Volumes of Restricted Minkowski Sums and the Free Analogue of the Entropy Power Inequality

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality has a counterpart for the free analogue of entropy . The free entropy (introduced recently by the second named author), consistently with Boltzmann's formula $S=k\log W$, was defined via volumes of matricial microstates. Proving the free entropy power inequality naturally becomes a geometric question. Restricting the Minkowski sum of two sets means to specify the set of pairs of points which will be added. The relevant inequality, which holds when the set of "addable" points is sufficiently large, differs from the Brunn-Minkowski inequality by having the exponent $1/n$ replaced by $2/n$. Its proof uses the rearrangement inequality of Brascamp-Lieb-L\"uttinger

Tailoring the magnetic properties of Fe asymmetric nanodots

Asymmetric dots as a function of their geometry have been investigated using three-dimensional (3D) object oriented micromagnetic framework (OOMMF) code. The effect of shape asymmetry of the disk on coercivity and remanence is studied. Angular dependence of the remanence and coercivity is also addressed. Asymmetric dots are found to reverse their magnetization by nucleation and propagation of a vortex, when the field is applied parallel to the direction of asymmetry. However, complex reversal modes appear when the angle at which the external field is applied is varied, leading to a non monotonic behavior of the coercivity and remanence.Comment: 5 pages, 7 figure

The new IOC and IAAF policies on female eligibility: old Emperor, new clothes?

The Caster Semenya debacle touched off by the 2009 Berlin World Athletics Championships resulted finally in IOC and IAAF abandonment of sex testing, which gave way to procedures that make female competition eligibility dependent upon the level of serum testosterone, which must be below the male range or instrumentally countered by androgen resistance. We argue that the new policy is unsustainable because (i) the testosterone-performance connection it posits is uncompelling; (ii) testosterone-induced female advantage is not ipso facto unfair advantage; (iii) the new policy reflects the gender policing impulses endemic to sport as well as the broader cultural impulses to monstrify women and to doctor women who have nothing wrong with them; (iv) female–male performance disparities are not the only reason for sex-segregated sport, but co-exist with respectable cultural and practical reasons, which (v) provide a powerful case for allowing athletes to compete in the sex category congruent with their gender identity

Observations and Modeling of Martian Auroras

peer reviewedObservations of planetary auroras form a new area of planetary exploration from space, especially for nonmagnetic planets since various kinds of auroras like Discrete, Proton and Diffuse auroras have been observed at Mars. We review the latest results of Martian auroras obtained by the instruments (1) SPICAM (Spectroscopy for the Investigation of the Characteristics of the Atmosphere of Mars) aboard Mars Express (MEX) and (2) IUVS (the Imaging Ultraviolet Spectrograph) on MAVEN (the Mars Atmosphere and Volatile Evolution mission). The MARSIS instrument (the Mars Advanced Radar for the Subsurface and Ionosphere Sounding) on MEX, in addition, exhibited strong ionizations in some electron density profiles, thus providing further evidence for the existence of Martian auroras. We review these MARSIS observations as well. In addition, we review various models of Martian auroras

A new silicon tracker for proton imaging and dosimetry

For many years, silicon micro-strip detectors have been successfully used as tracking detectors for particle and nuclear physics experiments. A new application of this technology is to the field of particle therapy where radiotherapy is carried out by use of charged particles such as protons or carbon ions. Such a treatment has been shown to have advantages over standard x-ray radiotherapy and as a result of this, many new centres offering particle therapy are currently under construction around the world today. The Proton Radiotherapy, Verification and Dosimetry Applications (PRaVDA) consortium are developing instrumentation for particle therapy based upon technology from high-energy physics. The characteristics of a new silicon micro-strip tracker for particle therapy will be presented. The array uses specifically designed, large area sensors with technology choices that follow closely those taken for the ATLAS experiment at the HL-LHC. These detectors will be arranged into four units each with three layers in an x–u–v configuration to be suitable for fast proton tracking with minimal ambiguities. The sensors will form a tracker capable of tracing the path of ~200 MeV protons entering and exiting a patient allowing a new mode of imaging known as proton computed tomography (pCT). This will aid the accurate delivery of treatment doses and in addition, the tracker will also be used to monitor the beam profile and total dose delivered during the high fluences used for treatment. We present here details of the design, construction and assembly of one of the four units that will make up the complete tracker along with its characterisation using radiation tests carried out using a 90 Sr source in the laboratory and a 60 MeV proton beam at the Clatterbridge Cancer Centre

Ability of the 4-D-Var analysis of the GOSAT BESD XCO₂ retrievals to characterize atmospheric CO₂ at large and synoptic scales

This study presents results from the European Centre for Medium-Range Weather Forecasts (ECMWF) carbon dioxide (CO₂) analysis system where the atmospheric CO₂ is controlled through the assimilation of column-averaged dry-air mole fractions of CO₂ (XCO₂) from the Greenhouse gases Observing Satellite (GOSAT). The analysis is compared to a free-run simulation (without assimilation of XCO₂), and they are both evaluated against XCO₂ data from the Total Carbon Column Observing Network (TCCON). We show that the assimilation of the GOSAT XCO₂ product from the Bremen Optimal Estimation Differential Optical Absorption Spectroscopy (BESD) algorithm during the year 2013 provides XCO₂ fields with an improved mean absolute error of 0.6 parts per million (ppm) and an improved station-to-station bias deviation of 0.7  ppm compared to the free run (1.1 and 1.4  ppm, respectively) and an improved estimated precision of 1  ppm compared to the GOSAT BESD data (3.3  ppm). We also show that the analysis has skill for synoptic situations in the vicinity of frontal systems, where the GOSAT retrievals are sparse due to cloud contamination. We finally computed the 10-day forecast from each analysis at 00:00  UTC, and we demonstrate that the CO₂ forecast shows synoptic skill for the largest-scale weather patterns (of the order of 1000  km) even up to day 5 compared to its own analysis

EVR-CB-004: An Inflated Hot Subdwarf O Star + Unseen WD Companion in a Compact Binary Discovered with the Evryscope

We present the discovery of EVR-CB-004, a close binary with a remnant stellar core and an unseen white dwarf (WD) companion. The analysis in this work reveals that the primary is potentially an inflated hot subdwarf (sdO) and more likely is a rarer post-blue horizontal branch (post-BHB) star. Post-BHBs are the short-lived shell-burning final stage of a blue horizontal star or hot subdwarf before transitioning to a WD. This object was discovered using Evryscope photometric data in a southern all-sky hot subdwarf variability survey. The photometric light curve for EVR-CB-004 shows multicomponent variability from ellipsoidal deformation of the primary and Doppler boosting, as well as gravitational limb darkening. The binary EVR-CB-004 is one of just a handful of known systems and has a long period (6.08426 hr) and large-amplitude ellipsoidal modulation (16.0% change in brightness from maximum to minimum) for these extremely close binary systems, while the properties of the primary make it a truly unique system. It also shows a peculiar low-amplitude (less than 1%) sinusoidal light-curve variation with a period that is a 1/3 resonance of the binary period. We tentatively identify this additional variation source as a tidally induced resonant pulsation, and we suggest follow-up observations that could verify this interpretation. From the evolutionary state of the system, its components, and its mass fraction, EVR-CB-004 is a strong merger candidate to form a single high-mass (1.2 M o˙) WD. It offers a glimpse into a brief phase of remnant core evolution and secondary variation not seen before in a compact binary

Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting