An analytic solution to the Busemann-Petty problem on sections of convex bodies

We derive a formula connecting the derivatives of parallel section functions of an origin-symmetric star body in R^n with the Fourier transform of powers of the radial function of the body. A parallel section function (or (n-1)-dimensional X-ray) gives the ((n-1)-dimensional) volumes of all hyperplane sections of the body orthogonal to a given direction. This formula provides a new characterization of intersection bodies in R^n and leads to a unified analytic solution to the Busemann-Petty problem: Suppose that K and L are two origin-symmetric convex bodies in R^n such that the ((n-1)-dimensional) volume of each central hyperplane section of K is smaller than the volume of the corresponding section of L; is the (n-dimensional) volume of K smaller than the volume of L? In conjunction with earlier established connections between the Busemann-Petty problem, intersection bodies, and positive definite distributions, our formula shows that the answer to the problem depends on the behavior of the (n-2)-nd derivative of the parallel section functions. The affirmative answer to the Busemann-Petty problem for n\le 4 and the negative answer for n\ge 5 now follow from the fact that convexity controls the second derivatives, but does not control the derivatives of higher orders.Comment: 13 pages, published versio

Chloride transport through concrete and implications for rapid chloride testing

Word processed copy. Includes bibliographical references (leaves 171-182)

Surface Activation Treatment of Wood and Its Effect on the Gel Time of Phenol-Formaldehyde Resin

Surface activation treatment of wood using hydrogen peroxide, nitric acid, and sodium hydroxide was examined to assess its effect on the gel time of phenol-formaldehyde resin. Four wood species comprising both hardwoods and softwoods, two treatment levels, and two treatment conditions (activation and activation followed by drying) were examined in the study. The effect of surface activation on the gel time of phenol-formaldehyde resin varies for a particular surface activator according to treatment level and treatment condition. Surface activated treated wood decreases the gel time of phenol-formaldehyde resin with hydrogen peroxide treatment having the greatest effect followed by nitric acid and sodium hydroxide treatments

Time-Frequency Ridge Analysis Based on the Reassignment Vector

International audienceThis paper considers the problem of detecting and estimating AM/FM components in the time-frequency plane. It introduces a new algorithm to estimate the ridges corresponding to the instantaneous frequencies of the components, and to segment the time-frequency plane into different `basins of attraction', each basin corresponding to one mode. The technique is based on the structure of the reassignment vector, which is commonly used for sharpening time-frequency representations. Compared with previous approaches, this new method does not need extra parameters, exhibits less sensitivity to the choice of the window and shows better reconstruction performance. Its effectiveness is demonstrated on simulated and real datasets

Sexual antagonism in haplodiploids

Funding: Royal Society (Grant Number(s): DHF\R1\180120; Grant recipient(s): Laura Ross). Natural Environment Research Council (Grant Number(s): NE/K009524/1; Grant recipient(s): Andy Gardner). University of St Andrews (Grant Number(s): PhD studentship; Grant recipient(s): Thomas Hitchcock). H2020 European Research Council (Grant Number(s): 771387; Grant recipient(s): Andy Gardner).Females and males may face different selection pressures, such that alleles conferring a benefit in one sex may be deleterious in the other. Such sexual antagonism has received a great deal of theoretical and empirical attention, almost all of which has focused on diploids. However, a sizeable minority of animals display an alternative haplodiploid mode of inheritance, encompassing both arrhenotoky, whereby males develop from unfertilized eggs, and paternal genome elimination (PGE), whereby males receive but do not transmit a paternal genome. Alongside unusual genetics, haplodiploids often exhibit social ecologies that modulate the relative value of females and males. Here, we develop a series of evolutionary-genetic models of sexual antagonism for haplodiploids, incorporating details of their molecular biology and social ecology. We find that: (1) PGE promotes female-beneficial alleles more than arrhenotoky, and to an extent determined by the timing of elimination—and degree of silencing of—the paternal genome; (2) sib-mating relatively promotes female-beneficial alleles, as do other forms of inbreeding including limited male-dispersal, oedipal-mating, and the pseudo-hermaphroditism of Icerya purchasi; (3) resource competition between related females inhibits the invasion of female-beneficial alleles; and (4) sexual antagonism foments conflicts between parents and offspring, endosymbionts and hosts, and maternal- and paternal-origin genes.Publisher PDFPeer reviewe

High frequency surface acoustic wave resonator-based sensor for particulate matter detection

This paper describes the characterization of high frequency Surface Acoustic Wave Resonator-based (SAWR) sensors, for the detection of micron and sub-micron sized particles. The sensor comprises two 262 MHz ST-cut quartz based Rayleigh wave SAWRs where one is used for particle detection and the other as a reference. Electro-acoustic detection of different sized particles shows a strong relationship between mass sensitivity (Δf/Δm) and particle diameter (Dp). This enables frequency-dependent SAWR sensitivity to be tailored to the size of particles, thus making these types of sensors good candidates for PM10, PM2.5 and ultrafine particle (UFP) detection. Our initial characterisation demonstrated a typical SAWR frequency shift of 60 Hz in response to a deposition of ca. 0.21 ng of 0.75 μm-sized gold particles (∼50 particles) on sensor’s surface. Sensor responses to different size particles, such as ∼30 μm diameter silicon, gold (diameters of ∼0.75 μm and ∼20 μm), ∼8 μm fine sugar, PTFE (∼1 μm and ∼15 μm), ∼4 μm talcum powder, and ∼2 μm molybdenum powder were evaluated, and an average mass sensitivity of 275 Hz/ng was obtained. Based on the results obtained in this study we believe that acoustic wave technology has great potential for application in airborne particle detection. Moreover, acoustic resonator devices can be integrated with CMOS interface circuitry to obtain sensitive, robust, low-power and low-cost particle detectors for variety of applications including outdoor environmental monitoring

Laser Guide Stars for Extremely Large Telescopes: Efficient Shack-Hartmann Wavefront Sensor Design using Weighted center-of-gravity algorithm

Over the last few years increasing consideration has been given to the study of Laser Guide Stars (LGS) for the measurement of the disturbance introduced by the atmosphere in optical and near-infrared astronomical observations from the ground. A possible method for the generation of a LGS is the excitation of the Sodium layer in the upper atmosphere at approximately 90 km of altitude. Since the Sodium layer is approximately 10 km thick, the artificial reference source looks elongated, especially when observed from the edge of a large aperture. The spot elongation strongly limits the performance of the most common wavefront sensors. The centroiding accuracy in a Shack-Hartmann wavefront sensor, for instance, decreases proportionally to the elongation (in a photon noise dominated regime). To compensate for this effect a straightforward solution is to increase the laser power, i.e. to increase the number of detected photons per subaperture. The scope of the work presented in this paper is twofold: an analysis of the performance of the Weighted Center of Gravity algorithm for centroiding with elongated spots and the determination of the required number of photons to achieve a certain average wavefront error over the telescope aperture.Comment: 10 pages, 14 figure

Superconducting Gatemon Qubit based on a Proximitized Two-Dimensional Electron Gas

The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies and interqubit coupling strengths, to the gain of parametric amplifiers for quantum-limited readout. The inductance is either set by tailoring the metal-oxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices (SQUIDs) with local current-biased flux lines. JJs based on superconductor-semiconductor hybrids represent a tantalizing all-electric alternative. The gatemon is a recently developed transmon variant which employs locally gated nanowire (NW) superconductor-semiconductor JJs for qubit control. Here, we go beyond proof-of-concept and demonstrate that semiconducting channels etched from a wafer-scale two-dimensional electron gas (2DEG) are a suitable platform for building a scalable gatemon-based quantum computer. We show 2DEG gatemons meet the requirements by performing voltage-controlled single qubit rotations and two-qubit swap operations. We measure qubit coherence times up to ~2 us, limited by dielectric loss in the 2DEG host substrate

The First Supernova Explosions: Energetics, Feedback, and Chemical Enrichment

We perform three-dimensional smoothed particle hydrodynamics simulations in a realistic cosmological setting to investigate the expansion, feedback, and chemical enrichment properties of a 200 M_sun pair-instability supernova in the high-redshift universe. We find that the SN remnant propagates for a Hubble time at z = 20 to a final mass-weighted mean shock radius of 2.5 kpc (proper), roughly half the size of the HII region, and in this process sweeps up a total gas mass of 2.5*10^5 M_sun. The morphology of the shock becomes highly anisotropic once it leaves the host halo and encounters filaments and neighboring minihalos, while the bulk of the shock propagates into the voids of the intergalactic medium. The SN entirely disrupts the host halo and terminates further star formation for at least 200 Myr, while in our specific case it exerts positive mechanical feedback on neighboring minihalos by shock-compressing their cores. In contrast, we do not observe secondary star formation in the dense shell via gravitational fragmentation, due to the previous photoheating by the progenitor star. We find that cooling by metal lines is unimportant for the entire evolution of the SN remnant, while the metal-enriched, interior bubble expands adiabatically into the cavities created by the shock, and ultimately into the voids with a maximum extent similar to the final mass-weighted mean shock radius. Finally, we conclude that dark matter halos of at least M_vir > 10^8 M_sun must be assembled to recollect all components of the swept-up gas.Comment: 16 pages, 14 figures, published in Ap