Marshall's Lemma for Convex Density Estimation

Marshall's (1970) lemma is an analytical result which implies root-n-consistency of the distribution function corresponding to the Grenander (1956) estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0,\infty).

An integral conservative gridding--algorithm using Hermitian curve interpolation

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).

On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series

Fossil pollen data from stratigraphic cores are irregularly spaced in time due to non-linear age-depth relations. Moreover, their marginal distributions may vary over time. We address these features in a nonparametric regression model with errors that are monotone transformations of a latent continuous-time Gaussian process Z(T). Although Z(T) is unobserved, due to monotonicity, under suitable regularity conditions, it can be recovered facilitating further computations such as estimation of the long-memory parameter and the Hermite coefficients. The estimation of Z(T) itself involves estimation of the marginal distribution function of the regression errors. These issues are considered in proposing a plug-in algorithm for optimal bandwidth selection and construction of confidence bands for the trend function. Some high-resolution time series of pollen records from Lago di Origlio in Switzerland, which go back ca. 20,000 years are used to illustrate the methods.

On low-dimensional projections of high-dimensional distributions

Let P be a probability distribution on q -dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension d<distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension q . It turns out, that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting P ^ be the empirical distribution of n independent random vectors with distribution P , we investigate the behavior of the empirical process n √ (P ^ −P) under random projections, conditional on P ^ .

Proton entry into the near-lunar plasma wake for magnetic field aligned flow

We report the first observation of protons in the near-lunar (100-200 km from the surface) and deeper (near anti-subsolar point) plasma wake when the interplanetary magnetic field (IMF) and solar wind velocity (vsw) are parallel (aligned flow; angle between IMF and vsw≤10°). More than 98% of the observations during aligned flow condition showed the presence of protons in the wake. These observations are obtained by the Solar Wind Monitor sensor of the Sub-keV Atom Reflecting Analyser experiment on Chandrayaan-1. The observation cannot be explained by the conventional fluid models for aligned flow. Back tracing of the observed protons suggests that their source is the solar wind. The larger gyroradii of the wake protons compared to that of solar wind suggest that they were part of the tail of the solar wind velocity distribution function. Such protons could enter the wake due to their large gyroradii even when the flow is aligned to IMF. However, the wake boundary electric field may also play a role in the entry of the protons into the wake.

Backscattered energetic neutral atoms from the Moon in the Earth's plasma sheet observed by Chandarayaan-1/Sub-keV Atom Reflecting Analyzer instrument

We present the observations of energetic neutral atoms (ENAs) produced at the lunar surface in the Earth's magnetotail. When the Moon was located in the terrestrial plasma sheet, Chandrayaan-1 Energetic Neutrals Analyzer (CENA) detected hydrogen ENAs from the Moon. Analysis of the data from CENA together with the Solar Wind Monitor (SWIM) onboard Chandrayaan-1 reveals the characteristic energy of the observed ENA energy spectrum (the e-folding energy of the distribution function) ∼100 eV and the ENA backscattering ratio (defined as the ratio of upward ENA flux to downward proton flux) <∼0.1. These characteristics are similar to those of the backscattered ENAs in the solar wind, suggesting that CENA detected plasma sheet particles backscattered as ENAs from the lunar surface. The observed ENA backscattering ratio in the plasma sheet exhibits no significant difference in the Southern Hemisphere, where a large and strong magnetized region exists, compared with that in the Northern Hemisphere. This is contrary to the CENA observations in the solar wind, when the backscattering ratio drops by ∼50% in the Southern Hemisphere. Our analysis and test particle simulations suggest that magnetic shielding of the lunar surface in the plasma sheet is less effective than in the solar wind due to the broad velocity distributions of the plasma sheet protons.

Measurement of the production of a W boson in association with a charm quark in pp collisions at sqrts = 7 TeV with the ATLAS detector

The production of a W boson in association with a single charm quark is studied using 4.6 fb−1 of pp collision data at ps = 7TeV collected with the ATLAS detector at the Large Hadron Collider. In events in which a W boson decays to an electron or muon, the charm quark is tagged either by its semileptonic decay to a muon or by the presence of a charmed meson. The integrated and differential cross sections as a function of the pseudorapidity of the lepton from the W-boson decay are measured. Results are compared to the predictions of next-to-leading-order QCD calculations obtained from various parton distribution function parameterisations. The ratio of the strange-to-down sea-quark distributions is determined to be 0.96+0.26−0.30 at Q2 = 1.9 GeV2, which supports the hypothesis of an SU(3)-symmetric composition of the light-quark sea. Additionally, the cross-section ratio ơ(W++c)/ơ(W−+c) is compared to the predictions obtained using parton distribution function parameterisations with different assumptions about the s–s quark asymmetry.

Bounding Standard Gaussian Tail Probabilities

We review various inequalities for Mills' ratio (1 - Φ)= Ø, where Ø and Φ denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving finite continued fractions lead to a general approximation scheme which implies and refines several known bounds.

Regularity conditions in the realisability problem in applications to point processes and random closed sets

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive ex-tension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extens ion can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed sets with given two-point covering function or contact distribution function. It is shown that the regularity condition can be efficiently checked in many cases in order to ensure that the obtained point processes are indeed locally finite and random sets have closed realisations.

Consistency of Concave Regression with an Application to Current-Status Data

We consider the problem of nonparametric estimation of a concave regression function F. We show that the supremum distance between the least square s estimatorand F on a compact interval is typically of order(log(n)/n)2/5. This entails rates of convergence for the estimator’s derivative. Moreover, we discuss the impact of additional constraints on F such as monotonicity and pointwise bounds. Then we apply these results to the analysis of current status data, where the distribution function of the event times is assumed to be concave.

Low-energy energetic neutral atom imaging of Io plasma and neutral tori

Io's plasma and neutral tori play significant roles in the Jovian magnetosphere. We present feasibility studies of measuring low-energy energetic neutral atoms (LENAs) generated from the Io tori. We calculate the LENA flux between 10 eV and 3 keV. The energy range includes the corotational plasma flow energy. The expected differential flux at Ganymede distance is typically 10(3)-10(5) cm(-2) s(-1) sr(-1) eV(-1) near the energy of the corotation. It is above the detection level of the planned LENA sensor that is to be flown to the Jupiter system with integration times of 0.01-1 s. The flux has strong asymmetry with respective to the Io phase. The observations will exhibit periodicities, which can be attributed to the Jovian magnetosphere rotation and the rotation of Io around Jupiter. The energy spectra will exhibit dispersion signatures, because of the non-negligible flight time of the LENAs from Io to the satellite. In 2030, the Jupiter exploration mission JUICE will conduct a LENA measurement with a LENA instrument, the Jovian Neutrals Analyzer (JNA). From the LENA observations collected by JNA, we will be able to derive characteristic quantities, such as the density, velocity, velocity distribution function, and composition of plasma-torus particles. We also discuss the possible physics to be explored by JNA in addition to the constraints for operating the sensor and analyzing the obtained dataset. (C) 2015 Elsevier Ltd. All rights reserved.

The Interstellar Neutral He haze in the heliosphere: what can we learn?

Neutral interstellar helium has been observed by the Interstellar Boundary Explorer (IBEX) since 2009, with a signal-to-noise ratio well above 1000. Because of the geometry of the observations, the signal observed from January to March each year is the easiest to identify. However, as we show via simulations, the portion of the signal in the range of intensities from 10(-3) to 10(-2) of the peak value, previously mostly left out from the analysis, may provide important information about the details of the distribution function of interstellar He gas in front of the heliosphere. In particular, these observations may inform us about possible departures of the parent interstellar He population from equilibrium. We compare the expected distribution of the signal for the canonical assumption of a single Maxwell-Boltzmann population with the distributions for a superposition of the Maxwell-Boltzmann primary population and the recently discovered Warm Breeze, and for a single primary population given by a kappa function. We identify the regions on the sky where the differences between those cases are expected to be the most visible against the background. We discuss the diagnostic potential of the fall peak of the interstellar signal, reduced by a factor of 50 due to the Compton-Getting effect but still above the detection limit of IBEX. We point out the strong energy dependence of the fall signal and suggest that searching for this signal in the data could bring an independent assessment of the low-energy measurement threshold of the IBEX-Lo sensor.

The dust environment of comet 67P/Churyumov-Gerasimenko from Rosetta OSIRIS and VLT observations in the 4.5 to 2.9 AU heliocentric distance range inbound

Context. The ESA Rosetta spacecraft, currently orbiting around cornet 67P/Churyumov-Gerasimenko, has already provided in situ measurements of the dust grain properties from several instruments, particularly OSIRIS and GIADA. We propose adding value to those measurements by combining them with ground-based observations of the dust tail to monitor the overall, time-dependent dust-production rate and size distribution. Aims. To constrain the dust grain properties, we take Rosetta OSIRIS and GIADA results into account, and combine OSIRIS data during the approach phase (from late April to early June 2014) with a large data set of ground-based images that were acquired with the ESO Very Large Telescope (VLT) from February to November 2014. Methods. A Monte Carlo dust tail code, which has already been used to characterise the dust environments of several comets and active asteroids, has been applied to retrieve the dust parameters. Key properties of the grains (density, velocity, and size distribution) were obtained from. Rosetta observations: these parameters were used as input of the code to considerably reduce the number of free parameters. In this way, the overall dust mass-loss rate and its dependence on the heliocentric distance could be obtained accurately. Results. The dust parameters derived from the inner coma measurements by OSIRIS and GIADA and from distant imaging using VLT data are consistent, except for the power index of the size-distribution function, which is alpha = -3, instead of alpha = -2, for grains smaller than 1 mm. This is possibly linked to the presence of fluffy aggregates in the coma. The onset of cometary activity occurs at approximately 4.3 AU, with a dust production rate of 0.5 kg/s, increasing up to 15 kg/s at 2.9 AU. This implies a dust-to-gas mass ratio varying between 3.8 and 6.5 for the best-fit model when combined with water-production rates from the MIRO experiment.