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Full-Text Articles in Physical Sciences and Mathematics

Mathematics For Biomedical Physics, Jogindra M. Wadehra Aug 2022

Mathematics For Biomedical Physics, Jogindra M. Wadehra

Open Textbooks

Mathematics for Biomedical Physics is an open access peer-reviewed textbook geared to introduce several mathematical topics at the rudimentary level so that students can appreciate the applications of mathematics to the interdisciplinary field of biomedical physics. Most of the topics are presented in their simplest but rigorous form so that students can easily understand the advanced form of these topics when the need arises. Several end-of-chapter problems and chapter examples relate the applications of mathematics to biomedical physics. After mastering the topics of this book, students would be ready to embark on quantitative thinking in various topics of biology and …


Actuator Cyberattack Handling Using Lyapunov-Based Economic Model Predictive Control, Keshav Kasturi Rangan, Henrique Oyama, Helen Durand Jun 2022

Actuator Cyberattack Handling Using Lyapunov-Based Economic Model Predictive Control, Keshav Kasturi Rangan, Henrique Oyama, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

Cybersecurity has gained increasing interest as a consequence of the potential impacts of cyberattacks on profits and safety. While attacks can affect various components of a plant, prior work from our group has focused on the impact of cyberattacks on control components such as process sensors and actuators and the development of detection strategies for cybersecurity derived from control theory. In this work, we provide greater focus on actuator attacks; specifically, we extend a detection and control strategy previously applied for sensor attacks and based on an optimization-based control technique called Lyapunov-based economic model predictive control (LEMPC) to detect attacks …


Test Methods For Image-Based Information In Next-Generation Manufacturing, Henrique Oyama, Dominic Messina, Renee O'Neill, Samantha Cherney, Minhazur Rahman, Keshav Kasturi Rangan, Govanni Gjonaj, Helen Durand Jun 2022

Test Methods For Image-Based Information In Next-Generation Manufacturing, Henrique Oyama, Dominic Messina, Renee O'Neill, Samantha Cherney, Minhazur Rahman, Keshav Kasturi Rangan, Govanni Gjonaj, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

Typical control designs in the process systems engineering literature have assumed that the primary sensing methodologies are traditional instruments such as thermocouples. Dig- italization is changing the landscape for manufacturing, and data-based sensing modalities (e.g., image-based sensing) are becoming of greater interest for plant control. These considerations require novel test/evaluation solutions. For example, process systems engineering researchers may wish to test image-based sensors in simulation. In this work, we provide preliminary thoughts on how image-based technologies might be evaluated via simulation for process systems.


Challenges And Opportunities For Next-Generation Manufacturing In Space, Kip Nieman, A. F. Leonard, Katie Tyrell, Dominic Messina, Rebecca Lopez, Helen Durand Jun 2022

Challenges And Opportunities For Next-Generation Manufacturing In Space, Kip Nieman, A. F. Leonard, Katie Tyrell, Dominic Messina, Rebecca Lopez, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

With commercial space travel now a reality, the idea that people might spend time on other planets in the future seems to have greater potential. To make this possible, however, there needs to be flexible means for manufacturing in space to enable tooling or resources to be created when needed to handle unexpected situations. Next-generation manufacturing paradigms offer significant potential for the kind of flexibility that might be needed; however, they can result in increases in computation time compared to traditional control methods that could make many of the computing resources already available on earth attractive for use. Furthermore, resilience …


Quantum Computing And Resilient Design Perspectives For Cybersecurity Of Feedback Systems, Keshav Kasturi Rangan, Jihan Abou Halloun, Henrique Oyama, Samantha Cherney, Ilham Azali Assoumani, Nazir Jairazbhoy, Helen Durand, Simon Ka Ng Jun 2022

Quantum Computing And Resilient Design Perspectives For Cybersecurity Of Feedback Systems, Keshav Kasturi Rangan, Jihan Abou Halloun, Henrique Oyama, Samantha Cherney, Ilham Azali Assoumani, Nazir Jairazbhoy, Helen Durand, Simon Ka Ng

Chemical Engineering and Materials Science Faculty Research Publications

Cybersecurity of control systems is an important issue in next-generation manufac- turing that can impact both operational objectives (safety and performance) as well as process designs (via hazard analysis). Cyberattacks differ from faults in that they can be coordinated efforts to exploit system vulnerabilities to create otherwise unlikely hazard scenarios. Because coordination and targeted process manipulation can be characteristics of attacks, some of the tactics previously analyzed in our group from a control system cybersecurity perspective have incorporated randomness to attempt to thwart attacks. The underlying assumption for the generation of this randomness has been that it can be achieved …


The Short-Term Effects Of Fine Airborne Particulate Matter And Climate On Covid-19 Disease Dynamics, El Hussain Shamsa, Kezhong Zhang Jun 2022

The Short-Term Effects Of Fine Airborne Particulate Matter And Climate On Covid-19 Disease Dynamics, El Hussain Shamsa, Kezhong Zhang

Medical Student Research Symposium

Background: Despite more than 60% of the United States population being fully vaccinated, COVID-19 cases continue to spike in a temporal pattern. These patterns in COVID-19 incidence and mortality may be linked to short-term changes in environmental factors.

Methods: Nationwide, county-wise measurements for COVID-19 cases and deaths, fine-airborne particulate matter (PM2.5), and maximum temperature were obtained from March 20, 2020 to March 20, 2021. Multivariate Linear Regression was used to analyze the association between environmental factors and COVID-19 incidence and mortality rates in each season. Negative Binomial Regression was used to analyze daily fluctuations of COVID-19 cases …


On-Line Process Physics Tests Via Lyapunov-Based Economic Model Predictive Control And Simulation-Based Testing Of Image-Based Process Control, Henrique Oyama, A. F. Leonard, Minhazur Rahman, Govanni Gjonaj, Michael Williamson, Helen Durand Jun 2022

On-Line Process Physics Tests Via Lyapunov-Based Economic Model Predictive Control And Simulation-Based Testing Of Image-Based Process Control, Henrique Oyama, A. F. Leonard, Minhazur Rahman, Govanni Gjonaj, Michael Williamson, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

Next-generation manufacturing involves increasing use of automation and data to enhance process efficiency. An important question for the chemical process industries, as new process systems (e.g., intensified processes) and new data modalities (e.g., images) are integrated with traditional plant automation concepts, will be how to best evaluate alternative strategies for data-driven modeling and synthesizing process data. Two methods which could be used to aid in this are those which aid in testing data-based techniques on-line, and those which enable various data-based techniques to be assessed in simulation. In this work, we discuss two techniques in this domain which can be …


The Gelfand Problem For The Infinity Laplacian, Fernando Charro, Byungjae Son, Peiyong Wang Apr 2022

The Gelfand Problem For The Infinity Laplacian, Fernando Charro, Byungjae Son, Peiyong Wang

Mathematics Faculty Research Publications

We study the asymptotic behavior as p → ∞ of the Gelfand problem

−Δpu = λeu in Ω ⊂ Rn, u = 0 on ∂Ω.

Under an appropriate rescaling on u and λ, we prove uniform convergence of solutions of the Gelfand problem to solutions of

min{|∇u|−Λeu, −Δu} = 0 in Ω, u = 0 on ∂Ω.

We discuss existence, non-existence, and multiplicity of solutions of the limit problem in terms of Λ.


Asymptotic Mean-Value Formulas For Solutions Of General Second-Order Elliptic Equations, Pablo Blanc, Fernando Charro, Juan J. Manfredi, Julio D. Rossi Apr 2022

Asymptotic Mean-Value Formulas For Solutions Of General Second-Order Elliptic Equations, Pablo Blanc, Fernando Charro, Juan J. Manfredi, Julio D. Rossi

Mathematics Faculty Research Publications

We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and supremum, of linear operators. The families of equations that we consider include well-known operators such as Pucci, Issacs, and k-Hessian operators.


Lyapunov-Based Economic Model Predictive Control For Detecting And Handling Actuator And Simultaneous Sensor/Actuator Cyberattacks On Process Control Systems, Henrique Oyama, Dominic Messina, Keshav Kasturi Rangan, Helen Durand Apr 2022

Lyapunov-Based Economic Model Predictive Control For Detecting And Handling Actuator And Simultaneous Sensor/Actuator Cyberattacks On Process Control Systems, Henrique Oyama, Dominic Messina, Keshav Kasturi Rangan, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

The controllers for a cyber-physical system may be impacted by sensor measurement cyberattacks, actuator signal cyberattacks, or both types of attacks. Prior work in our group has developed a theory for handling cyberattacks on process sensors. However, sensor and actuator cyberattacks have a different character from one another. Specifically, sensor measurement attacks prevent proper inputs from being applied to the process by manipulating the measurements that the controller receives, so that the control law plays a role in the impact of a given sensor measurement cyberattack on a process. In contrast, actuator signal attacks prevent proper inputs from being applied …


Parametric And Reliability Estimation Of The Kumaraswamy Generalized Distribution Based On Record Values, Mohd. Arshad, Qazi J. Azhad Jan 2022

Parametric And Reliability Estimation Of The Kumaraswamy Generalized Distribution Based On Record Values, Mohd. Arshad, Qazi J. Azhad

Journal of Modern Applied Statistical Methods

A general family of distributions, namely Kumaraswamy generalized family of (Kw-G) distribution, is considered for estimation of the unknown parameters and reliability function based on record data from Kw-G distribution. The maximum likelihood estimators (MLEs) are derived for unknown parameters and reliability function, along with its confidence intervals. A Bayesian study is carried out under symmetric and asymmetric loss functions in order to find the Bayes estimators for unknown parameters and reliability function. Future record values are predicted using Bayesian approach and non Bayesian approach, based on numerical examples and a monte carlo simulation.


Does The Type Of Records Affect The Estimates Of The Parameters?, Ayush Tripathi, Umesh Singh, Sanjay Kumar Singh Jan 2022

Does The Type Of Records Affect The Estimates Of The Parameters?, Ayush Tripathi, Umesh Singh, Sanjay Kumar Singh

Journal of Modern Applied Statistical Methods

The maximum likelihood estimation of the unknown parameters of inverse Rayleigh and exponential distributions are discussed based on lower and upper records. The aim is to study the effect of the type of records on the behavior of the corresponding estimators. Mean squared errors are calculated through simulation to study the behavior of the estimators. The results shall be of interest to those situations where the data can be obtained in the form of either of the two types of records and the experimenter must decide between these two for estimation of the unknown parameters of the distribution.


Design Of Sksp-R Plan For Popular Statistical Distributions, Jaffer Hussain, S. Balamurali, Muhammad Aslam Jan 2022

Design Of Sksp-R Plan For Popular Statistical Distributions, Jaffer Hussain, S. Balamurali, Muhammad Aslam

Journal of Modern Applied Statistical Methods

The design of a Skip-lot sampling plan of type SkSP-R is presented for time truncated life test for the Weibull, Exponentiated Weibull, and Birnbaum-Saunders lifetime distributions. The plan parameters of the SkSP-R plan under these three distributions are determined through a nonlinear optimization problem. Tables are also constructed for each distribution. The advantages of the proposed plan over the existing sampling schemes are discussed. Application of the proposed plan is explained with the help of an example. The Birnbaum-Saunders distribution is economically superior to other two distributions in terms of minimum average sample number.


Parameter Estimation Based On Double Ranked Set Samples With Applications To Weibull Distribution, Mohamed Abd Elhamed Sabry, Hiba Zeyada Muhammed, Mostafa Shaaban, Abd El Hady Nabih Jan 2022

Parameter Estimation Based On Double Ranked Set Samples With Applications To Weibull Distribution, Mohamed Abd Elhamed Sabry, Hiba Zeyada Muhammed, Mostafa Shaaban, Abd El Hady Nabih

Journal of Modern Applied Statistical Methods

In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating …


A New Goodness Of Fit Measure Based On Income Inequality Curves, Shahryar Mirzaei, S. M. A. Jahanshahi Jan 2022

A New Goodness Of Fit Measure Based On Income Inequality Curves, Shahryar Mirzaei, S. M. A. Jahanshahi

Journal of Modern Applied Statistical Methods

This paper uses inequality-measurement techniques to assess goodness of fit in income distribution models. It exposes the shortcomings of the use of conventional goodness of fit criteria in face of the big income data and proposes a new set of metrics, based on income inequality curves. In this note, we mentioned that the distance between theoretical and empirical inequality curves can be considered as a goodness of fit criterion. We demonstrate certain advantages of this measure over the other general goodness of fit criteria. Unlike other goodness of fit measures, this criterion is bounded. It is 0 in minimum difference …


Sequences Of Random Matrices Modulated By A Discrete-Time Markov Chain, Huy Nguyen Jan 2022

Sequences Of Random Matrices Modulated By A Discrete-Time Markov Chain, Huy Nguyen

Wayne State University Dissertations

In this dissertation, we consider a number of matrix-valued random sequences that are modulated by a discrete-time Markov chain having a finite space.Assuming that the state space of the Markov chain is large, our main effort in this work is devoted to reducing the complexity. To achieve this goal, our formulation uses time-scale separation of the Markov chain. The state-space of the Markov chain is split into subspaces. Next, the states of the Markov chain in each subspace are aggregated into a ``super'' state. Then we normalize the matrix-valued sequences that are modulated by the two-time-scale Markov chain. Under simple …


Optical Signal Processing With Discrete-Space Metamaterials, Mohammad Moein Moeini Jan 2022

Optical Signal Processing With Discrete-Space Metamaterials, Mohammad Moein Moeini

Wayne State University Dissertations

As digital circuits are approaching the limits of Moore’s law, a great deal of efforthas been directed to alternative computing approaches. Among them, the old concept of optical signal processing (OSP) has attracted attention, revisited in the light of metamaterials and nano-photonics. This approach has been successful in realizing basic mathematical operations, such as derivatives and integrals, but it is difficult to be applied to more complex ones. Inspired by digital filters, we propose a radically new OSP approach, able to realize arbitrary mathematical operations over a nano-photonic platform. We demonstrate this concept for the case of spatial differentiation, image …


Study Of Zyomogen Granule Movement Along Actin Filaments Using A Single Beam Optical Trap, Justin James Raupp Jan 2022

Study Of Zyomogen Granule Movement Along Actin Filaments Using A Single Beam Optical Trap, Justin James Raupp

Wayne State University Dissertations

Zymogen granules are enzymatic vesicles in the pancreas. The surface of these zymogen granules (ZGs) has several different kinds of myosin molecules, such as myosin 1c, 6, 5c, and 7b. These molecular motors may contribute to ZG transportation in cells. To understand the molecular motors involved in the vesicle trafficking, we observed the in vitro motility of purified ZGs from rat pancreas and examined the stepping behavior and force that is generated using a single beam optical trap. To be involved in trafficking, molecular motors have certain characteristics, a high duty ratio and the ability to move continuously along actin …


Non-Perturbative Processes In Standard Model \& New Physics: From Standard Calculations To Machine Learning, Cody Michael Grant Jan 2022

Non-Perturbative Processes In Standard Model \& New Physics: From Standard Calculations To Machine Learning, Cody Michael Grant

Wayne State University Dissertations

I calculated non-perturbative processes to study the Standard Model and probe areas of new physics. I found that invisible decays of heavy mesons are not dominated by the leading order contribution in the Standard Model. I argue that this affects neutrino mass constraints and avenues for discovering new physics, such as dark photons. In addition to this, I used a novel approach to approximate a semileptonic form factor with an artificial neural network (ANN). Comparing the results from the ANN to common phenomenological parameterizations, and using it to set a lower bound constraint on the CKM matrix element, $V_{cd}$. Finally, …


Electrochemistry Of Bubbles: Developing New Sensors, Promoting Gas Evolution Reactions, And Extraction Of Rare Earth Elements, Ruchiranga R. Ranaweera Jan 2022

Electrochemistry Of Bubbles: Developing New Sensors, Promoting Gas Evolution Reactions, And Extraction Of Rare Earth Elements, Ruchiranga R. Ranaweera

Wayne State University Dissertations

This dissertation presents new analytical, electrocatalysis, and separation strategies that utilize bubble behaviors in different electrochemical systems. The first part of this dissertation focuses on the method development for PFAS preconcentration and detection. First, we present the bubble-nucleation-based electrochemical method for the selective and sensitive detection of surfactants. Our method utilizes the high surface activity of surfactant analytes to affect the electrochemical bubble nucleation and then transduces the change in nucleation condition to an electrochemical signal for determining the surfactant concentration. Using this method, we demonstrate the quantitation of perfluorinated surfactants in water, a group of emerging environmental contaminants, with …


Defending Against Adversarial Attacks On Medical Imaging Ai Systems, Xin Li Jan 2022

Defending Against Adversarial Attacks On Medical Imaging Ai Systems, Xin Li

Wayne State University Theses

Although deep learning systems trained on medical images have shown state-of-the-art performance in many clinical prediction tasks, recent studies demonstrate that these systems can be fooled by carefully crafted adversarial images. It has raised concerns on the practical deployment of deep learning based medical image classification systems. Although an array of defense techniques have been developed and proved to be effective in computer vision, defending against adversarial attacks on medical images remains largely an uncharted territory due to their unique challenges: crafted adversarial noises added to a highly standardized medical image can make it a hard sample for model to …


Photophysics Of Metalloporphyrins Strongly Coupled To Cavity Photons, Aleksandr Avramenko Jan 2022

Photophysics Of Metalloporphyrins Strongly Coupled To Cavity Photons, Aleksandr Avramenko

Wayne State University Dissertations

This dissertation will discuss the photophysics of metalloporphyrins, mainly CuTPP, ZnTPP, and H2TPP under strong light-matter coupling conditions. Strong light-matter coupling was achieved by embedding the previously mentioned chromophores into a spun coated PMMA polymer coating which is then incorporated as a spacer layer in a FabryPérot nano-cavity. The cavity thickness is chosen so that the cavity photon is of similar energy as the B, or Soret transition (2nd excited state) of the porphyrin molecule. The exchange of energy between the cavity photon and the molecular mode leads to the formation of polariton states.

Increasing the concentration of the molecules …


Adversarial Machine Learning For Advanced Medical Imaging Systems, Xin Li Jan 2022

Adversarial Machine Learning For Advanced Medical Imaging Systems, Xin Li

Wayne State University Dissertations

Although deep neural networks (DNNs) have achieved significant advancement in various challenging tasks of computer vision, they are also known to be vulnerable to so-called adversarial attacks. With only imperceptibly small perturbations added to a clean image, adversarial samples can drastically change models’ prediction, resulting in a significant drop in DNN’s performance. This phenomenon poses a serious threat to security-critical applications of DNNs, such as medical imaging, autonomous driving, and surveillance systems. In this dissertation, we present adversarial machine learning approaches for natural image classification and advanced medical imaging systems.

We start by describing our advanced medical imaging systems to …


Kinase-Catalyzed Labeling To Identify Kinase-Substrate Pairs Using Γ-Phosphate Modified Atp Analogs, Rachel Beltman Jan 2022

Kinase-Catalyzed Labeling To Identify Kinase-Substrate Pairs Using Γ-Phosphate Modified Atp Analogs, Rachel Beltman

Wayne State University Dissertations

Post-translational modifications (PTMs) are responsible for a variety of cellular processes. One such PTM is protein phosphorylation, which is catalyzed by kinases. Kinase enzymes play important roles in cellular signaling pathways, but dysregulation of kinase-mediated events results in the formation of diseases, which make kinases favorable drug targets. To uncover the role kinases play in the development of diseases, kinase-mediated cellular events need to be better understood. The current gap in the field is the lack of tools available to identify the kinase that is responsible for specific phosphorylation events within the cell. To improve the gap in the field, …


Phenanthroline-Catalyzed 1,2-Cis Glycosylation: Scope And Mechanism, Jiayi Li Jan 2022

Phenanthroline-Catalyzed 1,2-Cis Glycosylation: Scope And Mechanism, Jiayi Li

Wayne State University Dissertations

Phenanthroline, a rigid and planar organic compound with two fused pyridine rings, has been used as a powerful ligand for metals and a binding agent for DNA/RNA. We recently discovered that phenanthroline could be used as a nucleophilic catalyst to access high yielding and diastereoselective α-1,2-cis glycosides through the coupling of hydroxyl acceptors with α-glycosyl bromide donors. The utility of the phenanthroline catalysis is expanded to sterically hindered hydroxyl nucleophiles and chemoselective coupling of an alkyl hydroxyl group in the presence of a free C1-hemiacetal functionality. In addition, the phenanthroline-based catalyst has a pronounced effect on site-selective couplings of triol …


Computational Single-Cell Analysis Of Confocal Fluorescence Images With Dapi-Generated Masks, Munirah Alduhailan Jan 2022

Computational Single-Cell Analysis Of Confocal Fluorescence Images With Dapi-Generated Masks, Munirah Alduhailan

Wayne State University Theses

Lipolysis is a metabolic pathway in which free fatty acids are mobilized from stored triglycerides. The rate-limiting enzyme in this process is adipose triglyceride lipase, which is regulated by α/β-hydrolase domain-containing protein 5 (ABHD5) via both natural and synthetic pathways. With advanced artificial neural networks, image processing methods can extract quantitative results from fluorescence images. The segmentation of complex biological images, in which regions of the image are labeled as distinct masks, is the first step in image analysis. Ilastik, a machine-learning software, performs image segmentation with a user-trained neural network and custom key feature labels. The software’s results are …


Integral Representations Of Sl_2(Z/Nz), Yatin Dinesh Patel Jan 2022

Integral Representations Of Sl_2(Z/Nz), Yatin Dinesh Patel

Wayne State University Dissertations

The aim of this work is to determine for which commutative rings integral representations of SL_2(Z/nZ) exist and to explicitly compute them. We start with R = Z/pZ and then consider Z=p^\lambda Z. A new approach will be used to do this based on the Weil representation. We then consider general finite rings Z/nZ by extending methods described in [26]. We make extensive use of group theory, linear representations of finite groups, ring theory, algebraic geometry, and number theory. From number theory we will employ results regarding modular forms, Legendre symbols, Hilbert symbols, and quadratic forms. We consider the works …


Correlations And Dynamic Fluctuations In High Energy Collisions, Zoulfekar Mazloum Jan 2022

Correlations And Dynamic Fluctuations In High Energy Collisions, Zoulfekar Mazloum

Wayne State University Dissertations

Is thermalization necessary for hydrodynamic flow in nuclear collisions? The discovery of flow-like azimuthal correlations in pA and high-multiplicity pp collisions raises profound questions about the onset of collective flow and its relation to hydrodynamics. We seek independent experimental information on the degree of thermalization in order to identify those hydrodynamic collision systems in which flow is sensitive to equilibrium QCD properties. We aim to develop a protocol for identifying the degree of thermalization using a combination of momentum and multiplicity correlation. To study the effect ofthermalization on these correlations, we use Boltzmann equation in the relaxation time approximation with …


Electrochemical Gelation Of Metal Chalcogenide Quantum Dots, Chathuranga Chinthana Hewa Rahinduwage Jan 2022

Electrochemical Gelation Of Metal Chalcogenide Quantum Dots, Chathuranga Chinthana Hewa Rahinduwage

Wayne State University Dissertations

Quantum dots (QDs) are attractive because of their unique size-dependent optical and electronic properties and high surface area. They are tested in research for diverse applications, including energy conversion, catalysis, and sensing. Assembling QDs into functional solid-state devices while preserving their attractive properties is a challenge. Methods currently under the research are not effective in directly fabricating QDs onto devices, making large area assemblies, maintaining the high surface area by forming 3D porous structures, and conducting electricity for applications such as sensing. QD gels are an example of QD assemblies that consist of a 3D porous interconnected QD network. They …


Lepton Flavor Violation And Effective Field Theories, Renae Conlin Jan 2022

Lepton Flavor Violation And Effective Field Theories, Renae Conlin

Wayne State University Dissertations

The Standard Model is believed to be a low energy effective theory of some completetheory at higher energies. This is already evidenced in the observation of neutrino oscillations. Standard Model processes conserve the lepton flavor quantum numbers. Adding massive neutrinos to the Standard Model, the branching ratios of lepton flavor violating processes are found to be incredibly small. For example, a process μ → eγ has a branching ratio order ∼ 10^−54. These tiny branching ratios of lepton flavor violating processes indicate that they are especially clean areas to look for beyond the Standard Model physics. Any observed flavor violation …