Algorithms for Kullback-Leibler Approximation of Probability Measures in Infinite Dimensions

In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the Kullback-Leibler divergence as a distance and find the best Gaussian approximation by minimizing this distance. It then follows that the approximate Gaussian must be equivalent to the Gaussian reference measure, defining a natural function space setting for the underlying calculus of variations problem. We introduce a computational algorithm which is well-adapted to the required minimization, seeking to find the mean as a function, and parameterizing the covariance in two different ways: through low rank perturbations of the reference covariance; and through Schr\"odinger potential perturbations of the inverse reference covariance. Two applications are shown: to a nonlinear inverse problem in elliptic PDEs, and to a conditioned diffusion process. We also show how the Gaussian approximations we obtain may be used to produce improved pCN-MCMC methods which are not only well-adapted to the high-dimensional setting, but also behave well with respect to small observational noise (resp. small temperatures) in the inverse problem (resp. conditioned diffusion).Comment: 28 page

Air quality in the Industrial Heartland of Alberta, Canada and potential impacts on human health.

The "Industrial Heartland" of Alberta is Canada's largest hydrocarbon processing center, with more than 40 major chemical, petrochemical, and oil and gas facilities. Emissions from these industries affect local air quality and human health. This paper characterizes ambient levels of 77 volatile organic compounds (VOCs) in the region using high-precision measurements collected in summer 2010. Remarkably strong enhancements of 43 VOCs were detected, and concentrations in the industrial plumes were often similar to or even higher than levels measured in some of the world's largest cities and industrial regions. For example maximum levels of propene and i-pentane exceeded 100 ppbv, and 1,3-butadiene, a known carcinogen, reached 27 ppbv. Major VOC sources included propene fractionation, diluent separation and bitumen processing. Emissions of the measured VOCs increased the hydroxyl radical reactivity (kOH), a measure of the potential to form downwind ozone, from 3.4 s-1 in background air to 62 s-1 in the most concentrated plumes. The plume value was comparable to polluted megacity values, and acetaldehyde, propene and 1,3-butadiene contributed over half of the plume kOH. Based on a 13-year record (1994-2006) at the county level, the incidence of male hematopoietic cancers (leukemia and non-Hodgkin lymphoma) was higher in communities closest to the Industrial Heartland compared to neighboring counties. While a causal association between these cancers and exposure to industrial emissions cannot be confirmed, this pattern and the elevated VOC levels warrant actions to reduce emissions of known carcinogens, including benzene and 1,3-butadiene

Exact solutions for diffusive transport on heterogeneous growing domains

From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely employed to investigate diffusive processes on growing domains. However, a standard assumption is that the domain growth is spatially uniform. There are many relevant examples where this is not the case, such as the colonisation of growing gut tissue by neural crest cells. As such, it is not straightforward to disentangle the individual roles of heterogeneous growth and diffusive transport. Here we present exact solutions to models of diffusive transport on domains undergoing spatially non-uniform growth. The exact solutions are obtained via a combination of transformation, convolution and superposition techniques. We verify the accuracy of these solutions via comparison with simulations of a corresponding lattice-based random walk. We explore various domain growth functions, including linear growth, exponential growth and contraction, and oscillatory growth. Provided the domain size remains positive, we find that the derived solutions are valid. The exact solutions reveal the relationship between model parameters, such as the diffusivity and the type and rate of domain growth, and key statistics, such as the survival and splitting probabilities

Exact sharp-fronted solutions for nonlinear diffusion on evolving domains

Models of diffusive processes that occur on evolving domains are frequently employed to describe biological and physical phenomena, such as diffusion within expanding tissues or substrates. Previous investigations into these models either report numerical solutions or require an assumption of linear diffusion to determine exact solutions. Unfortunately, numerical solutions do not reveal the relationship between the model parameters and the solution features. Additionally, experimental observations typically report the presence of sharp fronts, which are not captured by linear diffusion. Here we address both limitations by presenting exact sharp-fronted solutions to a model of degenerate nonlinear diffusion on a growing domain. We obtain the solution by identifying a series of transformations that converts the model of nonlinear diffusion on a growing domain to the porous medium equation on a fixed domain, which admits known exact solutions. We determine expressions for critical time scales and domain growth rates such that the diffusive population never reaches the domain boundaries and hence the solution remains valid

Occurrence of Injuries in Runners Using Heart-Rate Zone Based Training Load

Endurance athletes on both the recreational as well as higher competitive levels have regular access to tools that allow them to measure intensity of exercise. These tools may be beneficial in limiting injuries due to overtraining. PURPOSE: The purpose of this study is to identify the effects of heart-rate zone (HRZ) training in relation to the occurrence of injuries in recreational endurance runners that participate in events 5 kilometers or longer. METHODS: This study consists of data collected from 204 survey respondents; 2 respondents were removed due to being minors. The average age of participants was 40-44 with a range of 18-79 years old. This includes 148 females, 51 males, and 2 who declined to respond. The average experience of participation in events 5 kilometers or longer was 15-19 years. Participants completed a 19-question survey consisting of which 5 were Likert style, 4 yes or no, and 6 others. The remaining 4 were select all that apply. The survey was set that it would immediately be concluded if the participant selected ‘Under 18’ for age (Q1) or that they did not participate in running events of 5 kilometers or longer (Q4). RESULTS: Statistical analysis was performed using t-tests as well as ANOVA with SPSS software. Descriptive statistics were completed using the aid of the STAT IQ provided by Qualtrics. 53.8% of participants stated that they track their heart rate during training at least half of the time. However, only 12.7% utilize HRZ as an indicator of training intensity. Runners who selected HRZ most often trained in zone 3 which is 70-80% of maximal heart rate (MHR) which corresponded to 38.5% of this population. 84.6% of participants who indicated utilizing HRZ suffered an injury while training. Their rate of injury is not statistically significant when compared to those who did not indicate HRZ as a measure of training intensity as represented by p=0.791. Common injuries include strain, tendinitis, and other as reported by participants. Participants who suffered injury were equally likely to seek treatment by a medical professional regardless if they used HRZ or not as indicated by p=1. CONCLUSION: There was little statistical significance to indicate a likelihood of training related injuries in participants who utilize HRZ markers as a training tool when compared with those who do not. Further studies in controlled performance training could show a more reliable data set

A Discriminant Analysis Model of Alaskan Biomes Based on Spatial Climatic and Environmental Data

Classification of high-latitude landscapes into their appropriate biomes is important for many climate and global change-related issues. Unfortunately, large-scale, high-spatial-resolution observations of plant assemblages associated with these regions are generally unavailable, so accurate modeling of plant assemblages and biome boundaries is often needed. We built different discriminant analysis models and used them to “convert” various combinations of spatial climatic data (surface temperature and precipitation) and spatial environmental data (topography, soil, permafrost) into a biome-level map of Alaska. Five biomes (alpine tundra and ice fi elds, Arctic tundra, shrublands, boreal forest, and coastal rainforest) and one biome transition zone are modeled. Mean annual values of climatic variables were less useful than their annual extrema in this context. A quadratic discriminant analysis, combined with climate, topography, permafrost, and soil information, produced the most accurate Alaskan biome classification (skill = 74% when compared to independent data). The multivariate alteration detection transformation was used to identify Climatic Transition Zones (CTZs) with large interannual variability, and hence, less climatic consistency than other parts of Alaska. Biome classification was the least accurate in the CTZs, leading to the conclusion that large interannual climatic variability does not favor a unique biome. We interpret the CTZs as “transition biome areas” or ecotones between the five “core biomes” cited above. Both disturbance events (e.g., fires and subsequent plant succession sequences) and the partial intersection of the environmental variables used to characterize Alaskan biomes further complicate biome classification. Alaskan results obtained from the data-driven quadratic discriminant model compare favorably (based on Kappa statistics) with those produced by an equilibrium-based biome model for regions of Canada ecologically similar to the biomes we studied in Alaska. Climatic statistics are provided for each biome studied. Le classement des paysages de hautes latitudes dans les biomes adéquats revêt de l'importance dans le cadre de nombreux enjeux relatifs aux changements climatiques et à d'autres changements d'envergure mondiale. Malheureusement et en règle générale, il n'existe pas d'observations spatiales de haute résolution et à grande échelle pour ce qui est des assemblages de végétaux pour ces régions. C'est pourquoi il faut souvent procéder à la modélisation des assemblages de végétaux et des limites des biomes. Nous avons élaboré différents modèles d'analyses discriminantes dont nous nous sommes servis pour « transformer » divers ensembles de données climatiques spatiales (température de la surface et précipitation) et diverses données sur l'environnement spatial (topographie, sol, pergélisol) en carte des biomes de l'Alaska. La modélisation porte sur cinq biomes (toundra alpine et champs de glace, toundra arctique, arbustaie, forêt boréale et forêt pluviale côtière) et sur une zone de transition de biome. Les valeurs moyennes annuelles des variables climatiques ont été moins utiles que leurs extremas annuels dans ce contexte. Une analyse discriminante quadratique, combinée aux données relatives au climat, à la topographie, au pergélisol et au sol, a permis d'aboutir au classement de biomes alaskiens le plus précis (habileté = 74 % lorsque comparé aux données indépendantes). Nous avons recouru à la transformation de la détection de l'altération à variables multiples (multivariate alteration detection transformation) pour identifi er les zones de transition climatique (ZTC) ayant une importante variabilité interannuelle et, par conséquent, une moins grande uniformité climatique que d'autres parties de l'Alaska. Le classement des biomes était moins précis dans les ZTC, ce qui nous a amenés à conclure que l'importante variabilité climatique interannuelle ne favorise pas un biome unique. Nous interprétons les ZTC comme des « régions de biomes de transition » ou des écotones entre les cinq « biomes principaux » dont il est question ci-dessus. Les deux perturbations (c'est-à-dire les incendies et les séquences subséquentes des végétaux) et l'intersection partielle des variables environnementales utilisées pour caractériser les biomes alaskiens compliquent davantage le classement des biomes. Les résultats alaskiens obtenus à partir du modèle discriminant quadratique dérivant des données se comparent favorablement (en fonction des statistiques kappa) à ceux obtenus par un modèle de biome en équilibre pour des régions du Canada similaires du point de vue écologique aux biomes que nous avons étudiés en Alaska. Des statistiques climatiques sont fournies pour chaque biome étudié

Speaker sex effects on temporal and spectro-temporal measures of speech

This study investigated speaker sex differences in the temporal and spectro-temporal parameters of English monosyllabic words spoken by thirteen women and eleven men. Vowel and utterance duration were investigated. A number of formant frequency parameters were also analysed to assess the spectro-temporal dynamic structures of the monosyllabic words as a function of speaker sex. Absolute frequency changes were measured for the first (F1), second (F2), and third (F3) formant frequencies (ΔF1, ΔF2, and ΔF3, respectively). Rates of these absolute formant frequency changes were also measured and calculated to yield measurements for rF1, rF2, and rF3. Normalised frequency changes (normΔF1, normΔF2, and normΔF3), and normalised rates of change (normrF1, normrF2, and normrF3) were also calculated. F2 locus equations were then derived from the F2 measurements taken at the onset and temporal mid points of the vowels. Results indicated that there were significant sex differences in the spectro-temporal parameters associated with F2: ΔF2, normΔF2, rF2, and F2 locus equation slopes; women displayed significantly higher values for ΔF2, normΔF2 and rF2, and significantly shallower F2 locus equation slopes. Collectively, these results suggested lower levels of coarticulation in the speech samples of the women speakers, and corroborate evidence reported in earlier studies

Diffusive gradients in thin films technique provide robust prediction of metal bioavailability and toxicity in estuarine sediments

Many sediment quality assessment frameworks incorporate contaminant bioavailability as a critical factor regulating toxicity in aquatic ecosystems. However, current approaches do not always adequately predict metal bioavailability to organisms living in the oxidised sediment surface layers. The deployment of the diffusive gradients in thin films (DGT) probes in sediments allows labile metals present in pore waters and weakly-bound to the particulate phase to be assessed in a time-integrated manner in situ. In this study, relationships between DGT-labile metal fluxes within 5 mm of the sediment-water interface and lethal and sub-lethal effects to the amphipod Melita plumulosa were assessed in a range of contaminated estuarine sediments during 10-day laboratory-based bioassays. To account for differing toxicities of metals, DGT fluxes were normalised to water (WQG) or sediment quality guidelines or toxicity thresholds specific for the amphipod. The better dose-response relationships appeared to be the one based on WQG-normalized DGT fluxes, which successfully predicted toxicity despite the wide range of metals and large variations in sediment properties. The study indicated that the labile fraction of metals measured by DGT is useful for predicting metal toxicity to benthic invertebrates, supporting the applicability of this technique as a rapid monitoring tool for sediments quality assessments

Processes controlling metal transport and retention as metal-contaminated groundwaters efflux through estuarine sediments

Factors affecting the transport and retention of Cd, Cr, Cu, Ni, Pb and Zn in acidic groundwaters as they pass through estuarine sediments were investigated using column experiments. Acidic groundwaters caused the rapid dissolution of iron sulfide (AVS) and other iron and manganese phases from sediments that are important for metal binding and buffering. Metal breakthrough to overlying water occurred in the order of Ni\u3eZn\u3eCd\u3e\u3eCu\u3e\u3eCr/Pb. Metal transport increased as the sediment permeability increased, reflecting the low resistance to flow caused by larger sand-sized particles and the decreased abundance of metal adsorption sites on these materials. Metal mobility increased as the groundwater pH decreased, as flow rate or metal concentrations increased, and as the exposure duration increased. Groundwater Cr and Pb were promptly attenuated by the sediments, the mobility of Cu was low and decreased rapidly as sediment pH increased above 4.5, while Cd, Ni and Zn were the most easily transported to the surface sediments and released to the overlying waters. For groundwaters of pH 3, metal migration velocities through sandy sediments were generally 0.5-2% (Cr, Pb), 1-6% (Cu) and 4-13% (Cd, Ni, Zn) of the total groundwater velocity (9-700 m/year). The oxidative precipitation of Fe(II) and Mn(II) in the groundwaters did not affect metal mobility through the sediments. The results indicated that the efflux of acidic and metal-contaminated groundwater through estuarine sediments would affect organisms resident in sandy sediments more greatly than organisms resident in fine-grained, silty, sediments