Obesity in children is a nationwide problem. Physical activity is one way to help children stay fit and prevent obesity. Unfortunately, access to technology involving sedentary behavior is easier than ever. Fortunately, for this generation of students there is a way to combine physical activity and technology through exergaming. In order to encourage students to participate in exergaming, the students should be able to play games they prefer. The purpose of this study was to apply a paired choice preference assessment, rank order card sort, and social validity surveys to determine the preference order of six exergames for six elementary students and measure heart rates as the children played the six exergames. The results of this study show that children had different preferences as evident by the rank order card sort, social validity survey, and paired choice preference assessment. The pre-rank order card sort was significantly correlated with the paired choice assessment. On the other hand, the pre-social validity survey was not significantly correlated with the paired choice assessment.

In fields across science and engineering, we are increasingly faced with problems where the number of variables or features we need to estimate is much larger than the number of observations. Under such high-dimensional scaling, for any hope of statistically consistent estimation, it becomes vital to leverage any potential structure in the problem such as sparsity, low-rank structure or block sparsity. However, data may deviate significantly from any one such statistical model. The motivation of this thesis is: can we simultaneously leverage more than one such statistical structural model, to obtain consistency in a larger number of problems, and with fewer samples, than can be obtained by single models? Our approach involves combining via simple linear superposition, a technique we term dirty models. The idea is very simple: while any one structure might not capture the data, a superposition of structural classes might. Dirty models thus searches for a parameter that can be decomposed into a number of simpler structures such as (a) sparse plus block-sparse, (b) sparse plus low-rank and (c) low-rank plus block-sparse. In this thesis, we propose dirty model based algorithms for different problems such as multi-task learning, graph clustering and time-series analysis with latent factors. We analyze these algorithms in terms of the number of observations we need to estimate the variables. These algorithms are based on convex optimization and sometimes they are relatively slow. We provide a class of low-complexity greedy algorithms that not only can solve these optimizations faster, but also guarantee the solution. Other than theoretical results, in each case, we provide experimental results to illustrate the power of dirty models. / text

Quantifying uncertainties in large-scale forward and inverse PDE simulations has emerged as a central challenge facing the field of computational science and engineering. The promise of modeling and simulation for prediction, design, and control cannot be fully realized unless uncertainties in models are rigorously quantified, since this uncertainty can potentially overwhelm the computed result. While statistical inverse problems can be solved today for smaller models with a handful of uncertain parameters, this task is computationally intractable using contemporary algorithms for complex systems characterized by large-scale simulations and high-dimensional parameter spaces. In this dissertation, I address issues regarding the theoretical formulation, numerical approximation, and algorithms for solution of infinite-dimensional Bayesian statistical inverse problems, and apply the entire framework to a problem in global seismic wave propagation. Classical (deterministic) approaches to solving inverse problems attempt to recover the “best-fit” parameters that match given observation data, as measured in a particular metric. In the statistical inverse problem, we go one step further to return not only a point estimate of the best medium properties, but also a complete statistical description of the uncertain parameters. The result is a posterior probability distribution that describes our state of knowledge after learning from the available data, and provides a complete description of parameter uncertainty. In this dissertation, a computational framework for such problems is described that wraps around the existing forward solvers, as long as they are appropriately equipped, for a given physical problem. Then a collection of tools, insights and numerical methods may be applied to solve the problem, and interrogate the resulting posterior distribution, which describes our final state of knowledge. We demonstrate the framework with numerical examples, including inference of a heterogeneous compressional wavespeed field for a problem in global seismic wave propagation with 10⁶ parameters.

Με τον όρο «Έκτοπη Οστεοποίηση» περιγράφεται ο σχηματισμός οστού σε σημεία που υπό φυσιολογικές συνθήκες δεν υφίσταται. Τα σημεία αυτά μπορεί να είναι μύες, τένοντες ή σύνδεσμοι και γενικότερα μεσεγχυματικού τύπου μαλακά μόρια, κυρίως γύρω από τις μεγαλύτερες αρθρώσεις. Η επίκτητη μορφή της νόσου, που είναι και η πιο κοινή, εμφανίζεται μετά από μυοσκελετικούς τραυματισμούς, κακώσεις του νωτιαίου μυελού και του κεντρικού νευρικού συστήματος γενικότερα, αλλά και σε περιπτώσεις σοβαρών εγκαυμάτων. Η παθοφυσιολογία της έκτοπης οστεοποίησης παραμένει άγνωστη, αυτό που γνωρίζουμε με βεβαιότητα είναι ότι για τον σχηματισμό της απαιτούνται τρείς βασικές προϋποθέσεις που είναι α) τα οστεοπρογονικά κύτταρα, β) οι κατάλληλοι επαγωγικοί παράγοντες και γ) το ευνοϊκό οστεοεπαγωγικό περιβάλλον. Στην παρούσα εργασία με την χρήση κυτταρομετρίας ροής, δοκιμασιών με ηλεκτροχημειοφωταύγεια, Elisa και ανοσοπροσδιορισμού με χρήση Cytometric Bead Array προσδιορίσαμε τις συγκεντρώσεις των total procollagen type 1 amino-terminal propeptide (TP1NP), osteoprotegerin (OPG), β-isomerized C-terminal telopeptides (β- Crosslaps), soluble receptor activator of nuclear factor kappa-B ligand (sRANKL), N-MID osteocalcin, S100 και των κυτταροκινών IL-2, IL-4, IL-6, IL-10, INF-γ και TNF-a στον ορό ασθενών και υγιών μαρτύρων. Επιπλέον, στο ολικό αίμα προσδιορίσαμε τον πληθυσμό των θετικών στην οστεοκαλσίνη κυττάρων. Όλα τα προς μελέτη μόρια είχαν άμεση ή έμμεση σχέση με την οστική ανακατασκευή και τις φλεγμονώδεις αντιδράσεις. Συνολικά μελετήθηκαν 55 ασθενείς από τους οποίους ελήφθησαν δείγματα καθόλη την διάρκεια νοσηλείας τους. Οι ασθενείς μελετήθηκαν με βάση το είδος του τραύματος, την εμφάνιση ή όχι έκτοπης οστεοποίησης και την έκβαση της κατάστασης τους. Επιπλέον, οι επιμέρους ομάδες ασθενών μελετήθηκαν συναρτήσει του χρόνου. Τα αποτελέσματα μας έδειξαν ότι στο σύνολο των ασθενών παρατηρήθηκαν στατιστικά μειωμένα επίπεδα β- crosslaps, N-MID osteocalcin, sRANKL και S100 συγκριτικά με τους υγιείς μάρτυρες. Αντίθετα, τα επίπεδα των TP1NP, των θετικών στην οστεοκαλσίνη κυττάρων, της OPG, της INF-γ και της IL-6 ήταν στατιστικά σημαντικά αυξημένα. Επιπλέον, στατιστικά σημαντικά αυξημένα παρατηρήθηκαν τα επίπεδα του S100 στους ασθενείς που είχαν υποστεί κρανιοεγκεφαλικές κακώσεις κατά το πρώτο εικοσιτετράωρο μετά την επαγωγή της κάκωσης. Στατιστικά σημαντικά αυξημένο επίσης παρατηρήθηκε και στην ομάδα των ασθενών με κακή έκβαση συγκριτικά με τους υγιείς δότες. Στην ίδια ομάδα ασθενών παρατηρήθηκε μια γενικευμένη αύξηση των επιπέδων των κυτταροκινών που φαίνεται να σχετίζεται άμεσα με την κακή έκβαση της κατάστασης τους. Πιο συγκεκριμένα η αύξηση αυτή ήταν στατιστικώς σημαντική για τις IL-4, INF-γ και TNF-α. / Heterotopic ossification (HO) is the presence of bone in soft tissue where normally does not exist. The acquired form, which is also the most common, develops after musculoskeletal trauma, spinal cord injury or central nervous system injury and severe burns. Pathophysiology of OH still remains unclear, what we know is that the formation of ectopic bone requires three entities which are a) osteogenic precursor cells, b) inducing agents and c) an appropriate environment. In the present study using either flow cytometry, Elisa, electrochemiluminescence immunoassays or cytometric bead array assays we determined the concentrations of the osteoblast progenitors: osteocalcin positive cells in peripheral blood and the serum concentrations of total procollagen type 1 amino-terminal propeptide (TP1NP), osteoprotegerin (OPG), β-isomerized C-terminal telopeptides (β- Crosslaps), soluble receptor activator of nuclear factor kappa-B ligand (sRANKL), N-MID osteocalcin, S100 and the cytokines IL-2, IL-4, IL-6, IL-10, INF-γ and TNF-a. All measured molecules participate directly or indirectly in bone formation and metabolism and in inflammation. Our 55 patients were divided and studied in 3 different ways, regarding the kind of their injury, their outcome and the formation of HO. They were also monitored in course of time. Among our most interesting results is that patients had significantly lower levels of β- crosslaps, N-MID osteocalcin, sRANKL and S100 compared to healthy donors. On the other hand, levels of TP1NP, osteocalcin positive cells, OPG, INF-γ and IL-6 were significantly higher. S100 is significantly increased during the first 24 hours in patients who have sustained traumatic brain injury. In addition, S100 was significantly increased in patients with poor outcome compared to healthy donors. Furthermore, patients with poor outcome seem to develop a cytokine storm which is of great importance for their outcome. All measured cytokine levels were increased compared to patients with good outcome. Especially for IL-4, INF-γ, TNF-α this increase was statistically significant.

The Singular Value Decomposition (SVD) has many applications in image processing. The SVD can be used to restore a corrupted image by separating significant information from the noise in the image data set. This thesis outlines broad applications that address current problems in digital image processing. In conjunction with SVD filtering, image compression using the SVD is discussed, including the process of reconstructing or estimating a rank reduced matrix representing the compressed image. Numerical plots and error measurement calculations are used to compare results of the two SVD image restoration techniques, as well as SVD image compression. The filtering methods assume that the images have been degraded by the application of a blurring function and the addition of noise. Finally, we present numerical experiments for the SVD restoration and compression to evaluate our computation.

Fourier Transform Infrared (FTIR) microscopy is a sensitive method for detecting difference in the morphology of biological cells. In this study FTIR spectra were obtained for uninfected cells, and cells infected with two different viruses. The spectra obtained are difficult to discriminate visually. Here we apply advanced statistical methods to the analysis of the spectra, to test if such spectra are useful for diagnosing viral infections in cells. Logistic Regression (LR) and Partial Least Squares Regression (PLSR) were used to build models which allow us to diagnose if spectral differences are related to infection state of the cells. A three-fold, balanced cross-validation method was applied to estimate the shrinkages of the area under the receiving operator characteristic curve (AUC), and specificities at sensitivities of 95%, 90% and 80%. AUC, sensitivity and specificity were used to gauge the goodness of the discrimination methods. Our statistical results shows that the spectra associated with different cellular states are very effectively discriminated. We also find that the overall performance of PLSR is better than that of LR, especially for new data validation. Our analysis supports the idea that FTIR microscopy is a useful tool for detection of viral infections in biological cells.

Fourier transform infrared (FTIR) spectroscopy, one method of electromagnetic radiation for detecting specific cellular molecular structure, can be used to discriminate different types of cells. The objective is to find the minimum time (choice among 2 hour, 4 hour and 6 hour) to record FTIR readings such that different viruses can be discriminated. A new method is adopted for the datasets. Briefly, inner differences are created as the control group, and Wilcoxon Signed Rank Test is used as the first selecting variable procedure in order to prepare the next stage of discrimination. In the second stage we propose either partial least squares (PLS) method or simply taking significant differences as the discriminator. Finally, k-fold cross-validation method is used to estimate the shrinkages of the goodness measures, such as sensitivity, specificity and area under the ROC curve (AUC). There is no doubt in our mind 6 hour is enough for discriminating mock from Hsv1, and Coxsackie viruses. Adeno virus is an exception.

A hierarchical control system is proposed for automated flexible manufacturing cells (FMC) that operate in a job shop flow setting. The control system is made up of a higher level scheduler/reactive scheduler, which optimizes the production flow within the cell, and a lower level supervisor that implements the decisions of the scheduler on the shop floor. Previous studies have regularly considered the production scheduling and the supervisory control as two separate problems. This has led to: i) deadlock-prone optimized schedules that cannot be implemented in an automated setting, ii) deadlock-free optimized schedules that lack the means to be transformed into shop floor supervisors, or iii) supervisors that can safely drive the system with no consideration for production performance. The proposed control system combines mathematical models and an insertion heuristic to solve the deadlock-free scheduling problem in job shops, a deadlock-free reactive scheduling heuristic that can revise the schedules upon the occurrence of a wide variety of disruptions, and a systematic procedure that can transform schedules into readily implementable Petri net (PN) supervisors. The integration of these modules into one control hierarchy guarantees a correct, optimized and agile behavior of the controlled system. The performances of the mathematical models, the scheduling and the reactive scheduling heuristics were evaluated by comparison to performances of previous approaches. Experimental results showed that the proposed modules performed consistently better than the other corresponding approaches. The supervisor realization procedure and the overall control architecture were validated by simulation and implementation in an experimental robotic FMC. The control system developed was capable of driving the experimental cell to satisfactorily complete the processing of different product mixes that featured complex processing routes through the cell.

Inspired by the swapping algebra and the rank n cross-ratio introduced by F. Labourie, we construct a ring equipped with the swapping Poisson structure---the rank n swapping algebra Zn(P) to study the moduli spaces of cross ratios. We prove that Zn(P) inherits a Poisson structure form the swapping bracket. To consider the "cross-ratios" in the fraction ring, by interpreting Zn(P) by a geometric model in the study of geometry invariant theory, we prove that Zn(P) is an integral domain. Then we consider the ring Bn(P) generated by the cross ratios in the fraction ring of Zn(P). For n = 2,3, we embed in a Poisson way the ring generated by Fock-Goncharov coordinates for configuration space of flags in Rn into Bn(P). By studying the discrete integrable system for the configuration space MN,1 of N-twisted polygons in RP1, up to a discrete Fourier transformation, we asymptotically relate the swapping algebra to the Virasoro algebra on a hypersurface of MN,1.

A hierarchical control system is proposed for automated flexible manufacturing cells (FMC) that operate in a job shop flow setting. The control system is made up of a higher level scheduler/reactive scheduler, which optimizes the production flow within the cell, and a lower level supervisor that implements the decisions of the scheduler on the shop floor. Previous studies have regularly considered the production scheduling and the supervisory control as two separate problems. This has led to: i) deadlock-prone optimized schedules that cannot be implemented in an automated setting, ii) deadlock-free optimized schedules that lack the means to be transformed into shop floor supervisors, or iii) supervisors that can safely drive the system with no consideration for production performance. The proposed control system combines mathematical models and an insertion heuristic to solve the deadlock-free scheduling problem in job shops, a deadlock-free reactive scheduling heuristic that can revise the schedules upon the occurrence of a wide variety of disruptions, and a systematic procedure that can transform schedules into readily implementable Petri net (PN) supervisors. The integration of these modules into one control hierarchy guarantees a correct, optimized and agile behavior of the controlled system. The performances of the mathematical models, the scheduling and the reactive scheduling heuristics were evaluated by comparison to performances of previous approaches. Experimental results showed that the proposed modules performed consistently better than the other corresponding approaches. The supervisor realization procedure and the overall control architecture were validated by simulation and implementation in an experimental robotic FMC. The control system developed was capable of driving the experimental cell to satisfactorily complete the processing of different product mixes that featured complex processing routes through the cell.