A Direct Multigrid Poisson Solver for Oct-Tree Adaptive Meshes

We describe a finite-volume method for solving the Poisson equation on oct-tree adaptive meshes using direct solvers for individual mesh blocks. The method is a modified version of the method presented by Huang and Greengard (2000), which works with finite-difference meshes and does not allow for shared boundaries between refined patches. Our algorithm is implemented within the FLASH code framework and makes use of the PARAMESH library, permitting efficient use of parallel computers. We describe the algorithm and present test results that demonstrate its accuracy.Comment: 10 pages, 6 figures, accepted by the Astrophysical Journal; minor revisions in response to referee's comments; added char

Aircraft pollution: a futuristic view

International audienceImpacts of NOx, H2O and aerosol emissions from a projected 2050 aircraft fleet, provided in the EU project SCENIC, are investigated using the Oslo CTM2, a 3-D chemical transport model including comprehensive chemistry for the stratosphere and the troposphere. The aircraft emission scenarios comprise emissions from subsonic and supersonic aircraft. The increases in NOy due to emissions from the mixed fleet are comparable for subsonic (at 11–12 km) and supersonic (at 18–20 km) aircraft, with annual zonal means of 1.35 ppbv and 0.83 ppbv, respectively. H2O increases are also comparable at these altitudes: 630 and 599 ppbv, respectively. The aircraft emissions increase tropospheric ozone by about 10 ppbv in the Northern Hemisphere due to increased ozone production, mainly because of subsonic aircraft. Supersonic aircraft contribute to a reduction of stratospheric ozone due to increased ozone loss at higher altitudes. In the Northern Hemisphere the reduction is about 39 ppbv, but also in the Southern Hemisphere a 22 ppbv stratospheric decrease is modeled due to transport of supersonic aircraft emissions and ozone depleted air. The total ozone column is increased in lower and Northern mid-latitudes, otherwise the increase of ozone loss contributes to a decrease of the total ozone column. Two exceptions are the Northern Hemispheric spring, where the ozone loss increase is small due to transport processes, and tropical latitudes during summer where the effect of subsonic aircraft is low due to a high tropopause. Aerosol particles emitted by aircraft reduce both aircraft and background NOx, more than counterweighting the effect of NOx and H2O aircraft emissions in the stratosphere. Above about 20 km altitude, the NOx (and thus ozone loss) reduction is large enough to give an increase in ozone due to aircraft emissions. This effect is comparable in the Northern and Southern Hemisphere. At 11–20 km altitude, however, ozone production is reduced due to less NOx. Also ClONO2 is increased at this altitude due to enhanced heterogeneous reactions (lowered HCl), and ClO is increased due to less NOx, further enhancing ozone loss in this region. This results in a 14 ppbv further reduction of ozone. Mainly, this results in an increase of the total ozone column due to a decrease in ozone loss caused by the NOx cycle (at the highest altitudes). At the lowermost latitudes, the reduced loss due to the NOx cycle is small. However, ozone production at lower altitudes is reduced and the loss due to ClO is increased, giving a decrease in the total ozone column. Also, at high latitudes during spring the heterogeneous chemistry is more efficient on PSCs, increasing the ozone loss

Statistical inference of the generation probability of T-cell receptors from sequence repertoires

Stochastic rearrangement of germline DNA by VDJ recombination is at the origin of immune system diversity. This process is implemented via a series of stochastic molecular events involving gene choices and random nucleotide insertions between, and deletions from, genes. We use large sequence repertoires of the variable CDR3 region of human CD4+ T-cell receptor beta chains to infer the statistical properties of these basic biochemical events. Since any given CDR3 sequence can be produced in multiple ways, the probability distribution of hidden recombination events cannot be inferred directly from the observed sequences; we therefore develop a maximum likelihood inference method to achieve this end. To separate the properties of the molecular rearrangement mechanism from the effects of selection, we focus on non-productive CDR3 sequences in T-cell DNA. We infer the joint distribution of the various generative events that occur when a new T-cell receptor gene is created. We find a rich picture of correlation (and absence thereof), providing insight into the molecular mechanisms involved. The generative event statistics are consistent between individuals, suggesting a universal biochemical process. Our distribution predicts the generation probability of any specific CDR3 sequence by the primitive recombination process, allowing us to quantify the potential diversity of the T-cell repertoire and to understand why some sequences are shared between individuals. We argue that the use of formal statistical inference methods, of the kind presented in this paper, will be essential for quantitative understanding of the generation and evolution of diversity in the adaptive immune system.Comment: 20 pages, including Appendi

The Beta Generalized Exponential Distribution

We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the $r$th moment thus generalizing some results in the literature. Expressions for the density, moment generating function and $r$th moment of the order statistics also are obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix. We observe in one application to real data set that this model is quite flexible and can be used quite effectively in analyzing positive data in place of the beta exponential and generalized exponential distributions

Random perfect lattices and the sphere packing problem

Motivated by the search for best lattice sphere packings in Euclidean spaces of large dimensions we study randomly generated perfect lattices in moderately large dimensions (up to d=19 included). Perfect lattices are relevant in the solution of the problem of lattice sphere packing, because the best lattice packing is a perfect lattice and because they can be generated easily by an algorithm. Their number however grows super-exponentially with the dimension so to get an idea of their properties we propose to study a randomized version of the algorithm and to define a random ensemble with an effective temperature in a way reminiscent of a Monte-Carlo simulation. We therefore study the distribution of packing fractions and kissing numbers of these ensembles and show how as the temperature is decreased the best know packers are easily recovered. We find that, even at infinite temperature, the typical perfect lattices are considerably denser than known families (like A_d and D_d) and we propose two hypotheses between which we cannot distinguish in this paper: one in which they improve Minkowsky's bound phi\sim 2^{-(0.84+-0.06) d}, and a competitor, in which their packing fraction decreases super-exponentially, namely phi\sim d^{-a d} but with a very small coefficient a=0.06+-0.04. We also find properties of the random walk which are suggestive of a glassy system already for moderately small dimensions. We also analyze local structure of network of perfect lattices conjecturing that this is a scale-free network in all dimensions with constant scaling exponent 2.6+-0.1.Comment: 19 pages, 22 figure

Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions

The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had significant parameter correlation, but also contained multiple modes. We conclude that the mixture between two K distributions is the most applicable to this dataset.Comment: 15 pages, 7 figures, Accepted to the Journal of the Acoustical Society of Americ

Cryogenic R&D at the CERN Central Cryogenic Laboratory

The Central Cryogenic Laboratory operates since many years at CERN in the framework of cryogenic R&D for accelerators and experiments. The laboratory hosts several experimental posts for small cryogen ic tests, all implemented with pumping facility for GHe and vacuum, and is equipped with a He liquefier producing 6.105 l/year, which is distributed in dewars. Tests include thermomechanical qualifica tion of structural materials, cryogenic and vacuum qualification of prototypes, evaluation of thermal losses of components. Some of the most relevant results obtained at the laboratory in the last yea rs are outlined in this paper

Broadband classification and statistics of echoes from aggregations of fish measured by long-range, mid-frequency sonar

Author Posting. © Acoustical Society of America, 2017. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 141 (2017): 4354, doi:10.1121/1.4983446.For horizontal-looking sonar systems operating at mid-frequencies (1–10 kHz), scattering by fish with resonant gas-filled swimbladders can dominate seafloor and surface reverberation at long-ranges (i.e., distances much greater than the water depth). This source of scattering, which can be difficult to distinguish from other sources of scattering in the water column or at the boundaries, can add spatio-temporal variability to an already complex acoustic record. Sparsely distributed, spatially compact fish aggregations were measured in the Gulf of Maine using a long-range broadband sonar with continuous spectral coverage from 1.5 to 5 kHz. Observed echoes, that are at least 15 decibels above background levels in the horizontal-looking sonar data, are classified spectrally by the resonance features as due to swimbladder-bearing fish. Contemporaneous multi-frequency echosounder measurements (18, 38, and 120 kHz) and net samples are used in conjunction with physics-based acoustic models to validate this approach. Furthermore, the fish aggregations are statistically characterized in the long-range data by highly non-Rayleigh distributions of the echo magnitudes. These distributions are accurately predicted by a computationally efficient, physics-based model. The model accounts for beam-pattern and waveguide effects as well as the scattering response of aggregations of fish.This research was supported by the U.S. Office of Naval Research, the National Oceanographic Partnership Program, NOAA, WHOI, and the Oceanographer of the U.S. Navy

Complete Solving for Explicit Evaluation of Gauss Sums in the Index 2 Case

Let $p$ be a prime number, $q=p^f$ for some positive integer $f$, $N$ be a positive integer such that $\gcd(N,p)=1$, and let \k be a primitive multiplicative character of order $N$ over finite field \fq. This paper studies the problem of explicit evaluation of Gauss sums in "\textsl{index 2 case}" (i.e. f=\f{\p(N)}{2}=[\zn:\pp], where \p(\cd) is Euler function). Firstly, the classification of the Gauss sums in index 2 case is presented. Then, the explicit evaluation of Gauss sums G(\k^\la) (1\laN-1) in index 2 case with order $N$ being general even integer (i.e. N=2^{r}\cd N_0 where $r,N_0$ are positive integers and $N_03$ is odd.) is obtained. Thus, the problem of explicit evaluation of Gauss sums in index 2 case is completely solved

A note on the sign (unit root) ambiguities of Gauss sums in index 2 and 4 cases

Recently, the explicit evaluation of Gauss sums in the index 2 and 4 cases have been given in several papers (see [2,3,7,8]). In the course of evaluation, the sigh (or unit root) ambiguities are unavoidably occurred. This paper presents another method, different from [7] and [8], to determine the sigh (unit root) ambiguities of Gauss sums in the index 2 case, as well as the ones with odd order in the non-cyclic index 4 case. And we note that the method in this paper are more succinct and effective than [8] and [7]