Geodesically reversible Finsler 2-spheres of constant curvature

A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodesically reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily projectively flat. As a corollary, using a previous result of the author, it is shown that a reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily a Riemannian metric of constant Gauss curvature, thus settling a long- standing problem in Finsler geometry.

Estimation of in-canopy ammonia sources and sinks in a fertilized Zea mays field.

An analytical model was developed to describe in-canopy vertical distribution of ammonia (NH(3)) sources and sinks and vertical fluxes in a fertilized agricultural setting using measured in-canopy mean NH(3) concentration and wind speed profiles. This model was applied to quantify in-canopy air-surface exchange rates and above-canopy NH(3) fluxes in a fertilized corn (Zea mays) field. Modeled air-canopy NH(3) fluxes agreed well with independent above-canopy flux estimates. Based on the model results, the urea fertilized soil surface was a consistent source of NH(3) one month following the fertilizer application, whereas the vegetation canopy was typically a net NH(3) sink with the lower portion of the canopy being a constant sink. The model results suggested that the canopy was a sink for some 70% of the estimated soil NH(3) emissions. A logical conclusion is that parametrization of within-canopy processes in air quality models are necessary to explore the impact of agricultural field level management practices on regional air quality. Moreover, there are agronomic and environmental benefits to timing liquid fertilizer applications as close to canopy closure as possible. Finally, given the large within-canopy mean NH(3) concentration gradients in such agricultural settings, a discussion about the suitability of the proposed model is also presented.

Jamming for a 2D granular material

This paper focuses on the nature of jamming, as seen in two-dimensional frictional granular systems consisting of photoelastic particles. The photoelastic technique is unique at this time, in its capability to provide detailed particle-scale information on forces and kinematic quantities such as particle displacements and rotations. These experiments first explore isotropic stress states near point J through measurements of the mean contact number per particle, Z, and the pressure, P as functions of the packing fraction, . In this case, the experiments show some but not all aspects of jamming, as expected on the basis of simulations and models that typically assume conservative, hence frictionless, forces between particles. Specifically, there is a rapid growth in Z, at a reasonable which we identify with as c. It is possible to fit Z and P, to power law expressions in - c above c, and to obtain exponents that are in agreement with simulations and models. However, the experiments differ from theory on several points, as typified by the rounding that is observed in Z and P near c. The application of shear to these same 2D granular systems leads to phenomena that are qualitatively different from the standard picture of jamming. In particular, there is a range of packing fractions below c, where the application of shear strain at constant leads to jammed stress-anisotropic states, i.e. they have a non-zero shear stress, τ. The application of shear strain to an initially isotropically compressed (hence jammed) state, does not lead to an unjammed state per se. Rather, shear strain at constant first leads to an increase of both τ and P. Additional strain leads to a succession of jammed states interspersed with relatively localized failures of the force network leading to other stress-anisotropic states that are jammed at typically somewhat lower stress. The locus of jammed states requires a state space that involves not only and τ, but also P. P, τ, and Z are all hysteretic functions of shear strain for fixed . However, we find that both P and τ are roughly linear functions of Z for strains large enough to jam the system. This implies that these shear-jammed states satisfy a Coulomb like-relation, τ = μP. © 2010 The Royal Society of Chemistry.

Refractive changes after descemet stripping endothelial keratoplasty: a simplified mathematical model.

PURPOSE: To develop a mathematical model that can predict refractive changes after Descemet stripping endothelial keratoplasty (DSEK). METHODS: A mathematical formula based on the Gullstrand eye model was generated to estimate the change in refractive power of the eye after DSEK. This model was applied to four DSEK cases retrospectively, to compare measured and predicted refractive changes after DSEK. RESULTS: The refractive change after DSEK is determined by calculating the difference in the power of the eye before and after DSEK surgery. The power of the eye post-DSEK surgery can be calculated with modified Gullstrand eye model equations that incorporate the change in the posterior radius of curvature and change in the distance between the principal planes of the cornea and lens after DSEK. Analysis of this model suggests that the ratio of central to peripheral graft thickness (CP ratio) and central thickness can have significant effect on refractive change where smaller CP ratios and larger graft thicknesses result in larger hyperopic shifts. This model was applied to four patients, and the average predicted hyperopic shift in the overall power of the eye was calculated to be 0.83 D. This change reflected in a mean of 93% (range, 75%-110%) of patients' measured refractive shifts. CONCLUSIONS: This simplified DSEK mathematical model can be used as a first step for estimating the hyperopic shift after DSEK. Further studies are necessary to refine the validity of this model.

Identification of beta-adrenergic receptors in human lymphocytes by (-) (3H) alprenolol binding.

Human lymphocytes are known to posessess a catecholamine-responsive adenylate cyclase which has typical beta-adrenergic specificity. To identify directly and to quantitate these beta-adenergic receptors in human lymphocytes, (-) [3H] alprenolol, a potent beta-adrenergic antagonist, was used to label binding sites in homogenates of human mononuclear leukocytes. Binding of (-) [3H] alprenolol to these sites demonstrated the kinetics, affinity, and stereospecificity expected of binding to adenylate cyclase-coupled beta-adrenergic receptors. Binding was rapid (t1/2 less than 30 s) and rapidly reversible (t1/2 less than 3 min) at 37 degrees C. Binding was a saturable process with 75 +/- 12 fmol (-) [3H] alprenolol bound/mg protein (mean +/- SEM) at saturation, corresponding to about 2,000 sites/cell. Half-maximal saturation occurred at 10 nM (-) [3H] alprenolol, which provides an estimate of the dissociation constant of (-) [3H] alprenolol for the beta-adrenergic receptor. The beta-adrenergic antagonist, (-) propranolol, potently competed for the binding sites, causing half-maximal inhibition of binding at 9 nM. beta-Adrenergic agonists also competed for the binding sites. The order of potency was (-) isoproterenol greater than (-) epinephrine greater than (-)-norepinephrine which agreed with the order of potency of these agents in stimulating leukocyte adenylate cyclase. Dissociation constants computed from binding experiments were virtually identical to those obtained from adenylate cyclase activation studies. Marked stereospecificity was observed for both binding and activation of adenylate cyclase. (-)Stereoisomers of beta-adrenergic agonists and antagonists were 9- to 300-fold more potent than their corresponding (+) stereoisomers. Structurally related compounds devoid of beta-adrenergic activity such as dopamine, dihydroxymandelic acid, normetanephrine, pyrocatechol, and phentolamine did not effectively compete for the binding sites. (-) [3H] alprenolol binding to human mononuclear leukocyte preparations was almost entirely accounted for by binding to small lymphocytes, the predominant cell type in the preparations. No binding was detectable to human erythrocytes. These results demonstrate the feasibility of using direct binding methods to study beta-adrenergic receptors in a human tissue. They also provide an experimental approach to the study of states of altered sensitivity to catecholamines at the receptor level in man.

Spending on postapproval drug safety.

Withdrawals of high-profile pharmaceuticals have focused attention on post-approval safety surveillance. There have been no systematic assessments of spending on postapproval safety. We surveyed drug manufacturers regarding safety efforts. Mean spending on postapproval safety per company in 2003 was 56 million dollars (0.3 percent of sales). Assuming a constant safety-to-sales ratio, we estimated that total spending on postapproval safety by the top twenty drug manufacturers was 800 million dollars in 2003. We also examined, using regression analysis, the relationship between the number of safety personnel and the number of initial adverse-event reports. This study offers information for the debate on proposed changes to safety surveillance.

Sticky central limit theorems on open books

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fréchet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine.We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky). © Institute of Mathematical Statistics, 2013.

Locomotor head movements and semicircular canal morphology in primates.

Animal locomotion causes head rotations, which are detected by the semicircular canals of the inner ear. Morphologic features of the canals influence rotational sensitivity, and so it is hypothesized that locomotion and canal morphology are functionally related. Most prior research has compared subjective assessments of animal "agility" with a single determinant of rotational sensitivity: the mean canal radius of curvature (R). In fact, the paired variables of R and body mass are correlated with agility and have been used to infer locomotion in extinct species. To refine models of canal functional morphology and to improve locomotor inferences for extinct species, we compare 3D vector measurements of head rotation during locomotion with 3D vector measures of canal sensitivity. Contrary to the predictions of conventional models that are based upon R, we find that axes of rapid head rotation are not aligned with axes of either high or low sensitivity. Instead, animals with fast head rotations have similar sensitivities in all directions, which they achieve by orienting the three canals of each ear orthogonally (i.e., along planes at 90° angles to one another). The extent to which the canal configuration approaches orthogonality is correlated with rotational head speed independent of body mass and phylogeny, whereas R is not.