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

Measurements of the Diffuse Ultraviolet Background and the Terrestrial Airglow with the Space Telescope Imaging Spectrograph

Far-UV observations in and near the Hubble Deep Fields demonstrate that the Space Telescope Imaging Spectrograph (STIS) can potentially obtain unique and precise measurements of the diffuse far-ultraviolet background. Although STIS is not the ideal instrument for such measurements, high-resolution images allow Galactic and extragalactic objects to be masked to very faint magnitudes, thus ensuring a measurement of the truly diffuse UV signal. The programs we have analyzed were not designed for this scientific purpose, but would be sufficient to obtain a very sensitive measurement if it were not for a weak but larger-than-expected signal from airglow in the STIS 1450-1900 A bandpass. Our analysis shows that STIS far-UV crystal quartz observations taken near the limb during orbital day can detect a faint airglow signal, most likely from NI\1493, that is comparable to the dark rate and inseparable from the far-UV background. Discarding all but the night data from these datasets gives a diffuse far-ultraviolet background measurement of 501 +/- 103 ph/cm2/sec/ster/A, along a line of sight with very low Galactic neutral hydrogen column (N_HI = 1.5E20 cm-2) and extinction (E(B-V)=0.01 mag). This result is in good agreement with earlier measurements of the far-UV background, and should not include any significant contribution from airglow. We present our findings as a warning to other groups who may use the STIS far-UV camera to observe faint extended targets, and to demonstrate how this measurement may be properly obtained with STIS.Comment: 7 pages, Latex. 4 figures. Uses corrected version of emulateapj.sty and apjfonts.sty (included). Accepted for publication in A

A Mathematical Framework for Agent Based Models of Complex Biological Networks

Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis.Comment: To appear in Bulletin of Mathematical Biolog

Professional Organizations and Healthcare Industry Support: Ethical Conflict?

A good deal of attention has been recently focused on the presumed advertising excesses of the healthcare industry in its promotion techniques to healthcare professionals, whether through offering gratuities such as gifts, honoraria, or travel support2-6 or through deception. Two basic concerns have been expressed: Does the acceptance of gratuities bias the recipient, tainting his or her responsibilities as the patient's agent? Does acceptance of the gratuity by the healthcare professional contribute to the high cost of healthcare products? The California Society of Hospital Pharmacists was recently asked by its members to formulate a policy for an appropriate relationship between the Society and the healthcare industry, addressing these concerns. In formulating its policy, it became clear that the Society depended on healthcare industry support, gathered through journal advertising, fees for booths at its various educational events, and grants for speaker

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

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

Using domain-independent problems for introducing formal methods

The key to the integration of formal methods into engineering practice is education. In teaching, domain-independent problems i.e., not requiring prior engineering background-offer many advantages. Such problems are widely available, but this paper adds two dimensions that are lacking in typical solutions yet are crucial to formal methods: (i) the translation of informal statements into formal expressions; (ii) the role of formal calculation (including proofs) in exposing risks or misunderstandings and in discovering pathways to solutions. A few example problems illustrate this: (a) a small logical one showing the importance of fully capturing informal statements; (b) a combinatorial one showing how, in going from "real-world" formulations to mathematical ones, formal methods can cover more aspects than classical mathematics, and a half-page formal program semantics suitable for beginners is presented as a support; (c) a larger one showing how a single problem can contain enough elements to serve as a Leitmotiv for all notational and reasoning issues in a complete introductory course. An important final observation is that, in teaching formal methods, no approach can be a substitute for an open mind, as extreme mathphobia appears resistant to any motivation