Satellite operators as group actions on knot concordance

Any knot in a solid torus, called a pattern or satellite operator, acts on knots in the 3-sphere via the satellite construction. We introduce a generalization of satellite operators which form a group (unlike traditional satellite operators), modulo a generalization of concordance. This group has an action on the set of knots in homology spheres, using which we recover the recent result of Cochran and the authors that satellite operators with strong winding number $\pm 1$ give injective functions on topological concordance classes of knots, as well as smooth concordance classes of knots modulo the smooth 4--dimensional Poincare Conjecture. The notion of generalized satellite operators yields a characterization of surjective satellite operators, as well as a sufficient condition for a satellite operator to have an inverse. As a consequence, we are able to construct infinitely many non-trivial satellite operators P such that there is a satellite operator $\overline{P}$ for which $\overline{P}(P(K))$ is concordant to K (topologically as well as smoothly in a potentially exotic $S^3\times [0,1]$) for all knots K; we show that these satellite operators are distinct from all connected-sum operators, even up to concordance, and that they induce bijective functions on topological concordance classes of knots, as well as smooth concordance classes of knots modulo the smooth 4--dimensional Poincare Conjecture.Comment: 20 pages, 9 figures; in the second version, we have added several new results about surjectivity of satellite operators, and inverses of satellite operators, and the exposition and structure of the paper have been improve

Concordance of knots in S1×S2S^1\times S^2

We establish a number of results about smooth and topological concordance of knots in $S^1\times S^2$. The winding number of a knot in $S^1\times S^2$ is defined to be its class in $H_1(S^1\times S^2;\mathbb{Z})\cong \mathbb{Z}$. We show that there is a unique smooth concordance class of knots with winding number one. This improves the corresponding result of Friedl-Nagel-Orson-Powell in the topological category. We say a knot in $S^1\times S^2$ is slice (resp. topologically slice) if it bounds a smooth (resp. locally flat) disk in $D^2\times S^2$. We show that there are infinitely many topological concordance classes of non-slice knots, and moreover, for any winding number other than $\pm 1$, there are infinitely many topological concordance classes even within the collection of slice knots. Additionally we demonstrate the distinction between the smooth and topological categories by constructing infinite families of slice knots that are topologically but not smoothly concordant, as well as non-slice knots that are topologically slice and topologically concordant, but not smoothly concordant.Comment: 25 pages, 19 figures, final version, to appear in Journal of London Mathematical Societ

A comparison of geocoding baselayers for electronic medical record data analysis

Indiana University-Purdue University Indianapolis (IUPUI)Identifying spatial and temporal patterns of disease occurrence by mapping the residential locations of affected people can provide information that informs response by public health practitioners and improves understanding in epidemiological research. A common method of locating patients at the individual level is geocoding residential addresses stored in electronic medical records (EMRs) using address matching procedures in a geographic information system (GIS). While the process of geocoding is becoming more common in public health studies, few researchers take the time to examine the effects of using different address databases on match rate and positional accuracy of the geocoded results. This research examined and compared accuracy and match rate resulting from four commonly-used geocoding databases applied to sample of 59,341 subjects residing in and around Marion County/ Indianapolis, IN. The results are intended to inform researchers on the benefits and downsides to their selection of a database to geocode patient addresses in EMRs

Studies in ring D fragmentation of estrone

Includes bibliographical references.Studies have been conducted in synthesising 14-allyl 19-norsteroids. The eventual aim is to convert the 14-allyl derivatives into bridge-functionalised 19-norsteroids. Two approaches were investigated, with the immediate aim of generating fragmentation intermediates suitable for 14-allylation. The approaches were based on cleavage of the 16,17-bond via oxidative cleavage or fragmentation methodology. The oxidative cleavage routes involved the preparation of 3-methoxy-17 –methylestra-1,3,5(10), 16-tetraen-15-one, which was shown not to undergo regioselective 14-methylation. In an alternative approach 3-methoxy-17a-methylestra-1,3,5(10),14tetraene- 16β, 17β-diol was synthesised. However, the lability of the primary cleaved product prompted synthesis of 3-methoxy-16,17-seco-17a-homoestra-1,3,5(10)-triene16,17a- dione. Chemodifferentiation of the carbonyl groups of the seco derivative provided access to 16-acetoxy-3-methoxy-16, 17-seco-17a-homoestra-1,3,5(10)-trien-17a-one, in an overall yield of 60% from estrone 3-methyl ether. The fragmentation approaches involved conjugate stannylation and silylation of 3-methoxyestra-1,3,5,(10), 15-tetraen-17 -one to give the 15β-trimethylstannyl and 15β-trimethylsilyl 17 -ketones respectively. The stannyl ketone was converted to the 3-methoxy-17a-methyl-15β-trimethylstannylestra-1,3,5,(10)-trien-l7β-ol. Generation of the derived alkoxy radical resulted in formation of 3-methoxy-16, 17-seco-17a-homoestra1,3,5( 10),15-tetraen-17a-one, in low yield, The silyl ketone was converted to the 17acetoxyimino- 3 -methoxy-15β-trimethylsilylestra-l,3,5( 10)-trien, Fragmentation with the borontrifluoride diethyl ether complex resulted in formation of the undesired 3-methoxy13,17-secoestra-l ,3,5(1 0),l4-tetraen-17-nitrile. Since the 15β-trimethylsilyl group did not direct the fragmentation, the 17-acetoxyimino-3-methoxy-16β-trimethylsilylmethylestra-1,3,5(10)-triene was synthesised in the hope that it would be more amenable to silicon directed fragmentation, However, fragmentation with the boron trifluoride diethyl ether complex resulted In formation of the undesired 17-acetoxy-3-methoxy 16β-trimethylsilylmethyl-17a-aza-17a-homoestra-1,3,5(10), 17-tetraene

Didacticism and reconciliation: instructive discourse in the novels of Ignacio Manuel Altamirano

Ignacio Manuel Altamirano’s novelística is of insurmountable importance for any study of the development of Nineteenth century Mexican literary culture and the Mexican liberal national narrative. Nevertheless, the ample criticism which treats Altamirano’s novels has to date failed to grasp anything more than a tenuous unity latent in those works. This investigation provides a new framework for a unified interpretation of Altamirano’s three most widely read and commented novels, Clemencia, La navidad en las montañas, and El Zarco. By way of an examination of historiographic-political narratives contemporaneous with the period informing the writing of those novels, in conjunction with an appeal to the understanding of the function of the novelistic form following the theory of M.M. Bakhtin and others, Altamirano’s still controversial final novel will be shown to yield a new interpretation whose unitary function is dependent on all three of the novels examined herein. This unitary function will be shown to be constructed by way of the deployment of an innovatory instructive discourse which embraces all three of the novels examined and fundamentally determines their structure and content. As such, this investigation provides a new understanding of the works of this canonical author and propounds a more profound understanding of the interdependencies both literary and extraliterary that shape this part of the maestro’s work and the innovatory instructive discourse upon which it is founded

Bachelor of Arts

thesisThe essay has taken many forms throughout its long and storied history, but where does it stand today? With the advent of digital media propagated throughout theInternet the essay has again changed. The digital revolution has enabled authors to create essays in a multitude of new and often hybrid genres. In particular, digital technology has made combining images and sound possible for anyone with access to a computer. What follows is a personal exploration of t h e essay. I have included three prose essays and four multi-media essays that attempt to address the current state of the literary form

Facing the Past: Engendering the Study of Iron Age Celtic Human Imagery in Continental Europe

Iconography is an important tool in understanding the past because it may express apeople’s understanding of the world through representations of stories or figures, including human beings. The continental early Iron Age Celts left behind no written sources but did leave iconographic representations of humans in the form of full bodies as well as heads. How the Celts saw their world and how they perceived and gendered other humans or anthropomorphic beings can be partially accessed via these representations. This thesis examines a representative sample of statues and figures from Iberia, Gaul, and Central Europe from an intersectional perspective focused on status and gender. Details such as facial features, jewelry, or weapons have often been associated with certain genders or statuses, but to date, no systematic comparative analysis has been carried out to determine whether there are any geographic or temporal patterns in these representations. Items such as arm rings and belts have been reevaluated to test the idea that status may have been as important as gender in such representations. This study was able to demonstrate that images with masculine or male features appear more frequently in stone or metal than those with feminine or female features and that facial hair in emic imagery challenges the stereotypical view presented by Mediterranean sources that emphasize moustaches rather than beards. The presence and placement of belts and arm rings in iconographic representations likewise does not conform to expected patterns from mortuary contexts, possibly due to differential preservation. This project opens a dialogue for iii future analysis of gendered objects through iconographic analysis. An intersectional analysis of human figural representation in Celtic iconography has the potential to expand our understanding of gender in Iron Age Europe by interrogating objects intended to depict human or anthropomorphic beings

Double-Hinged Di-1,2,4-Triazoles for Synthesis of Breathing MOFs

Employing semi-rigid di-1,2,4-triazoles as ligands has led to the formation of a plethora of Metal-Organic Framework (MOF) architectures. The ability for the ligands to exhibit multiple conformations through a “hinge” effect allows for the formation of a multitude of MOF topologies and dimensionalities. Employment of a di-triazole containing a central trans-butene moiety was initially studied and led to the formation of two three-dimensional copper MOFs. The frameworks can be synthesized independently, but a reaction occurs in water wherein the kinetic product is used as a reagent to synthesize the topologically distinct thermodynamic product. Additional testing of reaction conditions with the butene-containing di-triazole led to the formation of a three-dimensional breathing framework by utilizing a mixed anion system. The framework structure flexes reversibly upon removal or addition of water to form semi-hydrated and dehydrated MOFs. Single crystal X-ray analysis demonstrated the 2-butene subunit of the ligand rotates between positions, causing changes in the solvent accessible volume. This double hinge within the ligand is a built-in breathing mechanism and suggests a general synthesis for breathing MOFs. Replacing the central butene moiety with a xylene moiety resulted in the di-triazole adopting a syn conformation between copper chains, forming two-dimensional MOFs that resemble fused 1D metal-organic nanotubes (MONTs). The 2D sheet layers can expand or contract, or, more remarkably, the phenyl ring can rotate between positions as a function of solvation. The transformations were followed by powder X-ray diffraction and solid state NMR. Additionally, frameworks which contain extended naphthyl and biphenyl linkers have been synthesized and characterized. The syn conformation adopted by the di-triazoles was further exploited for the formation of a series of 1D MONTs. The di-triazole ligands bridge rigid metal chains while appropriate anion choice provides a “capping” of the metal fragments, leading to nanotube formation instead of 2D sheets. The pore size of the MONTs can be adjusted by changing the central portion of the double-hinged ligand, allowing for a general synthesis of MONTs. Adsorption studies of MONTs revealed selective uptake of carbon dioxide and methane with copper MONTs exhibiting the highest uptake