarily large ) in with many pairs of strictly antipodal points. The two latter results significantly improve the previous bounds by Talata, and Makai and Martini, respectively.

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Title:

Outcome of Respiratory Syncytial Virus Lower Respiratory Tract Disease in Hematopoietic Cell Transplant Recipients Receiving Aerosolized Ribavirin: Significance of Stem Cell Source and Oxygen Requirement

Author Full Names:

Seo, Sachiko; Campbell, Angela P.; Xie, Hu; Chien, Jason W.; Leisenring, Wendy M.; Englund, Janet A.; Boeckh, Michael

Source:

BIOLOGY OF BLOOD AND MARROW TRANSPLANTATION, 19 (4):589-596; 10.1016/j.bbmt.2012.12.019 APR 2013

Abstract:

Respiratory syncytial virus (RSV) infection is an important complication after hematopoietic cell transplantation (HCT), and RSV lower respiratory tract disease (LRD) results in substantial early mortality and late airflow obstruction among survivors. Factors associated with poor outcome are unknown. We evaluated the effect of transplant and treatment factors on overall survival, mortality from respiratory failure, and pulmonary function among 82 HCT recipients who had RSV LRD between 1990 and 2011. All patients received aerosolized ribavirin. In multivariable analyses, only the use of marrow or cord blood as graft source (adjusted hazard ratio [aHR], 4.1; 95% confidence interval [CI], 1.8 to 9.0; P < .001) and oxygen requirement (aHR, 3.3; 95% CI, 1.5 to 6.7; P = .003) remained independently associated with overall mortality and death due to respiratory failure (aHR, 4.7; 95% CI, 1.8 to 13; P = .002 and aHR, 5.4; 95% CI, 1.8 to 16; P = .002, respectively). Antibody-based! treatments, including intravenous immunoglobulin and palivizumab, were not independently associated with improved outcome and did not alter the associations of the graft source and oxygen requirements in statistical models. In conclusion, use of peripheral blood stem cells as graft source and lack of oxygen requirement at diagnosis appear to be important factors associated with improved survival of HCT recipients with RSV LRD. These results may explain differences in outcomes reported from RSV infection over time and may guide the design of future interventional trials. (C) 2013 American Society for Blood and Marrow Transplantation.

Record 3 of 5.

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Title:

WRIGHT-FISHER DIFFUSION WITH NEGATIVE MUTATION RATES

Author Full Names:

Pal, Soumik

Source:

ANNALS OF PROBABILITY, 41 (2):503-526; 10.1214/11-AOP704 MAR 2013

Abstract:

We study a family of n-dimensional diffusions, taking values in the unit simplex of vectors with nonnegative coordinates that add up to one. These processes satisfy stochastic differential equations which are similar to the ones for the classical Wright-Fisher diffusions, except that the "mutation rates" are now nonpositive. This model, suggested by Aldous, appears in the study of a conjectured diffusion limit for a Markov chain on Cladograms. The striking feature of these models is that the boundary is not reflecting, and we kill the process once it hits the boundary. We derive the explicit exit distribution from the simplex and probabilistic bounds on the exit time. We also prove that these processes can be viewed as a "stochastic time-reversal" of a Wright-Fisher process of increasing dimensions and conditioned at a random time. A key idea in our proofs is a skew-product construction using certain one-dimensional diffusions called Bessel-square processes of negative dimen! sions, which have been recently introduced by Going-Jaeschke and Yor.

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Title:

SHY COUPLINGS, CAT(0) SPACES, AND THE LION AND MAN

Author Full Names:

Bramson, Maury; Burdzy, Krzysztof; Kendall, Wilfrid

Source:

ANNALS OF PROBABILITY, 41 (2):744-784; 10.1214/11-AOP723 MAR 2013

Abstract:

Two random processes X and Y on a metric space are said to be epsilon-shy coupled if there is positive probability of them staying at least a positive distance E apart from each other forever. Interest in the literature centres on nonexistence results subject to topological and geometric conditions; motivation arises from the desire to gain a better understanding of probabilistic coupling. Previous nonexistence results for co-adapted shy coupling of reflected Brownian motion required convexity conditions; we remove these conditions by showing the nonexistence of shy co-adapted couplings of reflecting Brownian motion in any bounded CAT(0) domain with boundary satisfying uniform exterior sphere and interior cone conditions, for example, simply-connected bounded planar domains with C-2 boundary.
The proof uses a Cameron-Martin-Girsanov argument, together with a continuity property of the Skorokhod transformation and properties of the intrinsic metric of the domain. To this end, a generalization of Gauss' lemma is established that shows differentiability of the intrinsic distance function for closures of CAT(0) domains with boundaries satisfying uniform exterior sphere and interior cone conditions. By this means, the shy coupling question is converted into a Lion and Man pursuit evasion problem.

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Title:

A modified Procrustes analysis for bilaterally symmetrical outlines, with an application to microevolution in Baculites

Author Full Names:

Bookstein, Fred L.; Ward, Peter D.

Source:

PALEOBIOLOGY, 39 (2):214-234; 10.1666/12038 SPR 2013

Abstract:

In quantitative paleobiology, one common format for image-derived information is the closed two-dimensional outline curve. Before the end of the last century a great variety of morphometric tools were on offer to deal with this data type, including diverse analyses of distance from a central point, "eigenshape analysis" of a carefully normalized tangent angle function, and Procrustes analysis of configurations of sliding semilandmarks. For the special case of outline forms that are nominally bilaterally symmetric, this paper offers a hybrid approach that fuses the Procrustes toolkit with a variant of a much older method, analysis of radial distance according to angles out of a center. The synthesis represents each outline as a regularly resampled data set of radially aligned shape coordinates analogous to bilateral Procrustes shape coordinates. When the center is iteratively located in one particular way, this representation has the same Procrustes distance statistics as a c! onventional radial representation, while the formalism of shape coordinates permits symmetrization, localizability, and thin-plate spline visualizations. We explain the method and sketch some of its advantages and limitations in the course of an example involving 99 Baculites inornatus outlines spanning 90 m of deposits from a high-precision measured section in the Campanian-age Rosario Formation cropping out at Punta San Jose, Baja California. This sequence shows substantial changes of pole curvature over time, changes that may involve a punctuation event regarding hydrostatics, hydrodynamics, or defense against predators. A concluding comment deals with implications of the developments here for Baculites microevolution and for morphometrics.

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Title:

Phase retrieval using nonlinear diversity

Author Full Names:

Lu, Chien-Hung; Barsi, Christopher; Williams, Matthew O.; Kutz, J. Nathan; Fleischer, Jason W.

Source:

APPLIED OPTICS, 52 (10):D92-D96; APR 1 2013

Abstract:

We extend the Gerchberg-Saxton algorithm to phase retrieval in a nonlinear system. Using a tunable photorefractive crystal, we experimentally demonstrate the noninterferometric technique by reconstructing an unknown phase object from optical intensity measurements taken at different nonlinear strengths. (C) 2013 Optical Society of America

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Title:

Transient Climate Response in Coupled Atmospheric-Ocean General Circulation Models

Author Full Names:

Liang, Mao-Chang; Lin, Li-Ching; Tung, Ka-Kit; Yung, Yuk L.; Sun, Shan

Source:

JOURNAL OF THE ATMOSPHERIC SCIENCES, 70 (4):1291-1296; 10.1175/JAS-D-12-0338.1 APR 2013

Abstract:

The equilibrium climate sensitivity (ECS) has a large uncertainty range among models participating in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) and has recently been presented as "inherently unpredictable.'' One way to circumvent this problem is to consider the transient climate response (TCR). However, the TCR among AR4 models also differs by more than a factor of 2. The authors argue that the situation may not necessarily be so pessimistic, because much of the intermodel difference may be due to the fact that the models were run with their oceans at various stages of flux adjustment with their atmosphere. This is shown by comparing multimillennium-long runs of the Goddard Institute for Space Studies model, version E, coupled with the Hybrid Coordinate Ocean Model (GISS-EH) and the Community Climate System Model, version 4 (CCSM4) with what were reported to AR4. The long model runs here reveal the range of variability (similar to 30! %) in their TCR within the same model with the same ECS. The commonly adopted remedy of subtracting the "climate drift" is ineffective and adds to the variability. The culprit is the natural variability of the control runs, which exists even at quasi equilibration. Fortunately, for simulations with multidecadal time horizon, robust solutions can be obtained by branching off thousand-year-long control runs that reach "quasi equilibration" using a new protocol, which takes advantage of the fact that forced solutions to radiative forcing forget their initial condition after 30-40 yr and instead depend mostly on the trajectory of the radiative forcing.

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Title:

Optimal Vaccine Allocation for the Early Mitigation of Pandemic Influenza

Author Full Names:

Matrajt, Laura; Halloran, M. Elizabeth; Longini, Ira M., Jr.

Source:

PLOS COMPUTATIONAL BIOLOGY, 9 (3):10.1371/journal.pcbi.1002964 MAR 2013

Abstract:

With new cases of avian influenza H5N1 (H5N1AV) arising frequently, the threat of a new influenza pandemic remains a challenge for public health. Several vaccines have been developed specifically targeting H5N1AV, but their production is limited and only a few million doses are readily available. Because there is an important time lag between the emergence of new pandemic strain and the development and distribution of a vaccine, shortage of vaccine is very likely at the beginning of a pandemic. We coupled a mathematical model with a genetic algorithm to optimally and dynamically distribute vaccine in a network of cities, connected by the airline transportation network. By minimizing the illness attack rate (i.e., the percentage of people in the population who become infected and ill), we focus on optimizing vaccine allocation in a network of 16 cities in Southeast Asia when only a few million doses are available. In our base case, we assume the vaccine is well-matched and va! ccination occurs 5 to 10 days after the beginning of the epidemic. The effectiveness of all the vaccination strategies drops off as the timing is delayed or the vaccine is less well-matched. Under the best assumptions, optimal vaccination strategies substantially reduced the illness attack rate, with a maximal reduction in the attack rate of 85%. Furthermore, our results suggest that cooperative strategies where the resources are optimally distributed among the cities perform much better than the strategies where the vaccine is equally distributed among the network, yielding an illness attack rate 17% lower. We show that it is possible to significantly mitigate a more global epidemic with limited quantities of vaccine, provided that the vaccination campaign is extremely fast and it occurs within the first weeks of transmission.

Mathematical Logic and Foundations

Probability Theory and Stochastic Processes

Statistics

Statistical Theory and Methods

Record 1 of 2.

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Title:

Discrete approximation of symmetric jump processes on metric measure spaces

Author Full Names:

Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi

Source:

PROBABILITY THEORY AND RELATED FIELDS, 155 (3-4):703-749; 10.1007/s00440-012-0411-x APR 2013

Abstract:

In this paper we give general criteria on tightness and weak convergence of discrete Markov chains to symmetric jump processes on metric measure spaces under mild conditions. As an application, we investigate discrete approximation for a large class of symmetric jump processes. We also discuss some application of our results to the scaling limit of random walk in random conductance.

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Title:

Reconstructing Past Populations With Uncertainty From Fragmentary Data

Author Full Names:

Wheldon, Mark C.; Raftery, Adrian E.; Clark, Samuel J.; Gerland, Patrick

Source:

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 108 (501):96-110; 10.1080/01621459.2012.737729 MAR 2013

Abstract:

Current methods for reconstructing human populations of the past by age and sex are deterministic or do not formally account for measurement error. We propose a method for simultaneously estimating age-specific population counts, fertility rates, mortality rates, and net international migration flows from fragmentary data that incorporates measurement error. Inference is based on joint posterior probability distributions that yield fully probabilistic interval estimates. It is designed for the kind of data commonly collected in modern demographic surveys and censuses. Population dynamics over the period of reconstruction are modeled by embedding formal demographic accounting relationships in a Bayesian hierarchical model. Informative priors are specified for vital rates, migration rates, population counts at baseline, and their respective measurement error variances. We investigate calibration of central posterior marginal probability intervals by simulation and demonstrate ! the method by reconstructing the female population of Burkina Faso from 1960 to 2005. Supplementary materials for this article are available online and the method is implemented in the R package "popReconstruct."

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Title:

Ecological bias in studies of the short-term effects of air pollution on health

Author Full Names:

Shaddick, Gavin; Lee, Duncan; Wakefield, Jonathan

Source:

INTERNATIONAL JOURNAL OF APPLIED EARTH OBSERVATION AND GEOINFORMATION, 22 65-74; SI 10.1016/j.jag.2012.03.011 JUN 2013

Abstract:

There has been a great deal of research into the short-term effects of air pollution on health with a large number of studies modelling the association between aggregate disease counts and environmental exposures measured at point locations, for example via air pollution monitors. In such cases, the standard approach is to average the observed measurements from the individual monitors and use this in a log-linear health model. Hence such studies are ecological in nature being based on spatially aggregated health and exposure data. Here we investigate the potential for bias in the estimates of the effects on health when estimating the short-term effects of air pollution on health. Such ecological bias may occur if a simple summary measure, such as a daily mean, is not a suitable summary of a spatially variable pollution surface. We assess the performance of commonly used models when confronted with such issues using simulation studies and compare their performance with a mode! l specifically designed to acknowledge the effects of exposure aggregation. In addition to simulation studies, we apply the models to a case study of the short-term effects of particulate matter on respiratory mortality using data from Greater London for the period 2002-2005. We found a significant increased risk of 3% (95% CI 1-5%) associated with the average of the previous three days exposure to particulate matter (per 10 mu g m(-3) PM10). (C) 2012 Elsevier B.V. All rights reserved.

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Title:

A proof of Crouzeix's conjecture for a class of matrices

Author Full Names:

Choi, Daeshik

Source:

LINEAR ALGEBRA AND ITS APPLICATIONS, 438 (8):3247-3257; 10.1016/j.laa.2012.12.045 APR 15 2013

Abstract:

Crouzeix's conjecture is that for any square matrix A and any polynomial p we have
vertical bar vertical bar p(A)vertical bar vertical bar <= 2 max{vertical bar P(z)vertical bar : z epsilon W (4)} where W(A)],
is the field of values of A and vertical bar vertical bar . vertical bar vertical bar denotes the spec-tral norm. In this paper, we show that the conjecture holds for the matrices of the form
[GRAPHICS]
where lambda epsilon C and alpha = (alpha(1),, alpha(n)) epsilon C-n. Published by Elsevier Inc.

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Title:

High-energy mode-locked fiber lasers using multiple transmission filters and a genetic algorithm

Author Full Names:

Fu, Xing; Kutz, J. Nathan

Source:

OPTICS EXPRESS, 21 (5):6526-6537; MAR 11 2013

Abstract:

We theoretically demonstrate that in a laser cavity mode-locked by nonlinear polarization rotation (NPR) using sets of waveplates and passive polarizer, the energy performance can be significantly increased by incorporating multiple NPR filters. The NPR filters are engineered so as to mitigate the multi-pulsing instability in the laser cavity which is responsible for limiting the single pulse per round trip energy in a myriad of mode-locked cavities. Engineering of the NPR filters for performance is accomplished by implementing a genetic algorithm that is capable of systematically identifying viable and optimal NPR settings in a vast parameter space. Our study shows that five NPR filters can increase the cavity energy by approximately a factor of five, with additional NPRs contributing little or no enhancements beyond this. With the advent and demonstration of electronic controls for waveplates and polarizers, the analysis suggests a general design and engineering principle ! that can potentially close the order of magnitude energy gap between fiber based mode-locked lasers and their solid state counterparts. (c) 2013 Optical Society of America

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Title:

Large Scale Distributed Acoustic Modeling With Back-Off N-Grams

Author Full Names:

Chelba, Ciprian; Xu, Peng; Pereira, Fernando; Richardson, Thomas

Source:

IEEE TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING, 21 (6):1158-1169; 10.1109/TASL.2013.2245649 JUN 2013

Abstract:

The paper revives an older approach to acoustic modeling that borrows from n-gram language modeling in an attempt to scale up both the amount of training data and model size (as measured by the number of parameters in the model), to approximately 100 times larger than current sizes used in automatic speech recognition. In such a data-rich setting, we can expand the phonetic context significantly beyond triphones, as well as increase the number of Gaussian mixture components for the context-dependent states that allow it. We have experimented with contexts that span seven or more context-independent phones, and up to 620 mixture components per state. Dealing with unseen phonetic contexts is accomplished using the familiar back-off technique used in language modeling due to implementation simplicity. The back-off acoustic model is estimated, stored and served using MapReduce distributed computing infrastructure. Speech recognition experiments are carried out in an N-best list ! rescoring framework for Google Voice Search. Training big models on large amounts of data proves to be an effective way to increase the accuracy of a state-of-the-art automatic speech recognition system. We use 87 000 hours of training data (speech along with transcription) obtained by filtering utterances in Voice Search logs on automatic speech recognition confidence. Models ranging in size between 20-40 million Gaussians are estimated using maximum likelihood training. They achieve relative reductions in word-error-rate of 11% and 6% when combined with first-pass models trained using maximum likelihood, and boosted maximum mutual information, respectively. Increasing the context size beyond five phones (quinphones) does not help.

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Title:

Motif statistics and spike correlations in neuronal networks

Author Full Names:

Hu, Yu; Trousdale, James; Josic, Kresimir; Shea-Brown, Eric

Source:

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 10.1088/1742-5468/2013/03/P03012 MAR 2013

Abstract:

Motifs are patterns of subgraphs of complex networks. We studied the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells in a recurrent network of integrate and fire neurons. For a range of network architectures, we find that the pairwise correlation coefficients, averaged across the network, can be closely approximated using only three statistics of network connectivity. These are the overall network connection probability and the frequencies of two second order motifs: diverging motifs, in which one cell provides input to two others, and chain motifs, in which two cells are connected via a third intermediary cell. Specifically, the prevalence of diverging and chain motifs tends to increase correlation. Our method is based on linear response theory, which enables us to express spiking statistics using linear algebra, and a resumming technique, which extrapolates from second order motifs to predict the ov! erall effect of coupling on network correlation. Our motif-based results seek to isolate the effect of network architecture perturbatively from a known network state.

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Title:

HIGH-RESOLUTION FINITE VOLUME MODELING OF WAVE PROPAGATION IN ORTHOTROPIC POROELASTIC MEDIA

Author Full Names:

Lemoine, Grady I.; Ou, M. Yvonne; Leveque, Randall J.

Source:

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 35 (1):B176-B206; 10.1137/120878720 2013

Abstract:

Poroelasticity theory models the dynamics of porous, fluid-saturated media. It was pioneered by Maurice Biot in the 1930s through the 1960s and has applications in several fields, including geophysics and modeling of in vivo bone. A wide variety of methods have been used to model poroelasticity, including finite difference, finite element, pseudospectral, and discontinuous Galerkin methods. In this work we use a Cartesian-grid high-resolution finite volume method to numerically solve Biot's equations in the time domain for orthotropic materials with the stiff relaxation source term in the equations incorporated using operator splitting. This class of finite volume method has several useful properties, including the ability to use wave limiters to reduce numerical artifacts in the solution, ease of incorporating material inhomogeneities, low memory overhead, and an explicit time-stepping approach. To the authors' knowledge, this is the first use of high-resolution finite volu! me methods to model poroelasticity. The solution code uses the CLAWPACK finite volume method software, which also includes block-structured adaptive mesh refinement in its AMRCLAW variant. We present convergence results for known analytic plane wave solutions, achieving second-order convergence rates outside of the stiff regime of the system. Our convergence rates are degraded in the stiff regime, but we still achieve similar levels of error on the finest grids examined. We also demonstrate good agreement against other numerical results from the literature.

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Title:

HIGH-ORDER WAVE PROPAGATION ALGORITHMS FOR HYPERBOLIC SYSTEMS

Author Full Names:

Ketcheson, David I.; Parsani, Matteo; Leveque, Randall J.

Source:

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 35 (1):A351-A377; 10.1137/110830320 2013

Abstract:

We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving Riemann problems and calculating fluctuations (not fluxes). The implementation employs weighted essentially nonoscillatory reconstruction in space and strong stability preserving Runge-Kutta integration in time. The method can be extended to arbitrarily high order of accuracy and allows a well-balanced implementation for capturing solutions of balance laws near steady state. This well-balancing is achieved through the f-wave Riemann solver and a novel wave-slope WENO reconstruction procedure. The wide applicability and advantageous properties of the method are demonstrated through numerical examples, including problems in nonconservative form, problems with spatially varying fluxes, and problems involving near-equilibrium solutions of balance l! aws.