Watermelon configurations with wall interaction: exact and asymptotic results

We perform an exact and asymptotic analysis of the model of $n$ vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially non-rigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.Comment: AmS-TeX, 41 page

On spherical averages of radial basis functions

A radial basis function (RBF) has the general form $$s(x)=\sum_{k=1}^{n}a_{k}\phi(x-b_{k}),\quad x\in\mathbb{R}^{d},$$ where the coefficients a 1,…,a n are real numbers, the points, or centres, b 1,…,b n lie in ℝ d , and φ:ℝ d →ℝ is a radially symmetric function. Such approximants are highly useful and enjoy rich theoretical properties; see, for instance (Buhmann, Radial Basis Functions: Theory and Implementations, [2003]; Fasshauer, Meshfree Approximation Methods with Matlab, [2007]; Light and Cheney, A Course in Approximation Theory, [2000]; or Wendland, Scattered Data Approximation, [2004]). The important special case of polyharmonic splines results when φ is the fundamental solution of the iterated Laplacian operator, and this class includes the Euclidean norm φ(x)=‖x‖ when d is an odd positive integer, the thin plate spline φ(x)=‖x‖2log  ‖x‖ when d is an even positive integer, and univariate splines. Now B-splines generate a compactly supported basis for univariate spline spaces, but an analyticity argument implies that a nontrivial polyharmonic spline generated by (1.1) cannot be compactly supported when d>1. However, a pioneering paper of Jackson (Constr. Approx. 4:243–264, [1988]) established that the spherical average of a radial basis function generated by the Euclidean norm can be compactly supported when the centres and coefficients satisfy certain moment conditions; Jackson then used this compactly supported spherical average to construct approximate identities, with which he was then able to derive some of the earliest uniform convergence results for a class of radial basis functions. Our work extends this earlier analysis, but our technique is entirely novel, and applies to all polyharmonic splines. Furthermore, we observe that the technique provides yet another way to generate compactly supported, radially symmetric, positive definite functions. Specifically, we find that the spherical averaging operator commutes with the Fourier transform operator, and we are then able to identify Fourier transforms of compactly supported functions using the Paley–Wiener theorem. Furthermore, the use of Haar measure on compact Lie groups would not have occurred without frequent exposure to Iserles’s study of geometric integration

Extending Halogen-based Medicinal Chemistry to Proteins: IODO-INSULIN AS A CASE STUDY

Insulin, a protein critical for metabolic homeostasis, provides a classical model for protein design with application to human health. Recent efforts to improve its pharmaceutical formulation demonstrated that iodination of a conserved tyrosine (Tyr(B26)) enhances key properties of a rapid-acting clinical analog. Moreover, the broad utility of halogens in medicinal chemistry has motivated the use of hybrid quantum- and molecular-mechanical methods to study proteins. Here, we (i) undertook quantitative atomistic simulations of 3-[iodo-Tyr(B26)]insulin to predict its structural features, and (ii) tested these predictions by X-ray crystallography. Using an electrostatic model of the modified aromatic ring based on quantum chemistry, the calculations suggested that the analog, as a dimer and hexamer, exhibits subtle differences in aromatic-aromatic interactions at the dimer interface. Aromatic rings (Tyr(B16), Phe(B24), Phe(B25), 3-I-Tyr(B26), and their symmetry-related mates) at this interface adjust to enable packing of the hydrophobic iodine atoms within the core of each monomer. Strikingly, these features were observed in the crystal structure of a 3-[iodo-Tyr(B26)]insulin analog (determined as an R6 zinc hexamer). Given that residues B24-B30 detach from the core on receptor binding, the environment of 3-I-Tyr(B26) in a receptor complex must differ from that in the free hormone. Based on the recent structure of a "micro-receptor" complex, we predict that 3-I-Tyr(B26) engages the receptor via directional halogen bonding and halogen-directed hydrogen bonding as follows: favorable electrostatic interactions exploiting, respectively, the halogen's electron-deficient σ-hole and electronegative equatorial band. Inspired by quantum chemistry and molecular dynamics, such "halogen engineering" promises to extend principles of medicinal chemistry to proteins

Shallow seafloor gas emissions near Heard and McDonald Islands on the Kerguelen Plateau, Southern Indian Ocean

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Spain, E. A., Johnson, S. C., Hutton, B., Whittaker, J. M., Lucieer, V., Watson, S. J., Fox, J. M., Lupton, J., Arculus, R., Bradney, A., & Coffin, M. F. Shallow seafloor gas emissions near Heard and McDonald Islands on the Kerguelen Plateau, Southern Indian Ocean. Earth and Space Science, 7(3), (2020): e2019EA000695, doi:10.1029/2019EA000695.Bubble emission mechanisms from submerged large igneous provinces remains enigmatic. The Kerguelen Plateau, a large igneous province in the southern Indian Ocean, has a long sustained history of active volcanism and glacial/interglacial cycles of sedimentation, both of which may cause seafloor bubble production. We present the results of hydroacoustic flare observations around the underexplored volcanically active Heard Island and McDonald Islands on the Central Kerguelen Plateau. Flares were observed with a split‐beam echosounder and characterized using multifrequency decibel differencing. Deep‐tow camera footage, water properties, water column δ3He, subbottom profile, and sediment δ13C and δ34S data were analyzed to consider flare mechanisms. Excess δ3He near McDonald Islands seeps, indicating mantle‐derived input, suggests proximal hydrothermal activity; McDonald Islands flares may thus indicate CO2, methane, and other minor gas bubbles associated with shallow diffuse hydrothermal venting. The Heard Island seep environment, with subbottom acoustic blanking in thick sediment, muted 3He signal, and δ13C and δ34S fractionation factors, suggest that Heard Island seeps may either be methane gas (possibly both shallow biogenic methane and deeper‐sourced thermogenic methane related to geothermal heat from onshore volcanism) or a combination of methane and CO2, such as seen in sediment‐hosted geothermal systems. These data provide the first evidence of submarine gas escape on the Central Kerguelen Plateau and expand our understanding of seafloor processes and carbon cycling in the data‐poor southern Indian Ocean. Extensive sedimentation of the Kerguelen Plateau and additional zones of submarine volcanic activity mean additional seeps or vents may lie outside the small survey area proximal to the islands.We thank the Australian Marine National Facility (MNF) for its support in the form of sea time on RV Investigator , support personnel, scientific equipment, and data management. We also thank the captain, crew, and fellow scientists of RV Investigator voyage IN2016_V01. We also thank specifically the following: T. Martin, F. Cooke, S. L. Sow, N. Bax, J. Ford, and F. Althaus, CSIRO (Commonwealth Scientific and Industrial Research Organisation); Echoview Software Pty. Ltd. (Hobart, Australia); C. Dietz and C. Cook, Central Science Laboratory, University of Tasmania; C. Wilkinson and T. Baumberger, National Oceanic and Atmospheric Administration; R. Carey, University of Tasmania; T. Holmes, Institute for Marine and Antarctic Studies, University of Tasmania; N. Polmear; and A. Post, Geoscience Australia. The overall science of the project is supported by Australian Antarctic Science Program (AASP) grant 4338. E.S.' PhD research is supported by the Australian Research Council's Special Research Initiative Antarctic Gateway Partnership (Project ID SR140300001) and by an Australian Government Research Training Program Scholarship. S.C.J. is supported by iCRAG under SFI, European Regional Development Fund, and industry partners, as well as ANZIC‐IODP. J.M.W. is supported by ARC grant DE140100376 and DP180102280. This is PMEL publication number 4910. All IN2016_V01 data and samples acquired on IN2016_V01 are made publicly available in accordance with MNF policy

Damage patterns at the head-stem taper junction helps understand the mechanisms of material loss

Background: Material loss at the taper junction of metal-on-metal total hip replacements (MOM THRs) has been implicated in their early failure. The mechanisms of material loss are not fully understood; analysis of the patterns of damage at the taper can help us better understand why material loss occurs at this junction. Methods: We mapped the patterns of material loss in a series of 155 MOM-THRs received at our centre by scanning the taper surface using a roundness-measuring machine. We examined these material loss maps to develop a five-tier classification system based on visual differences between different patterns. We correlated these patterns to surgical, implant and patient factors known to be important for head-stem taper damage. Results: We found that 63 implants had ‘minimal damage’ at the taper (material loss <1mm3 ) and the remaining 92 implants could be categorised by four distinct patterns of taper material loss. We found that (1) head diameter and (2) time to revision were key significant variables separating the groups. Conclusion: These material loss maps allow us to suggest different mechanisms that dominate the cause of the material loss in each pattern: (a) corrosion, (b) mechanically assisted corrosion or (c) intra-operative damage or poor size tolerances leading to toggling of trunnion in taper

Tumor Cell-Driven Extracellular Matrix Remodeling Drives Haptotaxis during Metastatic Progression

Fibronectin (FN) is a major component of the tumor microenvironment, but its role in promoting metastasis is incompletely understood. Here we show that FN gradients elicit directional movement of breast cancer cells, in vitro and in vivo. Haptotaxis on FN gradients requires direct interaction between α5β1 integrin and Mena, an actin regulator, and involves increases in focal complex signaling and tumor-cell-mediated extracellular matrix (ECM) remodeling. Compared to Mena, higher levels of the pro-metastatic MenaINV isoform associate with α5, which enables 3D haptotaxis of tumor cells towards the high FN concentrations typically present in perivascular space and in the periphery of breast tumor tissue. MenaINV and FN levels were correlated in two breast cancer cohorts, and high levels of MenaINV were significantly associated with increased tumor recurrence as well as decreased patient survival. Our results identify a novel tumor-cell-intrinsic mechanism that promotes metastasis through ECM remodeling and ECM guided directional migration

Fregene: Simulation of realistic sequence-level data in populations and ascertained samples

Background: FREGENE simulates sequence-level data over large genomic regions in large populations. Because, unlike coalescent simulators, it works forwards through time, it allows complex scenarios of selection, demography, and recombination to be modelled simultaneously. Detailed tracking of sites under selection is implemented in FREGENE and provides the opportunity to test theoretical predictions and gain new insights into mechanisms of selection. We describe here main functionalities of both FREGENE and SAMPLE, a companion program that can replicate association study datasets.Results: We report detailed analyses of six large simulated datasets that we have made publicly available. Three demographic scenarios are modelled: one panmictic, one substructured with migration, and one complex scenario that mimics the principle features of genetic variation in major worldwide human populations. For each scenario there is one neutral simulation, and one with a complex pattern of selection.Conclusion: FREGENE and the simulated datasets will be valuable for assessing the validity of models for selection, demography and population genetic parameters, as well as the efficacy of association studies. Its principle advantages are modelling flexibility and computational efficiency. It is open source and object-oriented. As such, it can be customised and the range of models extended

Estimating uncertainty in ecosystem budget calculations

© The Authors, 2010. This article is distributed under the terms of the Creative Commons Attribution-Noncommercial License. The definitive version was published in Ecosystems 13 (2010): 239-248, doi:10.1007/s10021-010-9315-8.Ecosystem nutrient budgets often report values for pools and fluxes without any indication of uncertainty, which makes it difficult to evaluate the significance of findings or make comparisons across systems. We present an example, implemented in Excel, of a Monte Carlo approach to estimating error in calculating the N content of vegetation at the Hubbard Brook Experimental Forest in New Hampshire. The total N content of trees was estimated at 847 kg ha−1 with an uncertainty of 8%, expressed as the standard deviation divided by the mean (the coefficient of variation). The individual sources of uncertainty were as follows: uncertainty in allometric equations (5%), uncertainty in tissue N concentrations (3%), uncertainty due to plot variability (6%, based on a sample of 15 plots of 0.05 ha), and uncertainty due to tree diameter measurement error (0.02%). In addition to allowing estimation of uncertainty in budget estimates, this approach can be used to assess which measurements should be improved to reduce uncertainty in the calculated values. This exercise was possible because the uncertainty in the parameters and equations that we used was made available by previous researchers. It is important to provide the error statistics with regression results if they are to be used in later calculations; archiving the data makes resampling analyses possible for future researchers. When conducted using a Monte Carlo framework, the analysis of uncertainty in complex calculations does not have to be difficult and should be standard practice when constructing ecosystem budgets