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Pattern recognition has over past decades become a fast growing area of chemometrics. Accurate, user-friendly, and fast pattern recognition methods are desired to accommodate the increased capacity of automated instruments to obtain large-scale data under complex circumstances. It has found significant applications in diverse fields such as environmental monitoring and biomedical diagnostics. In this dissertation, the capabilities of pattern recognition methods in case studies related to environmental remote sensing and biomedical sensing are investigated. For remote sensing applications, two types of airborne spectroscopic data, passive Fourier transform infrared (FTIR) and gamma-ray, are subject to analysis in order to develop automated classifiers for either ammonia vapor or the radioisotope cesium-137 in the open-air. Support vector machine (SVM) classification is the primary pattern recognition method used in this work. In order to overcome the limitation of available representative patterns associated with airborne data, and provide sufficient patterns presenting the analyte-active class for use in the training set, a spectral simulation protocol is employed to generate abundant patterns bearing both the signature of the target analyte and the background spectral profile. Signal processing procedures including segment selection and digital filtering are further used to extract the information most relevant to the target analyte out the acquired raw data. Also, to ease the computational demand from the SVM, an alternative pattern recognition method, piecewise linear discriminant analysis (PLDA) is applied to optimize signal processing conditions for final SVM classification. Process control techniques are applied to the SVM score profiles of prediction sets to improve pattern recognition performance by incorporating probabilities associated with every SVM score. Ammonia classifiers developed from this methodology result in classification performance with high sensitivity and selectivity, and the cesium-137 classifiers developed from the same concepts exhibit excellent sensitivity to test data with very low signal strengths. Under the case of ammonia classification, the relationship between the concentration profile of the active patterns in the training set and the limit of detection of the corresponding classifier is investigated. Classifiers built to detect low concentrations of ammonia are developed and tested through this work. For a glucose sensing application, studies are conducted to provide sound performance diagnostics for an established calibration model for glucose from near infrared spectroscopic data. Six-component aqueous matrixes of glucose in the presence of five other interfering species, all spanning physiological levels, serve as samples to be analyzed. A novel residual modeling protocol is proposed to retrieve the residual glucose concentrations, the concentration not being predicted by the calibration model, from the residual spectra, the portion of the raw spectra not being used by the calibration model. The recovered glucose concentration from the residual modeling can be used as a means, combined with process control techniques, to evaluate the performance of the established calibration model. Several modeling techniques are used for residual modeling, including PLS, support vector regression (SVR), a hybrid method, PLS-aided SVR, and an amplified version of the hybrid, amplified PLS-aided SVR. Through this work, a calibration updating strategy is developed which provides an effective way to monitor the established calibration model.

The 1641 rebellion is unique in early modern European violence and armed struggles because of the vast collection of over 8,000 eyewitness accounts known as the 1641 depositions. My dissertation seeks to utilize the depositions to uncover the religious worldviews of early modern Irish men and women. Through close readings of the depositions, as well as polemical literature which cited the depositions as source material, the following chapters analyze how survivors and polemicists alike invoked religious language to despicted confessional differences and the workings of divine providence in seventeenth-century Ireland. In particular, this dissertation focuses on two related themes: how refugees described the conflicts and violence they had experienced and how eyewitness accounts were co-opted and edited by later authors to serve as propaganda. The depositions clearly portray deponents' understandings of differences in religious identity and their familiarity with providential explanations of the crises to which they had f victim. While much subsequent polemical literature presented the conflict in strictly confessionalized terms, a comparative analysis of contemporary propaganda alongside the depositions shows that strategic editing of source materials betrayed the deponents' nuanced depictions of religious identity and their providential interpretations of the progress of the violence of the 1640s. Broadening the context of the rebellion to include similar providentialist propaganda from the Thirty Years War, this dissertation shows the extent to which providential imagery in eyewitness accounts and war propaganda polarized religious identities in print. In making this point, my research contributes to broader interests in the over-simplification of religious language and imagery to define in-groups and out-groups in wartime rhetoric.

The property of having a finite number of orbits under the regular action has been used to study properties of rings and algebras. For example, in ring theory, Yasuyuki Hirano was able to use this property to show that rings with finitely many orbits under the regular action can be decomposed as direct sum of uniserial rings and a finite ring. In this thesis, we study modules under the regular action. More precisely, if R is a unital ring and M is a left(right) R-module, we describe all modules M that have finitely many orbits under the regular action. Along the way, we give a (new) module theoretical proof to the theorem of Yasuyuki Hirano on the classification of rings with finitely many orbits under the regular action which was proven using using methods from ring theory. Our charaterization of modules with finitely many orbits under the regular action shows a connection between algebras with finitely many submodules and distributive modules. A particular algebra that is of interest to us is the incidence algebra of a finite poset. Incidence algebras were originally introduced in the 1960's by Gian-Carlo Rota as a way to study combinatorial problems but it became apparent later on that such algebras were an interesting object to study in their own right. They include ring theoretical examples such as the product of copies of a ring R and the upper triangular matrices over R. Robert B. Feinberg in his work on incidence algebras developed an internal characterization of incidence algebras of lower finite quasi-ordered sets. For example, he showed that an associative unital complete topological algebra Λ over a field K, where K has the discrete topology, is isomorphic to an incidence algebra if and only if 1. Λ has a faithful unital left module M with a distributive lattice of submodules. Further, every finitely generated submodule of M is finite dimensional and Λ has the coarset topology such that its action on M is continuous in Λ, when M has the discrete topology. 2. For every maximal closed ideal J, Λ/J is isomorphic to Mn(k) for some integer n. 3. For every closed ideal J, the center Λ/J is isomorphic to the direct product of copies of k. This thesis investigates the deformations of incidence algebras and how such deformations relate to cohomology. We show that distributivity of projective indecomposable modules of algebras largely characterizes precisely those algebras which are deformations of incidence algebras

Synapses undergo many stresses and plastic changes throughout the life of an organism. Homeostatic mechanisms respond to these stresses and maintain synaptic activity within a physiologically favorable range. When faced with a reduction in postsynaptic glutamate receptor activity, the Drosophila neuromuscular junction (NMJ) homeostatically compensates by sending a retrograde signal to the presynaptic nerve. This signal triggers an increase in the number of synaptic vesicles released from the presynaptic terminal during an action potential. One of the least well understood aspects of this process is how postsynaptic systems drive production of homeostatic retrograde signals. We have identified several factors that regulate homeostatic synaptic plasticity in the postsynaptic muscle through an RNAi- and electrophysiology-based screen. This screen revealed that C-terminal Src Kinase (Csk) and the fibroblast growth factor receptor (FGFR) Heartless (Htl) are required for homeostatic compensation at the NMJ. This led to the development of two projects, one focused on Csk and the other on Htl. Work with Csk mutant alleles shows that Csk is required for the long-term maintenance of synaptic homeostasis, but not the rapid induction of this process. Csk phosphorylates and inactivates Src Family Kinases (SFKs), of which there are two in Drosophila: Src64B and Src42A. Overexpression and suppression experiments indicate that the homeostatic defects of Csk mutants are due to elevated SFK activity in the postsynaptic muscle. Immunostaining reveals that Csk mutants have altered NMJ levels and localization of the neural cell adhesion molecule (NCAM) ortholog Fasciclin II (FasII). Western analysis reveals that the change in FasII levels in Csk mutants results from upregulation of a previously unreported FasII isoform. We examined a potential role for FasII in homeostatic plasticity and found that increasing FasII levels partially impairs this process. Additionally, reducing FasII in a Csk mutant background restores homeostatic compensation, suggesting that Csk and FasII regulate homeostatic compensation through a common pathway. We show that Htl/FGFR is required in the postsynaptic muscle for the maintenance, but not the induction, of homeostatic signaling. Htl is known to activate Src64B, and we show that Src64B is required for homeostasis in the postsynaptic muscle and link Src64B and Htl/FGFR signaling in the context of homeostatic compensation. We also determine that Htl signaling regulates homeostatic plasticity through activation of translation, likely through target of rapamycin (TOR). FasII has been implicated as a regulator of Htl activity in Drosophila, which is supported by our observation that FasII genetically interacts with Htl and Src64B during homeostatic compensation, connecting the homeostatic block of Csk mutants to Htl signaling. Collectively, these data shed light on postsynaptic mechanisms that work in a single pathway to regulate the production of a homeostatic retrograde signal.

The goal of this thesis is to study non-commutative deformation rings of representations of algebras. The main motivation is to provide a generalization of the deformation theory over commutative local rings studied by B. Mazur, M. Schlessinger and others. The latter deformation theory has played an important role in number theory, and in particular in the proof of Fermat's Last Theorem. The thesis is divided into two parts. In the first part, A is an arbitrary λ-algebra for a complete local commutative Noetherian ring λ with residue field k. A category Ĉ is defined whose objects are complete local λ-algebras R with residue field k such that R is a quotient ring of a power series algebra over λ in finitely many non-commuting variables. If V is a finite dimensional k-vector space that is also a left A-module and that satisfies a natural finiteness condition, it is proved that V has a so-called versal deformation ring R(A,V). More precisely, R(A,V) is an object in Ĉ such that the isomorphism class of every lift of V over an object R in Ĉ arises from a morphism α : R(A,V)→ R in Ĉ and α is unique if R is the ring of dual numbers k[ϵ]. In the second part, two particular examples of λ, A and V are studied and the versal deformation ring R(A,V) is determined in each of these cases. In the first example, λ=k, A is a series of non-commutative k-algebras depending on a parameter r≥2, and V is a particular quotient module of A; it is shown that R(A,V) is isomorphic to A. The second example builds on the first example when r=2 and uses that, if additionally the characteristic of k is 2, then A is isomorphic to the group ring k[D8] of a dihedral group D8 of order 8. It is shown that if k is perfect and W is the ring of infinite Witt vectors over k, then R(W[D8],V) is isomorphic to W[D8].

Chiral amine functionality is abundant in the world of natural products. In the past, many research groups have made use of the addition of carbanions to imine derivatives in order to achieve such functionality. Nucleophilic addition, however, can prove to be difficult when utilizing complex starting materials since many functional groups are not orthogonal to this approach. Radical addition to imine derivatives is an alternative strategy. There is a broader range of functional group tolerance with this method due to the mild nature and chemoselectivity of radical reactions. Further, secondary functionality may be included in either the radical precursor or acceptor, leading to subsequent formation of nitrogen heterocycles through a radical-polar crossover reaction. We have found that photolysis of alkyl iodides in the presence of Mn2(CO)10 leads to chemoselective iodine atom abstraction and radical addition to N-acylhydrazones without affecting alky chloride functionality. Using radical precursors or acceptors bearing a suitably positioned alkyl chloride, the radical addition is followed by further bond construction enabled by radical-polar crossover. After the alkyl radical adds to the imine bond, the resulting N-nucleophile displaces the alkyl chloride leaving group via 5-exo-tet or 6-exo-tet cyclizations, furnishing either pyrrolidine or piperidine functionality, respectively. When both 5-exo-tet and 6-exo-tet pathways are available, the 5-exo-tet cyclization is preferred. Isolation of the intermediate radical adduct, still bearing the alkyl chloride functionality, confirms the order of events in this radical-polar crossover annulation. A chiral oxazolidinone stereocontrol element in the N-acylhydrazones provides excellent stereocontol in these reactions. In the past, the Mn-mediated radical addition to N-acylhydrazones methodology was applied to the synthesis of γ-amino esters and synthetic studies of the tubulysin family of natural products. Throughout this work, it became apparent that there exists a need for a versatile, general approach to the installation of N,O-acetal functionality at peptide bonds. Initial results suggest that such a structure can be synthesized in a latent form, and later oxidized to reveal the N,O-acetal moiety.

In this dissertation, we present several structural studies carried out on some ionic liquids using molecular dynamics simulations. In fact, the cations found in ionic liquids are bulky and amphiphilic. Therefore, they basically govern the structure of these ionic liquids. However, the role of anions in ionic liquids in terms of X-ray scattering experiments was ambiguous. Therefore, one of the goals of this study was to determine the role of anions in ionic liquids in terms of X-ray scattering experiments. Through the molecular dynamics simulations carried out on three ammonium ionic liquids, we demonstrate that the anions play a fundamental role as reporters of structure in X-ray experiments. Moreover, we could identify a mathematical tool, the cation head - anion partial structure function that does not suffer from cancellations between peaks and anti peaks albeit can identify both polarity and charge alternations present in a system. A closer dissection of the total structure functions of a series of pyrrolidinium ionic liquids, into partial structure functions such as polar-apolar and cation head - anion reveal the types of alternations present in these ionic liquids. This study was also an attempt to reveal the association between peaks, antipeaks and different types of alternations. The enhancement of similar type group densities at a particular frequency, gives rise to 'peaks' in the structure function while the depletion of different type group densities (that has a phase offset) gives rise to 'antipeaks'. These peaks and antipeaks that appear at a particular frequency, occur due to some type of alternation,such as charge and polarity alternation. Hence, SAXS peaks and anti peaks unravel the larger length scale ordering present in an ionic liquid. A temperature dependent simulation study was performed on a phosphonium, namely tetradecyltrihexylphosphonium bis(tri fluoromethylsulfonyl)amide ionic liquid. The temperature dependent structural study carried out on this ionic liquid revealed that the intensity of the prepeak (or the first sharp diffraction peak) observed in the total structure function is largely enhanced at higher temperature. It was found that at lower temperature, the apolar alkyl tails are more organized at the expense of polar groups and at higher temperature, the polar groups are more organized at the expense of apolar alkyl tails. The development of the prepeak intensity at higher temperature is merely a consequence of the better organization of polar groups at higher temperature. Such phenomenon could be observed in many other phosphonium ionic liquids, while an opposite phenomenon was observed for the 1-methyl-3-octylimidazolium tetra fluoroborate ionic liquid. Ionic liquids that can form hydrogen bonds and have polar, apolar and fluoro domains have drawn a greater attention during the past decade. In our structural study, we show that both in the fluoroprotic and non- fluoroprotic ionic liquids of our interest namely, butylammonium pentadeca fluoro-octanoate and butylammonium octanoate, the separation between two filaments that comprises the continuous, polar, hydrogen bonded network gives rise to a prepeak, while these filaments are percolating the whole ionic liquid in both cases. Finally, the continuous phase that comprises the hydrogen bonded charge alternation and the phase that contains the alkyl and fluorocarbon tails make these systems bicontinuous.

Anions play a variety of roles in biology, bioinorganic chemistry, organic chemistry and mineralogy. As such, the directed coordination of anions in molecular complexation and the development of synthetic receptor molecules represent a burgeoning field for supramolecular chemistry in solution phase recognition and solid-state crystal engineering. The desire to develop solution phase anion sensors utilizing the optoelectronic properties of tetraphenylethylene (TPE), in particular its capacity to participate in aggregation-induced emission (AIE) enhancement has resulted in the synthesis of two new classes of TPE-based anion sensors. The first class features a series of ureas off of a tetrasubstituted TPE framework capable of detecting a range of anions with its sensitivity toward these anions directly influenced by the basicity of the anion. The second class of TPE-based sensors displays a unique sensitivity toward the presence of pyrophosphate anion and is the first known example of a neutral TPE-based pyrophosphate sensor that does not require a zinc cofactor as a requisite of detection. Our interest in utilizing anions in the self-assembly of organic materials resulted in the synthesis of twelve N-halophenyl pyridinium salts that are capable of assembling the solid state as a direct consequence of a combination of hydrogen- and halogen-bonding intermolecular forces and their interaction with a halide counterion. In four examples, the abundance of iodine halogen-bond donors relative to counterion acceptors resulted in the formation of extended halogen-bonded networks in the crystal structures that proved to be sufficiently strong to avoid disruption by an abundance of competing hydrogen bond donors. Five additional examples of TPE-based halopyridinium salts were analyzed via crystallographic methods to examine what role the counterion will play, if any, in the directed assembly of these materials with the aid of potentially strong halogen bond donors. Three examples feature the presence of a traditionally coordinating anion and two examples study the types of assembly motifs that may be encountered when the anion is noncoordinating. Conclusions from this study led to attempts to synthesize TPE-based pyridinium- and imidazolium salts capable of participating in anion recognition through solution phase halogen bonding. Though the results did not imply success, the potential to continue to refine our synthetic methodology and analytical techniques is being explored.

This dissertation consists of three chapters. The first chapter addresses the role of housing market dynamics in explaining the choice of public education finance systems at the state level. The second chapter assesses the effects of increased levels of state involvement in public education finance on total amount of resources for public schools by taking into account the differences in state aid formulae. The third chapter examines the relationship between spending per pupil in public schools and demographic characteristics of the population. In the first chapter, I analyze the welfare effects of different public education finance systems. Specifically, I show that the public education finance system that decreases intrastate spending inequality by setting a minimum spending per pupil, Foundation, would be chosen over the system that sets a guaranteed tax base for every district, Power-Equalizing, if they were subject to a majority voting. The main mechanism behind this is that higher property tax rates under a Power-Equalizing system compared to a Foundation system lead to lower housing wealth for the majority in the former. The model suggests that a high preference for education in the utility function, lower mean income in a state, and lower income inequality in a state results in a Foundation system being chosen by a majority. Finally, I provide suggestive evidence supporting these theoretical results. In the second chapter, I quantitatively address the effects of increased levels of state involvement in public education finance in the U.S.. By using district level data on K-12 public education finance, income and demographic composition in 2008, I conclude that state governments redistribute from wealthier districts to poorer districts. Local authorities, however, respond to the centralization of public education finance systems by decreasing their contributions. Thus, every dollar increase in state aid increases total expenditures by less than one dollar. Using the categorization of Jackson et al. (2014), I argue that the effect of state funds on total expenditures is different for different state aid formula types. In states with standard equalization plans and local effort equalization plans, a dollar increase in state aid increases total expenditures by as little as 35 cents. In states with minimum foundation plans, in contrast, a dollar increase in state aid increases total expenditures by as much as 70 to 83 cents. In the third chapter, I explore the underlying demographic factors that leads into a stronger preference for public education. Previous studies suggest that lower share of elderly, higher share of school age children, and higher share of college graduates in the population result in a higher level of spending per pupil in public schools. However, the existing literature does not take into account the differences in state aid formulae. This is important given that these formulae differ and they have direct effects on levels and dispersion of spending in the districts. My analysis suggests that the type of state aid formula affects the relationship between demographic characteristics and spending per pupil in public schools. Specifically, the effects of these three variables on public education expenditures are bigger in the states with Minimum Foundation plans compared to Equalization and Local Equalization plans. This is a direct result of the latter two state aid formulae being more centralized compared to Minimum Equalization plans. While they control for spending inequality at a higher degree, public education finance system in the state becomes more centralized which leads into a weaker relationship between each of these demographic variables and spending levels in the districts. These results are also seem to be robust to the type of the public education finance reform of the state.