In this paper, we turn the interpolation problem of coarsely-sampled data into a denoising problem. From this point of view, we illustrate the benefit of random sampling at sub-Nyquist rate over regular sampling at the same rate. We show that, using nonlinear sparsity promoting optimization, coarse random sampling may actually lead to significantly better wavefield reconstruction than equivalent regularly sampled data.

The intent of this thesis is to investigate, develop, and apply techniques to determine the reliability and maintainability of populations of items. These techniques are to be used in determining the total life-time operating costs of the populations so that those items with the lowest life-time costs can be bought. To do this, the author has explored current techniques for determining compliance to some minimum required Mean Time Between Failure (MTBF) in what is referred to as a Phase I testing. After the requirements of Phase I testing have been met, testing may be continued at the option of the contractor and confidence limits constructed about the Bid MTBF to determine compliance to it. Methods by which incentives or penalties may be rewarded or assessed to contractor as a result of the Phase II testing are included. The author next investigated techniques which can be used to determine the maintainability parameters and the accuracy of these parameters. Finally, since the reliability techniques explored were all based on the exponential distribution, techniques were included to prove if the failure rate was exponential. If not, discussions were incorporated on how to handle this situation. (85 pages)

Although sampling techniques have been used effectively in education research and practice it is not clear how stratified random sampling techniques apply to high-stakes testing in the current educational environment. The present study focused on representative sampling as a possible means for reducing the quantity of state-administered tests in Texas public education. The purpose of this study was two-fold: (1) to determine if stratified random sampling is a viable option for reducing the number of students participating in Texas state assessments, and (2) to determine which sampling rate provides consistent estimates of the actual test results among the population of students. The study examined students’ scaled scores, percent of students passing, and student growth over a three-year period on state-mandated assessments in reading, mathematics, science, and social studies. Four sampling rates were considered (10%, 15%, 20%, & 25%) when analyzing student performance across demographic variables, including population estimates by socioeconomic status, limited English proficiency, and placement in special education classes. The data set for this study included five school districts and 68,641 students. Factorial ANOVAs were used initially to examine the effects of sampling rate on bias in reading and mathematics scores and bias in percentage of students passing these tests. Also 95% confidence intervals (CIs) and effect sizes for each model were examined to aid in the interpretation of the results. The results showed main effects for sampling rate and campus as well as a two-way interaction between these variables. The results indicated that a 20% sampling rate would closely approximate the parameter values regarding the mean TAKS reading and mathematics scale scores and the percentage of students passing these assessments. However, as population size decreases, sampling rate may have to be increased. For example, in populations with 30 or fewer students in a subgroup it is recommended that all students be included in the testing program. This study situated in one state contributes to the growing body of research being conducted on an international basis in sample-based educational assessments.

Combinatorial control of transcription is a well established phenomenon in the cell. Multiple transcription factors often bind to the same transcriptional control region of a gene and interact with each other to control the expression of the gene. It is thus necessary to consider the joint conservation of sequence pairs in order to identify combinations of binding sites to which the transcription factors bind. Conventional motif finding algorithms fail to address this issue. We propose a novel biclustering algorithm based on random sampling to identify candidate binding site combinations. We establish bounds on the various parameters to the algorithm and study the conditions under which the algorithm is guaranteed to identify candidate binding sites. We analyzed a yeast cell cycle gene expression data set using our algorithm and recovered certain novel combinations of binding sites, besides those already reported in the literature. / Master of Science

Knowing the uncertainty of a calculated result is always important, but especially so when performing calculations for safety analysis. A traditional way of propagating the uncertainty of input parameters is Monte Carlo (MC) methods. A quicker alternative to MC, especially useful when computations are heavy, is Deterministic Sampling (DS). DS works by hand-picking a small set of samples, rather than randomizing a large set as in MC methods. The samples and its corresponding weights are chosen to represent the uncertainty one wants to propagate by encoding the first few statistical moments of the parameters' distributions. Finding a suitable ensemble for DS in not easy, however. Given a large enough set of samples, one can always calculate weights to encode the first couple of moments, but there is good reason to want an ensemble with only positive weights. How to choose the ensemble for DS so that all weights are positive is the problem investigated in this project. Several methods for generating such ensembles have been derived, and an algorithm for calculating weights while forcing them to be positive has been found. The methods and generated ensembles have been tested for use in uncertainty propagation in many different cases and the ensemble sizes have been compared. In general, encoding two or four moments in an ensemble seems to be enough to get a good result for the propagated mean value and standard deviation. Regarding size, the most favorable case is when the parameters are independent and have symmetrical distributions. In short, DS can work as a quicker alternative to MC methods in uncertainty propagation as well as in other applications.

High-frequency financial data are not only discretely sampled in time but the time separating successive observations is often random. We review the paper of Aït-Sahalia and Mykland (2003), that measure the effects of discreteness sampling and ignoring the randomness of the sampling for estimating the m.l.e of a continuous-time diffusion model. In that article, three different assumptions and restrict in one made on the sampling intervals, and the corresponding likelihood function, asymptotic normality, and covariance matrix are obtained. It is concluded that the effects due to discretely sampling are smaller than the effect of simply ignoring the sampling randomness. This study focuses on rechecking the results in the paper of A¡Lıt-Sahalia and Mykland (2003) including theory, simulation and application. We derive a different likelihood function expression from A¡Lıt-Sahalia and Mykland (2003)¡¦s result. However, the asymptotic covariance are consistent for both approaching in the O-U process. Furthermore, we conduct an empirical study on the high frequency transaction time data by using non-homogeneous Poisson Processes.

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Στην παρούσα διατριβή μελετήθηκαν οι απόψεις των καθηγητών/τριών δευτεροβάθμιας εκπαίδευσης του νομού Αχαΐας σε θέματα λειτουργίας, οργάνωσης και υλοποίησης της περιβαλλοντικής εκπαίδευσης. Αναλυτικά στα πλαίσια της διατριβής ερευνήθηκε ο τρόπος επιλογής των θεμάτων των προγραμμάτων περιβαλλοντικής εκπαίδευσης από τους καθηγητές/τριες δευτεροβάθμιας εκπαίδευσης. Επίσης μελετήθηκε και ο τρόπος υλοποίησης των προγραμμάτων περιβαλλοντικής εκπαίδευσης. Δηλαδή ερευνήθηκε αν τα προγράμματα αυτά υλοποιούνται ολιστικά σύμφωνα και με τις τρεις προσεγγίσεις της περιβαλλοντικής εκπαίδευσης (μέσω, για, προς όφελος του περιβάλλοντος) ή αν αυτά υλοποιούνται σύμφωνα με την κάθε προσέγγιση ξεχωριστά. Στη διατριβή χρησιμοποιήθηκε η ερευνητική περιγραφική μέθοδος «επισκόπηση». Πριν την κυρίως έρευνα πραγματοποιήθηκε πιλοτική επισκόπηση σε σκόπιμο δείγμα τριάντα καθηγητών/τριών δευτεροβάθμιας εκπαίδευσης από το νομό Αχαΐας με μεγάλη πείρα στην περιβαλλοντική εκπαίδευση με στόχο να διαμορφωθεί το τελικό ερωτηματολόγιο και να διεξαχθεί αποτελεσματικά η έρευνα. O συνολικός πληθυσμός κατά την κυρίως έρευνα περιλάμβανε 306 καθηγητές/τριες από το νομό Αχαΐας οι οποίοι εκπονούσαν προγράμματα περιβαλλοντικής εκπαίδευσης κατά το σχολικό έτος 2004-05. Από το συγκεκριμένο πληθυσμό επιλέχθηκε τυχαίο δείγμα με «απλή τυχαία δειγματοληψία». Το δείγμα περιλάμβανε 55 άτομα δηλαδή το 18% του πληθυσμού και προερχόταν από διαφορετικές περιοχές του νομού Αχαΐας και από διαφορετικά είδη σχολείων (γυμνάσια, λύκεια κ.λ.π). Για τη στατιστική ανάλυση των δεδομένων της παρούσας διατριβής χρησιμοποιήθηκαν «κατανομές συχνοτήτων» και στατιστικός έλεγχος X2. Μετά την επεξεργασία και ανάλυση των δεδομένων διαπιστώθηκε αντίθεση μεταξύ πρόθεσης και υλοποίησης κατά την επιλογή και υλοποίηση προγραμμάτων περιβαλλοντικής εκπαίδευσης από τους καθηγητές/τριες του νομού Αχαΐας. Συγκεκριμένα ενώ αναγνωρίζεται η εκπαιδευτική σημασία να εκπονηθούν προγράμματα περιβαλλοντικής εκπαίδευσης που αναφέρονται στην υποβάθμιση των οικοσυστημάτων τελικά υλοποιούνται προγράμματα περιβαλλοντικής εκπαίδευσης που αναφέρονται στο ευρύ περιβάλλον. Οι πιθανοί λόγοι που ευθύνονται για την προαναφερθείσα αντίθεση, όπως σκιαγραφήθηκαν από τις απαντήσεις των εκπαιδευτικών, είναι η έλλειψη αξιολόγησης της περιβαλλοντικής εκπαίδευσης στη δευτεροβάθμια εκπαίδευση, η αδιαφορία και η απουσία συνεργασίας μεταξύ των εκπαιδευτικών διαφορετικών ειδικοτήτων για την περιβαλλοντική εκπαίδευση και η θεώρηση εκ μέρους των εκπαιδευτικών ότι η περιβαλλοντική πολιτική των κρατών ευθύνεται κυρίως για την οικολογική κρίση και ότι η συμβολή τού εκπαιδευτικού συστήματος στην αντιμετώπισή της οικολογικής κρίσης είναι δευτερεύουσας σημασίας. Με βάση το στατιστικό έλεγχο Χ2 διαπιστώθηκε ότι υπάρχει σχέση μεταξύ των ετών υπηρεσίας των καθηγητών/τριών δευτεροβάθμιας εκπαίδευσης και του τύπου περιβαλλοντικής εκπαίδευσης που επιλέγουν (δηλαδή περιβαλλοντική εκπαίδευση για το ευρύ περιβάλλον ή για το περιβαλλοντικό ζήτημα). Με τη διερεύνηση αυτή διαπιστώθηκε ότι οι εκπαιδευτικοί με περισσότερα από 15 έτη υπηρεσίας προτιμούν προγράμματα περιβαλλοντικής εκπαίδευσης που αναφέρονται στο ευρύ περιβάλλον ενώ οι νεώτεροι εκπαιδευτικοί με λιγότερα από 15 έτη υπηρεσίας προτιμούν προγράμματα περιβαλλοντικής εκπαίδευσης που αναφέρονται στο «περιβαλλοντικό ζήτημα». Επίσης διαπιστώθηκε ότι ανεξάρτητα από την ειδικότητά τους οι καθηγητές/τριες του νομού Αχαΐας έχουν την πρόθεση να ασχοληθούν με προγράμματα περιβαλλοντικής εκπαίδευσης αλλά προτιμούν να ασχολούνται με προγράμματα που αναφέρονται στο ευρύ περιβάλλον. Με τη χρήση του στατιστικού ελέγχου Χ2 διαπιστώθηκε ότι δεν υπάρχει σχέση μεταξύ της ειδικότητας των καθηγητών/τριών δευτεροβάθμιας εκπαίδευσης και του τύπου περιβαλλοντικής εκπαίδευσης που επιλέγουν. Στα πλαίσια της επισκόπησης έγινε προσπάθεια να διερευνηθεί αν οι εκπαιδευτικοί θεωρούν επαρκή ή ανεπαρκή την εκπαίδευσή τους ώστε να αντιμετωπίσουν επιτυχώς προγράμματα περιβαλλοντικής εκπαίδευσης. Οι απαντήσεις των εκπαιδευτικών στις ερωτήσεις που τέθηκαν γι’αυτό το σκοπό δηλώνουν ανεπάρκεια εκπαίδευσης και ίσως σχετίζονται με το συμπέρασμα που προαναφέρθηκε ότι η πλειοψηφία των ερωτηθέντων εκπαιδευτικών προτιμά να εκπονήσει προγράμματα περιβαλλοντικής εκπαίδευσης που αναφέρονται στο ευρύ περιβάλλον. Με στατιστικό έλεγχο Χ2 διαπιστώθηκε ότι δεν υπάρχει σχέση μεταξύ της ειδικότητας των καθηγητών/τριών δευτεροβάθμιας εκπαίδευσης και της επάρκειας εκπαίδευσης τους σε θέματα περιβαλλοντικής εκπαίδευσης. Τέλος παρατηρήθηκε ότι κατά την εκπόνηση των προγραμμάτων περιβαλλοντικής εκπαίδευσης υπάρχει ολιστική αντιμετώπιση της περιβαλλοντικής εκπαίδευσης σύμφωνα και με τις τρεις προσεγγίσεις μέσω, για και προς όφελος του περιβάλλοντος. Σύμφωνα με τις απαντήσεις η συντριπτική πλειοψηφία των καθηγητών/τριών που εκπονούν περιβαλλοντικά προγράμματα στο σχολείο προτιμά την εκπαιδευτική επιλογή της περιβαλλοντικής εκπαίδευσης με αγωγή με σκοπό να μεταδοθεί περιβαλλοντική ευαισθησία προσφέροντας γνώσεις για το περιβάλλον. / The field of Environmental Education in Greek Secondary Education faces many problems due to different perceptions of teachers about the meaning of Environmental Education as well as its theory and practice. A characteristic example of this misinterpretation fact is that during the School year 2004-2005 teachers from Greek prefecture of Achaia chose Environmental Education programmes about “wide Environment” including everything except the natural Environment. This emphasizes that there is not ‘common parlance’ between the Secondary Education teachers and different Environmental Education definitions exist. Thus, it is not sure that the Greek Secondary Environmental Education programmes assist still to modify human Environmental behavior and improve the quality of life. In this research, the differences in views and perceptions about Environmental Education among the Greek Secondary Education teachers coming from the prefecture of Achaia were investigated in detail. The purpose was to investigate the process of making a choise between different Environmental Education programmes and how these programmes were materialized. An important issue was to specify if this materialization comprised totally or separately the three different approaches of Environmental Education (Environmental Education through the environment, about the environment, for the environment). The aim of this research was to give answers in all questions. The sampling method of this study was the “simple random sampling”. The total sample of this method, included 306 Greek Secondary Education teachers. This population has participated in Environmental Education programs during the School year 2004-2005. We determined random sample of 55 teachers, which represents the 18% of the population. The chosen teachers came from Secondary Education schools of the Achaia prefecture area (Patras center, suburbs etc.). For the collection of data in this research we used “structured questionnaire” which included 36 questions and was given to random sample of 55 teachers. For the statistical analysis of data we used “frequency-distribution” and “X2 –distribution”tests. The results of this research showed a gap between discourse and practice and an extent from theory to act during choise and materialization procedure in all Environmental Education programmes. The teachers declared that they haven’t sufficient understood many issues about Environmental Education subjects. The different speciality of teachers make them to choose the “wide Environment” Environmental Education programmes which includes natural, social and civilizing environment. The research showed also that teachers intend to materialize Environmental Education programmes using all three approaches (Environmental Education through, about, for the environment).

This thesis presents a framework for automatic recognition of human actions in uncontrolled, realistic video data such as movies, internet and surveillance videos. In this thesis, the human action recognition problem is solved from the perspective of local spatio-temporal feature and bag-of-features representation. The bag-of-features model only contains statistics of unordered low-level primitives, and any information concerning temporal ordering and spatial structure is lost. To address this issue, we proposed a novel multiscale local part model on the purpose of maintaining both structure information and ordering of local events for action recognition. The method includes both a coarse primitive level root feature covering event-content statistics and higher resolution overlapping part features incorporating local structure and temporal relationships. To extract the local spatio-temporal features, we investigated a random sampling strategy for efficient action recognition. We also introduced the idea of using very high sampling density for efficient and accurate classification. We further explored the potential of the method with the joint optimization of two constraints: the classification accuracy and its efficiency. On the performance side, we proposed a new local descriptor, called GBH, based on spatial and temporal gradients. It significantly improved the performance of the pure spatial gradient-based HOG descriptor on action recognition while preserving high computational efficiency. We have also shown that the performance of the state-of-the-art MBH descriptor can be improved with a discontinuity-preserving optical flow algorithm. In addition, a new method based on histogram intersection kernel was introduced to combine multiple channels of different descriptors. This method has the advantages of improving recognition accuracy with multiple descriptors and speeding up the classification process. On the efficiency side, we applied PCA to reduce the feature dimension which resulted in fast bag-of-features matching. We also evaluated the FLANN method on real-time action recognition. We conducted extensive experiments on real-world videos from challenging public action datasets. We showed that our methods achieved the state-of-the-art with real-time computational potential, thus highlighting the effectiveness and efficiency of the proposed methods.

Algorithms based on Markov chains are ubiquitous across scientific disciplines, as they provide a method for extracting statistical information about large, complicated systems. Although these algorithms may be applied to arbitrary graphs, many physical applications are more naturally studied under the restriction to regular lattices. We study several local Markov chains on lattices, exploring how small changes to some parameters can greatly influence efficiency of the algorithms. We begin by examining a natural Markov Chain that arises in the context of "monotonic surfaces", where some point on a surface is sightly raised or lowered each step, but with a greater rate of raising than lowering. We show that this chain is rapidly mixing (converges quickly to the equilibrium) using a coupling argument; the novelty of our proof is that it requires defining an exponentially increasing distance function on pairs of surfaces, allowing us to derive near optimal results in many settings. Next, we present new methods for lower bounding the time local chains may take to converge to equilibrium. For many models that we study, there seems to be a phase transition as a parameter is changed, so that the chain is rapidly mixing above a critical point and slow mixing below it. Unfortunately, it is not always possible to make this intuition rigorous. We present the first proofs of slow mixing for three sampling problems motivated by statistical physics and nanotechnology: independent sets on the triangular lattice (the hard-core lattice gas model), weighted even orientations of the two-dimensional Cartesian lattice (the 8-vertex model), and non-saturated Ising (tile-based self-assembly). Previous proofs of slow mixing for other models have been based on contour arguments that allow us prove that a bottleneck in the state space constricts the mixing. The standard contour arguments do not seem to apply to these problems, so we modify this approach by introducing the notion of "fat contours" that can have nontrivial area. We use these to prove that the local chains defined for these models are slow mixing. Finally, we study another important issue that arises in the context of phase transitions in physical systems, namely how the boundary of a lattice can affect the efficiency of the Markov chain. We examine a local chain on the perfect and near-perfect matchings of the square-octagon lattice, and show for one boundary condition the chain will mix in polynomial time, while for another it will mix exponentially slowly. Strikingly, the two boundary conditions only differ at four vertices. These are the first rigorous proofs of such a phenomenon on lattice graphs.