Simulation studies of a phenomenological model for elongated virus capsid formation

We study a phenomenological model in which the simulated packing of hard, attractive spheres on a prolate spheroid surface with convexity constraints produces structures identical to those of prolate virus capsid structures. Our simulation approach combines the traditional Monte Carlo method with a modified method of random sampling on an ellipsoidal surface and a convex hull searching algorithm. Using this approach we identify the minimum physical requirements for non-icosahedral, elongated virus capsids, such as two aberrant flock house virus (FHV) particles and the prolate prohead of bacteriophage $\phi_{29}$, and discuss the implication of our simulation results in the context of recent experimental findings. Our predicted structures may also be experimentally realized by evaporation-driven assembly of colloidal spheres

A Novel Approach for Ellipsoidal Outer-Approximation of the Intersection Region of Ellipses in the Plane

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection of the ellipses are found in an efficient manner. To do so, the intersection points of the ellipses that fall on the boundary of the intersection region are determined, and a set of points is generated on the elliptic arcs connecting every two neighbouring intersection points. By finding the tangent lines to the ellipses at the extended set of points, a set of half-planes is obtained, whose intersection forms a polygon. To find the polygon more efficiently, the points are given an order and the intersection of the half-planes corresponding to every two neighbouring points is calculated. If the polygon is convex and bounded, these calculated points together with the initially obtained intersection points will form its vertices. If the polygon is non-convex or unbounded, we can detect this situation and then generate additional discrete points only on the elliptical arc segment causing the issue, and restart the algorithm to obtain a bounded and convex polygon. Finally, the smallest area ellipse that contains the vertices of the polygon is obtained by solving a convex optimization problem. Through numerical experiments, it is illustrated that the proposed technique returns a tighter outer-approximation of the intersection of multiple ellipses, compared to conventional techniques, with only slightly higher computational cost

Wavelet Based Fractal Analysis of Airborne Pollen

The most abundant biological particles in the atmosphere are pollen grains and spores. Self protection of pollen allergy is possible through the information of future pollen contents in the air. In spite of the importance of airborne pol len concentration forecasting, it has not been possible to predict the pollen concentrations with great accuracy, and about 25% of the daily pollen forecasts have resulted in failures. Previous analysis of the dynamic characteristics of atmospheric pollen time series indicate that the system can be described by a low dimensional chaotic map. We apply the wavelet transform to study the multifractal characteristics of an a irborne pollen time series. We find the persistence behaviour associated to low pollen concentration values and to the most rare events of highest pollen co ncentration values. The information and the correlation dimensions correspond to a chaotic system showing loss of information with time evolution.Comment: 11 pages, 7 figure

Universal microscopic correlation functions for products of independent Ginibre matrices

We consider the product of n complex non-Hermitian, independent random matrices, each of size NxN with independent identically distributed Gaussian entries (Ginibre matrices). The joint probability distribution of the complex eigenvalues of the product matrix is found to be given by a determinantal point process as in the case of a single Ginibre matrix, but with a more complicated weight given by a Meijer G-function depending on n. Using the method of orthogonal polynomials we compute all eigenvalue density correlation functions exactly for finite N and fixed n. They are given by the determinant of the corresponding kernel which we construct explicitly. In the large-N limit at fixed n we first determine the microscopic correlation functions in the bulk and at the edge of the spectrum. After unfolding they are identical to that of the Ginibre ensemble with n=1 and thus universal. In contrast the microscopic correlations we find at the origin differ for each n>1 and generalise the known Bessel-law in the complex plane for n=2 to a new hypergeometric kernel 0_F_n-1.Comment: 20 pages, v2 published version: typos corrected and references adde

Rates of convergence for empirical spectral measures: a soft approach

Understanding the limiting behavior of eigenvalues of random matrices is the central problem of random matrix theory. Classical limit results are known for many models, and there has been significant recent progress in obtaining more quantitative, non-asymptotic results. In this paper, we describe a systematic approach to bounding rates of convergence and proving tail inequalities for the empirical spectral measures of a wide variety of random matrix ensembles. We illustrate the approach by proving asymptotically almost sure rates of convergence of the empirical spectral measure in the following ensembles: Wigner matrices, Wishart matrices, Haar-distributed matrices from the compact classical groups, powers of Haar matrices, randomized sums and random compressions of Hermitian matrices, a random matrix model for the Hamiltonians of quantum spin glasses, and finally the complex Ginibre ensemble. Many of the results appeared previously and are being collected and described here as illustrations of the general method; however, some details (particularly in the Wigner and Wishart cases) are new. Our approach makes use of techniques from probability in Banach spaces, in particular concentration of measure and bounds for suprema of stochastic processes, in combination with more classical tools from matrix analysis, approximation theory, and Fourier analysis. It is highly flexible, as evidenced by the broad list of examples. It is moreover based largely on "soft" methods, and involves little hard analysis

Beringia and the peopling of the Western Hemisphere

Did Beringian environments represent an ecological barrier to humans until less than 15 000 years ago or was access to the Americas controlled by the spatial–temporal distribution of North American ice sheets? Beringian environments varied with respect to climate and biota, especially in the two major areas of exposed continental shelf. The East Siberian Arctic Shelf (‘Great Arctic Plain’ (GAP)) supported a dry steppe-tundra biome inhabited by a diverse large-mammal community, while the southern Bering-Chukchi Platform (‘Bering Land Bridge’ (BLB)) supported mesic tundra and probably a lower large-mammal biomass. A human population with west Eurasian roots occupied the GAP before the Last Glacial Maximum (LGM) and may have accessed mid-latitude North America via an interior ice-free corridor. Re-opening of the corridor less than 14 000 years ago indicates that the primary ancestors of living First Peoples, who already had spread widely in the Americas at this time, probably dispersed from the NW Pacific coast. A genetic ‘arctic signal’ in non-arctic First Peoples suggests that their parent population inhabited the GAP during the LGM, before their split from the former. We infer a shift from GAP terrestrial to a subarctic maritime economy on the southern BLB coast before dispersal in the Americas from the NW Pacific coast

IgE to epitopes of Ara h 2 enhance the diagnostic accuracy of Ara h 2‐specific IgE

© 2020 The Authors. Allergy published by European Academy of Allergy and Clinical Immunology and John Wiley & Sons Ltd. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.Background: Understanding the discrepancy between IgE sensitization and allergic reactions to peanut could facilitate diagnosis and lead to novel means of treating peanut allergy. Objective: To identify differences in IgE and IgG4 binding to peanut peptides between peanut-allergic (PA) and peanut-sensitized but tolerant (PS) children. Methods: PA (n = 56), PS (n = 42) and nonsensitized nonallergic (NA, n = 10) patients were studied. Synthetic overlapping 15-mer peptides of peanut allergens (Ara h 1-11) were spotted onto microarray slides, and patients' samples were tested for IgE and IgG4 binding using immunofluorescence. IgE and IgG4 levels to selected peptides were quantified using ImmunoCAP. Diagnostic model comparisons were performed using likelihood-ratio tests between each specified nominal logistic regression models. Results: Seven peptides on Ara h 1, Ara h 2, and Ara h 3 were bound more by IgE of PA compared to PS patients on the microarray. IgE binding to one peptide on Ara h 5 and IgG4 binding to one Ara h 9 peptide were greater in PS than in PA patients. Using ImmunoCAP, IgE to the Ara h 2 peptides enhanced the diagnostic accuracy of Ara h 2-specific IgE. Ratios of IgG4/IgE to 4 out of the 7 peptides were higher in PS than in PA subjects. Conclusions: Ara h 2 peptide-specific IgE added diagnostic value to Ara h 2-specific IgE. Ability of peptide-specific IgG4 to surmount their IgE counterpart seems to be important in established peanut tolerance.This work was supported by the Medical Research Council (MRC Clinical Research Training Fellowship G090218, MRC Centenary Early Career Award and MRC Clinician Scientist Fellowship MR/M008517/1, all awarded to A. F. Santos), the Department of Health via the National Institute for Health Research (NIHR) comprehensive Biomedical Research Centre award to Guy's & St Thomas' NHS Foundation Trust in partnership with King's College London and King's College Hospital NHS Foundation Trust; the US Department of Agriculture, Agricultural Research Service (USDA-ARS6054-43440-046-00D; USDA-NIFA) and the National Peanut Board (GRANT12229460).info:eu-repo/semantics/publishedVersio

Spectral decomposition of internal gravity wave sea surface height in global models

Two global ocean models ranging in horizontal resolution from 1/12° to 1/48° are used to study the space and time scales of sea surface height (SSH) signals associated with internal gravity waves (IGWs). Frequency‐horizontal wavenumber SSH spectral densities are computed over seven regions of the world ocean from two simulations of the HYbrid Coordinate Ocean Model (HYCOM) and three simulations of the Massachusetts Institute of Technology general circulation model (MITgcm). High wavenumber, high‐frequency SSH variance follows the predicted IGW linear dispersion curves. The realism of high‐frequency motions (>0.87  cpd) in the models is tested through comparison of the frequency spectral density of dynamic height variance computed from the highest‐resolution runs of each model (1/25° HYCOM and 1/48° MITgcm) with dynamic height variance frequency spectral density computed from nine in situ profiling instruments. These high‐frequency motions are of particular interest because of their contributions to the small‐scale SSH variability that will be observed on a global scale in the upcoming Surface Water and Ocean Topography (SWOT) satellite altimetry mission. The variance at supertidal frequencies can be comparable to the tidal and low‐frequency variance for high wavenumbers (length scales smaller than ∼50 km), especially in the higher‐resolution simulations. In the highest‐resolution simulations, the high‐frequency variance can be greater than the low‐frequency variance at these scales.Key PointsTwo high‐resolution ocean models compare well against data in frequency spectral density of dynamic heightSea surface height frequency‐horizontal wavenumber spectral densities show high variance along internal gravity wave dispersion curvesTwo high‐resolution ocean models give different estimates of variance in high‐frequency, high wavenumber phenomenaPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/139946/1/jgrc22465-sup-0002-2017JC013009-fs01.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139946/2/jgrc22465-sup-0003-2017JC013009-fs02.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139946/3/jgrc22465_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139946/4/jgrc22465.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139946/5/jgrc22465-sup-0007-2017JC013009-fs06.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139946/6/jgrc22465-sup-0009-2017JC013009-fs08.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139946/7/jgrc22465-sup-0004-2017JC013009-fs03.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139946/8/jgrc22465-sup-0005-2017JC013009-fs04.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139946/9/jgrc22465-sup-0006-2017JC013009-fs05.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139946/10/jgrc22465-sup-0001-2017JC013009-s01.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139946/11/jgrc22465-sup-0008-2017JC013009-fs07.pd

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure