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This dissertation is an edition of the letters exchanged between Charles Peirce and the Open Court Publishing Company (OCP) 1890 to 1913, roughly the last twenty-three years of Peirce’s life. OCP published more of Peirce’s philosophical writings than any other publisher during his lifetime, and played a critical role in what little recognition and financial income he received during these difficult, yet philosophically rich, years. This correspondence is the basis for much of what is known surrounding Peirce’s publications in The Monist and The Open Court, and is referenced often in Peirce editions dealing with his later work. Peirce’s OCP correspondents included Paul Carus, editor; Edward C. Hegeler, founder and owner; Thomas J. McCormack, assistant editor and translator; Francis C. Russell, Chicago attorney and OCP editorial contractor; and various other OCP editors and staff members. Also included in this edition (Appendix) are enclosures and other material related to the letters, with some exclusions noted in the text. Not included are letters exchanged within the OCP organization that make reference to Peirce. Significant portions of these letters are quoted or referenced in editorial notes, but their entirety is not necessary for a full account of the Peirce–OCP relationship, and for now falls out of the scope of this edition. The objective of this edition is to provide for the first time a complete and accurate text of this oft-cited correspondence, with textual apparatus and contextual annotation. The edition is intended for Peirce readers, but is also a valuable reference for those interested in the history of OCP and, more generally, of Progressive Era American philosophy. / 2024-03-31T00:00:00Z

Esta tese é um estudo de estabilidade de modos quasinormais em um sistema que apresenta uma mudança de estabilidade ao variar continuamente os parâmetros físicos de um buraco negro. A mudança de estabilidade encontrada possui interpretações na correspondência AdS/CFT. A ferramenta principal utilizada neste trabalho para o cálculo de modos quasinormais foram métodos numéricos que podem ser utilizados em inúmeros trabalhos desta área de pesquisa, especialmente por não dependerem de suposições de simetria ou de comportamento conveniente do sistema físico. / This thesis is a study of stability of quasinormal modes in a system featuring a stability change if one continuously varies the physical parameters of a black hole. The stability change thus found has some possible interpretations in the AdS/CFT correspondence. The main tool used in this study for calculating quasinormal modes are numerical methods that can be used in numerous works in this area of research, especially because they do not depend on assumptions of symmetry or any convenient behavior of the physical system.

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Ontologies provide an organization of language, in the form of a network or graph, which is amenable to computational analysis while remaining human-readable. Although they are used in a variety of disciplines, ontologies in the biomedical field, such as Gene Ontology, are of interest for their role in organizing terminology used to describe—among other concepts—the functions, locations, and processes of genes and gene-products. Due to the consistency and level of automation that ontologies provide for such annotations, methods for finding enriched biological terminology from a set of differentially identified genes in a tissue or cell sample have been developed to aid in the elucidation of disease pathology and unknown biochemical pathways. However, despite their immense utility, biomedical ontologies have significant limitations and caveats. One major issue is that gene annotation enrichment analyses often result in many redundant, individually enriched ontological terms that are highly specific and weakly justified by statistical significance. These large sets of weakly enriched terms are difficult to interpret without manually sorting into appropriate functional or descriptive categories. Also, relationships that organize the terminology within these ontologies do not contain descriptions of semantic scoping or scaling among terms. Therefore, there exists some ambiguity, which complicates the automation of categorizing terms to improve interpretability. We emphasize that existing methods enable the danger of producing incorrect mappings to categories as a result of these ambiguities, unless simplified and incomplete versions of these ontologies are used which omit problematic relations. Such ambiguities could have a significant impact on term categorization, as we have calculated upper boundary estimates of potential false categorizations as high as 121,579 for the misinterpretation of a single scoping relation, has_part, which accounts for approximately 18% of the total possible mappings between terms in the Gene Ontology. However, the omission of problematic relationships results in a significant loss of retrievable information. In the Gene Ontology, this accounts for a 6% reduction for the omission of a single relation. However, this percentage should increase drastically when considering all relations in an ontology. To address these issues, we have developed methods which categorize individual ontology terms into broad, biologically-related concepts to improve the interpretability and statistical significance of gene-annotation enrichment studies, meanwhile addressing the lack of semantic scoping and scaling descriptions among ontological relationships so that annotation enrichment analyses can be performed across a more complete representation of the ontological graph. We show that, when compared to similar term categorization methods, our method produces categorizations that match hand-curated ones with similar or better accuracy, while not requiring the user to compile lists of individual ontology term IDs. Furthermore, our handling of problematic relations produces a more complete representation of ontological information from a scoping perspective, and we demonstrate instances where medically-relevant terms--and by extension putative gene targets--are identified in our annotation enrichment results that would be otherwise missed when using traditional methods. Additionally, we observed a marginal, yet consistent improvement of statistical power in enrichment results when our methods were used, compared to traditional enrichment analyses that utilize ontological ancestors. Finally, using scalable and reproducible data workflow pipelines, we have applied our methods to several genomic, transcriptomic, and proteomic collaborative projects.

The evolutionary forces that led to the unprecedented expansion of the human brain and the extreme cognitive prowess possessed by humans have always attracted a great deal of attention from the scientific community. Presented here is a novel theoretical perspective, where the driving force on human brain evolution was the need for enhanced ability to infer social values of conspecifics in the face of degradation and loss of chemosensory signalling mechanisms necessary for social communication present in most mammals. The lack of chemosensory communication of biologically relevant information between humans in the face of the need to make adaptive and accurate social evaluations, led to an exaption of mammalian chemosensory brain regions for the more complex task of inferring social values from behavioural cues that are variable, ambiguous, or otherwise difficult to detect and interpret. This change in social processing from perceptual evaluation to inferential computation placed a premium on cognitive capacity, thus selecting for larger more powerful brains. These selective processes would have left an indelible mark on the human brain, where the human homologues of regions involved in mammalian conspecific chemical communication, in particular the target regions of this study the amygdala and ventromedial prefrontal cortex (VMPC), should be involved in the processing of biologically relevant information and social inference. Several experiments were conducted to examine the role of these brain regions in social inferential processing using the lesion deficit method. First, given that conspecific chemical communication is particularly relevant for biologically imperative evaluation for the purposes of reproduction, VMPC and amygdala damage may result in abnormal mate-related decisions. Second, normal social attributions exhibit the correspondence bias, however damage to the target regions may result in an abnormal lack correspondence bias. Third, the current hypothesis is contrasted with another leading hypothesis, the Social Brain Hypothesis whose proponents predict a relationship between group-size and social cognition. Finally, if the target brain regions are truly integral in inferring social information, then damage to these regions will interfere with the ability to utilize transitive inference in social situations, and potentially in using transitive inference in general. Damage to the target areas produces limited effects on mate-related decisions and preferences. However, the current hypothesis may suggest that the target brain regions are only involved when the problem is inferential in nature rather than simpler perception of social information. In support of this notion, damage to the target regions results in a lack of the correspondence bias when making economic decisions. This alteration in social attributions actually leads to more `rational' decision-making in this context. In contrast to the predictions of the Social Brain Hypothesis, damage to the target regions produces no observed reduction in social group size, nor is there any observed relationship between perspective-taking ability and group size. Finally, damage to the VMPC produces deficits in using transitive inference in a non-social context perhaps hinting at the underlying computations of this region in inferring social information. In conclusion, it appears that the notion that the human brain regions that have been exapted from their duties in chemosensation and communication in mammalian brains has at least some validity. Moreover, these brain regions have been shifted by evolution to a more computationally complex process of social inference possibly providing the push toward larger and more powerful human brains.

There are two primary sources of motivation for the contents of this thesis. The first is an effort to generalize classical dilation theory, a brief history of which is given in Section 2.1. The second source of motivation is the study of the representation theory of tensor algebras associated to C*-correspondences; these concepts are discussed in Sections 2.2 and 2.4. Although seemingly unrelated, there is a close connection between these two motivating theories. The link between classical dilation theory and the representation theory of tensor algebras over C*-correspondences was established by Muhly and Solel in their 1998 paper Tensor Algebras over C*-Correspondences: Representations, Dilations, and C*-Envelopes. In that paper, the authors not only introduced the concept of (operator-theoretic) tensor algebras – non-selfadjoint operator algebras that generalize algebraic tensor algebras – but they also developed the representation theory of these algebras. In order to do so, they introduced and made extensive use of a generalized dilation theory for contractions on Hilbert space. In analogy with classical dilation theory, they developed notions of “isometric dilation” and “coisometric extension” for completely contractive representations of the tensor algebra. The process of forming isometric dilations proceeded smoothly, but constructing coisometric extensions proved more problematic. In contrast to the classical case, Muhly and Solel showed that there is a high degree of nonuniqueness involved when building coisometric extensions. This lack of uniqueness proved to be an impediment to developing a full generalization of the dilation and model theories of Sz.-Nagy and Foias. In this thesis, we introduce a way to manage the ambiguities that arise when forming coisometric extensions. More specifically, we show that the notion of a transfer operator from classical dynamics can be adapted to this setting, and we prove that when a transfer operator is fixed in advance, every completely contractive representation of the tensor algebra admits a unique coisometric extension that respects the transfer operator in a fashion that we describe in Chapter 5. We also prove a commutant lifting theorem in the context of coisometric extensions.

An operator-theoretic formulation of the interpolation problem posed by Nevanlinna and Pick in the early twentieth century asks for conditions under which there exists a multiplier of a reproducing kernel Hilbert space that interpolates a specified set of data. Paul S. Muhly and Baruch Solel have shown that their theory for operator algebras built from W*-correspondences provides an appropriate context for generalizing this classic question. Their reproducing kernel W*-correspondences are spaces of functions that generalize the reproducing kernel Hilbert spaces. Their Nevanlinna-Pick interpolation theorem, which is proved using commutant lifting, implies that the algebra of multipliers of the reproducing kernel W*-correspondence associated with a certain W*-version of the classic Szegö kernel may be identified with their primary operator algebra of interest, the Hardy algebra. To provide a context for generalizing another familiar topic in operator theory, the study of the weighted Hardy spaces, Muhly and Solel have recently expanded their theory to include operator-valued weights. This creates a new family of reproducing kernel W*-correspondences that includes certain, though not all, classic weighted Hardy spaces. It is the purpose of this thesis to generalize several of Muhly and Solel's results to the weighted setting and investigate the function-theoretic properties of the resulting spaces. We give two principal results. The first is a weighted version of Muhly and Solel's commutant lifting theorem, which we obtain by making use of Parrott's lemma. The second main result, which in fact follows from the first, is a weighted Nevanlinna-Pick interpolation theorem. Other results, several of which follow from the two primary results, include the construction of an orthonormal basis for the nonzero tensor product of two W*-corrrespondences, a double commutant theorem, the identification of several function-theoretic properties of the elements in the reproducing kernel W*-correspondence associated with a weighted W*-Szegö kernel as well as the elements in its algebra of mutlipliers, and the presentation of a relationship between this algebra of multipliers and a weighted Hardy algebra. In addition, we consider a candidate for a W*-version of the complete Pick property and investigate the aforementioned weighted W*-Szegö kernel in its light.

This thesis uses the results of limited testing at the Fort Dade (1836-1842) and Hope Homestead (1842-ca. 1900) archaeological sites to establish a method for quickly identifying threatened sites with minimal disturbance to surrounding areas. Artifact analysis, pattern recognition, and comparison with similar known sites are key elements. Pedestrian survey, metal detection, posthole and shovel testing, and test excavation are tools used to accomplish this. Artifact analysis is used to establish date ranges for the sites, as well as the material variation between military and homestead occupations. Artifacts used for analysis include glass, ceramics, nails, arms and personal items. Quantitative analysis of artifact assemblages is utilized to determine broad site type classification, and further contribute to preliminary identification. Correspondence analysis helps differentiate sites according to length and type of occupation. With refinement, this method could be used for preliminary identification of many Seminole War sites. Rapid and widespread development in Florida has made identification of Seminole War sites a priority, so they can be recorded and preserved before they are lost forever.

Predicting breast tissue deformation is of great significance in several medical applications such as surgery, biopsy and imaging. In breast surgery, surgeons are often concerned with a specific portion of the breast, e.g., tumor, which must be located accurately beforehand. Also clinically it is important for combining the information provided by images from several modalities or at different times, for the planning and guidance of interventions. Multi-modality imaging of the breast obtained by mammography, MRI and PET is thought to be best achieved through some form of data fusion technique. However, images taken by these various techniques are often obtained under entirely different tissue configurations, compression, orientation or body position. In these cases some form of spatial transformation of image data from one geometry to another is required such that the tissues are represented in an equivalent configuration. We constructed the 3D biomechanical models for this purpose using Finite Element Methods (FEM). The models were based on phantom and patient MRIs and could be used to model the interrelation between different types of tissue by applying displacements of forces and to register multimodality medical images.