Discrete wavelet transforms have many applications, including those in image compression and edge detection. Transforms constructed using orthogonal filters are extremely useful in that they can easily be inverted as well as coded. We review the major properties of three well-known orthogonal filters, namely, the Haar, Daubechies, and Coiflet filters. Subsequently, we analyze the Fourier series that corresponds to each of those filters and recall some important results about the smoothness of the modulus of those Fourier series. We consider a specialized case in which the length of the discrete wavelet transform is not much longer than the length of the filter used in its construction. For this case, we prove the existence of additional degrees of freedom in the system of equations used in the construction of the aforementioned orthogonal filters. We suggest a modified Coiflet filter which takes advantage of the extra degrees of freedom by imposing further conditions on the derivative of the Fourier series.

The method described here for recovering the shape of a surface from a shaded image can deal with complex, wrinkled surfaces. Integrability can be enforced easily because both surface height and gradient are represented. The robustness of the method stems in part from linearization of the reflectance map about the current estimate of the surface orientation at each picture cell. The new scheme can find an exact solution of a given shape-from-shading problem even though a regularizing term is included. This is a reflection of the fact that shape-from-shading problems are not ill-posed when boundary conditions are available or when the image contains singular points.

This quantitative study investigated the effect of client self-disclosure on the physiological arousal of the therapist and subsequent ratings of the therapeutic alliance, session smoothness, and session depth. Three therapists and 10 clients participated in a 40-minute videotaped therapy session while being attached to sensors that measured heart rate and skin conductance. The participants completed self-report questionnaires designed to assess the therapeutic alliance and session smoothness and depth immediately following the therapy session. The videotaped therapy sessions were later transcribed and coded by two independent coders for the occurrence of client self-disclosure. Correlation analyses were utilized to determine whether or not a relationship existed between client self-disclosure and the physiological arousal of the therapist. No significant relationships were found to exist between client self-disclosure and the physiological arousal of the therapist. Positive correlations were found to exist between the occurrence of client self-disclosure and the physiological arousal of the therapist as well as between the occurrence of client self-disclosure and the therapeutic alliance. The physiological arousal of the therapist was also found to be positively correlated with the strength of the therapeutic alliance.

Neste trabalho, primeiramente, exploramos certos módulos de suavidade e K - funcionais definidos na esfera unitária m - dimensional e suas propriedades, dando prioridade a suas equivalências assintóticas e comparação com o erro de melhor aproximação. Uma das principais referências utilizadas foi (DAI; XU, 2010). Posteriormente, consideramos um módulo de suavidade e um K-funcional em espaços mais gerais, os espaços compactos 2-homogêneos, classe de espaços esta que contém a classe das esferas. A relação entre estes objetos e o raio de aproximação do operador translação (translação esférica, no contexto esférico) foi estudada. As principais referências foram (PLATONOV, 2009) e (PLATONOV, 1997). / In this work, we firstly explored certain moduli of smoothness and K - functionals defined on the m-dimensional unit sphere and their properties, mainly their asymptotic equivalence and relation to the best approximation error. The main reference is (DAI; XU, 2010). Later we consider a moduli of smoothness and a K-functional on a general setting, namely two-point homogeneous spaces, which has the unit spheres as one of its classes. Relations between those tools and the rate of approximation of the shiffting operator were studied. The main references here were (PLATONOV, 2009) and (PLATONOV, 1997).

Cette thèse est principalement consacrée à des problèmes de dynamique linéaire dans les espaces de Banach. Répondant à une question récente de Hajek et Smith, on construit notamment, dans tout espace de Banach séparable, un opérateur borné tel que ses orbites tendent vers l'infini sur une partie ni vide, ni dense. On relie également, à l'aide d'un autre résultat, le module de lissité asymptotique au comportement des opérateurs bornés. / This work is mainly devoted to some problems of linear dynamics in Banach spaces. In particular, we answer a recent question of Hajek and Smith by constructing, in any separable Banach space, a bounded operator such that its orbits tending to infinity form a set which is neither empty, nor dense. We also connect the behaviour of bounded operators with the asymptotic modulus of smoothness.

It is well-known that the basic properties of a bivariate spline space such as dimension and approximation order depend on the geometric structure of the partition. The dependence of geometric structure results in the fact that the dimension of a C1 cubic spline space over an arbitrary triangulation becomes a well-known open problem. In this paper, by employing a new group of smoothness conditions and conformality conditions, we determine the dimension of bivariate C1 cubic spline spaces over a so-called even stratified triangulation.

Vehicle trajectory data has played a critical role in the recent history of traffic flow and CAV operations-related studies. However, available trajectories have limited coverage, either spatial or temporal. The implementation of CAV technology is expected to produce a large-scale trajectory dataset. However, at the initial implementation level, the trajectory data produced is expected to have gaps in terms of completeness. This research develops a data model for large-scale trajectory data that can be built on CAV-collected trajectories and easily manipulated to produce traffic parameters for CAV control and operation research. A benchmarking process has been applied to test a trajectory reconstruction approach to develop a population database from partial trajectories to fill the expected data gap in CAV feedback. The large-scale trajectory data is then used in CAV operations-related studies focusing on CAV's integration with human drivers and developing performance matrices for CAV-controlled optimized trajectories. This research used large-scale vehicle trajectory data from Wide Area Motion Imagery (WAMI) developed by PVLabs for modeling and analyzing traffic characteristics as a surrogate of CAV-collected trajectories. This timestamped location data capture provides trajectory information at an interval of one second. Trajectories from an approximate area of four-square kilometers in downtown Hamilton, Canada, are used to develop a data model to extract and store traffic characteristics. The video data was collected for two three-hour continuous periods, one in the morning and one in the evening of the same day. Like other moving object detection-based algorithms, this data suffers from false-positive detection, false-negative detection, and other positional inaccuracies caused by faulty image registration. A context-based trajectory filtering algorithm has been developed and validated against ten minutes of vehicle counts from actual WAMI images. The filtered data provides a sample of trajectories over the area, including complete and partial vehicle trajectories, excluding undetected ones. The missing trajectory reconstruction process using a dynamic state estimation process is developed to reconstruct partial and missing trajectories. A data analytics approach predicts the number of missing trajectories between two successive detections in the traffic stream on a roadway lane. A benchmarking test of the performance of the missing trajectory prediction algorithm is conducted using the NGSIM I80 database. A frame-by-frame learning method is developed to join the identified missing trajectories. This data analytics approach preserves the naturalistic property of the trajectory, which was a concern of previous traffic-flow model-based approaches. Joining partial/split trajectories provides a more comprehensive picture of the trajectory population. Due to data structure similarities, including the nature of the split and missing trajectories, the methods developed in this study to recover trajectories can be adopted for future CAV feedback data in a mixed traffic scenario. The applicability of using the large-scale trajectory data model is explored in two performance areas of CAV operations. The first is a scenario-based testing process, which evaluates the "intelligence" of a CAV in handling interactions with Human driven Vehicles (HV) by artificially replacing an HV in the traffic stream with a CAV. Scenario-based testing is conducted for a particular Operational Design Domain (ODD). The ODD is defined as operating conditions under which particular driver assistance or automated control systems are designed to function. Existing literature on scenario-based testing primarily focuses on CAV-HV interaction on highways as large-scale naturalistic trajectory data are available to facilitate such studies. This research explores car-following and lane-changing aspects of arterial CAV testing. The large-scale trajectory data model generates testing scenarios and calibrates the surrogate model for CAV operation. The modification to the trajectory data model to accommodate the scenario-based testing is illustrated. The second consists of using the large-scale trajectory data model to estimate a new trajectory smoothness parameter that can indicate the impact of intersection stop-and-go movement on the smoothness of the entire trajectory. This smoothness parameter can be applied as an optimization variable in future trajectory control-based intersection management. Long-duration trajectories from the large-scale trajectory data are used to estimate the spectral arc length parameter for trajectory smoothness. This research only estimates smoothness parameters for human-driven vehicles to illustrate its applicability for vehicle trajectories. This research developed a framework for applying expected partial trajectories from CAV technology in estimating near-complete trajectories. The large-scale data application process in two CAV operations-related studies is also provided. / Doctor of Philosophy / The decision-making process undertaken by transportation agencies for planning, evaluating, and operating transportation facilities relies on analyzing traffic and driver behavior for prevailing and future traffic conditions. The analytical tools for policy, design, decision-making, and safety analysis use aggregated and disaggregated traffic parameters. Traffic parameters are information about the dynamic state of the traffic. In the case of a vehicle, the dynamic state information can be location, speed, acceleration, heading, and spacing with other vehicles in the traffic stream. The sequence of these dynamic parameters is called vehicle trajectories in a broader term. The trajectory information is collected using several direct and indirect collection systems. The implementation of CAV technologies is expected to provide a new source of vehicle trajectory information. Trajectory data are integral to CAV safety, operational evaluation, and optimization control algorithms. Trajectory data are also used to develop, calibrate, and validate the models representing a particular aspect of human driver behavior, and the recent development of CAV has elevated the necessity and application of trajectory data. As a result, a significant demand exists in academia and industry for the procedure to create trajectories of the vehicle population in the traffic stream. The trajectory population represents the dynamic properties of all the vehicles moving over the data collection area. The primary goal of this research is to develop and apply a large-scale trajectory population database. Trajectories are typically stored in a Moving Object Database (MOD). This research leverages a MOD database collected by a new generation of Wide-Area Motion Imagery (WAMI). The WAMI system collects images from a high-altitude moving aerial platform with high-definition cameras at a fixed time interval, which captures the trajectories of vehicles in the collection area. However, validating the created trajectories for completeness and data noise revealed continuity and consistency gaps in trajectories. A multistep data mining process is undertaken to filter, process, and extract sample trajectories with reduced data noise. A trajectory reconstruction task is undertaken to reduce the data gap. A benchmarking performance test for trajectory reconstruction is conducted using NGSIM I80 data because it has been validated in multiple studies and contains trajectories of all vehicles during the collection period (i.e., trajectory population). The trajectory reconstruction methodology developed in this research can be adapted for future CAV-collected partial trajectory data. The development of the trajectory reconstruction methodology and training data created from NGSIM I80 is one of the main contributions of this research in the field of trajectory reconstruction. Several traffic flow measures are then estimated from the sample trajectories that outline the analytical requirements to integrate trajectory data with roadway infrastructure. A data model is developed to store and manipulate dynamic trajectory parameters efficiently. The resulting data processing and integration process can be applied to CAV-collected trajectories to create an analytical trajectory database. The large-scale trajectory database is used to illustrate its capability in evaluating CAV operating models, specifically the car-following and lane-changing models on an arterial network. The car-following model mimics the longitudinal movement of real-world drivers following another vehicle. The lane-changing model predicts lane-changing behavior due to path-planning requirements and navigating surrounding traffic conditions. The overall operational model evaluation process is called accelerated evaluation, in which the naturalistic vehicle movement data is used to measure CAV's operational and safety performance. For a second application of the large-scale trajectory data, long-duration trajectories are used to develop a trajectory smoothness performance measure that can be used to test different trajectory control approaches for intersection movement management. This research is one of the early attempts to leverage large-scale vehicle trajectory datasets in transportation engineering applications. Its primary contribution is the development of a comprehensive trajectory validation methodology that can be applied to future CAV feedback to produce a trajectory population database with enhanced analytical capability. The secondary output of this research is benchmarking results for different analytical methodologies to develop the trajectories that can be used in future research and development as a reference.

While moment matching can effectively reduce the dimension of a linear, time-invariant system, it can simultaneously fail to improve the stable time-step for the forward Euler scheme. In the context of a semi-discrete heat equation with spatially smooth forcing, the high frequency modes are virtually insignificant. Eliminating such modes dramatically improves the stable time-step without sacrificing output accuracy. This is accomplished by modal filtration, whose computational cost is relatively palatable when applied following an initial reduction stage by moment matching. A bound on the norm of the difference between the transfer functions of the moment-matched system and its modally-filtered counterpart yields an intelligent choice for the mode of truncation. The dual-stage algorithm disappoints in the context of highly nonnormal semi-discrete convection-diffusion equations. There, moment matching can be ineffective in dimension reduction, precluding a cost-effective modal filtering step.

A capacidade de resistência à corrosão sofrida pelas próteses dentais confeccionadas com ligas metálicas é de grande importância na clínica odontológica devido à ocorrência de possíveis reações biológicas, como por exemplo, sintomas alérgicos e degradação das restaurações. Em razão da presença de fatores diversos agindo no meio oral, todo material restaurador, metálico ou não, sofre uma ação de deterioração em sua superfície, seja por variação de pH, dieta alimentar, temperatura ou mastigação. Houve evolução de novas ligas metálicas, entre elas o titânio (Ti), que apresenta propriedades físicas e biocompatíveis excelentes, sendo um material muito utilizado em vários setores relacionados à área odontológica, principalmente na indústria de implantes dentais. Nesse estudo foi avaliada a rugosidade superficial de duas ligas metálicas (Ti e Ni Cr ) em três fases distintas, através de leituras realizadas pelo rugosímetro de superfície nos corpos de prova, submetidos à ciclagem térmica e submersos em saliva artificial à temperatura constante de 37 graus centígrados, por um período de 8 meses. Através dos resultados estatísticos obtidos, conclui-se que não existe diferença entre as ligas, no tocante aos fatores tempo e aspecto visual, havendo somente diferença significante entre as fases I e III do estudo. / The resistance capacity to corrosion to which the dental prosthesis made in mettalic alloys are subject has a major importance in the dental clinic, due to the occurance of possible biological reactions such as, for example, allergic symptoms and degradation of restorations. As there are several factors acting in the oral medium, every restoration material, either metallic or not, is subject to a deterioration action in its surface, caused by pH variation, alimentary diet, temperature and chewing. New metallic alloys have been developed, among them the Titanium (Ti), which presents excellent acceptance in the dentistry area , mainly in the industry of dental implants. This study appraised the superficial rugosity of two metallic alloys Titanium e Nickel Chromium (Ni Cr) in three different phases , through readings made by the surface rugosimeter in the test bodies, submitted to thermal cycling and submerged in artificial saliva at constant temperature of 37 degrees, for a period of 8 months. Through the achieved statistic results, it may be concluded that there is no difference between the alloys, concerning the time and visual aspect factors, there being a significant difference only between phases I and III of the study.

In this abstract, we present a nonlinear curvelet-based sparsity-promoting formulation of a seismic processing flow, consisting of the following steps: seismic data regularization and the restoration of migration amplitudes. We show that the curvelet's wavefront detection capability and invariance under the migration-demigration operator lead to a formulation that is stable under noise and missing data.