The problem of shot selection in basketball

In basketball, every time the offense produces a shot opportunity the player with the ball must decide whether the shot is worth taking. In this paper, I explore the question of when a team should shoot and when they should pass up the shot by considering a simple theoretical model of the shot selection process, in which the quality of shot opportunities generated by the offense is assumed to fall randomly within a uniform distribution. I derive an answer to the question "how likely must the shot be to go in before the player should take it?", and show that this "lower cutoff" for shot quality $f$ depends crucially on the number $n$ of shot opportunities remaining (say, before the shot clock expires), with larger $n$ demanding that only higher-quality shots should be taken. The function $f(n)$ is also derived in the presence of a finite turnover rate and used to predict the shooting rate of an optimal-shooting team as a function of time. This prediction is compared to observed shooting rates from the National Basketball Association (NBA), and the comparison suggests that NBA players tend to wait too long before shooting and undervalue the probability of committing a turnover.Comment: 7 pages, 2 figures; comparison to NBA data adde

Provenance and geochemistry of exotic clasts in conglomerates of the Oligocene Torehina Formation, Coromandel Peninsula, New Zealand

Non-marine pebble to cobble conglomerates of the lower Torehina Formation (Oligocene) crop out along western Coromandel Peninsula and overlie, with strong angular discordance, continental-margin metasedimentary rocks (Manaia Hill Group) of Mesozoic (Late Jurassic to ?Early Cretaceous) age. The conglomerates contain provenance information that identifies a pre-Oligocene depositional history obscured by the unconformable juxtaposition of these Tertiary and Mesozoic strata. Most clasts in the lower Torehina Formation are visually similar to local bedrock lithologies, including metamorphosed sandstones and argillites, but are kaolinitic and contain more detrital and authigenic chert, quartz, and potash feldspar. Local derivation of these clasts seems unlikely. By comparing geochemical ratios with those defined for continental margin sandstones, and well characterised New Zealand tectonic terranes, we interpret the majority of clasts in the lower Torehina Formation to have been derived from a dissected orogen, with mixtures of felsic and volcanogenic-derived sediment. The most likely sources are the Waipapa and Torlesse Terranes. The remaining 20–30% of the clasts in the lower Torehina Formation were originally friable, are coarse grained, and appear to be lithologically exotic relative to known metamorphosed sandstones in basement terrane sources on North Island. Some clasts contain coal laminae and particles, and all contain detrital kaolinite as lithic fragments and matrix. Such characteristics imply a non-marine to marginal-marine source containing sediment derived from strongly weathered granite or granodiorite. Mechanical fragility implies a likely proximal, easily erodible source. We propose that this group of clasts was derived from an Upper Cretaceous sedimentary cover, either part of a locally developed basin fill or part of a once regionally extensive cover on North Island. Either case defines a more widely distributed Cretaceous source than found today

Io: IUE observations of its atmosphere and the plasma torus

Two of the main components of the atmosphere of Io, neutral oxygen and sulfur, were detected with the IUE. Four observations yield brightnesses that are similar, regardless of whether the upstream or the downstream sides of the torus plasma flow around Io is observed. A simple model requires the emissions to be produced by the interaction of O and S columns in the exospheric range with 2 eV electrons. Cooling of the 5 eV torus electrons is required prior to their interaction with the atmosphere of Io. Inconsistencies in the characteristics of the spectra that cannot be accounted for in this model require further analysis with improved atomic data. The Io plasma torus was monitored with the IUE. The long-term stability of the warm torus is established. The observed brightnesses were analyzed using a model of the torus, and variations of less than 30 percent in the composition are observed, the quantitative results being model dependent

Inverse remodelling algorithm identifies habitual manual activities of primates based on metacarpal bone architecture

Previously, a micro-finite element (micro-FE)-based inverse remodelling method was presented in the literature that reconstructs the loading history of a bone based on its architecture alone. Despite promising preliminary results, it remains unclear whether this method is sensitive enough to detect differences of bone loading related to pathologies or habitual activities. The goal of this study was to test the sensitivity of the inverse remodelling method by predicting joint loading histories of metacarpal bones of species with similar anatomy but clearly distinct habitual hand use. Three groups of habitual hand use were defined using the most representative primate species: manipulation (human), suspensory locomotion (orangutan), and knuckle-walking locomotion (bonobo, chimpanzee, gorilla). Nine to ten micro-computed tomography scans of each species ($$n=48$$n=48in total) were used to create micro-FE models of the metacarpal head region. The most probable joint loading history was predicted by optimally scaling six load cases representing joint postures ranging from $$-\,75^{\circ }$$-75∘(extension) to $$+\,75^{\circ }$$+75∘(flexion). Predicted mean joint load directions were significantly different between knuckle-walking and non-knuckle-walking groups ($$p<0.05$$p<0.05) and in line with expected primary hand postures. Mean joint load magnitudes tended to be larger in species using their hands for locomotion compared to species using them for manipulation. In conclusion, this study shows that the micro-FE-based inverse remodelling method is sensitive enough to detect differences of joint loading related to habitual manual activities of primates and might, therefore, be useful for palaeoanthropologists to reconstruct the behaviour of extinct species and for biomedical applications such as detecting pathological joint loading

Ionic conductivity on a wetting surface

Recent experiments measuring the electrical conductivity of DNA molecules highlight the need for a theoretical model of ion transport along a charged surface. Here we present a simple theory based on the idea of unbinding of ion pairs. The strong humidity dependence of conductivity is explained by the decrease in the electrostatic self-energy of a separated pair when a layer of water (with high dielectric constant) is adsorbed to the surface. We compare our prediction for conductivity to experiment, and discuss the limits of its applicability.Comment: 5 pages, 3 figures; one section and two illustrations added; figures updated and discussion added; typo fixe

A Single Circumbinary Disk in the HD 98800 Quadruple System

We present sub-arcsecond thermal infrared imaging of HD 98800, a young quadruple system composed of a pair of low-mass spectroscopic binaries separated by 0.8'' (38 AU), each with a K-dwarf primary. Images at wavelengths ranging from 5 to 24.5 microns show unequivocally that the optically fainter binary, HD 98800B, is the sole source of a comparatively large infrared excess upon which a silicate emission feature is superposed. The excess is detected only at wavelengths of 7.9 microns and longer, peaks at 25 microns, and has a best-fit black-body temperature of 150 K, indicating that most of the dust lies at distances greater than the orbital separation of the spectroscopic binary. We estimate the radial extent of the dust with a disk model that approximates radiation from the spectroscopic binary as a single source of equivalent luminosity. Given the data, the most-likely values of disk properties in the ranges considered are R_in = 5.0 +/- 2.5 AU, DeltaR = 13+/-8 AU, lambda_0 = 2(+4/-1.5) microns, gamma = 0+/-2.5, and sigma_total = 16+/-3 AU^2, where R_in is the inner radius, DeltaR is the radial extent of the disk, lambda_0 is the effective grain size, gamma is the radial power-law exponent of the optical depth, tau, and sigma_total is the total cross-section of the grains. The range of implied disk masses is 0.001--0.1 times that of the moon. These results show that, for a wide range of possible disk properties, a circumbinary disk is far more likely than a narrow ring.Comment: 11 page Latex manuscript with 3 postscript figures. Accepted for publication in Astrophysical Journal Letters. Postscript version of complete paper also available at http://www.hep.upenn.edu/PORG/web/papers/koerner00a.p

Low-Frequency Radio Transients in the Galactic Center

We report the detection of a new radio transient source, GCRT J1746-2757, located only 1.1 degrees north of the Galactic center. Consistent with other radio transients toward the Galactic center, this source brightened and faded on a time scale of a few months. No X-ray counterpart was detected. We also report new 0.33 GHz measurements of the radio counterpart to the X-ray transient source, XTE J1748-288, previously detected and monitored at higher radio frequencies. We show that the spectrum of XTE J1748-288 steepened considerably during a period of a few months after its peak. We also discuss the need for a more efficient means of finding additional radio transients

Imaging and burst location with the EXIST high-energy telescope

The primary instrument of the proposed EXIST mission is a coded mask high energy telescope (the HET), that must have a wide field of view and extremely good sensitivity. It will be crucial to minimize systematic errors so that even for very long total integration times the imaging performance is close to the statistical photon limit. There is also a requirement to be able to reconstruct images on-board in near real time in order to detect and localize gamma-ray bursts. This must be done while the spacecraft is scanning the sky. The scanning provides all-sky coverage and is key to reducing systematic errors. The on-board computational problem is made even more challenging for EXIST by the very large number of detector pixels. Numerous alternative designs for the HET have been evaluated. The baseline concept adopted depends on a unique coded mask with two spatial scales. Monte Carlo simulations and analytic analysis techniques have been used to demonstrate the capabilities of the design and of the proposed two-step burst localization procedure