Recurrent neural network for optimization with application to computer vision.

by Cheung Kwok-wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 1993.Includes bibliographical references (leaves [146-154]).Chapter Chapter 1 --- IntroductionChapter 1.1 --- Programmed computing vs. neurocomputing --- p.1-1Chapter 1.2 --- Development of neural networks - feedforward and feedback models --- p.1-2Chapter 1.3 --- State of art of applying recurrent neural network towards computer vision problem --- p.1-3Chapter 1.4 --- Objective of the Research --- p.1-6Chapter 1.5 --- Plan of the thesis --- p.1-7Chapter Chapter 2 --- BackgroundChapter 2.1 --- Short history on development of Hopfield-like neural network --- p.2-1Chapter 2.2 --- Hopfield network model --- p.2-3Chapter 2.2.1 --- Neuron's transfer function --- p.2-3Chapter 2.2.2 --- Updating sequence --- p.2-6Chapter 2.3 --- Hopfield energy function and network convergence properties --- p.2-1Chapter 2.4 --- Generalized Hopfield network --- p.2-13Chapter 2.4.1 --- Network order and generalized Hopfield network --- p.2-13Chapter 2.4.2 --- Associated energy function and network convergence property --- p.2-13Chapter 2.4.3 --- Hardware implementation consideration --- p.2-15Chapter Chapter 3 --- Recurrent neural network for optimizationChapter 3.1 --- Mapping to Neural Network formulation --- p.3-1Chapter 3.2 --- Network stability verse Self-reinforcement --- p.3-5Chapter 3.2.1 --- Quadratic problem and Hopfield network --- p.3-6Chapter 3.2.2 --- Higher-order case and reshaping strategy --- p.3-8Chapter 3.2.3 --- Numerical Example --- p.3-10Chapter 3.3 --- Local minimum limitation and existing solutions in the literature --- p.3-12Chapter 3.3.1 --- Simulated Annealing --- p.3-13Chapter 3.3.2 --- Mean Field Annealing --- p.3-15Chapter 3.3.3 --- Adaptively changing neural network --- p.3-16Chapter 3.3.4 --- Correcting Current Method --- p.3-16Chapter 3.4 --- Conclusions --- p.3-17Chapter Chapter 4 --- A Novel Neural Network for Global Optimization - Tunneling NetworkChapter 4.1 --- Tunneling Algorithm --- p.4-1Chapter 4.1.1 --- Description of Tunneling Algorithm --- p.4-1Chapter 4.1.2 --- Tunneling Phase --- p.4-2Chapter 4.2 --- A Neural Network with tunneling capability Tunneling network --- p.4-8Chapter 4.2.1 --- Network Specifications --- p.4-8Chapter 4.2.2 --- Tunneling function for Hopfield network and the corresponding updating rule --- p.4-9Chapter 4.3 --- Tunneling network stability and global convergence property --- p.4-12Chapter 4.3.1 --- Tunneling network stability --- p.4-12Chapter 4.3.2 --- Global convergence property --- p.4-15Chapter 4.3.2.1 --- Markov chain model for Hopfield network --- p.4-15Chapter 4.3.2.2 --- Classification of the Hopfield markov chain --- p.4-16Chapter 4.3.2.3 --- Markov chain model for tunneling network and its convergence towards global minimum --- p.4-18Chapter 4.3.3 --- Variation of pole strength and its effect --- p.4-20Chapter 4.3.3.1 --- Energy Profile analysis --- p.4-21Chapter 4.3.3.2 --- Size of attractive basin and pole strength required --- p.4-24Chapter 4.3.3.3 --- A new type of pole eases the implementation problem --- p.4-30Chapter 4.4 --- Simulation Results and Performance comparison --- p.4-31Chapter 4.4.1 --- Simulation Experiments --- p.4-32Chapter 4.4.2 --- Simulation Results and Discussions --- p.4-37Chapter 4.4.2.1 --- Comparisons on optimal path obtained and the convergence rate --- p.4-37Chapter 4.4.2.2 --- On decomposition of Tunneling network --- p.4-38Chapter 4.5 --- Suggested hardware implementation of Tunneling network --- p.4-48Chapter 4.5.1 --- Tunneling network hardware implementation --- p.4-48Chapter 4.5.2 --- Alternative implementation theory --- p.4-52Chapter 4.6 --- Conclusions --- p.4-54Chapter Chapter 5 --- Recurrent Neural Network for Gaussian FilteringChapter 5.1 --- Introduction --- p.5-1Chapter 5.1.1 --- Silicon Retina --- p.5-3Chapter 5.1.2 --- An Active Resistor Network for Gaussian Filtering of Image --- p.5-5Chapter 5.1.3 --- Motivations of using recurrent neural network --- p.5-7Chapter 5.1.4 --- Difference between the active resistor network model and recurrent neural network model for gaussian filtering --- p.5-8Chapter 5.2 --- From Problem formulation to Neural Network formulation --- p.5-9Chapter 5.2.1 --- One Dimensional Case --- p.5-9Chapter 5.2.2 --- Two Dimensional Case --- p.5-13Chapter 5.3 --- Simulation Results and Discussions --- p.5-14Chapter 5.3.1 --- Spatial impulse response of the 1-D network --- p.5-14Chapter 5.3.2 --- Filtering property of the 1-D network --- p.5-14Chapter 5.3.3 --- Spatial impulse response of the 2-D network and some filtering results --- p.5-15Chapter 5.4 --- Conclusions --- p.5-16Chapter Chapter 6 --- Recurrent Neural Network for Boundary DetectionChapter 6.1 --- Introduction --- p.6-1Chapter 6.2 --- From Problem formulation to Neural Network formulation --- p.6-3Chapter 6.2.1 --- Problem Formulation --- p.6-3Chapter 6.2.2 --- Recurrent Neural Network Model used --- p.6-4Chapter 6.2.3 --- Neural Network formulation --- p.6-5Chapter 6.3 --- Simulation Results and Discussions --- p.6-7Chapter 6.3.1 --- Feasibility study and Performance comparison --- p.6-7Chapter 6.3.2 --- Smoothing and Boundary Detection --- p.6-9Chapter 6.3.3 --- Convergence improvement by network decomposition --- p.6-10Chapter 6.3.4 --- Hardware implementation consideration --- p.6-10Chapter 6.4 --- Conclusions --- p.6-11Chapter Chapter 7 --- Conclusions and Future ResearchesChapter 7.1 --- Contributions and Conclusions --- p.7-1Chapter 7.2 --- Limitations and Suggested Future Researches --- p.7-3References --- p.R-lAppendix I The assignment of the boundary connection of 2-D recurrent neural network for gaussian filtering --- p.Al-1Appendix II Formula for connection weight assignment of 2-D recurrent neural network for gaussian filtering and the proof on symmetric property --- p.A2-1Appendix III Details on reshaping strategy --- p.A3-

Review : Deep learning in electron microscopy

Deep learning is transforming most areas of science and technology, including electron microscopy. This review paper offers a practical perspective aimed at developers with limited familiarity. For context, we review popular applications of deep learning in electron microscopy. Following, we discuss hardware and software needed to get started with deep learning and interface with electron microscopes. We then review neural network components, popular architectures, and their optimization. Finally, we discuss future directions of deep learning in electron microscopy

Algorithm and Hardware Co-design for Learning On-a-chip

abstract: Machine learning technology has made a lot of incredible achievements in recent years. It has rivalled or exceeded human performance in many intellectual tasks including image recognition, face detection and the Go game. Many machine learning algorithms require huge amount of computation such as in multiplication of large matrices. As silicon technology has scaled to sub-14nm regime, simply scaling down the device cannot provide enough speed-up any more. New device technologies and system architectures are needed to improve the computing capacity. Designing specific hardware for machine learning is highly in demand. Efforts need to be made on a joint design and optimization of both hardware and algorithm. For machine learning acceleration, traditional SRAM and DRAM based system suffer from low capacity, high latency, and high standby power. Instead, emerging memories, such as Phase Change Random Access Memory (PRAM), Spin-Transfer Torque Magnetic Random Access Memory (STT-MRAM), and Resistive Random Access Memory (RRAM), are promising candidates providing low standby power, high data density, fast access and excellent scalability. This dissertation proposes a hierarchical memory modeling framework and models PRAM and STT-MRAM in four different levels of abstraction. With the proposed models, various simulations are conducted to investigate the performance, optimization, variability, reliability, and scalability. Emerging memory devices such as RRAM can work as a 2-D crosspoint array to speed up the multiplication and accumulation in machine learning algorithms. This dissertation proposes a new parallel programming scheme to achieve in-memory learning with RRAM crosspoint array. The programming circuitry is designed and simulated in TSMC 65nm technology showing 900X speedup for the dictionary learning task compared to the CPU performance. From the algorithm perspective, inspired by the high accuracy and low power of the brain, this dissertation proposes a bio-plausible feedforward inhibition spiking neural network with Spike-Rate-Dependent-Plasticity (SRDP) learning rule. It achieves more than 95% accuracy on the MNIST dataset, which is comparable to the sparse coding algorithm, but requires far fewer number of computations. The role of inhibition in this network is systematically studied and shown to improve the hardware efficiency in learning.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Models for time series prediction based on neural networks. Case study : GLP sales prediction from ANCAP.

A time series is a sequence of real values that can be considered as observations of a certain system. In this work, we are interested in time series coming from dynamical systems. Such systems can be sometimes described by a set of equations that model the underlying mechanism from where the samples come. However, in several real systems, those equations are unknown, and the only information available is a set of temporal measures, that constitute a time series. On the other hand, by practical reasons it is usually required to have a prediction, v.g. to know the (approximated) value of the series in a future instant t. The goal of this thesis is to solve one of such real-world prediction problem: given historical data related with the lique ed bottled propane gas sales, predict the future gas sales, as accurately as possible. This time series prediction problem is addressed by means of neural networks, using both (dynamic) reconstruction and prediction. The problem of to dynamically reconstruct the original system consists in building a model that captures certain characteristics of it in order to have a correspondence between the long-term behavior of the model and of the system. The networks design process is basically guided by three ingredients. The dimensionality of the problem is explored by our rst ingredient, the Takens-Mañé's theorem. By means of this theorem, the optimal dimension of the (neural) network input can be investigated. Our second ingredient is a strong theorem: neural networks with a single hidden layer are universal approximators. As the third ingredient, we faced the search of the optimal size of the hidden layer by means of genetic algorithms, used to suggest the number of hidden neurons that maximizes a target tness function (related with prediction errors). These algorithms are also used to nd the most in uential networks inputs in some cases. The determination of the hidden layer size is a central (and hard) problem in the determination of the network topology. This thesis includes a state of the art of neural networks design for time series prediction, including related topics such as dynamical systems, universal approximators, gradient-descent searches and variations, as well as meta-heuristics. The survey of the related literature is intended to be extensive, for both printed material and electronic format, in order to have a landscape of the main aspects for the state of the art in time series prediction using neural networks. The material found was sometimes extremely redundant (as in the case of the back-propagation algorithm and its improvements) and scarce in others (memory structures or estimation of the signal subspace dimension in the stochastic case). The surveyed literature includes classical research works ([27], [50], [52]) as well as more recent ones ([79] , [16] or [82]), which pretends to be another contribution of this thesis. Special attention is given to the available software tools for neural networks design and time series processing. After a review of the available software packages, the most promising computational tools for both approaches are discussed. As a result, a whole framework based on mature software tools was set and used. In order to work with such dynamical systems, software intended speci cally for the analysis and processing of time series was employed, and then chaotic series were part of our focus. Since not all randomness is attributable to chaos, in order to characterize the dynamical system generating the time series, an exploration of chaotic-stochastic systems is required, as well as network models to predict a time series associated to one of them. Here we pretend to show how the knowledge of the domain, something extensively treated in the bibliography, can be someway sophisticated (such as the Lyapunov's spectrum for a series or the embedding dimension). In order to model the dynamical system generated by the time series we used the state-space model, so the time series prediction was translated in the prediction of the next system state. This state-space model, together with the delays method (delayed coordinates) have practical importance for the development of this work, speci cally, the design of the input layer in some networks (multi-layer perceptrons - MLPs) and other parameters (taps in the TFLNs). Additionally, the rest of the network components where determined in many cases through procedures traditionally used in neural networks : genetic algorithms. The criteria of model (network) selection are discussed and a trade-o between performance and network complexity is further explored, inspired in the Rissanen's minimum description length and its estimation given by the chosen software. Regarding the employed network models, the network topologies suggested from the literature as adequate for the prediction are used (TLFNs and recurrent networks) together with MLPs (a classic of arti cial neural networks) and networks committees. The e ectiveness of each method is con rmed for the proposed prediction problem. Network committees, where the predictions are a naive convex combination of predictions from individual networks, are also extensively used. The need of criteria to compare the behaviors of the model and of the real system, in the long run, for a dynamic stochastic systems, is presented and two alternatives are commented. The obtained results proof the existence of a solution to the problem of learning of the dependence Input ! Output . We also conjecture that the system is dynamic-stochastic but not chaotic, because we only have a realization of the random process corresponding to the sales. As a non-chaotic system, the mean of the predictions of the sales would improve as the available data increase, although the probability of a prediction with a big error is always non-null due to the randomness present. This solution is found in a constructive and exhaustive way. The exhaustiveness can be deduced from the next ve statements: the design of a neural network requires knowing the input and output dimension,the number of the hidden layers and of the neurons in each of them. the use of the Takens-Mañé's theorem allows to derive the dimension of the input data by theorems such as the Kolmogorov's and Cybenko's ones the use of multi-layer perceptrons with only one hidden layer is justi ed so several of such models were tested the number of neurons in the hidden layer is determined many times heuristically using genetic algorithms a neuron in the output gives the desired prediction As we said, two tasks are carried out: the development of a time series prediction model and the analysis of a feasible model for the dynamic reconstruction of the system. With the best predictive model, obtained by an ensemble of two networks, an acceptable average error was obtained when the week to be predicted is not adjacent to the training set (7.04% for the week 46/2011). We believe that these results are acceptable provided the quantity of information available, and represent an additional validation that neural networks are useful for time series prediction coming from dynamical systems, no matter whether they are stochastic or not. Finally, the results con rmed several already known facts (such as that adding noise to the inputs and outputs of the training values can improve the results; that recurrent networks trained with the back-propagation algorithm don't have the problem of vanishing gradients in short periods and that the use of committees - which can be seen as a very basic of distributed arti cial intelligence - allows to improve signi cantly the predictions).Una serie temporal es una secuencia de valores reales que pueden ser considerados como observaciones de un cierto sistema. En este trabajo, estamos interesados en series temporales provenientes de sistemas dinámicos. Tales sistemas pueden ser algunas veces descriptos por un conjunto de ecuaciones que modelan el mecanismo subyacente que genera las muestras. sin embargo, en muchos sistemas reales, esas ecuaciones son desconocidas, y la única información disponible es un conjunto de medidas en el tiempo, que constituyen la serie temporal. Por otra parte, por razones prácticas es generalmente requerida una predicción, es decir, conocer el valor (aproximado) de la serie en un instante futuro t. La meta de esta tesis es resolver un problema de predicción del mundo real: dados los datos históricos relacionados con las ventas de gas propano licuado, predecir las ventas futuras, tan aproximadamente como sea posible. Este problema de predicción de series temporales es abordado por medio de redes neuronales, tanto para la reconstrucción como para la predicción. El problema de reconstruir dinámicamente el sistema original consiste en construir un modelo que capture ciertas características de él de forma de tener una correspondencia entre el comportamiento a largo plazo del modelo y del sistema. El proceso de diseño de las redes es guiado básicamente por tres ingredientes. La dimensionalidad del problema es explorada por nuestro primer ingrediente, el teorema de Takens-Mañé. Por medio de este teorema, la dimensión óptima de la entrada de la red neuronal puede ser investigada. Nuestro segundo ingrediente es un teorema muy fuerte: las redes neuronales con una sola capa oculta son un aproximador universal. Como tercer ingrediente, encaramos la búsqueda del tamaño oculta de la capa oculta por medio de algoritmos genéticos, usados para sugerir el número de neuronas ocultas que maximizan una función objetivo (relacionada con los errores de predicción). Estos algoritmos se usan además para encontrar las entradas a la red que influyen más en la salida en algunos casos. La determinación del tamaño de la capa oculta es un problema central (y duro) en la determinación de la topología de la red. Esta tesis incluye un estado del arte del diseño de redes neuronales para la predicción de series temporales, incluyendo tópicos relacionados tales como sistemas dinámicos, aproximadores universales, búsquedas basadas en el gradiente y sus variaciones, así como meta-heurísticas. El relevamiento de la literatura relacionada busca ser extenso, para tanto el material impreso como para el que esta en formato electrónico, de forma de tener un panorama de los principales aspectos del estado del arte en la predicción de series temporales usando redes neuronales. El material hallado fue algunas veces extremadamente redundante (como en el caso del algoritmo de retropropagación y sus mejoras) y escaso en otros (estructuras de memoria o estimación de la dimensión del sub-espacio de señal en el caso estocástico). La literatura consultada incluye trabajos de investigación clásicos ( ([27], [50], [52])' así como de los más reciente ([79] , [16] or [82]). Se presta especial atención a las herramientas de software disponibles para el diseño de redes neuronales y el procesamiento de series temporales. Luego de una revisión de los paquetes de software disponibles, las herramientas más promisiorias para ambas tareas son discutidas. Como resultado, un entorno de trabajo completo basado en herramientas de software maduras fue definido y usado. Para trabajar con los mencionados sistemas dinámicos, software especializado en el análisis y proceso de las series temporales fue empleado, y entonces las series caóticas fueron estudiadas. Ya que no toda la aleatoriedad es atribuible al caos, para caracterizar al sistema dinámico que genera la serie temporal se requiere una exploración de los sistemas caóticos-estocásticos, así como de los modelos de red para predecir una serie temporal asociada a uno de ellos. Aquí se pretende mostrar cómo el conocimiento del dominio, algo extensamente tratado en la literatura, puede ser de alguna manera sofisticado (tal como el espectro de Lyapunov de la serie o la dimensión del sub-espacio de señal). Para modelar el sistema dinámico generado por la serie temporal se usa el modelo de espacio de estados, por lo que la predicción de la serie temporal es traducida en la predicción del siguiente estado del sistema. Este modelo de espacio de estados, junto con el método de los delays (coordenadas demoradas) tiene importancia práctica en el desarrollo de este trabajo, específicamente, en el diseño de la capa de entrada en algunas redes (los perceptrones multicapa) y otros parámetros (los taps de las redes TLFN). Adicionalmente, el resto de los componentes de la red con determinados en varios casos a través de procedimientos tradicionalmente usados en las redes neuronales: los algoritmos genéticos. Los criterios para la selección de modelo (red) son discutidos y un balance entre performance y complejidad de la red es explorado luego, inspirado en el minimum description length de Rissanen y su estimación dada por el software elegido. Con respecto a los modelos de red empleados, las topologóas de sugeridas en la literatura como adecuadas para la predicción son usadas (TLFNs y redes recurrentes) junto con perceptrones multicapa (un clásico de las redes neuronales) y comités de redes. La efectividad de cada método es confirmada por el problema de predicción propuesto. Los comités de redes, donde las predicciones son una combinación convexa de las predicciones dadas por las redes individuales, son también usados extensamente. La necesidad de criterios para comparar el comportamiento del modelo con el del sistema real, a largo plazo, para un sistema dinámico estocástico, es presentada y dos alternativas son comentadas. Los resultados obtenidos prueban la existencia de una solución al problema del aprendizaje de la dependencia Entrada - Salida . Conjeturamos además que el sistema generador de serie de las ventas es dinámico-estocástico pero no caótico, ya que sólo tenemos una realización del proceso aleatorio correspondiente a las ventas. Al ser un sistema no caótico, la media de las predicciones de las ventas debería mejorar a medida que los datos disponibles aumentan, aunque la probabilidad de una predicción con un gran error es siempre no nula debido a la aleatoriedad presente. Esta solución es encontrada en una forma constructiva y exhaustiva. La exhaustividad puede deducirse de las siguiente cinco afirmaciones : el diseño de una red neuronal requiere conocer la dimensión de la entrada y de la salida, el número de capas ocultas y las neuronas en cada una de ellas el uso del teorema de takens-Mañé permite derivar la dimensión de la entrada por teoremas tales como los de Kolmogorov y Cybenko el uso de perceptrones con solo una capa oculta es justificado, por lo que varios de tales modelos son probados el número de neuronas en la capa oculta es determinada varias veces heurísticamente a través de algoritmos genéticos una sola neurona de salida da la predicción deseada. Como se dijo, dos tareas son llevadas a cabo: el desarrollo de un modelo para la predicción de la serie temporal y el análisis de un modelo factible para la reconstrucción dinámica del sistema. Con el mejor modelo predictivo, obtenido por el comité de dos redes se logró obtener un error aceptable en la predicción de una semana no contigua al conjunto de entrenamiento (7.04% para la semana 46/2011). Creemos que este es un resultado aceptable dada la cantidad de información disponible y representa una validación adicional de que las redes neuronales son útiles para la predicción de series temporales provenientes de sistemas dinámicos, sin importar si son estocásticos o no. Finalmente, los resultados experimentales confirmaron algunos hechos ya conocidos (tales como que agregar ruido a los datos de entrada y de salida de los valores de entrenamiento puede mejorar los resultados: que las redes recurrentes entrenadas con el algoritmo de retropropagación no presentan el problema del gradiente evanescente en periodos cortos y que el uso de de comités - que puede ser visto como una forma muy básica de inteligencia artificial distribuida - permite mejorar significativamente las predicciones)

Quantum Inspired Machine Learning Algorithms for Adaptive Radiotherapy

Adaptive radiotherapy (ART) refers to the modification of radiotherapy treatment plans in response to patient anatomical and physiological changes over the course of treatment and has been recognized as an important step towards maximizing the curative potential of radiation therapy through personalized medicine. This dissertation explores the novel application of quantum physics principles and deep machine learning techniques to address three challenges towards the clinical implementation of ART: (1) efficient calculation of optimal treatment parameters, (2) adaptation to geometrical changes over the treatment period while mitigating associated uncertainties, and (3) understanding the relationship between individual patient characteristics and clinical outcomes. Applications of quantum and machine learning modeling in other fields support the potential of this novel approach. For efficient optimization, we developed and tested a quantum-inspired, stochastic algorithm for intensity-modulated radiotherapy: quantum tunnel annealing (QTA). By modeling the likelihood probability of accepting a higher energy solution after a particle tunneling through a potential energy barrier, QTA features an additional degree of freedom not shared by traditional stochastic optimization methods such as simulated annealing (SA). QTA achieved convergence up to 46.6% (26.8%) faster than SA for beamlet weight optimization and direct aperture optimization respectively. The results of this study suggest that the additional degree of freedom provided by QTA can improve convergence rates and achieve a more efficient and, potentially, effective treatment planning process. For geometrical adaptation, we investigated the feasibility of predicting patient changes across a fractionated treatment schedule using two approaches. The first was based on a joint framework (referred to as QRNN) employing quantum mechanics in combination with deep recurrent neural networks (RNNs). The second approach was developed based on a classical framework (MRNN), which modelled patient anatomical changes as a Markov process. We evaluated and compared these two approaches’ performance characteristics using a dataset of 125 head and neck cancer patients who received fractionated radiotherapy. The MRNN framework exhibited slightly better performance than the QRNN framework, with MRNN(QRNN) validation area under the receiver operating characteristic curve (AUC) scores [95% CI] of 0.742 [0.721-0.763] (0.675 [0.64-0.71]), 0.709 [0.683-0.735] (0.656 [0.634-0.677]), 0.724 [0.688-0.76] (0.652 [0.608-0.696]), and 0.698 [0.682-0.714] (0.605 [0.57-0.64]) for system state vector sizes of 4, 6, 8, and 10, respectively. A similar trend was also observed when the fully trained models were applied to an external testing dataset of 20 patients. These results suggest that these stochastic models provide added value in predicting patient changes during the course of adaptive radiotherapy. Towards understanding the relationship between patient characteristics and clinical outcomes, we performed a series of studies which investigated the use of quantitative patient features for predicting clinical outcomes in laryngeal cancer patients who underwent treatment in a bioselection paradigm based on surgeon-assessed response to induction chemotherapy. Among the features investigated from CT scans taken before and after induction chemotherapy, two (gross tumor volume change between pre- and post-induction chemotherapy, and nodal stage) had prognostic value for predicting patient outcomes using standard regression models. Artificial neural networks did not improve predictive performance in this case. Taken together, the significance of these studies lies in their contribution to the body of knowledge of medical physics and in their demonstration of the use of novel techniques which incorporate quantum mechanics and machine learning as a joint framework for treatment planning optimization and prediction of anatomical patient changes over time.PHDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169954/1/jpakela_1.pd