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Patients with a history of lateral ankle sprain (LAS) may experience different levels of mechanical and/or sensorimotor deficits following their injuries. Although various factors, such as structural damage, sensorimotor adaptation, perceived instability, swelling and/or pain, can develop and perpetuate the condition of chronic ankle instability (CAI), most previous CAI research on biomechanics has considered all patients with CAI as a homogeneous group. Recent research has clustered patients with CAI into six distinct movement patterns during a maximal jump-landing/cutting task. This approach could motivate clinicians to develop appropriate rehabilitation programs for each patient with CAI depending on their movement patterns. However, evaluating patients with CAI for the quality of movement and sensorimotor deficits using a 3D motion capture system and a force plate is not easily accessible in clinical settings. PURPOSE: (i) to identify subgroups within the CAI population based on their movement patterns using inertial measurement unit (IMU) devices and (ii) to characterize each subgroup's functional movement patterns during maximal jump-landing/cutting relative to the uninjured controls. METHODS: A total of 100 patients with CAI (height = 1.76 ± 0.1 m, mass = 74.0 ± 14.9 kg) were assessed according to the Foot and Ankle Ability Measure (FAAM) (ADL: 84.3 ± 7.6%, Sport: 63.6 ± 8.6%) and the Ankle Instability Instrument (AII) (6.7 ± 1.2) and were fit into clusters based on their movement strategy during the maximal jump-landing/cutting task. A total of 21 uninjured controls (height = 1.74 ± 0.1 m, mass = 70.7 ± 13.4 kg) were compared with each cluster. Seven IMU sensors were placed on the base of the lumbar spine, lower and upper legs, and feet and participants performed 5 trials of the maximal jump-landing/cutting test. Joint kinematics in the lower extremity were collected during the task using IMU sensors. Data were reduced to functional curves; kinematic data from the sagittal and frontal planes were reduced to a single representative curve for each plane. Then, representative curves were clustered using a Bayesian clustering technique. Functional analyses of variance were used to identify between-group differences for outcome measures and describe specific movement characteristics of each subgroup. Pairwise comparison functions as well as 95% confidence interval (CI) bands were plotted to determine specific differences. If 95% CI bands did not cross the zero line, we considered the difference significant. RESULTS: Four distinct clusters were identified from the sagittal- and frontal-plane kinematic data. Specific movement patterns in each cluster compared to either uninjured controls or rest of patients with CAI were also identified. CONCLUSION: The IMUs were able to distinguish 4 clusters within the CAI population based on distinct movement patterns during a maximal jump-landing/cutting task. Thus, IMUs can be effective measuring devices to distinguish and characterize multiple distinct movement patterns without relying on a traditional 3D motion capture system. Clinicians should consider utilizing IMU devices to measure and evaluate specific movement patterns in the CAI population during multiplanar demanding tests before developing appropriate treatment interventions in clinical settings.

Increasing habitat fragmentation and rapid global warming is changing the conditions for species populations and ecological communities around the world. This presents challenges for the maintenance of biodiversity and a dominant paradigm for conservation in fragmented habitats is given by island biogeography and metapopulation (or metacommunity) ecology. In this thesis I approach key concepts (area, connectivity and community assembly) in island biogeography and metacommunity ecology within the context of a dynamic land uplift archipelago. The presented work consists of two interwoven themes: (i) A methodological theme in which statistical approaches are developed to deal with the complexities of multispecies dynamic systems, and (ii) an applied theme dealing with community assembly and island biogeography of bryophytes on young land uplift islands. To describe island connectivity for entire species assemblages, an approach using functional principal component analysis (fPCA) on patch connectivity functions (the connectivity of an island as a continuous function of a variable representing the spatial scale of species dispersal capacities) was developed. In addition, a new statistical method, functional co-inertia analysis (fCoIA), for analyzing co-variation between multivariate species data and continuous functions was developed and applied to the relation between bryophyte species incidences and the island age/area-dynamics. Primarily asexual bryophyte species are dispersal limited and presence probabilities are related to island connectivity. No such patterns were found for species, at least occasionally, producing spores. Our results suggest that bryophyte dispersal is regulated by the contribution of spores to a regional spore rain and that bryophyte species with low spore output at the landscape level may be extra vulnerable under habitat fragmentation and loss. Having specialized asexual propagules increases the presence probabilities on islands, partly compensating for the dispersal limitation in asexual species. This suggests a trade-off between dispersal and establishment capacity, but also points to the importance of local dispersal for maintaining populations under the succession driven spatial turnover of microsites on the islands. Bryophyte colonization is strongly limited by habitat availability when a given habitats is rare, but there seems to exist a threshold over which other processes (e.g. dispersal limitation) become more important. Species with more vagile life history strategies appear to be stronger affected by the area of available habitats than many perennial species

As adults age, they lose the ability to produce maximal power and speed of movement. Success in daily living is often dependent upon power and speed. Thus these age-related decrements in performance can reduce physical independence and quality of life. An active lifestyle in older adulthood is associated with more successful aging. The purpose of this research program was to define the link between habitual activity and performance, specifically in regard to activities requiring power and speed. The hypothesis was that active older adults, compared to sedentary older adults, would be characterized by greater power production in maximal- and submaximal-effort tasks. Grouping older adults by activity level, coactivation was associated with activity level. Functional tasks are performed with a range of power requirements. Coactivation was used to distinguish groups in a maximal power task (Study 1) and submaximal power tasks (Study 2). In Study 1, the young adults demonstrated a greater maximal power than the older adults. While maximal power was not different between the older active and sedentary groups, the groups did differ on how they created maximal power. The active older adults produced a greater coactivation in the lower leg muscles compared to the older sedentary adults. In Study 2, the active older adults responded to different speeds during a submaximal power task with greater coactivation in the muscles of the lower leg at slow speeds compared with the sedentary older adults. Both older adults groups increased coactivation in the thigh muscles at high speeds. The sedentary older adults responded to speed with increased coactivation in the lower leg at fast speeds. The active older adults increased proximal thigh coactivation, EMG index, at the fastest speed compared with the sedentary older adults. Both older adult groups showed muscle activation adaptation to the change in task demands. The results of this dissertation increase our understanding about the link between physical activity and performance. Age-related differences in coactivation were observed during both maximal and submaximal tasks. Activity-related differences were observed suggesting the active older adults have a greater capability to adjust muscle activity to meet the challenges of community living. / text

This thesis presents a contribution to the active research area of functional data analysis (FDA) and is concerned with the analysis of data from complex experimental designs in which the responses are curves. High resolution, closely correlated data sets are encountered in many research fields, but current statistical methodologies often analyse simplistic summary measures and therefore limit the completeness and accuracy of conclusions drawn. Specifically the nature of the curves and experimental design are not taken into account. Mathematically, such curves can be modelled either as sample paths of a stochastic process or as random elements in a Hilbert space. Despite this more complex type of response, the structure of experiments which yield functional data is often the same as in classical experimentation. Thus, classical experimental design principles and results can be adapted to the FDA setting. More specifically, we are interested in the functional analysis of variance (ANOVA) of experiments which use orthogonal designs. Most of the existing functional ANOVA approaches consider only completely randomised designs. However, we are interested in more complex experimental arrangements such as, for example, split-plot and row-column designs. Similar to univariate responses, such complex designs imply that the response curves for different observational units are correlated. We use the design to derive a functional mixed-effects model and adapt the classical projection approach in order to derive the functional ANOVA. As a main result, we derive new functional F tests for hypotheses about treatment effects in the appropriate strata of the design. The approximate null distribution of these tests is derived by applying the Karhunen- Lo`eve expansion to the covariance functions in the relevant strata. These results extend existing work on functional F tests for completely randomised designs. The methodology developed in the thesis has wide applicability. In particular, we consider novel applications of functional F tests to gait analysis. Results are presented for two empirical studies. In the first study, gait data of patients with cerebral palsy were collected during barefoot walking and walking with ankle-foot orthoses. The effects of ankle-foot orthoses are assessed by functional F tests and compared with pointwise F tests and the traditional univariate repeated-measurements ANOVA. The second study is a designed experiment in which a split-plot design was used to collect gait data from healthy subjects. This is commonly done in gait research in order to better understand, for example, the effects of orthoses while avoiding confounded analysis from the high variability observed in abnormal gait. Moreover, from a technical point of view the study may be regarded as a real-world alternative to simulation studies. By using healthy individuals it is possible to collect data which are in better agreement with the underlying model assumptions. The penultimate chapter of the thesis presents a qualitative study with clinical experts to investigate the utility of gait analysis for the management of cerebral palsy. We explore potential pathways by which the statistical analyses in the thesis might influence patient outcomes. The thesis has six chapters. After describing motivation and introduction in Chapter 1, mathematical representations of functional data are presented in Chapter 2. Chapter 3 considers orthogonal designs in the context of functional data analysis. New functional F tests for complex designs are derived in Chapter 4 and applied in two gait studies. Chapter 5 is devoted to a qualitative study. The thesis concludes with a discussion which details the extent to which the research question has been addressed, the limitations of the work and the degree to which it has been answered.

The present study is divided into two parts: the first is on developing the statistical analysis and modeling of mortality (or incidence) trends using Bayesian joinpoint regression and the second is on fitting differential equations from time series data to derive the rate of change of carbon dioxide in the atmosphere. Joinpoint regression model identifies significant changes in the trends of the incidence, mortality, and survival of a specific disease in a given population. Bayesian approach of joinpoint regression is widely used in modeling statistical data to identify the points in the trend where the significant changes occur. The purpose of the present study is to develop an age-stratified Bayesian joinpoint regression model to describe mortality trends assuming that the observed counts are probabilistically characterized by the Poisson distribution. The proposed model is based on Bayesian model selection criteria with the smallest number of joinpoints that are sufficient to explain the Annual Percentage Change (APC). The prior probability distributions are chosen in such a way that they are automatically derived from the model index contained in the model space. The proposed model and methodology estimates the age-adjusted mortality rates in different epidemiological studies to compare the trends by accounting the confounding effects of age. The future mortality rates are predicted using the Bayesian Model Averaging (BMA) approach. As an application of the Bayesian joinpoint regression, first we study the childhood brain cancer mortality rates (non age-adjusted rates) and their Annual Percentage Change (APC) per year using the existing Bayesian joinpoint regression models in the literature. We use annual observed mortality counts of children ages 0-19 from 1969-2009 obtained from Surveillance Epidemiology and End Results (SEER) database of the National Cancer Institute (NCI). The predictive distributions are used to predict the future mortality rates. We also compare this result with the mortality trend obtained using joinpoint software of NCI, and to fit the age-stratified model, we use the cancer mortality counts of adult lung and bronchus cancer (25-85+ years), and brain and other Central Nervous System (CNS) cancer (25-85+ years) patients obtained from the Surveillance Epidemiology and End Results (SEER) data base of the National Cancer Institute (NCI). The second part of this study is the statistical analysis and modeling of noisy data using functional data analysis approach. Carbon dioxide is one of the major contributors to Global Warming. In this study, we develop a system of differential equations using time series data of the major sources of the significant contributable variables of carbon dioxide in the atmosphere. We define the differential operator as data smoother and use the penalized least square fitting criteria to smooth the data. Finally, we optimize the profile error sum of squares to estimate the necessary differential operator. The proposed models will give us an estimate of the rate of change of carbon dioxide in the atmosphere at a particular time. We apply the model to fit emission of carbon dioxide data in the continental United States. The data set is obtained from the Carbon Dioxide Information Analysis Center (CDIAC), the primary climate-change data and information analysis center of the United States Department of Energy. The first four chapters of this dissertation contribute to the development and application of joinpiont and the last chapter discusses the statistical modeling and application of differential equations through data using functional data analysis approach.

This thesis presents a new human-like upper limb and hand motion generating method. The work is based on Functional Principal Component Analysis and Quadratic Programming. The human-like motion generating problem is formulated in a framework of minimizing the difference of the dynamic profile of the optimal trajectory and the known types of trajectory. Statistical analysis is applied to the pre-captured human motion records to work in a low dimensional space. A novel PCA FPCA hybrid motion recognition method is proposed. This method is implemented on human grasping data to demonstrate its advantage in human motion recognition. One human grasping hierarchy is also proposed during the study. The proposed method of generating human-like upper limb and hand motion explores the ability to learn the motion kernels from human demonstration. Issues in acquiring motion kernels are also discussed. The trajectory planning method applies different weight on the extracted motion kernels to approximate the kinematic constraints of the task. Multiple means of evaluation are implemented to illustrate the quality of the generated optimal human-like trajectory compared to the real human motion records.

Medical research currently involves the collection of large and complex data. One such type of data is functional data where the unit of measurement is a curve measured over a grid. Functional data comes in a variety of forms depending on the nature of the research. Novel methodologies are required to accommodate this growing volume of functional data alongside new testing procedures to provide valid inferences. In this dissertation, I propose three novel methods to accommodate a variety of questions involving functional data of multiple forms. I consider three novel methods: (1) a function-on-function regression for Gaussian data; (2) a historical functional linear models for repeated measures; and (3) a generalized functional outcome regression for ordinal data. For each method, I discuss the existing shortcomings of the literature and demonstrate how my method fills those gaps. The abilities of each method are demonstrated via simulation and data application.

A disseminação de sistemas de aquisição de dados sobre a qualidade e o desempenho de produtos e processos de fabricação deu origem a novos tipos de dados. Dado funcional é um conjunto de dados que formam um perfil ou uma curva. No perfil, a característica de qualidade é uma função dependente de uma ou mais variáveis exploratórias ou independentes. A análise de dados funcionais é um tema de pesquisa recente praticado em diversas áreas do conhecimento. Na indústria, os dados funcionais aparecem no controle de qualidade. A ausência de métodos apropriados a dados funcionais pode levar ao uso de métodos ineficientes e reduzir o desempenho e a qualidade de um produto ou processo. A análise de dados funcionais através de métodos multivariados pode ser inadequada devido à alta dimensionalidade e estruturas de variância e covariância dos dados. O desenvolvimento teórico de métodos para a análise de dados funcionais na área de Engenharia da Qualidade encontra-se defasado em relação ao potencial de aplicações práticas. Este trabalho identificou a existência dos dados funcionais tratados por métodos ineficientes. Os métodos atuais para controle de qualidade de dados são adaptados a situações específicas, conforme o tipo de dado funcional e a fase do monitoramento. Este trabalho apresenta propostas para métodos de análise de dados funcionais aplicáveis a questões relevantes da área de pesquisa em Engenharia da Qualidade, tais como: (i) o uso da análise de variância em experimentos com dados funcionais; (ii) gráficos de controle para monitoramento de perfis; e (iii) a análise e seleção de perfis de fornecedores em projetos inovadores. / The dissemination of data acquisition systems on the quality and performance of products and manufacturing process has given rise to new types of data. Functional data are a collection of data points organized as a profile or curve. In profile, the quality characteristic is a function dependent on one or more exploratory or independent variables. The functional data analysis is a recent research topic practiced in various areas of knowledge. In industry, the functional data appears in quality control. The lack of suitable methods can lead to use of inefficient methods and reducing the performance and quality of a product or process. The analysis of functional data by multivariate methods may be inadequate due to the high dimensionality and variance and covariance structures of the data. The development of theoretical methods for the analysis of functional data in Quality Engineering area is lagged behind the potential for practical applications. This work identified the existence of functional data processed by inefficient methods. Current methods for data quality control are adapted to specific situations, depending on the type of functional data and the phase of monitoring. This paper presents proposals for functional data analysis methods applicable to relevant research questions in the area of Quality Engineering such as: (i) the use of analysis of variance in experiments with functional data; (ii) control charts for monitoring profiles; and (iii) the analysis and selection of supplier profiles on innovative projects.