Marshall's Lemma for Convex Density Estimation

Marshall's (1970) lemma is an analytical result which implies root-n-consistency of the distribution function corresponding to the Grenander (1956) estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0,\infty).

The First Density Estimation of an Isolated Eurasian Lynx Population in Southwest Asia

During November 2010–February 2011, we used camera traps to estimate the population density of Eurasian lynx Lynx lynx in Ciglikara Nature Reserve, Turkey, an isolated population in southwest Asia. Lynx density was calculated through spatial capture—recapture models. In a sampling eff ort of 1093 camera trap days, we identifi ed 15 independent individuals and estimated a density of 4.20 independent lynx per 100 km2, an unreported high density for this species. Camera trap results also indicated that the lynx is likely to be preying on brown hare Lepus europaeus, which accounted for 63% of the non-target species pictured. As lagomorph populations tend to fl uctuate, the high lynx density recorded in Ciglikara may be temporary and may decline with prey fl uctuation. Therefore we recommend to survey other protected areas in southwestern Turkey where lynx is known or assumed to exist, and continuously monitor the lynx populations with reliable methods in order to understand the populations structure and dynamics, defi ne sensible measures and management plans to conserve this important species.

KDENS: Stata module for univariate kernel density estimation

kdens produces univariate kernel density estimates and graphs the result. kdens supplements official Stata's kdensity. Important additions are: adaptive (i.e. variable bandwidth) kernel density estimation, several automatic bandwidth selectors including the Sheather-Jones plug-in estimator, pointwise variability bands and confidence intervals, boundary correction for variables with bounded domain, fast binned approximation estimation. Note that the moremata package, also available from SSC, is required.

Non-invasive quantitative estimation of bone density in rats throughout the life cycle and in arthritic osteopenia: preliminary results

A longitudinal bone survey was conducted in 86 female Wistar rats in order to assess mineral density kinetics from young age (5 weeks: 115 g) till late adulthood (64 weeks: 586 g). In vivo quantitative radiographic scanning was performed on the caudal vertebrae, taking trabecular mass as the parameter. Measurements were expressed as Relative Optical Density (ROD) units by means of a high resolution densitometric device. Results showed a progressive increase in mineral density throughout the life cycle, with a tendency to level in the higher weight range, indicating that progressive mineral aposition occurs in rats in dependency of age. This phenomenon, however, should be always considered within the context of continuous skeletal growth and related changes typical of this species. Twelve different animals were also examined following induction of articular inflammation with Freund's adjuvant in six of them. Bone survey conducted 12 to 18 days after inoculation revealed a significant (P less than 0.01) reduction in trabecular bone mass of scanned vertebrae in comparison with the weight-matched untreated controls. It is concluded that the in vivo quantitative assessment of bone density illustrated in this report represents a sensitive and useful tool for the long-term survey of naturally occurring or experimentally induced bone changes. Scanning of the same part of the skeleton can be repeated, thereby avoiding sacrifice of the animal and time-consuming preparation of post-mortem material.

Estimation of tool pose based on force-density correlation during robotic drilling

The application of image-guided systems with or without support by surgical robots relies on the accuracy of the navigation process, including patient-to-image registration. The surgeon must carry out the procedure based on the information provided by the navigation system, usually without being able to verify its correctness beyond visual inspection. Misleading surrogate parameters such as the fiducial registration error are often used to describe the success of the registration process, while a lack of methods describing the effects of navigation errors, such as those caused by tracking or calibration, may prevent the application of image guidance in certain accuracy-critical interventions. During minimally invasive mastoidectomy for cochlear implantation, a direct tunnel is drilled from the outside of the mastoid to a target on the cochlea based on registration using landmarks solely on the surface of the skull. Using this methodology, it is impossible to detect if the drill is advancing in the correct direction and that injury of the facial nerve will be avoided. To overcome this problem, a tool localization method based on drilling process information is proposed. The algorithm estimates the pose of a robot-guided surgical tool during a drilling task based on the correlation of the observed axial drilling force and the heterogeneous bone density in the mastoid extracted from 3-D image data. We present here one possible implementation of this method tested on ten tunnels drilled into three human cadaver specimens where an average tool localization accuracy of 0.29 mm was observed.

Noninvasive estimation of organ weights by postmortem magnetic resonance imaging and multislice computed tomography

OBJECTIVE: Computed tomography (CT) and magnetic resonance imaging (MRI) are introduced as an alternative to traditional autopsy. The purpose of this study was to investigate their accuracy in mass estimation of liver and spleen. METHODS: In 44 cases, the weights of spleen and liver were estimated based on MRI and CT data using a volume-analysis software and a postmortem tissue-specific density factor. In a blinded approach, the results were compared with the weights noted at autopsy. RESULTS: Excellent correlation between estimated and real weights (r = 0.997 for MRI, r = 0.997 for CT) was found. Putrefaction gas and venous air embolism led to an overestimation. Venous congestion and drowning caused higher estimated weights. CONCLUSION: Postmortem weights of liver and spleen can accurately be assessed by nondestructive imaging. Multislice CT overcomes the limitation of putrefaction and venous air embolism by the possibility to exclude gas. Congestion seems to be even better assessed.

Low bone mineral density, renal dysfunction, and fracture risk in HIV infection: a cross-sectional study

BACKGROUND: Reduced bone mineral density (BMD) is common in adults infected with human immunodeficiency virus (HIV). The role of proximal renal tubular dysfunction (PRTD) and alterations in bone metabolism in HIV-related low BMD are incompletely understood. METHODS: We quantified BMD (dual-energy x-ray absorptiometry), blood and urinary markers of bone metabolism and renal function, and risk factors for low BMD (hip or spine T score, -1 or less) in an ambulatory care setting. We determined factors associated with low BMD and calculated 10-year fracture risks using the World Health Organization FRAX equation. RESULTS: We studied 153 adults (98% men; median age, 48 years; median body mass index, 24.5; 67 [44%] were receiving tenofovir, 81 [53%] were receiving a boosted protease inhibitor [PI]). Sixty-five participants (42%) had low BMD, and 11 (7%) had PRTD. PI therapy was associated with low BMD in multivariable analysis (odds ratio, 2.69; 95% confidence interval, 1.09-6.63). Tenofovir use was associated with increased osteoblast and osteoclast activity (P< or = .002). The mean estimated 10-year risks were 1.2% for hip fracture and 5.4% for any major osteoporotic fracture. CONCLUSIONS: In this mostly male population, low BMD was significantly associated with PI therapy. Tenofovir recipients showed evidence of increased bone turnover. Measurement of BMD and estimation of fracture risk may be warranted in treated HIV-infected adults.

Calculation of crystal optical properties from molecular electron density

We have recently developed a method to obtain distributed atomic polarizabilities adopting a partitioning of the molecular electron density (for example, the Quantum Theory of Atoms in Molecules, [1]), calculated with or without an applied electric field. The procedure [2] allows to obtained atomic polarizability tensors, which are perfectly exportable, because quite representative of an atom in a given functional group. Among the many applications of this idea, the calculation of crystal susceptibility is easily available, either from a rough estimation (the polarizability of the isolated molecule is used) or from a more precise estimation (the polarizability of a molecule embedded in a cluster representing the first coordination sphere is used). Lorentz factor is applied to include the long range effect of packing, which is enhancing the molecular polarizability. Simple properties like linear refractive index or the gyration tensor can be calculated at relatively low costs and with good precision. This approach is particularly useful within the field of crystal engineering of organic/organometallic materials, because it would allow a relatively easy prediction of a property as a function of the packing, thus allowing "reverse crystal engineering". Examples of some amino acid crystals and salts of amino acids [3] will be illustrated, together with other crystallographic or non-crystallographic applications. For example, the induction and dispersion energies of intermolecular interactions could be calculated with superior precision (allowing anisotropic van der Waals interactions). This could allow revision of some commonly misunderstood intermolecular interactions, like the halogen bonding (see for example the recent remarks by Stone or Gilli [4]). Moreover, the chemical reactivity of coordination complexes could be reinvestigated, by coupling the conventional analysis of the electrostatic potential (useful only in the circumstances of hard nucleophilic/electrophilic interaction) with the distributed atomic polarizability. The enhanced reactivity of coordinated organic ligands would be better appreciated. [1] R. F. W. Bader, Atoms in Molecules: A Quantum Theory. Oxford Univ. Press, 1990. [2] A. Krawczuk-Pantula, D. Pérez, K. Stadnicka, P. Macchi, Trans. Amer. Cryst. Ass. 2011, 1-25 [3] A. S. Chimpri1, M. Gryl, L. H.R. Dos Santos1, A. Krawczuk, P. Macchi Crystal Growth & Design, in the press. [4] a) A. J. Stone, J. Am. Chem. Soc. 2013, 135, 7005−7009; b) V. Bertolasi, P. Gilli, G. Gilli Crystal Growth & Design, 2013, 12, 4758-4770.