This thesis consists of an introduction and five papers, of which two contribute to the theory of directed random graphs and three to the theory of greedy walks on point processes.           We consider a directed random graph on a partially ordered vertex set, with an edge between any two comparable vertices present with probability p, independently of all other edges, and each edge is directed from the vertex with smaller label to the vertex with larger label. In Paper I we consider a directed random graph on ℤ2 with the vertices ordered according to the product order and we show that the limiting distribution of the centered and rescaled length of the longest path from (0,0) to (n, [na] ), a<3/14, is the Tracy-Widom distribution. In Paper II we show that, under a suitable rescaling, the closure of vertex 0 of a directed random graph on ℤ with edge probability n−1 converges in distribution to the Poisson-weighted infinite tree. Moreover, we derive limit theorems for the length of the longest path of the Poisson-weighted infinite tree.           The greedy walk is a deterministic walk on a point process that always moves from its current position to the nearest not yet visited point. Since the greedy walk on a homogeneous Poisson process on the real line, starting from 0, almost surely does not visit all points, in Paper III we find the distribution of the number of visited points on the negative half-line and the distribution of the index at which the walk achieves its minimum. In Paper IV we place homogeneous Poisson processes first on two intersecting lines and then on two parallel lines and we study whether the greedy walk visits all points of the processes. In Paper V we consider the greedy walk on an inhomogeneous Poisson process on the real line and we determine sufficient and necessary conditions on the mean measure of the process for the walk to visit all points.

We develop a numerical method for solving singular differential equations and demonstrate the method on a variety of singular problems including first order ordinary differential equations, second order ordinary differential equations which have variational principles, and one partial differential equation.

Northeastern forests are being impacted by unprecedented environmental stressors, including acid deposition, invasive pests, and climate change. Forest health monitoring at a landscape scale is necessary to evaluate the changing condition of forest resources and to inform management of forest stressors. Traditional forest health monitoring is often limited to specific sites experiencing catastrophic decline or widespread mortality. Satellite remote sensing can complement these efforts by providing comprehensive forest health assessments over broad regions. Subtle changes in canopy health can be monitored over time by applying spectral vegetation indices to multitemporal satellite imagery. This project used historical archives of Landsat-5 TM imagery and geographic information systems to examine forest health trends in the northern Green Mountains of Vermont from 1984 to 2009. Results indicate that canopy health has remained relatively stable across most of the landscape, although decline was present in localized areas. Significant but weak relationships were discovered between declining forest health and spruce-fir-paper birch forests at high elevations. Possible causes of decline include the interacting effects of acid deposition, windthrow, and stressful growing environments typical of montane forests.

Context. The advances in location-acquisition and mobile computing techniques have generated massive spatial trajectory data. Such spatial trajectory data accumulated by telecommunication operators is huge, analyzing the data with a right tool or method can uncover patterns and connections which can be used for improving telecom services. Forecasting trajectory data or predicting next location of users is one of such analysis. It can be used for producing synthetic data and also to determine the network capacity needed for a cell tower in future. Objectives. The objectives of this thesis is, Firstly, to have a new application for CWT (Collapsed Weighted Tensor) method. Secondly, to modify the CWT method to predict the location of a user. Thirdly, to provide a suitable method for the given Telenor dataset to predict the user’s location over a period of time.   Methods. The thesis work has been carried out by implementing the modified CWT method. The predicted location obtained by modified CWT cannot be determined to which time stamp it belongs as the given Telenor dataset contains missing time stamps. So, the modified CWT method is implemented in two different methods. Replacing missing values with first value in dataset. Replacing missing values with second value in dataset. These two methods are implemented and determined which method can predict the location of users with minimal error.   Results. The results are carried by assuming that the given Telenor dataset for one week will be same as that for the next week. Users are selected in a random sample and above mentioned methods are performed. Furthermore, RMSD values and computational time are calculated for each method and selected users.   Conclusion. Based on the analysis of the results, Firstly, it can be concluded that CWT method have been modified and used for predicting the user’s location for next time stamp. Secondly, the method can be extended to predict over a period of time. Finally, modified CWT method predicts location of the user with minimal error when missing values are replaced by first value in the dataset.

Drinking groundwater is the primary way humans accumulate arsenic. Chronic exposure to inorganic arsenic (iAs) (over decades) has been shown to be associated with multiple health effects at low levels (5-10 ppb) including: cancer, elevated blood pressure and cardiovascular disease, skin lesions, renal failure, and peripheral neuropathy. Using hypertension (or high blood pressure) as a surrogate marker for cardiovascular disease, we examined the effect of iAs alone and in a mixture with other metals using a cross-sectional study of adults in United States (National Health and Examination Survey, NHANES, 2005-2010) adjusting for covariates: urinary creatinine level (mg/dL), poverty index ratio (PIR, measure of socioeconomic status, 1 to 5), age, smoking (yes/no), alcohol usage, gender, non-Hispanic Black, and overweight (BMI>=25). A logistic regression model suggests that a one-unit increase in log of inorganic arsenic increases the odds of hypertension by a factor of 1.093 (95% Confidence Interval=0.935, 1.277) adjusted for these covariates , which indicates that there was not significant evidence to claim that inorganic arsenic is a risk factor for hypertension. Biomonitoring data provides evidence that humans are not only exposed to inorganic arsenic but also to mixtures of chemicals including inorganic arsenic, total mercury, cadmium, and lead. We tested for a mixture effect of these four environmental chemicals using weighted quantile sum (WQS) regression, which takes into account the correlation among the chemicals and with the outcome. For one-unit increase in the weighted sum, the adjusted odds of developing hypertension increases by a factor of 1.027 (95% CI=0.882,1.196), which is also not significant after taking into account the same covariates. The insignificant finding may be due to the low inorganic arsenic concentration (8-620 μg /L) in US drinking water, compared to those in countries like Bangladesh where the concentrations are much higher. Literature provides conflicting evidence of the association of inorganic arsenic and hypertension in low/moderate regions; future studies, especially a large cohort study, are needed to confirm if inorganic arsenic alone or with other metals is associated with hypertension in the United States.

A fuzzy set is one in which membership in a category is not Boolean, rather items have a degree of membership. Fuzzy databases expand on this idea by storing fuzzy data and allowing data to be retrieved based on its degree of membership. Determining the degree of membership that satisfies the largest number of users is difficult. Five different methods of determining the membership function: the Direct Rating Method, the Random Method with step sizes of .02 and .03, the Steplock Method, and the Weighted Average Method, were compared on the basis of convergence and user satisfaction. The results support use of the Direct Rating Method and the Steplock Method in conjunction with each other, to produce the membership function in the least time and with the highest user satisfaction.

Title: Optimal pairs of function spaces for weighted Hardy operators Author: Rastislav Ol'hava Department: Department of Mathematical Analysis Supervisor of the master thesis: Prof. RNDr. Luboš Pick, CSc., DSc., Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic Abstrakt: We focus on a certain weighted Hardy operator, with a continuous, quasi- concave weight, defined on a rearrangement-invariant Banach function spaces. The op- erators of Hardy type are of great use to the theory of function spaces. The mentioned operator is a more general version of the Hardy operator, whose boundedness was shown to be equivalent to a Sobolev-type embedding inequality. This thesis is con- cerned with the proof of existence of domain and range spaces of our Hardy operator that are optimal. This optimality should lead to the optimality in the Sobolev-type embedding equalities. Our another aim is to study supremum operators, which are also closely related to this issue, and establish some of their basic properties. Keywords: optimality, weighted Hardy operator, supremum operator

Doctor of Philosophy / Department of Geography / Douglas G. Goodin / Jesse A. Poland / Kevin Price / Wheat breeders are in a race for genetic gain to secure the future nutritional needs of a growing population. Multiple barriers exist in the acceleration of crop improvement. Emerging technologies are reducing these obstacles. Advances in genotyping technologies have significantly decreased the cost of characterizing the genetic make-up of candidate breeding lines. However, this is just part of the equation. Field-based phenotyping informs a breeder’s decision as to which lines move forward in the breeding cycle. This has long been the most expensive and time-consuming, though most critical, aspect of breeding. The grand challenge remains in connecting genetic variants to observed phenotypes followed by predicting phenotypes based on the genetic composition of lines or cultivars. In this context, the current study was undertaken to investigate the utility of UAS in assessment field trials in wheat breeding programs. The major objective was to integrate remotely sensed data with geospatial analysis for high throughput phenotyping of large wheat breeding nurseries. The initial step was to develop and validate a semi-automated high-throughput phenotyping pipeline using a low-cost UAS and NIR camera, image processing, and radiometric calibration to build orthomosaic imagery and 3D models. The relationship between plot-level data (vegetation indices and height) extracted from UAS imagery and manual measurements were examined and found to have a high correlation. Data derived from UAS imagery performed as well as manual measurements while exponentially increasing the amount of data available. The high-resolution, high-temporal HTP data extracted from this pipeline offered the opportunity to develop a within season grain yield prediction model. Due to the variety in genotypes and environmental conditions, breeding trials are inherently spatial in nature and vary non-randomly across the field. This makes geographically weighted regression models a good choice as a geospatial prediction model. Finally, with the addition of georeferenced and spatial data integral in HTP and imagery, we were able to reduce the environmental effect from the data and increase the accuracy of UAS plot-level data. The models developed through this research, when combined with genotyping technologies, increase the volume, accuracy, and reliability of phenotypic data to better inform breeder selections. This increased accuracy with evaluating and predicting grain yield will help breeders to rapidly identify and advance the most promising candidate wheat varieties.

<div>Classification is an important supervised learning technique with numerous applications. This dissertation addresses two research problems in this area. The first is multicategory classification methods for high dimensional data. To handle high dimension low sample size (HDLSS) data with uneven group sizes (i.e., imbalanced data), we develop a new classification method called angle-based multicategory distance-weighted support vector machine (MDWSVM). It is motivated from its binary counterpart and has the merits of both the support vector machine (SVM) and distance-weighted discrimination (DWD) methods while alleviating both the data piling issue of SVM and the imbalanced data issue of DWD. Theoretical results and numerical studies are used to demonstrate the advantages of our MDWSVM method over existing methods.</div><div><br></div><div>The second part of the dissertation is on the application of classification methods to precision medicine problems. Because one-stage precision medicine problems can be reformulated as weighted classification problems, the subtle differences between classification methods may lead to different application performances under this setting. Among the margin-based classification methods, we propose to use the distance weighted discrimination outcome weighted learning (DWD-OWL) method. We also extend the model to handle negative rewards for better generality and apply the angle-based idea to handle multiple treatments. The proofs of Fisher consistency for DWD-OWL in both the binary and multicategory cases are provided. Under mild conditions, the insensitivity of DWD-OWL for imbalanced setting is also demonstrated.</div>

This study aims to answer whether a heuristic that trades cycles between the tours in a solution would show good results when trying to solve the Weighted k-Chinese Postman Problem for undirected graphs, of varying size, representing neighbourhoods in Sweden.A tabu search heuristic was implemented with each iteration consisting of giving a cycle from the most expensive tour to the cheapest. The heuristic performed increasingly well for graphs of increasing size, although the solution quality decreased when increasing the number of tours to be used in the solution. It is suspected that the cause for this behavior is due to the heuristic only giving cycles from the most expensive tour, not considering trading cycles from other tours in the solution. It is believed that a heuristic considering more than only the most expensive tour when trading cycles would produce even better solutions.