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In computer graphics, algorithms that attempt to create photographic images by simulating light transport are collectively known as Global Illumination methods. The most versatile of these are based on ray tracing (following ray paths through a scene), and numerical integration using random or quasi-random sampling. While ray tracing and sampling methods in global illumination have progressed much in the last two decades, the goal of fast and accurate simulation of light transport remains elusive. This dissertation presents a number of new sampling methods that attempt to address some of the shortcomings of existing global illumination algorithms. The first part of the dissertation concentrates on memory issues related to ray tracing of large scenes. In this part, we present memory-efficient lightweight bounding volumes as a data structure that can substantially reduce the memory overhead of a ray tracer, allowing more complicated scenes to be ray traced without complicated caching schemes. Part two of the dissertation concerns itself with sampling algorithms related to direct lighting, an important subset of global illumination. In this part, we develop two stage importance sampling} to sample the product of the BRDF function and a large light source such as an environment map. We then extend this method to include all three terms of the direct lighting equation, sampling the triple product of the BRDF, lighting and visibility. We show that the new sampling methods have a number of advantages over existing direct lighting algorithms, including comparatively low memory overhead, little precomputation, and the ability to sample all three terms of the direct lighting equation. Finally, the third part of the dissertation discusses sampling algorithms in the context of general global illumination. In this part, we develop two new algorithms that attempt to improve the sampling distribution over existing techniques by exploiting information gained during the course of sampling. The first of these methods, energy redistribution path tracing, works by using path mutation to spread energy, and thus share sampling information, between pixels. The second method, sample swarming, shares information gained during sampling by keeping importance maps for each pixel in the rendered image. Whenever a new pixel is to be rendered, the maps from neighboring pixels are averaged, propagating importance information through the scene. We demonstrate that both of these methods can perform substantially better than existing global illumination algorithms in a number of common rendering contexts.

Inductively coupled plasma - mass spectrometry (ICP-MS) is the technique of choice worldwide for trace elemental determinations because of its excellent ionization ability, low detection limits and fast analysis speeds. However, the ICP-MS still suffers from some disadvantages, such as spectral overlap and severe matrix effects. Matrix effects or interferences, partly arise from changes in the analyte transmission through the interfacial region between the ICP and mass spectrometer with changes in sample matrix. Better understanding of the transmission behaviors of analyte through the sampling and skimmer cones will provide the insights needed to alleviate matrix interferences and to improve the interface design between the ICP and mass spectrometer. Laser induced fluorescence is a highly sensitive, non-invasive and element specific detection method. The research herein endeavors to explain the transport behaviors of analytes upstream and downstream from the sampling cone in an ICP-MS. The final goal of this research is to improve the consistency and efficiency with which ions are transported from an ICP source to a mass analyzer. Several issues related to analyte transmission through the sampling and skimmer cones have been explored and discussed in this dissertation. First, it is found that the existence of the sampling cone not only disturbs the local thermodynamic equilibrium of the plasma, but also changes the spatial distributions and number densities of analyte species. Second, it has been verified that the spread of analyte species in the first vacuum stage is mass-dependent and can be explained by ambiploar diffusion theory. Finally, the current research suggests that the transmission efficiencies of the skimmer cone are impacted by the nebulizer flow and first vacuum stage pressure of the ICP-MS. To better elucidate the analyte transport behaviors from the plasma to the ion detector in an ICP-MS, more investigation needs to be carried out. Further research, such as the entire measurements of analyte transmission efficiency through the skimmer cone, the variation of doubly charged ions under different plasma operational conditions, and the functions of argon metastable atoms on analyte ionization inside the plasma will require much additional work.

The ability to robustly fit structures in datasets that contain outliers is a very important task in Image Processing, Pattern Recognition and Computer Vision. Random Sampling Consensus or RANSAC is a very popular method for this task, due to its ability to handle over 50% outliers. The problem with RANSAC is that it is only capable of finding a single structure. Therefore, if a dataset contains multiple structures, they must be found sequentially by finding the best fit, removing the points, and repeating the process. However, removing incorrect points from the dataset could prove disastrous. This thesis offers a novel approach to sampling consensus that extends its ability to discover multiple structures in a single iteration through the dataset. The process introduced is an unsupervised method, requiring no previous knowledge to the distribution of the input data. It uniquely assigns labels to different instances of similar structures. The algorithm is thus called Labeled Sampling Consensus or L-SAC. These unique instances will tend to cluster around one another allowing the individual structures to be extracted using simple clustering techniques. Since divisions instead of modes are analyzed, only a single instance of a structure need be recovered. This ability of L-SAC allows a novel sampling procedure to be presented “compressing” the required samples needed compared to traditional sampling schemes while ensuring all structures have been found. L-SAC is a flexible framework that can be applied to many problem domains.

Sampling and interpolation are two important topics in signal processing. Signal processing is a vast field of study that deals with analysis and operations of signals such as sounds, images, sensor data, telecommunications and so on. It also utilizes many mathematical theories such as approximation theory, analysis and wavelets. This dissertation is divided into two chapters: Modified Pal´ Interpolation and Sampling Bilevel Signals with Finite Rate of Innovation. In the first chapter, we introduce a new interpolation process, the modified Pal interpolation, based on papers by P ´ al, J ´ oo´ and Szabo, and we establish the existence and uniqueness of interpolation polynomials of modified ´ Pal type. ´ The paradigm to recover signals with finite rate of innovation from their samples is a fairly recent field of study. In the second chapter, we show that causal bilevel signals with finite rate of innovation can be stably recovered from their samples provided that the sampling period is at or above the maximal local rate of innovation, and that the sampling kernel is causal and positive on the first sampling period. Numerical simulations are presented to discuss the recovery of bilevel causal signals in the presence of noise.

Studies investigating Escherichia coli strain diversity and demographics in human hosts are frequently inconsistent regarding sampling effort and methodology while current strain typing methods are often expensive or laborious. To rectify these inconsistencies, sampling effort was investigated by comparing the diversity of 15-isolate collections to 100-isolate collections from 3 human subjects. Temporal variation in E. coli strain diversity was also studied by collecting 15 isolates once every 6 months. Additionally, strain identification and diversity collected by different sampling methods (fecal swabs vs. anal swabs collected at different times around defecation) were compared to identify any inherent biases in sampling method. This study employed pyroprinting, a new inexpensive and simple strain typing method using pyrosequencing, to generate DNA fingerprints (or pyroprints) based on the Intergenic Transcribed Spacer sequences in the ribosomal RNA operon to differentiate E. coli strains. Differences in strain diversity were apparent when comparing sampling efforts. The sampling effort investigation suggested that certain subjects hosted very large and highly diverse E. coli strain populations such that even 100 isolates may not fully represent E. coli strain populations in human hosts. Instead, the sampling effort required to accurately represent strain demographics may depend on strain richness and evenness within each host. The temporal investigation yielded similar or greater strain abundance and diversity compared to other typing methods in the literature suggesting pyroprinting is a similarly discriminating tool. When agglomerated over time or by subject, no significant differences in diversity were observed between subjects or between sampling methods despite visible differences in strain richness and evenness.

Social and computer networks permeate our lives. Large networks, such as the Internet, the World Wide Web (WWW), AND wireless smartphones, have indisputable economic and social importance. These networks have non-trivial topological features, i.e., features that do not occur in simple networks such as lattices or random networks. Estimating characteristics of these networks from incomplete (sampled) data is a challenging task. This thesis provides two frameworks within which common measurement tasks are analyzed and new, principled, measurement methods are designed. The first framework focuses on sampling directly observable network characteristics. This framework is applied to design a novel multidimensional random walk to efficiently sample loosely connected networks. The second framework focuses on the design of measurement methods to estimate indirectly observable network characteristics. This framework is applied to design two new, principled, estimators of flow size distributions over Internet routers using (1) randomly sampled IP packets and (2) a data stream algorithm.

Converting an analog signal to digital involves more than just digitizing some measurements. Consequences result from sampling an analog signal and care has to be taken to capture all the desired frequencies and avoid creating new ones.

This thesis is in two parts. Part A is about the study of the LD-4 Regenerator and Part B is about Lasing Action. Both are essential for the completion of Stephen Brown's Master of Engineering Degree. / <p>The switching mechanism of the LD-4 regenerator is studied by applying triangular signals with variable slope and phasing with respect to the sampling pulse in order to investigate their effect on the output signal voltage. Experimental results are obtained in the form of finite sampling crosshairs. These represent the family of input signals that produce all output between the 0 and 1 state. In effect they characterize PST input signals at the N^(th) regenerator to the eventual PST signals at the N+1^(th) regenerator input. </p><p> An attempt is a 1 so made to correlate the experimenta 1 data with either a constant voltage or constant charge sensitivity model in order to understand the mechanism of sampling. </p><p>Results of a detailed investigation of the time-dependence of the stimulated emission from electron-beam pumped CdS platelets are reported. Unlike lower threshold platelets previously reported (1), the platelet examined here exhibits rapid tuning with time of the stimulated emission to longer wavelength. The rate of this frequency tuning canpares favourably with the value reported by Shewchun et al (2) for CdS crystals many times thicker and with a higher threshold than the one measured in this report. Furthermore, there is a temporal variation of the angular position of the spatial mode. This temporal variation or angular tuning rate was compared with angular tuning data reported for GaAs and CdSe as well as with the theory that predicts such tuning in these crystals (3). </p> / Thesis / Master of Engineering (ME)

The Frank-Wolfe (FW) optimization algorithm, due to its projection free property, has gained popularity in recent years with typical application within the field of machine learning. In the stochastic setting, it is still relatively understudied in comparison to the more expensive projected method of Stochastic Gradient Descent (SGD). We propose a novel Stochastic Frank-Wolfe (SFW) algorithm, inspired by SGDo where random sampling is considered without replacement. In analogy to this abbreviation, we call the proposed algorithm SFWo. We consider a convex setting of gradient Lipschitz (smooth) functions over compact domains. Depending on experiment design (LASSO, Matrix Sensing, Matrix Completion), the SFWo algorithm, exhibits a faster or matching empirical convergence, and a tendency of bounded suboptimality by the precursor SFW. Benchmarks on both synthetic and real world data display that SFWo improves on the number of stochastic gradient evaluations needed to achieve the same guarantee as SFW. / Intresset för Frank-Wolfes (FW) optimeringsalgoritm har tack vare dess projektionsfria egenskap ökat de senaste åren med typisk tillämpning inom området maskininlärning. I sitt stokastiska uförande är den fortfarande relativt understuderad i jämförelse med den dyrare projicerande metoden Stochastic Gradient Descent (SGD). Vi föreslår en ny Stochastic Frank-Wolfe(SFW) algoritm, inspirerad av SGDo där slumpmässigt urval görs utan återläggning. I analogi med denna förkortning så kallar vi den föreslagna algoritmen SFWo. Vi betraktar en konvex miljö och gradient Lipschitz kontinuerliga (släta) funktioner över kompakta definitionsmängder. Beroende på experimentdesign (LASSO, Matrix Sensing, Matrix Completion) så visar den föreslagna algoritmen SFWo på en snabbare eller matchande empirisk konvergens och tenderar vara begränsad i suboptimalitet av föregångaren SFW. Prestandajämförelser på både syntetisk och verklig data visar att SFWo förbättrarantalet stokastiska gradientevalueringar som behövs för att uppnå samma garanti som för SFW.