Multiplex networks describe a set of entities, with multiple relationships among them, as a collection of networks over a common vertex set. Multiplex networks naturally describe complex systems where units connect across different modalities whereas single network data only permits a single relationship type. Joint spectral embedding methods facilitate analysis of multiplex network data by simultaneously mapping vertices in each network to points in Euclidean space, entitled node embeddings, where statistical inference is then performed. This mapping is performed by spectrally decomposing a matrix that summarizes the multiplex network. Different methods decompose different matrices and hence yield different node embeddings. This dissertation analyzes a class of joint spectral embedding methods which provides a foundation to compare these different approaches to multiple network inference. We compare joint spectral embedding methods in three ways. First, we extend the Random Dot Product Graph model to multiplex network data and establish the statistical properties of node embeddings produced by each method under this model. This analysis facilitates a full bias-variance analysis of each method and uncovers connections between these methods and methods for dimensionality reduction. Second, we compare the accuracy of algorithms which utilize these different node embeddings in a variety of multiple network inference tasks including community detection, vertex anomaly detection, and graph hypothesis testing. Finally, we perform a time and space complexity analysis of each method and present a case study in which we analyze interactions between New England sports fans on the social news aggregation and discussion website, Reddit. These findings provide a theoretical and practical guide to compare joint spectral embedding techniques and highlight the benefits and drawbacks of utilizing each method in practice.

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This study examines the ways early leaders can influence the process of institutionalization in public organizations. Using Schein's (1983, 1991) model of cultural creation and embedding as a heuristic device, secondary historical sources detailing the creation and development of the Central Intelligence Agency (CIA) and the Federal Bureau of Investigation (FBI) and the careers of three significant leaders are used to understand the institutionalizing effects of those leaders, how they created those effects, and what happened to those effects over time. The case studies of William Donovan and Allen Dulles at CIA and J. Edgar Hoover at the FBI, provide evidence that these early leaders explicitly and implicitly used several of the cultural creation and embedding mechanisms identified by Schein to entrench their beliefs and predispositions into their organizations. These ensconced attitudes and tendencies seemingly played significant roles in the institutionalization of beliefs, rules, and roles that have developed, persisted, and affected the historical evolution of both CIA and the FBI. / Ph. D.

The Collaborative for Academic, Social, and Emotional Learning (CASEL) (2018) specified that "integrating SEL (Social-Emotional Learning) with instructional practices and academic content has become a growing priority" (p. 1). This priority originates from research that suggests SEL promotes positive student and long-term community outcomes, particularly in secondary schools. This canon of research, however, only reviews the outcomes of implementing purchasable curricula, not content-embedded SEL. The effectiveness of content-embedded SEL instruction, which comprises a large portion of how SEL is implemented at the secondary level (CASEL, 2018; Hart et al., 2013), cannot be effectively measured or predicted because there is little to no identified research regarding three essential factors: how teachers embed SEL, how teachers assess content-embedded SEL, and teachers' perceived readiness to embed SEL. The purpose of this research was to identify the methods secondary teachers indicate they use to implement and assess content-embedded SEL instruction and their perceived preparedness to do so. Educational leaders may be better able to evaluate the effectiveness of content-embedded SEL instruction and improve its implementation with this knowledge. Using a qualitative design, secondary teachers were interviewed to identify how they embed SEL into their instruction, how they assess SEL, and how prepared they perceive they are to deliver content-embedded SEL instruction. This research suggests that expectations for embedding and documenting SEL vary, but teachers appear to be implementing content-embedded SEL nevertheless. Furthermore, teachers recognize that pre-curated resources or lessons are provided to assist them in embedding SEL but appear to rely heavily upon their own teacher-created resources. Among these activities, teachers rely upon opportunities for reflection and choice and voice activities, but no one instructional strategy or manipulative was preferred overall. Teachers perceive student progress in SEL via observation of student behaviors, interactions, and responses both formally and informally. Regarding their preparedness to teach SEL, teachers perceive that their personal SEL proficiencies directly affect their abilities to teach them. Finally, teachers prefer experiential professional learning situations for SEL, and perceive that time to revisit and reflect in smaller, collaborative settings is an effective process for learning to implement SEL, including the use of specialists. / Doctor of Education / Social-Emotional Learning (SEL) is an improvement strategy that has gained popularity in the past decade. Results from research that suggest SEL develops beneficial student and long-term community effects have led to substantial efforts to spread SEL instruction, especially in middle and high schools. However, the research upon which these efforts are based only reviews the benefits of using purchasable programming, not SEL that teachers embed into their content. The success of content-embedded SEL, which makes up a large percentage of how SEL is employed in middle and high schools (CASEL, 2018; Hart et al., 2013), cannot be accurately measured or predicted because there is little to no identified information about three important factors: how teachers embed SEL, how teachers measure content-embedded SEL, and teachers' perceived readiness to embed SEL. The purpose of this research was to identify the methods middle and high school teachers indicate they use to embed and measure SEL and their perceived preparedness to do so. Educational leaders may be better able to measure the success of content-embedded SEL and improve its use with this knowledge. Middle and high school teachers were interviewed to identify how they embed SEL, how they measure SEL, and how prepared they perceive they are to embed SEL. This research suggests that expectations for embedding and recording SEL vary, but teachers still appear to be embedding SEL. Additionally, teachers understand that pre-curated resources or lessons are provided to assist them in embedding SEL but appear to rely more heavily upon their own resources. Among these activities, teachers rely upon opportunities for reflection and choice and voice activities, but no one teaching strategy was preferred overall. Teachers recognize student development in SEL via observation of their behaviors, interactions, and responses; they grade this development about half of the time. Teachers believe their personal SEL proficiencies directly affect their abilities to teach them. Finally, teachers prefer hands-on situations for learning how to embed SEL, and perceive that time to revisit and reflect in smaller, collaborative settings to be an effective process for learning to implement SEL, including the use of specialists.

Short-term load forecasting (STLF) deals with forecasting of hourly system demand with a lead time ranging from one hour to 168 hours. The basic objective of the STLF is to provide for economic, reliable and secure operation of the power system. This dissertation establishes a new approach to artificial neural network (ANN) based STLF. It first decomposes the prediction problem into representation and function approximation problems. The representation problem is solved using phase-space embedding which identifies time delay variables from load time series that are used in forecasting. The concept is inherently different from the methods used so far because it does not use correlated variables for forecasting. Temperature variables are included as well using identified embedding parameters. Function approximation problem is approached using ANN ensemble and active selection of a training set. Training set is selected based on predicted weather parameters for a prediction horizon. Selection is done applying the k-nearest neighbors technique in a temperature-based vector space. A novel approach of pilot set simulation is used to determine the number of hidden units for every forecast period. Ensemble consists of two ANNs which are trained and cross validated on complementary training sets. Final prediction is obtained by a simple average of two trained ANNs. The described technique is used for predicting one week’s load in four selected months in summer peaking and winter peaking US utilities. Mean absolute percent errors (MAPEs) for 24-hour lead time predictions are slightly greater than 2% for all months. For 120-hour lead time (weekday) predictions, MAPEs are around 2.3%. MAPEs for 48- hour lead time (weekend) predictions are around 2.5%. Maximal errors for these cases are around 7%. Predictions for one-hour lead time are slightly higher than 1% for all months, with maximal errors not exceeding 4.99%. Peak load MAPEs are 2.3% for both utilities. Maximal peak-load errors do not exceed 6%. The technique shows very good performance faced with sudden and large changes in weather. For changes in temperature larger than 20° F for two consecutive days, forecasting error is smaller than 3.58%. / Ph. D.

<p dir="ltr">Theoretical development and implementation of Partition Density Functional Theory, a quantum density embedding framework for electronic structure simulation.</p>

This dissertations represents a composite of three papers which have been submitted for publication: The first chapter deals with a non-convex knapsack which is inspired by a simplified political districting problem. We present and derive a constant time solution to the problem via a reduced-dimensional reformulation, the Karash-Kuhn-Tucker optimality conditions, and gradient descent. The second chapter covers a more complete form of the political districting problem. We attempt to overcome the non-convex objective function and combinatorially massive solution space through a variety of linearization techniques and cutting planes. Our focus on dual bounds is novel in the space. The final chapter develops a framework for identifying ideal mixed binary linear programs and applies it to several rectangle packing formulations. These include both existing and novel formulations for the underlying disjunctive program. Additionally, we investigate the poor performance of branch-and-cut on the example problems. / Doctor of Philosophy / This dissertation is made up of three papers dealing with two problems: Political Districting (the process of partitioning land into voting districts for United States Congressional Representatives) and Rectangle Packing (the process of fitting rectangular objects onto a floorspace in some efficient or optimal manner). Both problems receive thorough descriptions in their respective chapters. Rather than generating real, usable solutions, our focus for the districting problem is on producing upper bounds against which the myriad existing solutions can be compared. This is useful in evaluating whether or not said solutions fairly represent the voting populous of a state. The first chapter deals with the difficulty of political districting by reducing the space of solutions; rather than assigning discrete tracts of land to districts, we assign individual voters. We present two fast methods for solving this reduced problem and achieving viable upper bounds. The second chapter covers a more complete form of the political districting problem as we attempt to overcome the difficulty associated with the objective function rather than the solution space. We propose a variety of techniques for efficiently approximating said function within exiting optimization frameworks and perform a number of experiments to demonstrate their effectiveness. The final chapter shifts focus to the rectangle packing problem described above. This problem is most naturally given as a Disjunctive Program (an optimization problem which requires `or' statements to properly describe). The approximation schemes given in Chapter 2 can also be accurately described as disjunctive programs, so some of the same techniques apply. There exist several good methods for formulating this problem, but we seek to establish a theoretical aspect of these methods. We say that a model is Ideal if any integer requirements can be safely ignored without destroying the solution; Chapter 3 develops a framework for identifying ideal formulations and uses it to prove and correct the idealness of existing methods.

Yes / This paper reports on a regionally based UK study uncovering what has worked well in learning from adverse incidents in hospitals. The purpose of this paper is to review the incident investigation methodology used in identifying strengths or weaknesses and explore the use of a database as a tool to embed learning. Documentary examination was conducted of all adverse incidents reported between 1 June 2011 and 30 June 2012 by three UK National Health Service hospitals. One root cause analysis report per adverse incident for each individual hospital was sent to an advisory group for a review. Using terms of reference supplied, the advisory group feedback was analysed using an inductive thematic approach. The emergent themes led to the generation of questions which informed seven in-depth semi-structured interviews. “Time” and “work pressures” were identified as barriers to using adverse incident investigations as tools for quality enhancement. Methodologically, a weakness in approach was that no criteria influenced the techniques which were used in investigating adverse incidents. Regarding the sharing of learning, the use of a database as a tool to embed learning across the region was not supported. Softer intelligence from adverse incident investigations could be usefully shared between hospitals through a regional forum. The use of a database as a tool to facilitate the sharing of learning from adverse incidents across the health economy is not supported.

State observers for nonlinear systems are often designed for a canonical form of this system. However, this form may possess singular points, where the vector field is not defined or a Lipschitz condition is not fulfilled. This unpleasant behavior can possibly be avoided using an embedding into a higher dimensional space. A construction of such an embedding and the corresponding inverse map is discussed for polynomial systems using methods from algebraic geometry.

This work explores a continuum representation for diffuse layer models, thereby endowing continuum embedding models the ability to capture electrostatic phenomena in the environment such as the existence of electrolyte ions, and the nature of ionic liquids. It introduces a new field-aware continuum model that adjusts the size of the quantum regime per atom based on the distribution of charge in a system. The model accounts for the asymmetric nature of solvent distribution when applied to cations versus anions; it also overcomes the need to parameterize continuum interface models for different charged systems. The continuum representation of cavitation in water does not account for the tendency for water to form a hydrogen bonding network that is broken due to the formation of cavities. This effect is a major contributor to hydrophobic solvation and is an important precondition to the investigation of solvated proteins with continuum embedding. A new model inspired by machine learning advances is trained on molecular dynamics simulations due to the difficulty of isolating the cavitation energy term in experiment. Thermodynamic integration is used to calculate the energy from a step-like repulsive potential from cavities in TIP4P water, cavities ranging from small organic molecules, to small proteins. Predictions from this new model show a small improvement for small molecules and scale much better with respect to the size of the system.