On blocks and runs estimators of extremal index

Given a sample from a stationary sequence of random variables, we study the blocks and runs estimators of the extremal index. Conditions are given for consistency and asymptotic normality of these estimators. We show that moment restrictions assumed by Hsing (1991, 1993) may be relaxed if a stronger mixing condition holds. The CLT for the runs estimator seems to be proven for the first time

First Amendment Scrutiny of FDA'S Fight Against Misbranding: Placing Labeling on the Spectrum of Speech

In order to further the Food and Drug Administration's (FDA) mission of "assur[ing] that the products it regulates are safe and truthfully labeled," the Federal Food, Drug, and Cosmetic Act (FD&C Act) gives FDA the power to enforce prohibitions on labeling that causes a food, drug, cosmetic, or medical device to be misbranded. The FD&C Act defines labeling as "all labels and other written, printed, or graphic matter (1) upon any article or any of its containers or wrappers, or (2) accompanying such article." Because of the expansive nature of this definition, independently written pamphlets, newspapers, and books that accompany products covered by the FD&C Act constitute labeling in certain circumstances. This exacerbates the tension between the First Amendment's free speech guarantee and FDA's mandate, and raises the question of how courts should scrutinize FDA's ability to seize or enjoin the sale of misleading labeling. The importance of both the Free Speech Clause and the protection of consumers makes this a difficult issue to resolve, and as of yet, "no case has squarely confronted the issue.

Keck Pencil-Beam Survey for Faint Kuiper Belt Objects

We present the results of a pencil-beam survey of the Kuiper Belt using the Keck 10-m telescope. A single 0.01 square degree field is imaged 29 times for a total integration time of 4.8 hr. Combining exposures in software allows the detection of Kuiper Belt Objects (KBOs) having visual magnitude V < 27.9. Two new KBOs are discovered. One object having V = 25.5 lies at a probable heliocentric distance d = 33 AU. The second object at V = 27.2 is located at d = 44 AU. Both KBOs have diameters of about 50 km, assuming comet-like albedos of 4%. Data from all surveys are pooled to construct the luminosity function from red magnitude R = 20 to 27. The cumulative number of objects per square degree, N (< R), is fitted to a power law of the form log_(10) N = 0.52 (R - 23.5). Differences between power laws reported in the literature are due mainly to which survey data are incorporated, and not to the method of fitting. The luminosity function is consistent with a power-law size distribution for objects having diameters s = 50 to 500 km; dn ~ s^(-q) ds, where the differential size index q = 3.6 +/- 0.1. The distribution is such that the smallest objects possess most of the surface area, but the largest bodies contain the bulk of the mass. Though our inferred size index nearly matches that derived by Dohnanyi (1969), it is unknown whether catastrophic collisions are responsible for shaping the size distribution. Implications of the absence of detections of classical KBOs beyond 50 AU are discussed.Comment: Accepted to AJ. Final proof-edited version: references added, discussion of G98 revised in sections 4.3 and 5.

Functional kernel estimators of conditional extreme quantiles

We address the estimation of "extreme" conditional quantiles i.e. when their order converges to one as the sample size increases. Conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian distributed kernel estimators. A Weissman-type estimator and kernel estimators of the conditional tail-index are derived, permitting to estimate extreme conditional quantiles of arbitrary order.Comment: arXiv admin note: text overlap with arXiv:1107.226

Ganglion-specific splicing of TRPV1 underlies infrared sensation in vampire bats.

Vampire bats (Desmodus rotundus) are obligate blood feeders that have evolved specialized systems to suit their sanguinary lifestyle. Chief among such adaptations is the ability to detect infrared radiation as a means of locating hotspots on warm-blooded prey. Among vertebrates, only vampire bats, boas, pythons and pit vipers are capable of detecting infrared radiation. In each case, infrared signals are detected by trigeminal nerve fibres that innervate specialized pit organs on the animal's face. Thus, vampire bats and snakes have taken thermosensation to the extreme by developing specialized systems for detecting infrared radiation. As such, these creatures provide a window into the molecular and genetic mechanisms underlying evolutionary tuning of thermoreceptors in a species-specific or cell-type-specific manner. Previously, we have shown that snakes co-opt a non-heat-sensitive channel, vertebrate TRPA1 (transient receptor potential cation channel A1), to produce an infrared detector. Here we show that vampire bats tune a channel that is already heat-sensitive, TRPV1, by lowering its thermal activation threshold to about 30 °C. This is achieved through alternative splicing of TRPV1 transcripts to produce a channel with a truncated carboxy-terminal cytoplasmic domain. These splicing events occur exclusively in trigeminal ganglia, and not in dorsal root ganglia, thereby maintaining a role for TRPV1 as a detector of noxious heat in somatic afferents. This reflects a unique organization of the bat Trpv1 gene that we show to be characteristic of Laurasiatheria mammals (cows, dogs and moles), supporting a close phylogenetic relationship with bats. These findings reveal a novel molecular mechanism for physiological tuning of thermosensory nerve fibres

Coherent oscillations and incoherent tunnelling in one - dimensional asymmetric double - well potential

For a model 1d asymmetric double-well potential we calculated so-called survival probability (i.e. the probability for a particle initially localised in one well to remain there). We use a semiclassical (WKB) solution of Schroedinger equation. It is shown that behaviour essentially depends on transition probability, and on dimensionless parameter which is a ratio of characteristic frequencies for low energy non-linear in-well oscillations and inter wells tunnelling. For the potential describing a finite motion (double-well) one has always a regular behaviour. For the small value of the parameter there is well defined resonance pairs of levels and the survival probability has coherent oscillations related to resonance splitting. However for the large value of the parameter no oscillations at all for the survival probability, and there is almost an exponential decay with the characteristic time determined by Fermi golden rule. In this case one may not restrict oneself to only resonance pair levels. The number of perturbed by tunnelling levels grows proportionally to the value of this parameter (by other words instead of isolated pairs there appear the resonance regions containing the sets of strongly coupled levels). In the region of intermediate values of the parameter one has a crossover between both limiting cases, namely the exponential decay with subsequent long period recurrent behaviour.Comment: 19 pages, 7 figures, Revtex, revised version. Accepted to Phys. Rev.

Triton's surface age and impactor population revisited in light of Kuiper Belt fluxes: Evidence for small Kuiper Belt objects and recent geological activity

Neptune's largest satellite, Triton, is one of the most fascinating and enigmatic bodies in the solar system. Among its numerous interesting traits, Triton appears to have far fewer craters than would be expected if its surface was primordial. Here we combine the best available crater count data for Triton with improved estimates of impact rates by including the Kuiper Belt as a source of impactors. We find that the population of impactors creating the smallest observed craters on Triton must be sub-km in scale, and that this small-impactor population can be best fit by a differential power-law size index near -3. Such results provide interesting, indirect probes of the unseen small body population of the Kuiper Belt. Based on the modern, Kuiper Belt and Oort Cloud impactor flux estimates, we also recalculate estimated ages for several regions of Triton's surface imaged by Voyager 2, and find that Triton was probably active on a time scale no greater than 0.1-0.3 Gyr ago (indicating Triton was still active after some 90% to 98% of the age of the solar system), and perhaps even more recently. The time-averaged volumetric resurfacing rate on Triton implied by these results, 0.01 km$^3$ yr$^{-1}$ or more, is likely second only to Io and Europa in the outer solar system, and is within an order of magnitude of estimates for Venus and for the Earth's intraplate zones. This finding indicates that Triton likely remains a highly geologically active world at present, some 4.5 Gyr after its formation. We briefly speculate on how such a situation might obtain.Comment: 14 pages (TeX), plus 2 postscript figures Stern & McKinnon, 2000, AJ, in pres