Technology: a cross-curricular catalyst

This paper reports results of the first year of an innovative cross-curricular project. The technology laboratory (TEC-Lab) serves as the setting for classes in geometry, government, economics, literature, physical science and technology. TEC-Lab is used in grades 9 through 12 (ages 15-18) in a Texas (USA.) high school for their usual academic pursuits. TEC-Lab incorporates a wide range of technologies, including computers, audio and video equipment, computer numerically controlled (CNC) machine tools, and satellite communication equipment. Comparisons are made between the achievement of students who studied in the TEC-Lab environment and the achievement of students who studied the subjects with the same teachers in regular classrooms. Changes in attitude toward technology are compared between students who worked in the TEC-Lab and students who worked in regular classrooms. Also, attitude shifts are compared among students who studied the respective subjects

Covariance-based rational approximations of fractional SPDEs for computationally efficient Bayesian inference

The stochastic partial differential equation (SPDE) approach is widely used for modeling large spatial datasets. It is based on representing a Gaussian random field $u$ on $\mathbb{R}^d$ as the solution of an elliptic SPDE $L^\beta u = \mathcal{W}$ where $L$ is a second-order differential operator, $2\beta$ (belongs to natural number starting from 1) is a positive parameter that controls the smoothness of $u$ and $\mathcal{W}$ is Gaussian white noise. A few approaches have been suggested in the literature to extend the approach to allow for any smoothness parameter satisfying $\beta>d/4$. Even though those approaches work well for simulating SPDEs with general smoothness, they are less suitable for Bayesian inference since they do not provide approximations which are Gaussian Markov random fields (GMRFs) as in the original SPDE approach. We address this issue by proposing a new method based on approximating the covariance operator $L^{-2\beta}$ of the Gaussian field $u$ by a finite element method combined with a rational approximation of the fractional power. This results in a numerically stable GMRF approximation which can be combined with the integrated nested Laplace approximation (INLA) method for fast Bayesian inference. A rigorous convergence analysis of the method is performed and the accuracy of the method is investigated with simulated data. Finally, we illustrate the approach and corresponding implementation in the R package rSPDE via an application to precipitation data which is analyzed by combining the rSPDE package with the R-INLA software for full Bayesian inference

Gaussian Whittle-Mat\'ern fields on metric graphs

We define a new class of Gaussian processes on compact metric graphs such as street or river networks. The proposed models, the Whittle--Mat\'ern fields, are defined via a fractional stochastic differential equation on the compact metric graph and are a natural extension of Gaussian fields with Mat\'ern covariance functions on Euclidean domains to the non-Euclidean metric graph setting. Existence of the processes, as well as some of their main properties, such as sample path regularity are derived. The model class in particular contains differentiable processes. To the best of our knowledge, this is the first construction of a differentiable Gaussian process on general compact metric graphs. Further, we prove an intrinsic property of these processes: that they do not change upon addition or removal of vertices with degree two. Finally, we obtain Karhunen--Lo\`eve expansions of the processes, provide numerical experiments, and compare them to Gaussian processes with isotropic covariance functions.Comment: 28 pages, 4 figure

Wasserstein complexity penalization priors: a new class of penalizing complexity priors

Penalizing complexity (PC) priors is a principled framework for designing priors that reduce model complexity. PC priors penalize the Kullback-Leibler Divergence (KLD) between the distributions induced by a ``simple'' model and that of a more complex model. However, in many common cases, it is impossible to construct a prior in this way because the KLD is infinite. Various approximations are used to mitigate this problem, but the resulting priors then fail to follow the designed principles. We propose a new class of priors, the Wasserstein complexity penalization (WCP) priors, by replacing KLD with the Wasserstein distance in the PC prior framework. These priors avoid the infinite model distance issues and can be derived by following the principles exactly, making them more interpretable. Furthermore, principles and recipes to construct joint WCP priors for multiple parameters analytically and numerically are proposed and we show that they can be easily obtained, either numerically or analytically, for a general class of models. The methods are illustrated through several examples for which PC priors have previously been applied

Rotation periods and colours of 10-m scale near-Earth asteroids from CFHT target of opportunity streak photometry

The rotational properties of $\sim$10~m-scale asteroids are poorly understood with only a few measurements. Additionally, collisions or thermal recoil can spin their rotations to periods less than a few seconds obfuscating their study due to the observational cadence imposed by the long read-out times of charge-coupled device imagers. We present a method to measure the rotation periods of 10~m-scale asteroids using the target of opportunity capability of the Canada France Hawaii Telescope and its MegaCam imager by intentionally streaking their detections in single exposures when they are at their brightest. Periodic changes in brightness as small as $\sim$0.05 mag along the streak can be measured as short as a few seconds. Additionally, the streak photometry is taken in multiple g, r, and i filter exposures enabling the measurement of asteroid colours. The streak photometry method was tested on CFHT observations of three 10~m-scale asteroids, 2016 GE$_1$, 2016 CG$_{18}$, and 2016 EV$_{84}$. Our 3 targets are among the smallest known asteroids with measured rotation periods/colours having some of the shortest known rotation periods. We compare our rotation period and taxonomic results with independent data from the literature and discuss applications of the method to future small asteroid observations.Comment: Revised version, MNRAS:L, 13 pages, 10 figures, 3 table

Regularity and numerical approximation of fractional elliptic differential equations on compact metric graphs

The fractional differential equation $L^\beta u = f$ posed on a compact metric graph is considered, where $\beta>0$ and $L = \kappa^2 - \nabla(a\nabla)$ is a second-order elliptic operator equipped with certain vertex conditions and sufficiently smooth and positive coefficients $\kappa, a$. We demonstrate the existence of a unique solution for a general class of vertex conditions and derive the regularity of the solution in the specific case of Kirchhoff vertex conditions. These results are extended to the stochastic setting when $f$ is replaced by Gaussian white noise. For the deterministic and stochastic settings under generalized Kirchhoff vertex conditions, we propose a numerical solution based on a finite element approximation combined with a rational approximation of the fractional power $L^{-\beta}$. For the resulting approximation, the strong error is analyzed in the deterministic case, and the strong mean squared error as well as the $L_2(\Gamma\times \Gamma)$-error of the covariance function of the solution are analyzed in the stochastic setting. Explicit rates of convergences are derived for all cases. Numerical experiments for ${L = \kappa^2 - \Delta, \kappa>0}$ are performed to illustrate the results.Comment: Accepted for publication in Mathematics of Computatio

MPEC 2020-A99: 2020 AV2

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In Vivo Quantitation of Adipose Tissue by Differential Absorptiometry Using Penetrating Isotopic Radiation

The physical principles for determining tissue lipid content In vivo by selective radiation attenuation have been studied and are compared to other methods of body composition analysis. Two penetrating photon beams, each monoenergetic but of differing energies, are simultaneously passed through the low Z components of tissue and the relative beam absorption measured. A mathematical function incorporating the unabsorbed and absorbed photon beam intensities is applied to determine experimentally the relative proportion of fat and lean in the tissue. \u27 Cd is used as the radioactive source of both xrays and gamma radiation. Results of experiments on low 2 phantom material and in vitro animal tissue indicate that the dual photon absorption principle provides accurate two-component quantitation. The fractional lipid content of in vitro mammalian tissue samples has been determined by dual beam photon absorption, with an error of less than 2%. In vivo values are reproducible to better than 2%. Skinfold thickness was measured simultaneously in vivo with adipose tissue content by dual beam absorptiometry. The experimental coefficient of correlation between these two measurements was .98

A Study of the Persistence of Mycobacterium bovis in the Environment under Natural Weather Conditions in Michigan, USA

Reisolation of Mycobacterium bovis from inoculated substrates was used to follow the persistence of viable M. bovis bacteria exposed to natural weather conditions over a 12-month period. Environmental factors were recorded continuously, and factors affecting M. bovis persistence (i.e., temperature, season, and substrate) were studied using survival analysis and Cox's proportional hazards regression. Persistence of M. bovis in the environment was significantly shorter in the spring/summer season, characterized by the highest average daily temperatures over the 12-month period. M. bovis persisted up to 88 days in soil, 58 days in water and hay, and 43 days on corn. These studies demonstrate that M. bovis bacteria persist long enough to represent a risk of exposure for cattle and/or wildlife and strengthen evidence that suggests cattle farm biosecurity and efforts to eliminate supplemental feeding of white-tailed deer will decrease the risk of bovine TB transmission among and between cattle and deer populations