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Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
The Application Of Synthetic Signals For Ecg Beat Classification, Elliot Morgan Brown
The Application Of Synthetic Signals For Ecg Beat Classification, Elliot Morgan Brown
Theses and Dissertations
A brief overview of electrocardiogram (ECG) properties and the characteristics of various cardiac conditions is given. Two different models are used to generate synthetic ECG signals. Domain knowledge is used to create synthetic examples of 16 different heart beat types with these models. Other techniques for synthesizing ECG signals are explored. Various machine learning models with different combinations of real and synthetic data are used to classify individual heart beats. The performance of the different methods and models are compared, and synthetic data is shown to be useful in beat classification.
Developing Understanding Of The Chain Rule, Implicit Differentiation, And Related Rates: Towards A Hypothetical Learning Trajectory Rooted In Nested Multivariation, Haley Paige Jeppson
Developing Understanding Of The Chain Rule, Implicit Differentiation, And Related Rates: Towards A Hypothetical Learning Trajectory Rooted In Nested Multivariation, Haley Paige Jeppson
Theses and Dissertations
There is an overemphasis on procedures and manipulation of symbols in calculus and not enough emphasis on conceptual understanding of the subject. Specifically, students struggle to understand and correctly apply concepts in calculus such as the chain rule, implicit differentiation, and related rates. Students can learn mathematics more deeply when they make connections between different mathematical ideas. I have hypothesized that students can make powerful connections between the chain rule, implicit differentiation, and related rates through the mathematical concept of nested multivariation. Based on this hypothesis, I created a hypothetical learning trajectory (HLT) rooted in nested multivariation for students to …
Extensions Of The Power Group Enumeration Theorem, Shawn Jeffrey Green
Extensions Of The Power Group Enumeration Theorem, Shawn Jeffrey Green
Theses and Dissertations
The goal of this paper is to develop extensions of Polya enumeration methods which count orbits of functions. De Bruijn, Harary, and Palmer all worked on this problem and created generalizations which involve permuting the codomain and domain of functions simultaneously. We cover their results and specifically extend them to the case where the group of permutations need not be a direct product of groups. In this situation, we develop a way of breaking the orbits into subclasses based on a characteristic of the functions involved. Additionally, we develop a formula for the number of orbits made up of bijective …
Sequential Survival Analysis With Deep Learning, Seth William Glazier
Sequential Survival Analysis With Deep Learning, Seth William Glazier
Theses and Dissertations
Survival Analysis is the collection of statistical techniques used to model the time of occurrence, i.e. survival time, of an event of interest such as death, marriage, the lifespan of a consumer product or the onset of a disease. Traditional survival analysis methods rely on assumptions that make it difficult, if not impossible to learn complex non-linear relationships between the covariates and survival time that is inherent in many real world applications. We first demonstrate that a recurrent neural network (RNN) is better suited to model problems with non-linear dependencies in synthetic time-dependent and non-time-dependent experiments.
Hyperparameters For Dense Neural Networks, Christopher James Hettinger
Hyperparameters For Dense Neural Networks, Christopher James Hettinger
Theses and Dissertations
Neural networks can perform an incredible array of complex tasks, but successfully training a network is difficult because it requires us to minimize a function about which we know very little. In practice, developing a good model requires both intuition and a lot of guess-and-check. In this dissertation, we study a type of fully-connected neural network that improves on standard rectifier networks while retaining their useful properties. We then examine this type of network and its loss function from a probabilistic perspective. This analysis leads to a new rule for parameter initialization and a new method for predicting effective learning …
Mirror Symmetry For Non-Abelian Landau-Ginzburg Models, Matthew Michael Williams
Mirror Symmetry For Non-Abelian Landau-Ginzburg Models, Matthew Michael Williams
Theses and Dissertations
We consider Landau-Ginzburg models stemming from non-abelian groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group G*, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors in general.
Secondary Preservice Mathematics Teachers' Curricular Reasoning, Kimber Anne Mathis
Secondary Preservice Mathematics Teachers' Curricular Reasoning, Kimber Anne Mathis
Theses and Dissertations
Researchers have found that teachers' decisions affect students' opportunity to learn. Prior researchers have investigated teachers' decisions while planning, implementing, or reflecting on lessons, but few researchers have studied teachers' decisions and their reasoning throughout the teaching process. It is important to study teachers' reasoning for why they make the decisions they do throughout the teaching process. Furthermore, because inservice and preservice teachers differ in experience and available resources that they draw on while making decisions, it is helpful to consider the resources PSTs' draw on while reasoning. Curricular reasoning is a framework that describes teachers' thinking processes when making …
Regular Fibrations Over The Hawaiian Earring, Stewart Mason Mcginnis
Regular Fibrations Over The Hawaiian Earring, Stewart Mason Mcginnis
Theses and Dissertations
We present a family of fibrations over the Hawaiian earring that are inverse limits of regular covering spaces over the Hawaiian earring. These fibrations satisfy unique path lifting, and as such serve as a good extension of covering space theory in the case of nonsemi-locally simply connected spaces. We give a condition for when these fibrations are path-connected.
Exponential Stability Of Intrinsically Stable Dynamical Networks And Switched Networks With Time-Varying Time Delays, David Patrick Reber
Exponential Stability Of Intrinsically Stable Dynamical Networks And Switched Networks With Time-Varying Time Delays, David Patrick Reber
Theses and Dissertations
Dynamic processes on real-world networks are time-delayed due to finite processing speeds and the need to transmit data over nonzero distances. These time-delays often destabilize the network's dynamics, but are difficult to analyze because they increase the dimension of the network.We present results outlining an alternative means of analyzing these networks, by focusing analysis on the Lipschitz matrix of the relatively low-dimensional undelayed network. The key criteria, intrinsic stability, is computationally efficient to verify by use of the power method. We demonstrate applications from control theory and neural networks.
Schur Rings Over Infinite Groups, Cache Porter Dexter
Schur Rings Over Infinite Groups, Cache Porter Dexter
Theses and Dissertations
A Schur ring is a subring of the group algebra with a basis that is formed by a partition of the group. These subrings were initially used to study finite permutation groups, and classifications of Schur rings over various finite groups have been studied. Here we investigate Schur rings over various infinite groups, including free groups. We classify Schur rings over the infinite cyclic group.