Master of Landscape Architecture / Department of Landscape Architecture/Regional and Community Planning / Timothy D. Keane / Camp Adventure, a summer camp for the physically disabled, has obtained a site for the future Camp Adventure Conference and Retreat Center at Perry Lake, Ozawkie, Kansas. The camp serves youth and adults with cerebral palsy and spina bifida. Past rental facilities have been far from adequate for the camp’s basic needs of accessibility and has led the camp to seek a specially designed permanent home. As a counselor for 9 years, I have experienced firsthand the barriers and frustrations with inadequate facilities. Seeking to find solutions to the camp’s specific needs, I found William H. Whyte’s research methods and environmental psychology studies fitting to discover human preference and experiential qualities. To understand the best methods of adaptation, a series of user based research methods have been conducted to gather user input. The campers understand, from daily experience, what it takes to make an element or activity accessible, and their guidance will inform the design of select program elements. User input is not only being gathered from the camp, but from educational sources at Kansas State University, practicing professionals at Ochsner Hare and Hare, and local government representatives. Collaboratively molding the site’s existing form, the campers accessibility needs, and a complex program has created an exciting and challenging project. The program consists of 24 elements and activities, many of which are not traditionally handicap friendly. In-depth design studies and application of the user input has created the form and experience of seven program elements. This book contains literature and precedent studies, user based research results, the master plan for the entire site, and design details of seven program elements. It is to be used by Camp Adventure as a guide to implementation of the camp design. It is the path for Camp Adventure to achieve their dream: a barrier free, fully accessible, adventure; Camp Adventure.

<p> In this thesis, both direct and inverse elastic scattering problems are considered. For a given incident wave, the direct problem is to determine the displacement of wave field from the known structure, which could be an obstacle or a surface in this thesis; The inverse problem is to determine the structure from the measurement of displacement on an artificial boundary.</p><p>In the second chapter, we consider the scattering of an elastic plane wave by a rigid obstacle, which is immersed in a homogeneous and isotropic elastic medium in two dimensions. Based on a Dirichlet-to-Neumann (DtN) operator, an exact transparent boundary condition is introduced and the scattering problem is formulated as a boundary value problem of the elastic wave equation in a bounded domain. By developing a new duality argument, an a posteriori error estimate is derived for the discrete problem by using the finite element method with the truncated DtN operator. The a posteriori error estimate consists of the finite element approximation error and the truncation error of the DtN operator which decays exponentially with respect to the truncation parameter. An adaptive finite element algorithm is proposed to solve the elastic obstacle scattering problem, where the truncation parameter is determined through the truncation error and the mesh elements for local refinements are chosen through the finite element discretization error.<br></p><p>In chapter 3, we extend the argument developed in chapter 2 to elastic surface grating problem, where the surface is assumed to be periodic and elastic rigid; Then, we treat the obstacle scattering in three dimensional space; The direct problem is shown to have a unique weak solution by examining its variational formulation. The domain derivative is studied and a frequency continuation method is developed for the inverse problem. Finally, in chapter 4, a rigorous mathematical model and an efficient computational method are proposed to solve the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. The surface is assumed to be a small and smooth perturbation of an elastically rigid plane. By placing a rectangle slab of a homogeneous and isotropic elastic medium with larger mass density above the surface, more propagating wave modes can be utilized from the far-field data which contributes to the reconstruction resolution. Requiring only a single illumination, the method begins with the far-to-near field data conversion and utilized the transformed field expansion to derive an analytic solution for the direct problem, which leads to an explicit inversion formula for the inverse problem; Moreover, a nonlinear correction scheme is developed to improve the accuracy of the reconstruction; Numerical examples are presented to demonstrate the effectiveness of the proposed methods for solving the questions mentioned above.<br></p>

At the atomic scale, interactive physically-based modeling tools are more and more in demand. Unfortunately, solving the underlying physics equations at interactive rates is computationally challenging. In this dissertation, we propose new algorithms that allow for interactive modeling of chemical structures. We first present a modeling tool to construct structural models of hydrocarbon systems. The physically-based feedbacks are based on the Brenner potential. In order to be able to interactively edit systems containing numerous atoms, we introduce a new adaptive simulation algorithm. Then, we introduce what we believe to be the first interactive quantum chemistry simulation algorithm at the Atom Superposition and Electron Delocalization Molecular Orbital (ASED-MO) level of theory. This method is based on the divide-and-conquer (D&C) approach, which we show is accurate and efficient for this non-self-consistent semi-empirical theory. We then propose a novel Block-Adaptive Quantum Mechanics (BAQM) approach to interactive quantum chemistry. BAQM constrains some nuclei positions and some electronic degrees of freedom on the fly to simplify the simulation. Finally, we demonstrate several applications, including one study of graphane formation, interactive simulation for education purposes, and virtual prototyping at the atomic scale, both on desktop computers and in virtual reality environments.

A l'échelle atomique, les outils de modélisation interactive sont de plus en plus nécessaires. Cependant, résoudre les équations de la physique sous-jacente en temps interactif est un défi numérique difficile. Dans cette dissertation, nous proposons des nouveaux algorithmes qui permettent la modélisation interactive de structures chimiques. Tout d'abord, nous présentons un outil de modélisation pour construire des modèles structuraux de systèmes hydrocarbonés. Les retours physiques sont basés sur le potentiel de Brenner. Pour obtenir des taux interactifs lors de l'édition de systèmes contenant un grand nombre d'atomes, nous introduisons un nouvel algorithme adaptatif. Ensuite, nous introduisons ce que nous pensons être le premier algorithme de chimie quantique interactif au niveau de théorie “Atom Superposition and Electron Delocalization Molecular Orbital”. Cette méthode est basée sur une approche diviser-pour-régner qui, comme nous le montrons, est précise et efficace pour cette théorie semi-empirique non auto-cohérente. Nous proposons ensuite une nouvelle approche pour la chimie quantique interactive : “Block-Adaptive Quantum Mechanics” (BAQM). BAQM contraint la position des noyaux et les degrés de liberté électronique à la volée pour simplifier la simulation. Finalement, nous présentons plusieurs applications : une étude de la formation du graphane, la simulation interactive à des fins pédagogiques, et le prototypage virtuel à l'échelle atomique, à la fois sur des ordinateurs de bureau et dans des environnements de réalité virtuelle. / At the atomic scale, interactive physically-based modeling tools are more and more in demand. Unfortunately, solving the underlying physics equations at interactive rates is computationally challenging. In this dissertation, we propose new algorithms that allow for interactive modeling of chemical structures. We first present a modeling tool to construct structural models of hydrocarbon systems. The physically-based feedbacks are based on the Brenner potential. In order to be able to interactively edit systems containing numerous atoms, we introduce a new adaptive simulation algorithm. Then, we introduce what we believe to be the first interactive quantum chemistry simulation algorithm at the Atom Superposition and Electron Delocalization Molecular Orbital (ASED-MO) level of theory. This method is based on the divide-and-conquer (D&C) approach, which we show is accurate and efficient for this non-self-consistent semi-empirical theory. We then propose a novel Block-Adaptive Quantum Mechanics (BAQM) approach to interactive quantum chemistry. BAQM constrains some nuclei positions and some electronic degrees of freedom on the fly to simplify the simulation. 
 Finally, we demonstrate several applications, including one study of graphane formation, interactive simulation for education purposes, and virtual prototyping at the atomic scale, both on desktop computers and in virtual reality environments.

Lorsque les internautes naviguent sur le Web, ils laissent de nombreuses traces que nous nous proposons d’exploiter pour améliorer les applications d'accès à l'information. Nous étudions des techniques centrées sur les utilisateurs qui tirent parti des nombreux types de rétroaction pour perfectionner les services offerts aux utilisateurs. Nous nous concentrons sur des applications telles que la recommandation et le marketing d’influence dans lesquelles les utilisateurs génèrent des signaux (clics, "j'aime", etc.) que nous intégrons dans nos algorithmes afin de fournir des services fortement contextualisés. La première partie de cette thèse est consacrée à une approche interactive de la recherche d'information sur les médias sociaux. Le problème consiste à récupérer un ensemble de k résultats dans un réseau social sous la contrainte que la requête peut être incomplète (par exemple, si le dernier terme est un préfixe). Chaque fois que l'utilisateur met à jour sa requête, le système met à jour l'ensemble des résultats de recherche en conséquence. Nous adoptons une interprétation de la pertinence de l'information qui tient compte du réseau, selon laquelle l'information produite par les utilisateurs proches de l'utilisateur faisant la requête est jugée plus pertinente. Ensuite, nous étudions une version générique de la maximisation de l'influence, dans laquelle nous voulons maximiser l'influence des campagnes d'information ou de marketing en sélectionnant de manière adaptative les utilisateurs initiant la propagation de l'information parmi un petit sous-ensemble de la population. Notre approche ne fait aucune hypothèse sur le modèle de diffusion sous-jacent ni même sur la structure du réseau de diffusion. Notre méthode a d'importantes applications dans le marketing d’influence qui vise à s’appuyer sur les influenceurs de réseaux sociaux pour promouvoir des produits ou des idées. Enfin, nous abordons le problème bien connu du démarrage à froid auquel sont confrontés les systèmes de recommandation par une approche adaptative. Si aucune information n’est disponible concernant l'appréciation d’un article, le système de recommandation doit recueillir des signaux (clics, etc.) afin d'estimer la valeur de l'article. Cependant, afin de minimiser les mauvaises recommandations faites aux utilisateurs, le système ne doit pas recueillir ces signaux de façon négligente. Nous introduisons un algorithme dynamique qui vise à alterner intelligemment les recommandations visant à accumuler de l'information et celles s'appuyant sur les données déjà recueillies. / When users interact on modern Web systems, they let numerous footprints which we propose to exploit in order to develop better applications for information access. We study a family of techniques centered on users, which take advantage of the many types of feedback to adapt and improve services provided to users. We focus on applications like recommendation and influencer marketing in which users generate discrete feedback (e.g. clicks, "likes", reposts, etc.) that we incorporate in our algorithms in order to deliver strongly contextualized services. The first part of this dissertation is dedicated to an approach for as-you-type search on social media. The problem consists in retrieving a set of k search results in a social-aware environment under the constraint that the query may be incomplete (e.g., if the last term is a prefix). Every time the user updates his / her query, the system updates the set of search results accordingly. We adopt a "network-aware" interpretation of information relevance, by which information produced by users who are closer to the user issuing a request is considered more relevant. Then, we study a generic version of influence maximization, in which we want to maximize the influence of marketing or information campaigns by adaptively selecting "spread seeds" from a small subset of the population. Influencer marketing is a straightforward application of this, in which the focus of a campaign is placed on precise key individuals who are typically able to reach millions of consumers. This represents an unprecedented tool for online marketing that we propose to improve using an adaptive approach. Notably, our approach makes no assumptions on the underlying diffusion model and no diffusion network is needed. Finally, we propose to address the well-known cold start problem faced by recommender systems with an adaptive approach. If no information is available regarding the user appreciation of an item, the recommender system needs to gather feedback (e.g., clicks) so as to estimate the value of the item. However, in order to minimize "bad" recommendations, a well-designed system should not collect feedback carelessly. We introduce a dynamic algorithm that aims to intelligently achieve the balance between "bad" and "good" recommendations.

L’objet de cette thèse a été de développer une méthode numérique multi-approche et multiéchelle appliquée à la simulation d’écoulements diphasiques de fluides non miscibles, incompressibles et isothermiques et plus particulièrement à l’atomisation primaire. Cette méthode repose sur une approche couplée entre un maillage local raffiné et un maillage global plus large. Le couplage est explicite avec raffinement en temps, c’est-à-dire que chaque domaine évolue selon son propre pas de temps. Afin de prendre en compte les différentes échelles en temps et en espace dans le processus d’atomisation, cette méthode numérique couple deux méthodes numériques diphasiques différentes : une méthode de capture de l’interface dans le domaine local raffiné près de l’injecteur et une méthode de sous-maille dans le domaine global grossier et la région du spray dispersé. Le code développé et parallélisé dans le logiciel OpenFOAMR s’avère capable de réduire de manière significative le temps de calcul d’une simulation aux grandes échelles de l’atomisation dans un injecteur coaxial, tout en prédisant de manière fiable les données expérimentales. / The purpose of this work has been to develop a multi-approach and multi-scale numerical method applied to the simulation of two-phase flows involving non miscible, incompressible and isothermal fluids, and more specifically primary atomization. This method is based on a coupled approach between a refined local mesh and a coarser global mesh. The coupling is explicit with refinement in time, i.e. each domain evolves following its own time-step. In order to account for the different scales in space and time of the atomization process, this numerical method couples two different two-phase numerical methods: an interface capturing method in the refined local domain near the injector and a sub-grid method in the coarser global domain in the dispersed spray region. The code has been developed and parallelized in the OpenFOAMR software. It is able to reduce significantly the computational cost of a large eddy simulation of a coaxial atomization, while predicting with accuracy the experimental data.

Dieser Artikel enthält vier Kapitel. Das erste Kapitel ist berechtigt, '''' lokalen Quantil Regression"und seine Zusammenfassung: Quantil Regression ist eine Technik, bedingte Quantil Kurven zu schätzen. Es bietet ein umfassendes Bild über ein Antwort-Kontingent auf erklärenden Variablen. In einem Rahmen flexible Modellierung ist eine besondere Form der bedingten Quantil-Kurve nicht von vornherein festgelegt. Dies motiviert eine lokale parametrische anstatt einer globalen feste Modell passend Ansatz. Eine nichtparametrische Glättung Schätzung der bedingte Quantil Kurve erfordert, zwischen lokalen Krümmung und stochastische auszugleichen Variabilität. In den ersten Essay empfehlen wir eine lokale Modellauswahl Technik, die eine adaptive Schätzung der bedingte bietet Quantil-Regression-Kurve bei jedem Entwurf-Punkt. Theoretische Ergebnisse behaupten, dass das vorgeschlagene adaptive Verfahren als führt gut als Orakel die würde das Risiko der lokalen Abschätzung für die Aufgabenstellung minimieren. Wir veranschaulichen die Leistung der Trolle. / This article includes four chapters. The first chapter is entitled ``Local Quantile Regression", and its summary: Quantile regression is a technique to estimate conditional quantile curves. It provides a comprehensive picture of a response contingent on explanatory variables. In a flexible modeling framework, a specific form of the conditional quantile curve is not a priori fixed. This motivates a local parametric rather than a global fixed model fitting approach. A nonparametric smoothing estimate of the conditional quantile curve requires to balance between local curvature and stochastic variability. In the first essay, we suggest a local model selection technique that provides an adaptive estimate of the conditional quantile regression curve at each design point. Theoretical results claim that the proposed adaptive procedure performs as good as an oracle which would minimize the local estimation risk for the problem at hand. We illustrate the performance of the procedure by an extensive simulation study and consider a couple of applications: to tail dependence analysis for the Hong Kong stock market and to analysis of the distributions of the risk factors of temperature dynamics.

The thesis consists of four papers on numerical complexityanalysis of weak approximation of ordinary and partialstochastic differential equations, including illustrativenumerical examples. Here by numerical complexity we mean thecomputational work needed by a numerical method to solve aproblem with a given accuracy. This notion offers a way tounderstand the efficiency of different numerical methods. The first paper develops new expansions of the weakcomputational error for Itˆo stochastic differentialequations using Malliavin calculus. These expansions have acomputable leading order term in a posteriori form, and arebased on stochastic flows and discrete dual backward problems.Beside this, these expansions lead to efficient and accuratecomputation of error estimates and give the basis for adaptivealgorithms with either deterministic or stochastic time steps.The second paper proves convergence rates of adaptivealgorithms for Itˆo stochastic differential equations. Twoalgorithms based either on stochastic or deterministic timesteps are studied. The analysis of their numerical complexitycombines the error expansions from the first paper and anextension of the convergence results for adaptive algorithmsapproximating deterministic ordinary differential equations.Both adaptive algorithms are proven to stop with an optimalnumber of time steps up to a problem independent factor definedin the algorithm. The third paper extends the techniques to theframework of Itˆo stochastic differential equations ininfinite dimensional spaces, arising in the Heath Jarrow Mortonterm structure model for financial applications in bondmarkets. Error expansions are derived to identify differenterror contributions arising from time and maturitydiscretization, as well as the classical statistical error dueto finite sampling. The last paper studies the approximation of linear ellipticstochastic partial differential equations, describing andanalyzing two numerical methods. The first method generates iidMonte Carlo approximations of the solution by sampling thecoefficients of the equation and using a standard Galerkinfinite elements variational formulation. The second method isbased on a finite dimensional Karhunen- Lo`eve approximation ofthe stochastic coefficients, turning the original stochasticproblem into a high dimensional deterministic parametricelliptic problem. Then, adeterministic Galerkin finite elementmethod, of either h or p version, approximates the stochasticpartial differential equation. The paper concludes by comparingthe numerical complexity of the Monte Carlo method with theparametric finite element method, suggesting intuitiveconditions for an optimal selection of these methods. 2000Mathematics Subject Classification. Primary 65C05, 60H10,60H35, 65C30, 65C20; Secondary 91B28, 91B70. / QC 20100825

This thesis consists of a summary and four scientific articles. All four articles consider various aspects of stochastic differential equations and the purpose of the summary is to provide an introduction to this subject and to supply the notions required in order to fully understand the articles. In the first article we conduct a thorough study of the multi-dimensional Skorohod problem in time-dependent domains. In particular we prove the existence of cádlág solutions to the Skorohod problem with oblique reflection in time-independent domains with corners. We use this existence result to construct weak solutions to stochastic differential equations with oblique reflection in time-dependent domains. In the process of obtaining these results we also establish convergence results for sequences of solutions to the Skorohod problem and a number of estimates for solutions, with bounded jumps, to the Skorohod problem. The second article considers the problem of determining the sensitivities of a solution to a second order parabolic partial differential equation with respect to perturbations in the parameters of the equation. We derive an approximate representation of the sensitivities and an estimate of the discretization error arising in the sensitivity approximation. We apply these theoretical results to the problem of determining the sensitivities of the price of European swaptions in a LIBOR market model with respect to perturbations in the volatility structure (the so-called ‘Greeks’). The third article treats stopped diffusions in time-dependent graph domains with low regularity. We compare, numerically, the performance of one adaptive and three non-adaptive numerical methods with respect to order of convergence, efficiency and stability. In particular we investigate if the performance of the algorithms can be improved by a transformation which increases the regularity of the domain but, at the same time, reduces the regularity of the parameters of the diffusion. In the fourth article we use the existence results obtained in Article I to construct a projected Euler scheme for weak approximation of stochastic differential equations with oblique reflection in time-dependent domains. We prove theoretically that the order of convergence of the proposed algorithm is 1/2 and conduct numerical simulations which support this claim.