The histogram is an analysis tool in widespread use within many sciences, with high energy physic... more The histogram is an analysis tool in widespread use within many sciences, with high energy physics as a prime example. However, there exists an inherent bias in the choice of binning for the histogram, with different choices potentially leading to different interpretations. This paper aims to eliminate this bias using two "debinning" algorithms. Both algorithms generate an observed cumulative distribution function from the data, and use it to construct a representation of the underlying probability distribution function. The strengths and weaknesses of these two algorithms are compared and contrasted. The applicability and future prospects of these algorithms is also discussed.
The main result of this thesis is the development of a theory of semidefinite facial reduction fo... more The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean dis-tance matrix and faces of the ...
Page 1. NUMERICAL SOLUTION OF SEMIDEFINITE CONSTRAINED LEAST SQUARES PROBLEMS by NATHAN GAVIN BEA... more Page 1. NUMERICAL SOLUTION OF SEMIDEFINITE CONSTRAINED LEAST SQUARES PROBLEMS by NATHAN GAVIN BEAUREGARD KRISLOCK B.Sc. Hon. (Combined Math/Computer Science) University of Regina, 2000 ...
We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with ... more We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with anchors and with noisy distance information. The main point of the paper is to view \SNL as a (nearest) Euclidean Distance Matrix, \EDM, completion problem and to show the advantages for using this latter, well studied model. We first show that the current popular \SDP relaxation is equivalent
The sensor network localization, SNL, problem in embedding dimension r, consists of locating the ... more The sensor network localization, SNL, problem in embedding dimension r, consists of locating the positions of wireless sensors, given only the distances between sensors that are within radio range and the positions of a subset of the sensors (called anchors). Current solu- tion techniques relax this problem to a weighted, nearest, (positive) semidefinite programming, SDP,completion problem, by using the linear
Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reason... more Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reasons. The first reason is that the many applications of EDMs, such as molecular conformation in bioinformatics, dimensionality reduction in machine learning and statistics, and especially the problem of wireless sensor network localization, have all become very active areas of research. The second reason for this increased interest is the close connection between EDMs and semidefinite matrices. Our recent ability to solve semidefinite programs efficiently means we can now also solve many problems involving EDMs efficiently. This chapter connects the classical approaches for EDMs with the more recent tools from semidefinite programming. We emphasize the application to sensor network localization.
Introduction. The quality of municipal water supplies has become an issue of great importance for... more Introduction. The quality of municipal water supplies has become an issue of great importance for large, urban centres. Widespread industrialisation, pollution, and development of areas close to traditional water sources have all contributed to the degradation of our drinking water, and made the topic a subject of heated debate. Officials and planners at all levels of government have recognised the need to manage water distribution networks so as to maintain acceptable levels of water quality. Because of the complexity of even the simplest of flow networks, numerical computations have become an essential tool in the water quality management process, and simulations of networks with hundreds of junctions, pumping stations, tanks and reservoirs are commonplace [4]. The forward or dynamic simulation of water networks with known characteristics and contaminant inputs is fairly well-understood, and software packages such as Epanet [5], which is freely-available ove
The histogram is an analysis tool in widespread use within many sciences, with high energy physic... more The histogram is an analysis tool in widespread use within many sciences, with high energy physics as a prime example. However, there exists an inherent bias in the choice of binning for the histogram, with different choices potentially leading to different interpretations. This paper aims to eliminate this bias using two "debinning" algorithms. Both algorithms generate an observed cumulative distribution function from the data, and use it to construct a representation of the underlying probability distribution function. The strengths and weaknesses of these two algorithms are compared and contrasted. The applicability and future prospects of these algorithms is also discussed.
The main result of this thesis is the development of a theory of semidefinite facial reduction fo... more The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean dis-tance matrix and faces of the ...
Page 1. NUMERICAL SOLUTION OF SEMIDEFINITE CONSTRAINED LEAST SQUARES PROBLEMS by NATHAN GAVIN BEA... more Page 1. NUMERICAL SOLUTION OF SEMIDEFINITE CONSTRAINED LEAST SQUARES PROBLEMS by NATHAN GAVIN BEAUREGARD KRISLOCK B.Sc. Hon. (Combined Math/Computer Science) University of Regina, 2000 ...
We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with ... more We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with anchors and with noisy distance information. The main point of the paper is to view \SNL as a (nearest) Euclidean Distance Matrix, \EDM, completion problem and to show the advantages for using this latter, well studied model. We first show that the current popular \SDP relaxation is equivalent
The sensor network localization, SNL, problem in embedding dimension r, consists of locating the ... more The sensor network localization, SNL, problem in embedding dimension r, consists of locating the positions of wireless sensors, given only the distances between sensors that are within radio range and the positions of a subset of the sensors (called anchors). Current solu- tion techniques relax this problem to a weighted, nearest, (positive) semidefinite programming, SDP,completion problem, by using the linear
Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reason... more Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reasons. The first reason is that the many applications of EDMs, such as molecular conformation in bioinformatics, dimensionality reduction in machine learning and statistics, and especially the problem of wireless sensor network localization, have all become very active areas of research. The second reason for this increased interest is the close connection between EDMs and semidefinite matrices. Our recent ability to solve semidefinite programs efficiently means we can now also solve many problems involving EDMs efficiently. This chapter connects the classical approaches for EDMs with the more recent tools from semidefinite programming. We emphasize the application to sensor network localization.
Introduction. The quality of municipal water supplies has become an issue of great importance for... more Introduction. The quality of municipal water supplies has become an issue of great importance for large, urban centres. Widespread industrialisation, pollution, and development of areas close to traditional water sources have all contributed to the degradation of our drinking water, and made the topic a subject of heated debate. Officials and planners at all levels of government have recognised the need to manage water distribution networks so as to maintain acceptable levels of water quality. Because of the complexity of even the simplest of flow networks, numerical computations have become an essential tool in the water quality management process, and simulations of networks with hundreds of junctions, pumping stations, tanks and reservoirs are commonplace [4]. The forward or dynamic simulation of water networks with known characteristics and contaminant inputs is fairly well-understood, and software packages such as Epanet [5], which is freely-available ove
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