Large scale data processing using MapReduce

As massive data sets become increasingly available, people are facing the problem of how to effectively process and understand these data. Traditional sequential computing models are giving way to parallel and distributed computing models, such as MapReduce, both due to the large size of the data sets and their high dimensionality. This dissertation, as in the same direction of other researches that are based on MapReduce, tries to develop effective techniques and applications using MapReduce that can help people solve large-scale problems. Three different problems are tackled in the dissertation. The first one deals with processing terabytes of raster data in a spatial data management system. Aerial imagery files are broken into tiles to enable data parallel computation. The second and third problems deal with dimension reduction techniques that can be used to handle data sets of high dimensionality. Three variants of the nonnegative matrix factorization technique are scaled up to factorize matrices of dimensions in the order of millions in MapReduce based on different matrix multiplication implementations. Two algorithms, which compute CANDECOMP/PARAFAC and Tucker tensor decompositions respectively, are parallelized in MapReduce based on carefully partitioning the data and arranging the computation to maximize data locality and parallelism.

Text analytics of social media: Sentiment analysis, event detection and summarization

In the last decade, large numbers of social media services have emerged and been widely used in people's daily life as important information sharing and acquisition tools. With a substantial amount of user-contributed text data on social media, it becomes a necessity to develop methods and tools for text analysis for this emerging data, in order to better utilize it to deliver meaningful information to users. ^ Previous work on text analytics in last several decades is mainly focused on traditional types of text like emails, news and academic literatures, and several critical issues to text data on social media have not been well explored: 1) how to detect sentiment from text on social media; 2) how to make use of social media's real-time nature; 3) how to address information overload for flexible information needs. ^ In this dissertation, we focus on these three problems. First, to detect sentiment of text on social media, we propose a non-negative matrix tri-factorization (tri-NMF) based dual active supervision method to minimize human labeling efforts for the new type of data. Second, to make use of social media's real-time nature, we propose approaches to detect events from text streams on social media. Third, to address information overload for flexible information needs, we propose two summarization framework, dominating set based summarization framework and learning-to-rank based summarization framework. The dominating set based summarization framework can be applied for different types of summarization problems, while the learning-to-rank based summarization framework helps utilize the existing training data to guild the new summarization tasks. In addition, we integrate these techneques in an application study of event summarization for sports games as an example of how to better utilize social media data. ^

Text Analytics of Social Media: Sentiment Analysis, Event Detection and Summarization

In the last decade, large numbers of social media services have emerged and been widely used in people's daily life as important information sharing and acquisition tools. With a substantial amount of user-contributed text data on social media, it becomes a necessity to develop methods and tools for text analysis for this emerging data, in order to better utilize it to deliver meaningful information to users. Previous work on text analytics in last several decades is mainly focused on traditional types of text like emails, news and academic literatures, and several critical issues to text data on social media have not been well explored: 1) how to detect sentiment from text on social media; 2) how to make use of social media's real-time nature; 3) how to address information overload for flexible information needs. In this dissertation, we focus on these three problems. First, to detect sentiment of text on social media, we propose a non-negative matrix tri-factorization (tri-NMF) based dual active supervision method to minimize human labeling efforts for the new type of data. Second, to make use of social media's real-time nature, we propose approaches to detect events from text streams on social media. Third, to address information overload for flexible information needs, we propose two summarization framework, dominating set based summarization framework and learning-to-rank based summarization framework. The dominating set based summarization framework can be applied for different types of summarization problems, while the learning-to-rank based summarization framework helps utilize the existing training data to guild the new summarization tasks. In addition, we integrate these techneques in an application study of event summarization for sports games as an example of how to better utilize social media data.

Sobre a integração indefinida de funções racionais complexas: teoria e implementação de algoritmos racionais

We present indefinite integration algorithms for rational functions over subfields of the complex numbers, through an algebraic approach. We study the local algorithm of Bernoulli and rational algorithms for the class of functions in concern, namely, the algorithms of Hermite; Horowitz-Ostrogradsky; Rothstein-Trager and Lazard-Rioboo-Trager. We also study the algorithm of Rioboo for conversion of logarithms involving complex extensions into real arctangent functions, when these logarithms arise from the integration of rational functions with real coefficients. We conclude presenting pseudocodes and codes for implementation in the software Maxima concerning the algorithms studied in this work, as well as to algorithms for polynomial gcd computation; partial fraction decomposition; squarefree factorization; subresultant computation, among other side algorithms for the work. We also present the algorithm of Zeilberger-Almkvist for integration of hyperexpontential functions, as well as its pseudocode and code for Maxima. As an alternative for the algorithms of Rothstein-Trager and Lazard-Rioboo-Trager, we yet present a code for Benoulli’s algorithm for square-free denominators; and another for Czichowski’s algorithm, although this one is not studied in detail in the present work, due to the theoretical basis necessary to understand it, which is beyond this work’s scope. Several examples are provided in order to illustrate the working of the integration algorithms in this text

Optimización de la factorización de matrices no negativas en Bioinformática

En los últimos años se ha incrementado el interés de la comunidad científica en la Factorización de matrices no negativas (Non-negative Matrix Factorization, NMF). Este método permite transformar un conjunto de datos de grandes dimensiones en una pequeña colección de elementos que poseen semántica propia en el contexto del análisis. En el caso de Bioinformática, NMF suele emplearse como base de algunos métodos de agrupamiento de datos, que emplean un modelo estadístico para determinar el número de clases más favorable. Este modelo requiere de una gran cantidad de ejecuciones de NMF con distintos parámetros de entrada, lo que representa una enorme carga de trabajo a nivel computacional. La mayoría de las implementaciones de NMF han ido quedando obsoletas ante el constante crecimiento de los datos que la comunidad científica busca analizar, bien sea porque los tiempos de cómputo llegan a alargarse hasta convertirse en inviables, o porque el tamaño de esos datos desborda los recursos del sistema. Por ello, esta tesis doctoral se centra en la optimización y paralelización de la factorización NMF, pero no solo a nivel teórico, sino con el objetivo de proporcionarle a la comunidad científica una nueva herramienta para el análisis de datos de origen biológico. NMF expone un alto grado de paralelismo a nivel de datos, de granularidad variable; mientras que los métodos de agrupamiento mencionados anteriormente presentan un paralelismo a nivel de cómputo, ya que las diversas instancias de NMF que se ejecutan son independientes. Por tanto, desde un punto de vista global, se plantea un modelo de optimización por capas donde se emplean diferentes tecnologías de alto rendimiento...

Enhancing non-refractory aerosol apportionment from an urban industrial site through receptor modelling of complete high time-resolution aerosol mass spectra

Receptor modelling was performed on quadrupole unit mass resolution aerosol mass spectrometer (Q-AMS) sub-micron particulate matter (PM) chemical speciation measurements from Windsor, Ontario, an industrial city situated across the Detroit River from Detroit, Michigan. Aerosol and trace gas measurements were collected on board Environment Canada’s CRUISER mobile laboratory. Positive matrix factorization (PMF) was performed on the AMS full particle-phase mass spectrum (PMFFull MS) encompassing both organic and inorganic components. This approach was compared to the more common method of analysing only the organic mass spectra (PMFOrg MS). PMF of the full mass spectrum revealed that variability in the non-refractory sub-micron aerosol concentration and composition was best explained by six factors: an amine-containing factor (Amine); an ammonium sulphate and oxygenated organic aerosol containing factor (Sulphate-OA); an ammonium nitrate and oxygenated organic aerosol containing factor (Nitrate-OA); an ammonium chloride containing factor (Chloride); a hydrocarbon like organic aerosol (HOA) factor; and a moderately oxygenated organic aerosol factor (OOA). PMF of the organic mass spectrum revealed three factors of similar composition to some of those revealed through PMFFull MS: Amine, HOA and OOA. Including both the inorganic and organic mass proved to be a beneficial approach to analysing the unit mass resolution AMS data for several reasons. First, it provided a method for potentially calculating more accurate sub-micron PM mass concentrations, particularly when unusual factors are present, in this case, an Amine factor. As this method does not rely on a priori knowledge of chemical species, it circumvents the need for any adjustments to the traditional AMS species fragmentation patterns to account for atypical species, and can thus lead to more complete factor profiles. It is expected that this method would be even more useful for HR-ToF-AMS data, due to the ability to better understand the chemical nature of atypical factors from high resolution mass spectra. Second, utilizing PMF to extract factors containing inorganic species allowed for the determination of extent of neutralization, which could have implications for aerosol parameterization. Third, subtler differences in organic aerosol components were resolved through the incorporation of inorganic mass into the PMF matrix. The additional temporal features provided by the inorganic aerosol components allowed for the resolution of more types of oxygenated organic aerosol than could be reliably re-solved from PMF of organics alone. Comparison of findings from the PMFFull MS and PMFOrg MS methods showed that for the Windsor airshed, the PMFFull MS method enabled additional conclusions to be drawn in terms of aerosol sources and chemical processes. While performing PMFOrg MS can provide important distinctions between types of organic aerosol, it is shown that including inorganic species in the PMF analysis can permit further apportionment of organics for unit mass resolution AMS mass spectra.

Characterization of urban aerosol in Cork city (Ireland) using aerosol mass spectrometry

Ambient wintertime background urban aerosol in Cork city, Ireland, was characterized using aerosol mass spectrometry. During the three-week measurement study in 2009, 93% of the ca. 1 350 000 single particles characterized by an Aerosol Time-of-Flight Mass Spectrometer (TSI ATOFMS) were classified into five organic-rich particle types, internally mixed to different proportions with elemental carbon (EC), sulphate and nitrate, while the remaining 7% was predominantly inorganic in nature. Non-refractory PM1 aerosol was characterized using a High Resolution Time-of-Flight Aerosol Mass Spectrometer (Aerodyne HR-ToF-AMS) and was also found to comprise organic aerosol as the most abundant species (62 %), followed by nitrate (15 %), sulphate (9 %) and ammonium (9 %), and chloride (5 %). Positive matrix factorization (PMF) was applied to the HR-ToF-AMS organic matrix, and a five-factor solution was found to describe the variance in the data well. Specifically, "hydrocarbon-like" organic aerosol (HOA) comprised 20% of the mass, "low-volatility" oxygenated organic aerosol (LV-OOA) comprised 18 %, "biomass burning" organic aerosol (BBOA) comprised 23 %, non-wood solid-fuel combustion "peat and coal" organic aerosol (PCOA) comprised 21 %, and finally a species type characterized by primary m/z peaks at 41 and 55, similar to previously reported "cooking" organic aerosol (COA), but possessing different diurnal variations to what would be expected for cooking activities, contributed 18 %. Correlations between the different particle types obtained by the two aerosol mass spectrometers are also discussed. Despite wood, coal and peat being minor fuel types used for domestic space heating in urban areas, their relatively low combustion efficiencies result in a significant contribution to PM1 aerosol mass (44% and 28% of the total organic aerosol mass and non-refractory total PM1, respectively).Ambient wintertime background urban aerosol in Cork city, Ireland, was characterized using aerosol mass spectrometry. During the three-week measurement study in 2009, 93% of the ca. 1 350 000 single particles characterized by an Aerosol Time-of-Flight Mass Spectrometer (TSI ATOFMS) were classified into five organic-rich particle types, internally mixed to different proportions with elemental carbon (EC), sulphate and nitrate, while the remaining 7% was predominantly inorganic in nature. Non-refractory PM1 aerosol was characterized using a High Resolution Time-of-Flight Aerosol Mass Spectrometer (Aerodyne HR-ToF-AMS) and was also found to comprise organic aerosol as the most abundant species (62 %), followed by nitrate (15 %), sulphate (9 %) and ammonium (9 %), and chloride (5 %). Positive matrix factorization (PMF) was applied to the HR-ToF-AMS organic matrix, and a five-factor solution was found to describe the variance in the data well. Specifically, "hydrocarbon-like" organic aerosol (HOA) comprised 20% of the mass, "low-volatility" oxygenated organic aerosol (LV-OOA) comprised 18 %, "biomass burning" organic aerosol (BBOA) comprised 23 %, non-wood solid-fuel combustion "peat and coal" organic aerosol (PCOA) comprised 21 %, and finally a species type characterized by primary m/z peaks at 41 and 55, similar to previously reported "cooking" organic aerosol (COA), but possessing different diurnal variations to what would be expected for cooking activities, contributed 18 %. Correlations between the different particle types obtained by the two aerosol mass spectrometers are also discussed. Despite wood, coal and peat being minor fuel types used for domestic space heating in urban areas, their relatively low combustion efficiencies result in a significant contribution to PM1 aerosol mass (44% and 28% of the total organic aerosol mass and non-refractory total PM1, respectively).

Single particle characterization using the soot particle aerosol mass spectrometer (SP-AMS)

Understanding the impact of atmospheric black carbon (BC) containing particles on human health and radiative forcing requires knowledge of the mixing state of BC, including the characteristics of the materials with which it is internally mixed. In this study, we demonstrate for the first time the capabilities of the Aerodyne Soot-Particle Aerosol Mass Spectrometer equipped with a light scattering module (LS-SP-AMS) to examine the mixing state of refractory BC (rBC) and other aerosol components in an urban environment (downtown Toronto). K-means clustering analysis was used to classify single particle mass spectra into chemically distinct groups. One resultant cluster is dominated by rBC mass spectral signals (C+1 to C+5) while the organic signals fall into a few major clusters, identified as hydrocarbon-like organic aerosol (HOA), oxygenated organic aerosol (OOA), and cooking emission organic aerosol (COA). A nearly external mixing is observed with small BC particles only thinly coated by HOA ( 28% by mass on average), while over 90% of the HOA-rich particles did not contain detectable amounts of rBC. Most of the particles classified into other inorganic and organic clusters were not significantly associated with BC. The single particle results also suggest that HOA and COA emitted from anthropogenic sources were likely major contributors to organic-rich particles with low to mid-range aerodynamic diameter (dva). The similar temporal profiles and mass spectral features of the organic clusters and the factors from a positive matrix factorization (PMF) analysis of the ensemble aerosol dataset validate the conventional interpretation of the PMF results.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Methods for Imputing Missing Values and Synthesizing Confidential Values for Continuous and Magnitude Data

Abstract

Continuous variable is one of the major data types collected by the survey organizations. It can be incomplete such that the data collectors need to fill in the missingness. Or, it can contain sensitive information which needs protection from re-identification. One of the approaches to protect continuous microdata is to sum them up according to different cells of features. In this thesis, I represents novel methods of multiple imputation (MI) that can be applied to impute missing values and synthesize confidential values for continuous and magnitude data.

The first method is for limiting the disclosure risk of the continuous microdata whose marginal sums are fixed. The motivation for developing such a method comes from the magnitude tables of non-negative integer values in economic surveys. I present approaches based on a mixture of Poisson distributions to describe the multivariate distribution so that the marginals of the synthetic data are guaranteed to sum to the original totals. At the same time, I present methods for assessing disclosure risks in releasing such synthetic magnitude microdata. The illustration on a survey of manufacturing establishments shows that the disclosure risks are low while the information loss is acceptable.

The second method is for releasing synthetic continuous micro data by a nonstandard MI method. Traditionally, MI fits a model on the confidential values and then generates multiple synthetic datasets from this model. Its disclosure risk tends to be high, especially when the original data contain extreme values. I present a nonstandard MI approach conditioned on the protective intervals. Its basic idea is to estimate the model parameters from these intervals rather than the confidential values. The encouraging results of simple simulation studies suggest the potential of this new approach in limiting the posterior disclosure risk.

The third method is for imputing missing values in continuous and categorical variables. It is extended from a hierarchically coupled mixture model with local dependence. However, the new method separates the variables into non-focused (e.g., almost-fully-observed) and focused (e.g., missing-a-lot) ones. The sub-model structure of focused variables is more complex than that of non-focused ones. At the same time, their cluster indicators are linked together by tensor factorization and the focused continuous variables depend locally on non-focused values. The model properties suggest that moving the strongly associated non-focused variables to the side of focused ones can help to improve estimation accuracy, which is examined by several simulation studies. And this method is applied to data from the American Community Survey.

(Table 2) Contents of U, P2O5, CO2, and TOC in phosphorites from Pacific seamounts

Uranium content of in phosphorites from Pacific seamounts does not exceed 10ppm; it is significantly lower than in phosphorites from submarine continental margins and deposits on land. Phosphate is not the main carrier of uranium, which is inhomogeneously distributed in ferromanganese hydroxide-, phosphate-, silicate- and carbonate materials. Uranium associated with phosphate is not isomorphic admixture. Uranium occurs in rocks in fine particles of unknown composition. Ultramicroscopic inclusions of U(IV) oxides have been also found.

Long-term chemical characterization of aerosols at CVAO from 2007 to 2011

The first long-term aerosol sampling and chemical characterization results from measurements at the Cape Verde Atmospheric Observatory (CVAO) on the island of São Vicente are presented and are discussed with respect to air mass origin and seasonal trends. In total 671 samples were collected using a high-volume PM10 sampler on quartz fiber filters from January 2007 to December 2011. The samples were analyzed for their aerosol chemical composition, including their ionic and organic constituents. Back trajectory analyses showed that the aerosol at CVAO was strongly influenced by emissions from Europe and Africa, with the latter often responsible for high mineral dust loading. Sea salt and mineral dust dominated the aerosol mass and made up in total about 80% of the aerosol mass. The 5-year PM10 mean was 47.1 ± 55.5 µg/m**2, while the mineral dust and sea salt means were 27.9 ± 48.7 and 11.1 ± 5.5 µg/m**2, respectively. Non-sea-salt (nss) sulfate made up 62% of the total sulfate and originated from both long-range transport from Africa or Europe and marine sources. Strong seasonal variation was observed for the aerosol components. While nitrate showed no clear seasonal variation with an annual mean of 1.1 ± 0.6 µg/m**3, the aerosol mass, OC (organic carbon) and EC (elemental carbon), showed strong winter maxima due to strong influence of African air mass inflow. Additionally during summer, elevated concentrations of OM were observed originating from marine emissions. A summer maximum was observed for non-sea-salt sulfate and was connected to periods when air mass inflow was predominantly of marine origin, indicating that marine biogenic emissions were a significant source. Ammonium showed a distinct maximum in spring and coincided with ocean surface water chlorophyll a concentrations. Good correlations were also observed between nss-sulfate and oxalate during the summer and winter seasons, indicating a likely photochemical in-cloud processing of the marine and anthropogenic precursors of these species. High temporal variability was observed in both chloride and bromide depletion, differing significantly within the seasons, air mass history and Saharan dust concentration. Chloride (bromide) depletion varied from 8.8 ± 8.5% (62 ± 42%) in Saharan-dust-dominated air mass to 30 ± 12% (87 ± 11%) in polluted Europe air masses. During summer, bromide depletion often reached 100% in marine as well as in polluted continental samples. In addition to the influence of the aerosol acidic components, photochemistry was one of the main drivers of halogenide depletion during the summer; while during dust events, displacement reaction with nitric acid was found to be the dominant mechanism. Positive matrix factorization (PMF) analysis identified three major aerosol sources: sea salt, aged sea salt and long-range transport. The ionic budget was dominated by the first two of these factors, while the long-range transport factor could only account for about 14% of the total observed ionic mass.

Multivariate Techniques in Biomechanical Analysis

This work outlines the theoretical advantages of multivariate methods in biomechanical data, validates the proposed methods and outlines new clinical findings relating to knee osteoarthritis that were made possible by this approach. New techniques were based on existing multivariate approaches, Partial Least Squares (PLS) and Non-negative Matrix Factorization (NMF) and validated using existing data sets. The new techniques developed, PCA-PLS-LDA (Principal Component Analysis – Partial Least Squares – Linear Discriminant Analysis), PCA-PLS-MLR (Principal Component Analysis – Partial Least Squares –Multiple Linear Regression) and Waveform Similarity (based on NMF) were developed to address the challenging characteristics of biomechanical data, variability and correlation. As a result, these new structure-seeking technique revealed new clinical findings. The first new clinical finding relates to the relationship between pain, radiographic severity and mechanics. Simultaneous analysis of pain and radiographic severity outcomes, a first in biomechanics, revealed that the knee adduction moment’s relationship to radiographic features is mediated by pain in subjects with moderate osteoarthritis. The second clinical finding was quantifying the importance of neuromuscular patterns in brace effectiveness for patients with knee osteoarthritis. I found that brace effectiveness was more related to the patient’s unbraced neuromuscular patterns than it was to mechanics, and that these neuromuscular patterns were more complicated than simply increased overall muscle activity, as previously thought.

Testing After Worked Example Study Does Not Enhance Delayed Problem-Solving Performance Compared to Restudy

Four experiments investigated whether the testing effect also applies to the acquisition of problem-solving skills from worked examples. Experiment 1 (n=120) showed no beneficial effects of testing consisting of isomorphic problem solving or example recall on final test performance, which consisted of isomorphic problem solving, compared to continued study of isomorphic examples. Experiment 2 (n=124) showed no beneficial effects of testing consisting of identical problem solving compared to restudying an identical example. Interestingly, participants who took both an immediate and a delayed final test outperformed those taking only a delayed test. This finding suggested that testing might become beneficial for retention but only after a certain level of schema acquisition has taken place through restudying several examples. However, experiment 2 had no control condition restudying examples instead of taking the immediate test. Experiment 3 (n=129) included such a restudy condition, and there was no evidence that testing after studying four examples was more effective for final delayed test performance than restudying, regardless of whether restudied/tested problems were isomorphic or identical. Experiment 4 (n=75) used a similar design as experiment 3 (i.e., testing/restudy after four examples), but with examples on a different topic and with a different participant population. Again, no evidence of a testing effect was found. Thus, across four experiments, with different types of initial tests, different problem-solving domains, and different participant populations, we found no evidence that testing enhanced delayed test performance compared to restudy. These findings suggest that the testing effect might not apply to acquiring problem-solving skills from worked examples

Orbital and strongly orbital spaces

We say that a (countably dimensional) topological vector space X is orbital if there is T∈L(X) and a vector x∈X such that X is the linear span of the orbit {Tnx:n=0,1,…}. We say that X is strongly orbital if, additionally, x can be chosen to be a hypercyclic vector for T. Of course, X can be orbital only if the algebraic dimension of X is finite or infinite countable. We characterize orbital and strongly orbital metrizable locally convex spaces. We also show that every countably dimensional metrizable locally convex space X does not have the invariant subset property. That is, there is T∈L(X) such that every non-zero x∈X is a hypercyclic vector for T. Finally, assuming the Continuum Hypothesis, we construct a complete strongly orbital locally convex space.

As a byproduct of our constructions, we determine the number of isomorphism classes in the set of dense countably dimensional subspaces of any given separable infinite dimensional Fréchet space X. For instance, in X=ℓ2×ω, there are exactly 3 pairwise non-isomorphic (as topological vector spaces) dense countably dimensional subspaces.