The calculation of expectations for classes of diffusion processes by Lie symmetry methods

This paper uses Lie symmetry methods to calculate certain expectations for a large class of It\^{o} diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form $E_x(e^{-\lambda X_t-\int_0^tg(X_s) ds})$ can be reduced to evaluating a single integral of known functions. Given a drift $f$ we determine the functions $g$ for which the corresponding functional can be calculated by symmetry. Conversely, given $g$, we can determine precisely those drifts $f$ for which the transition density and the functional may be computed by symmetry. Many examples are presented to illustrate the method.Comment: Published in at http://dx.doi.org/10.1214/08-AAP534 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Lie Symmetry Methods for Multidimensional Linear, Parabolic PDES and Diffusions

In this paper we introduce methods based upon Lie symmetry analysis for the construction of explicit fundamental solutions of multidimensional parabolic PDEs. We give applications to the problem of finding transition probability densities for multidimensional diffusions and to representation theory.Lie symmetry groups; fundamental solutions; transition densities; representation theory

Lie Group Symmetries as Integral Transforms of Fundamental Solutions

We obtain fundamental solutions for PDEs of the form ut = x uxx +f(x)ux ??xru by showing that if the symmetry group of the PDE is nontrivial, it contains a standard integral transform of the fundamental solution. We show that in this case, the problem of finding a fundamental solution can be reduced to inverting a Laplace transform or some other classical transform.lie symmetry groups; fundamental solutions; transition densities; short range models; zero coupon bond pricing

Price effects of an emissions trading scheme in New Zealand

Implementation of a New Zealand Emission Trading Scheme (NZ ETS) will begin in 2008, beginning with forestry, subsequently including energy and industrial emissions, and finally, agricultural GHGs from 2013. Reducing agricultural emissions is a major challenge for New Zealand as they account for over half its total GHG emissions. On the other hand, agriculture is critical to the economy, with its basic and processed products accounting for a third of exports. We use an environmental input-output model to analyse direct and indirect cost impacts of emissions pricing on food and fibre sectors. At NZ $25/t CO₂-eq, costs of energy-related emissions on the food and fibre sectors are very small; however, costs of agricultural emissions post 2013 would substantially impact on sheep, beef and dairy farming. Costeffective mitigation measures and land use changes should help reduce micro- and macroeconomic impacts, but the latter may also risk 'emissions leakage'.emissions trading, input-output price model, agricultural greenhouse gases, Demand and Price Analysis, Environmental Economics and Policy, Land Economics/Use,

Salmonella Infection After Craniotomy.

Salmonella is an uncommon cause of meningitis, especially after neurosurgery. Here, we present a case of Salmonella meningitis after craniotomy, likely due to physical contact with a snake after surgery, with contiguous spread from the patient's hand to her wound. The purpose of this report is to serve as a reminder that patients undergoing neurosurgery should avoid contact with pets, including snakes and other reptiles, in the postoperative period and practice good hand hygiene

The Density of Lyman-alpha Emitters at Very High Redshift

We describe narrowband and spectroscopic searches for emission-line star forming galaxies in the redshift range 3 to 6 with the 10 m Keck II Telescope. These searches yield a substantial population of objects with only a single strong (equivalent width >> 100 Angstrom) emission line, lying in the 4000 - 10,000 Angstrom range. Spectra of the objects found in narrowband-selected samples at lambda ~5390 Angstroms and ~6741 Angstroms show that these very high equivalent width emission lines are generally redshifted Lyman alpha 1216 Angstrom at z~3.4 and 4.5. The density of these emitters above the 5 sigma detection limit of 1.5 e-17 ergs/cm^2/s is roughly 15,000 per square degree per unit redshift interval at both z~3.4 and 4.5. A complementary deeper (1 sigma \~1.0 e-18 ergs/cm^2/s) slit spectroscopic search covering a wide redshift range but a more limited spatial area (200 square arcminutes) shows such objects can be found over the redshift range 3 to 6, with the currently highest redshift detected being at z=5.64. The Lyman alpha flux distribution can be used to estimate a minimum star formation rate in the absence of reddening of roughly 0.01 solar masses/Mpc^3/year (H_0 = 65 km/s/Mpc and q_0 = 0.5). Corrections for reddening are likely to be no larger than a factor of two, since observed equivalent widths are close to the maximum values obtainable from ionization by a massive star population. Within the still significant uncertainties, the star formation rate from the Lyman alpha-selected sample is comparable to that of the color-break-selected samples at z~3, but may represent an increasing fraction of the total rates at higher redshifts. This higher-z population can be readily studied with large ground-based telescopes.Comment: 7 pages, 5 encapsulated figures; aastex, emulateapj, psfig and lscape style files. Separate gif files for 2 gray-scale images also available at http://www.ifa.hawaii.edu/faculty/hu/emitters.html . Added discussion of foreground contaminants. Updated discussion of comparison with external surveys (Sec. 5 and Fig. 5). Note: continuum break strength limits (Fig. 3 caption) are correct here -- published ApJL text has a sign erro

Comprehensive health assessments during de-institutionalization: An observational study

Background: People with intellectual disability (ID) leaving institutions pass through a transition stage that makes them vulnerable to inadequate health care. They enter into community care under general practitioners (GPs) who are often untrained and inexperienced in their needs. Specifically designed health reviews may be of assistance to both them and their new GPs as they go through that phase

Peer mentorship and positive effects on student mentor and mentee retention and academic success

This study examined how the introduction of peer mentorship in an undergraduate health and social welfare programme at a large northern university affected student learning. Using an ethnographic case study approach, the study draws upon data collected from a small group of mentors and their mentees over a period of one academic year using interviews, reflective journals, assessment and course evaluation data. Analysis of the data collected identified a number of key findings: peer mentorship improves assessment performance for both mentee and mentor; reduces stress and anxiety, enhances participation and engagement in the academic community, and adds value to student outcomes

Galaxy Halo Masses from Galaxy-Galaxy Lensing

We present measurements of the extended dark halo profiles of bright early type galaxies at redshifts 0.1 to 0.9 obtained via galaxy-galaxy lensing analysis of images taken at the CFHT using the UH8K CCD mosaic camera. Six half degree fields were observed for a total of 2 hours each in I and V, resulting in catalogs containing ~20 000 galaxies per field. We used V-I color and I magnitude to select bright early type galaxies as the lens galaxies, yielding a sample of massive lenses with fairly well determined redshifts and absolute magnitudes M ~ M_* \pm 1. We paired these with faint galaxies lying at angular distances 20" to 60", corresponding to physical radii of 26 to 77 kpc (z = 0.1) and 105 to 315 kpc (z = 0.9), and computed the mean tangential shear of the faint galaxies. The shear falls off with radius roughly as expected for flat rotation curve halos. The shear values were weighted in proportion to the square root of the luminosity of the lens galaxy. Our results give a value for the average mean rotation velocity of an L_* galaxy halo at r~50-200 kpc of v_* = 238^{+27}_{-30} km per sec for a flat lambda (Omega_m0 = 0.3, Omega_l0 = 0.7) cosmology (v_* = 269^{+34}_{-39} km per sec for Einstein-de Sitter), and with little evidence for evolution with redshift. We compare to halo masses measured by other groups/techniques. We find a mass-to-light ratio of ~121\pm28h(r/100 kpc) and these halos constitute Omega ~0.04 \pm 0.01(r/100 kpc) of closure density. (abridged)Comment: Accepted for publication in ApJ (minor modifications) - 32 pages, 11 figs, 5 table