Nevanlinna representations in several variables

We generalize two integral representation formulae of Nevanlinna to functions of several variables. We show that for a large class of analytic functions that have non-negative imaginary part on the upper polyhalfplane there are representation formulae in terms of densely defined self-adjoint operators on a Hilbert space. We introduce three types of structured resolvent of a self-adjoint operator and identify four different types of representation in terms of these resolvents. We relate the types of representation that a function admits to its growth at infinity.Comment: 37 pages. In this version we have added some references and expanded the introductio

Boundary behavior of analytic functions of two variables via generalized models

We describe a generalization of the notion of a Hilbert space model of a function in the Schur class of the bidisc. This generalization is well adapted to the investigation of boundary behavior at a mild singularity of the function on the 2-torus. We prove the existence of a generalized model with certain properties corresponding to such a singularity and use this result to solve two function-theoretic problems. The first of these is to characterise the directional derivatives of a function in the Schur class at a singular point on the torus for which the Carath\'eodory condition holds. The second is to obtain a representation theorem for functions in the two-variable Pick class analogous to the refined Nevanlinna representation of functions in the one-variable Pick class.Comment: 30 page

The purposes of school:an instrumental case study

Abstract. This thesis is a qualitative study about the purposes of school using a combination of theoretical and empirical data. The school under study is the collection of schools and corresponding social imaginary that emerged in the 19th century in the compulsory mass education movement. This is the social imaginary of a “relatively uniform model” of compulsory mass schooling, or education for all, as a state or government responsibility. The research aims to answer the following questions: i) How have the purposes of school been understood by different researchers since the spread of mass schooling? ii) How do the purposes of school appear to be understood by different agents within an education community in Ontario? As the research is framed as a case study of the education community in Ontario, along with a section summarizing the history of school, the first data set, a collection of literature by a diverse group of educational authors, was used in order to inform the analysis of a second data set and contribute to the case. This data set was analyzed using inductive qualitative content analysis, with themes emerging from the data. The second data set, data from the case itself, was a selection of interviews with educators as well as one student interview and 30 student productions about the topic. These were analyzed using deductive qualitative content analysis, whereas the themes induced in the first data set were used to analyze the second data set, with space for new themes to emerge. The findings of the study suggest that there is quite a panoply of perceptions of the purposes of school. On the theoretical side, much depends on the context and history of schools in the given context, and vary in terms of temporal purposes (preparation for adulthood and for the present moment), as well as in terms of individual or collective purposes, and finally as an oppressive or enlightening force. For the educators in Ontario, the purposes seem to be more fluid and depend on the students’ and school board’s initiatives. The purposes have been found to also relate to individual beliefs and values. As will be discussed below, every purpose but one found in the literature, was also mentioned in the interviews. Interestingly, new themes emerged. There also seems to be a major issue with respect to the lack of time available and taken by educators to reflect on the purposes of school. It is possible that we are stuck in a cycle of accepting that this school under study has no viable alternative in our societies, without necessarily understanding or reflecting on the “why” behind its existence.Abstract . Ce mémoire consiste d’une étude qualitative sur la raison d’être de l’école. L’étude se base sur une combinaison de données théoriques et empiriques. L’école étudiée est celle qui a émergé au XIXe siècle durant la période qui a commencé le mouvement vers l’éducation obligatoire pour tous. Ce mouvement s’est transformé dans un imaginaire social puissant d’un «modèle relativement uniforme» de la scolarité en tant que responsabilité de l’État ou du gouvernement. La recherche vise à répondre aux questions suivantes: i) Comment la raison d’être de l’école a-t-elle été comprise par différents chercheurs depuis la diffusion de la scolarisation des masses? ii) Comment la raison d’être de l’école semble-t-elle être comprise par différents agents au sein d’une communauté scolaire en Ontario? La recherche est présentée comme une étude de cas d’une communauté éducative en Ontario, avec une section résumant l’histoire de l’école. Le premier ensemble de données, une collection de littérature par un groupe diversifié d’auteurs pédagogiques, a été utilisé afin d’éclairer l’analyse du deuxième ensemble de données. Le deuxième ensemble de données consistait d’entretiens avec les agents de la communauté scolaire ainsi que des contributions d’élèves. Le tout a été analysé à l’aide d’une méthode d’analyse de contenu qualitative déductive. Les thèmes induits du le premier ensemble de données ont été utilisés pour analyser le deuxième ensemble de données, avec un espace pour l’émergence de nouveaux thèmes. Les résultats de l’étude suggèrent qu’il existe une panoplie de perceptions sur la raison d’être de l’école. Sur le plan théorique, beaucoup dépend du contexte et de l’histoire des écoles dans le contexte donné, et varie en termes d’objectifs temporels, ainsi qu’en termes d’objectifs individuels ou collectifs, et enfin comme une force oppressive ou éclairante. Pour les éducateurs de l’Ontario, les objectifs semblent plus fluides et dépendent de la réalité des élèves et des initiatives conseils scolaires. Il a été constaté que les raisons d’être qui ont emergés des données concernaient également les croyances et les valeurs individuelles. Comme nous le verrons ci-dessous, toutes les raisons d’être sauf un trouvés dans la littérature ont également été mentionnés dans les entretiens. De plus, de nouveaux thèmes ont émergé. Il semble également avoir un problème majeur en ce qui concerne le manque de temps dis-ponible et pris par les éducateurs pour réfléchir à la raison d’être de l’école. Il est possible que nous soyons coincés dans un cycle d’accepter que ce modèle, celui de l’école obligatoire et pour tous, n’a pas d’alternative viable dans nos sociétés, sans nécessairement comprendre ou réfléchir sur le «pourquoi» derrière son existence

MISSION ENGINEERING METHODOLOGY FOR REALIZATION OF UNMANNED SURFACE VESSEL OPERATIONS

The Navy has included unmanned systems as a key enabler for the future fleet. Congress has mandated that the Navy (PMS 406) provide demonstrated testing and documentation sufficient to support transition of Unmanned Surface Vessels (USVs) from prototype to operational. Commercial USV certification examples only address safety of navigation and do not provide certification requirements for autonomy, nor do they consider the operational mission context or requirements for the USVs. No current methodology exists that decomposes the certification metrics and standards, including the complexity of the intended USV missions. Mission engineering (ME) provides the systems engineering rigor and methodology to ensure that the USV prototypes are evaluated in their intended missions. The mission objectives were captured in Design Reference Missions (DRMs). The DRMs provided the operational sequence of events for the USVs to accomplish their mission in support of commander's intent. The DRMs decomposed into mission essential tasks (METs). The METs were mapped to the critical systems performing the METs. This methodology can be further analyzed to produce the complete complement of certification requirements for PMS 406. Analysis revealed several gaps. The communications systems and the human-in-the-loop interaction with the USVs need to be reevaluated based upon the mission analysis.Civilian, Department of the NavyApproved for public release. Distribution is unlimited

Developing the Quantitative Histopathology Image Ontology : A case study using the hot spot detection problem

Interoperability across data sets is a key challenge for quantitative histopathological imaging. There is a need for an ontology that can support effective merging of pathological image data with associated clinical and demographic data. To foster organized, cross-disciplinary, information-driven collaborations in the pathological imaging field, we propose to develop an ontology to represent imaging data and methods used in pathological imaging and analysis, and call it Quantitative Histopathological Imaging Ontology – QHIO. We apply QHIO to breast cancer hot-spot detection with the goal of enhancing reliability of detection by promoting the sharing of data between image analysts

A MATHEMATICAL PROGRAMMING MODEL FOR VEGETABLE ROTATIONS

Rotations have historically been used to alleviate pest problems in crop production. This paper considers methods of modeling rotations in linear programming models for Southeastern vegetable production. In such models, entering each possible crop rotation as a separate activity can be burdensome because of the large numbers of possible rotational alternatives. Conventional methodology for double crop rotations reduces the number of activities but must be adapted to accommodate triple crop rotational requirements in vegetable production. This paper demonstrates these methods both for a simple example and an empirical problem with numerous rotation alternatives. While the methods presented in this paper may have computational disadvantages compared to entering each rotation as a separate activity, they do have advantages in model design and data management.Crop Production/Industries,

Nucleation at the DNA supercoiling transition

Twisting DNA under a constant applied force reveals a thermally activated transition into a state with a supercoiled structure known as a plectoneme. Using transition state theory, we predict the rate of this plectoneme nucleation to be of order 10^4 Hz. We reconcile this with experiments that have measured hopping rates of order 10 Hz by noting that the viscosity of the bead used to manipulate the DNA limits the measured rate. We find that the intrinsic bending caused by disorder in the base-pair sequence is important for understanding the free energy barrier that governs the transition. Both analytic and numerical methods are used in the calculations. We provide extensive details on the numerical methods for simulating the elastic rod model with and without disorder.Comment: 18 pages, 15 figure