Advances in information technology in the past two decades have seen innovations in the field of domestic and industrial computing that led to a paradigm shift in the management and operation of urban water systems by water utility companies. The traditional public management policy that focused on ensuring a minimum quality of service regardless of the costs associated with the processes of catchment, treatment and distribution of water, in many cases even unknown, have evolved towards more efficient cost sensitive models. These new wholly or partly public funded management systems improve not only the quality of service offered to users, but also optimize resources by reducing the cost and causing the minimum environmental impact. The new challenges raised by the European Water Framework1 Directive by imposing cost recovery to improve water efficiency and environmental sustainability have led to a significant change at all levels of water management. Consequently, new priorities have been established in terms of infrastructure management that require the reduction of water losses and the improvement of the water efficiency in urban networks for human consumption. Likewise, in a broader context which includes the water--energy binomial, it is also desirable to improve the energy efficiency and carbon emissions of these systems. Today, network sectoring is the most commonly used strategy to improve management and increase network performance. It basically consists of dividing the network into several smaller hydraulic sectors, where water inlets and outlets are perfectly controlled. This simplifies the task of carrying out periodic water balances in each of the sectors, and allows water loss volume to be assessed for a given period of time. As configuring network sectors is not a trivial task, it is therefore important to have appropriate tools to perform the task efficiently and effectively. Mathematical models can play an important role as decision support tools to help water managers assess the performance of water network distribution systems. This thesis aims to address the current problems of managing urban water networks by combining new information-processing technologies with innovative network modelling techniques. It intends to facilitate the system diagnosis and extend the use of models on the decision-making process to provide better solutions to the management of urban water networks. For this purpose a software extension that works on a geographic information system (GIS) has been developed. It integrates: the hydraulic and water quality simulation program EPANET 2, innovative tools for model analysis and diagnostic, automatic tools for sectoring and computing tools to conduct water balances in the sectors using actual measurements. The work demonstrates the compatibility and complementarity of GIS and hydraulic models as technologies that can be used to support the assessment and diagnosis of water distribution networks. Considering that the majority of information linked to the network system has some geographic reference, it is not surprising that GIS has become a popular tool for dealing with such information. At the same time, the integration of mathematical modelling and simulation tools, offers the GIS a new dimension in the realm of hydraulic study of water networks. Furthermore, if this specific integration is provided with new features aimed not only to facilitate the model building, but also to assist the user in decision-making using powerful algorithms based on the application of the graph theory, the result is a powerful up-to-date analytical tool, which opens up new possibilities in the field of management and efficient operation of urban water supply systems. / Bartolín Ayala, HJ. (2013). Confección de modelos de redes de distribución de agua desde un Sig y desarrollo de herramientas de apoyo a la toma de decisiones [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/33152

<p dir="ltr">This work will introduce a channel conceptualization and possible coding scheme for Graph-and-Symbol (GS) Communication. While Claude Shannon’s mathematical model for communication employed graphs to describe relationships and confusability among traditional time-sequenced signals, little work as been done to describe non-linear communication <i>with</i> graphs where we transmit and receive physical structures of information. The principal contribution of this work is to introduce a mathematical framework for communication with graphs which have symbols assigned to vertices. This looks like a molecule, and so we may think of these messages as coded forms of molecular communication.</p><p dir="ltr">At this time, many problems in this area will (and may remain) computationally intractable, but as the field of graph theory continues to develop, new tools and techniques may emerge to solve standing problems in this new subfield of communication.</p><p dir="ltr">Graphs present two difficulties: first, they contain ambiguities among their vertices and do not have an <i>a priori</i> canonical ordering, and second, the relationships among graphs lack structural regularities which we see in traditional error control coding lattices. There are no Galois fields to exploit over graph-based codes as we have with cyclic codes, for example. Furthermore, the shear number of graphs of order n grows so rapidly that it is difficult to account for the neighborhoods around codewords and effectively reduce communication errors which may occur. The more asymmetric a graph is, the more orderings on symbols it can support. However, asymmetries complicate the computation of channel transition probabilities, which are the cornerstone of all communication theory.</p><p dir="ltr">In the prologue, the reader will be introduced to a new educational tool for designing traditional binary cyclic codes.</p><p dir="ltr">1 through 10 will detail the development of Graph-and-Symbol (GS) Commu- nication to date followed by two example codes which demonstrate the power of structuring information on graphs.</p><p dir="ltr">Chapter 13 onward will review the preliminary work in another area of research, disjoint from the main body. It is included here for posterity and special interests in applying graphs to solving other problems in signal processing. It begins with an introduction of spacetime raythic graphs. We propose a new chamfering paradigm for connecting neighboring pixels which approximates solutions to the eikonal equation. We show that some raythic graphs possess structures with multiple, differing solutions to eikonal wavefront propagation which are essential to the construction of the Umbral Transform. This umbral transform emulates ray casting effects, such as shadows and diffraction within an image space, from a network-flow algorithm.</p><p dir="ltr">This work may be duplicated in whole or in part for educational purposes only. All other rights of this work are reserved by the author, Timothy Arthur Terlep Jr., of Rose-Hulman Institute of Technology, Terre Haute, IN (effective August 2024), and subject to the rules and regulations of the Graduate School of Purdue University.</p><p dir="ltr">Readers may contact the author with any comments and questions at <b>taterlep@gmail.com</b></p>

This thesis deals with cohomologies on the symplectic quotient of a Frölicher space which is locally diffeomorphic to a Euclidean Frölicher subspace of Rn of constant dimension equal to n. The symplectic reduction under consideration in this thesis is an extension of the Marsden-Weinstein quotient (also called, the reduced space) well-known from the finite-dimensional smooth manifold case. That is, starting with a proper and free action of a Frölicher-Lie-group on a locally Euclidean Frölicher space of finite constant dimension, we study the smooth structure and the topology induced on a small subspace of the orbit space. It is on this topological space that we will construct selected cohomologies such as : sheaf cohomology, Alexander-Spanier cohomology, singular cohomology, ~Cech cohomology and de Rham cohomology. Some natural questions that will be investigated are for instance: the impact of the symplectic structure on these di erent cohomologies; the cohomology that will give a good description of the topology on the objects of category of Frölicher spaces; the extension of the de Rham cohomology theorem in order to establish an isomorphism between the five cohomologies. Beside the algebraic, topological and geometric study of these new objects, the thesis contains a modern formalism of Hamiltonian mechanics on the reduced space under symplectic and Poisson structures. / Mathematical Sciences / D. Phil. (Mathematics)

<p>Land use change constitutes a primary driving force in shaping social-ecological systems world wide, and its effects reach far beyond the directly impacted areas. Graph based landscape ecological tools have become established as a promising way to efficiently explore and analyze the complex, spatial systems dynamics of ecological networks in physical landscapes. However, little attention has been paid to making these approaches operational within ecological assessments, physical planning, and design. This thesis presents a network based, landscape-ecological tool that can be implemented for effective use by practitioners within physical planning and design, and ecological assessments related to these activities. The tool is based on an ecological profile system, a common generalized network model of the ecological infrastructure, graph theoretic metrics, and a spatially explicit, geographically defined representation, deployable in a GIS. Graph theoretic metrics and analysis techniques are able to capture the spatio-temporal dynamics of complex systems, and the generalized network model places the graph theoretic toolbox in a geographically defined landscape. This provides completely new insights for physical planning, and environmental assessment activities. The design of the model is based on the experience gained through seven real-world cases, commissioned by different governmental organizations within Stockholm County. A participatory approach was used in these case studies, involving stakeholders of different backgrounds, in which the tool proved to be flexible and effective in the communication and negotiation of indicators, targets, and impacts. In addition to successful impact predictions for alternative planning scenarios, the tool was able to highlight critical ecological structures within the landscape, both from a system-centric, and a site-centric perspective. In already being deployed and used in planning, assessments, inventories, and monitoring by several of the involved organizations, the tool has proved to effectively meet some of the challenges of application in a multidisciplinary landscape.</p>

This thesis deals with cohomologies on the symplectic quotient of a Frölicher space which is locally diffeomorphic to a Euclidean Frölicher subspace of Rn of constant dimension equal to n. The symplectic reduction under consideration in this thesis is an extension of the Marsden-Weinstein quotient (also called, the reduced space) well-known from the finite-dimensional smooth manifold case. That is, starting with a proper and free action of a Frölicher-Lie-group on a locally Euclidean Frölicher space of finite constant dimension, we study the smooth structure and the topology induced on a small subspace of the orbit space. It is on this topological space that we will construct selected cohomologies such as : sheaf cohomology, Alexander-Spanier cohomology, singular cohomology, ~Cech cohomology and de Rham cohomology. Some natural questions that will be investigated are for instance: the impact of the symplectic structure on these di erent cohomologies; the cohomology that will give a good description of the topology on the objects of category of Frölicher spaces; the extension of the de Rham cohomology theorem in order to establish an isomorphism between the five cohomologies. Beside the algebraic, topological and geometric study of these new objects, the thesis contains a modern formalism of Hamiltonian mechanics on the reduced space under symplectic and Poisson structures. / Mathematical Sciences / D. Phil. (Mathematics)

Land use change constitutes a primary driving force in shaping social-ecological systems world wide, and its effects reach far beyond the directly impacted areas. Graph based landscape ecological tools have become established as a promising way to efficiently explore and analyze the complex, spatial systems dynamics of ecological networks in physical landscapes. However, little attention has been paid to making these approaches operational within ecological assessments, physical planning, and design. This thesis presents a network based, landscape-ecological tool that can be implemented for effective use by practitioners within physical planning and design, and ecological assessments related to these activities. The tool is based on an ecological profile system, a common generalized network model of the ecological infrastructure, graph theoretic metrics, and a spatially explicit, geographically defined representation, deployable in a GIS. Graph theoretic metrics and analysis techniques are able to capture the spatio-temporal dynamics of complex systems, and the generalized network model places the graph theoretic toolbox in a geographically defined landscape. This provides completely new insights for physical planning, and environmental assessment activities. The design of the model is based on the experience gained through seven real-world cases, commissioned by different governmental organizations within Stockholm County. A participatory approach was used in these case studies, involving stakeholders of different backgrounds, in which the tool proved to be flexible and effective in the communication and negotiation of indicators, targets, and impacts. In addition to successful impact predictions for alternative planning scenarios, the tool was able to highlight critical ecological structures within the landscape, both from a system-centric, and a site-centric perspective. In already being deployed and used in planning, assessments, inventories, and monitoring by several of the involved organizations, the tool has proved to effectively meet some of the challenges of application in a multidisciplinary landscape.

Indiana University-Purdue University Indianapolis (IUPUI) / Symptoms of post-traumatic stress disorder (PTSD) are a common comorbidity in veterans seeking treatment of chronic musculoskeletal pain (CMP). However, little is known regarding the mutual influence of PTSD and CMP in this population. Using cross-sectional and longitudinal data from a randomized clinical trial evaluating a stepped care intervention for CMP in Iraq/Afghanistan veterans (ESCAPE), this dissertation examined the relationships between PTSD and CMP along with other factors including depression, anxiety, catastrophizing and health-related quality of life. The Classification and Regression Tree (CART) analysis was conducted to identify key factors associated with baseline PTSD besides CMP severity. A series of statistical analyses including logistical regression analysis, mixed model repeated measure analysis, confirmatory factor analysis and cross-lagged panel analysis via structural equation modeling were conducted to test five competing models of PTSD symptom clusters, and to examine the mutual influences of PTSD symptom clusters and CMP outcomes. Results showed baseline pain intensity and pain disability predicted PTSD at 9 months. And baseline PTSD predicted improvement of pain disability at 9 months. Moreover, direct relationships were found between PTSD and the disability component of CMP, and indirect relationships were found between PTSD, CMP and CMP components (intensity and disability) mediated by depression, anxiety and pain catastrophizing. Finally, the coexistence of PTSD and more severe pain was associated with worse SF-36 Physical Component Summary (PCS) and Mental Component Summary (MCS) scores. Together these findings provided empirical support for the mutual maintenance theory.

This Master Thesis deals with the drawing algorithms of graphs known from the mathematical theory. These algorithms deals with an appropriate distribution of the graph vertices in order to obtain the most clear and readable graphs for human readers. The main objective of this work was also to implement the drawing algorithm in the application that would allow to edit the graph. This work deals also with graphs representation in computers.

[ES] La interoperabilidad entre los objetos comunicados es el objetivo principal del internet de las cosas (IoT). Algunos esfuerzos para lograrlo han generado diversas propuestas de arquitecturas, sin embargo, aún no se ha llegado a un conceso. Estas arquitecturas difieren en el tipo de estructura, grado de centralización, algoritmo de enrutamiento, métricas de enrutamiento, técnicas de descubrimiento, algoritmos de búsqueda, segmentación, calidad de servicio y seguridad, entre otros. Algunas son mejores que otras, dependiendo del entorno en el que se desempeñan y del tipo de parámetro que se use. Las más populares son las orientadas a eventos o acciones basadas en reglas, las cuales han permitido que IoT ingrese en el mercado y logre una rápida masificación. Sin embargo, su interoperabilidad se basa en alianzas entre fabricantes para lograr su compatibilidad. Esta solución se logra en la nube con una plataforma que unifica a las diferentes marcas aliadas. Esto permite la introducción de estas tecnologías a la vida común de los usuarios pero no resuelve problemas de autonomía ni de interoperabilidad. Además, no incluye a la nueva generación de redes inteligentes basadas en cosas inteligentes. La arquitectura propuesta en esta tesis toma los aspectos más relevantes de las cuatro arquitecturas IoT más aceptadas y las integra en una, separando la capa IoT (comúnmente presente en estas arquitecturas), en tres capas. Además, está pensada para abarcar redes de proximidad (integrando diferentes tecnologías de interconexión IoT) y basar su funcionamiento en inteligencia artificial (AI). Por lo tanto, esta propuesta aumenta la posibilidad de lograr la interoperabilidad esperada y aumenta la funcionalidad de cada objeto en la red enfocada en prestar un servicio al usuario. Aunque el sistema que se propone incluye el procesamiento de una inteligencia artificial, sigue los mismos aspectos técnicos que sus antecesoras, ya que su operación y comunicación continúan basándose en la capa de aplicación y trasporte de la pila de protocolo TCP/IP. Sin embargo, con el fin de aprovechar los protocolos IoT sin modificar su funcionamiento, se crea un protocolo adicional que se encapsula y adapta a su carga útil. Se trata de un protocolo que se encarga de descubrir las características de un objeto (DFSP) divididas en funciones, servicios, capacidades y recursos, y las extrae para centralizarla en el administrador de la red (IoT-Gateway). Con esta información el IoT-Gateway puede tomar decisiones como crear grupos de trabajo autónomos que presten un servicio al usuario y enrutar a los objetos de este grupo que prestan el servicio, además de medir la calidad de la experiencia (QoE) del servicio; también administra el acceso a internet e integra a otras redes IoT, utilizando inteligencia artificial en la nube. Al basarse esta propuesta en un nuevo sistema jerárquico para interconectar objetos de diferente tipo controlados por AI con una gestión centralizada, se reduce la tolerancia a fallos y seguridad, y se mejora el procesamiento de los datos. Los datos son preprocesados en tres niveles dependiendo del tipo de servicio y enviados a través de una interfaz. Sin embargo, si se trata de datos sobre sus características estos no requieren mucho procesamiento, por lo que cada objeto los preprocesa de forma independiente, los estructura y los envía a la administración central. La red IoT basada en esta arquitectura tiene la capacidad de clasificar un objeto nuevo que llegue a la red en un grupo de trabajo sin la intervención del usuario. Además de tener la capacidad de prestar un servicio que requiera un alto procesamiento (por ejemplo, multimedia), y un seguimiento del usuario en otras redes IoT a través de la nube. / [CA] La interoperabilitat entre els objectes comunicats és l'objectiu principal de la internet de les coses (IoT). Alguns esforços per aconseguir-ho han generat diverses propostes d'arquitectures, però, encara no s'arriba a un concens. Aquestes arquitectures difereixen en el tipus d'estructura, grau de centralització, algoritme d'encaminament, mètriques d'enrutament, tècniques de descobriment, algoritmes de cerca, segmentació, qualitat de servei i seguretat entre d'altres. Algunes són millors que altres depenent de l'entorn en què es desenvolupen i de el tipus de paràmetre que es faci servir. Les més populars són les orientades a esdeveniments o accions basades en regles. Les quals li han permès entrar al mercat i aconseguir una ràpida massificació. No obstant això, la seva interoperabilitat es basa en aliances entre fabricants per aconseguir la seva compatibilitat. Aquesta solució s'aconsegueix en el núvol amb una plataforma que unifica les diferents marques aliades. Això permet la introducció d'aquestes tecnologies a la vida comuna dels usuaris però no resol problemes d'autonomia ni d'interoperabilitat. A més, no inclou a la nova generació de xarxes intel·ligents basades en coses intel·ligents. L'arquitectura proposada en aquesta tesi, pren els aspectes més rellevants de les quatre arquitectures IoT mes acceptades i les integra en una, separant la capa IoT (comunament present en aquestes arquitectures), en tres capes. A més aquesta pensada en abastar xarxes de proximitat (integrant diferents tecnologies d'interconnexió IoT) i basar el seu funcionament en intel·ligència artificial. Per tant, aquesta proposta augmenta la possibilitat d'aconseguir la interoperabilitat esperada i augmenta la funcionalitat de cada objecte a la xarxa enfocada a prestar un servei a l'usuari. Tot i que el sistema que es proposa inclou el processament d'una intel·ligència artificial, segueix els mateixos aspectes tècnics que les seves antecessores, ja que, la seva operació i comunicació se segueix basant en la capa d'aplicació i transport de la pila de protocol TCP / IP. No obstant això, per tal d'aprofitar els protocols IoT sense modificar el seu funcionament es crea un protocol addicional que s'encapsula i s'adapta a la seva càrrega útil. Es tracta d'un protocol que s'encarrega de descobrir les característiques d'un objecte (DFSP) dividides en funcions, serveis, capacitats i recursos, i les extreu per centralitzar-la en l'administrador de la xarxa (IoT-Gateway). Amb aquesta informació l'IoT-Gateway pot prendre decisions com crear grups de treball autònoms que prestin un servei a l'usuari i encaminar als objectes d'aquest grup que presten el servei. A més de mesurar la qualitat de l'experiència (QoE) de el servei. També administra l'accés a internet i integra a altres xarxes Iot, utilitzant intel·ligència artificial en el núvol. A l'basar-se aquesta proposta en un nou sistema jeràrquic per interconnectar objectes de diferent tipus controlats per AI amb una gestió centralitzada, es redueix la tolerància a fallades i seguretat, i es millora el processament de les dades. Les dades són processats en tres nivells depenent de el tipus de servei i enviats a través d'una interfície. No obstant això, si es tracta de dades sobre les seves característiques aquests no requereixen molt processament, de manera que cada objecte els processa de forma independent, els estructura i els envia a l'administració central. La xarxa IoT basada en aquesta arquitectura té la capacitat de classificar un objecte nou que arribi a la xarxa en un grup de treball sense la intervenció de l'usuari. A més de tenir la capacitat de prestar un servei que requereixi un alt processament (per exemple multimèdia), i un seguiment de l'usuari en altres xarxes IoT a través del núvol. / [EN] Interoperability between communicating objects is the main goal of the Internet of Things (IoT). Efforts to achieve this have generated several architectures' proposals; however, no consensus has yet been reached. These architectures differ in structure, degree of centralisation, routing algorithm, routing metrics, discovery techniques, search algorithms, segmentation, quality of service, and security. Some are better than others depending on the environment in which they perform, and the type of parameter used. The most popular are those oriented to events or actions based on rules, which has allowed them to enter the market and achieve rapid massification. However, their interoperability is based on alliances between manufacturers to achieve compatibility. This solution is achieved in the cloud with a dashboard that unifies the different allied brands, allowing the introduction of these technologies into users' everyday lives but does not solve problems of autonomy or interoperability. Moreover, it does not include the new generation of smart grids based on smart things. The architecture proposed in this thesis takes the most relevant aspects of the four most accepted IoT-Architectures and integrates them into one, separating the IoT layer (commonly present in these architectures) into three layers. It is also intended to cover proximity networks (integrating different IoT interconnection technologies) and base its operation on artificial intelligence (AI). Therefore, this proposal increases the possibility of achieving the expected interoperability and increases the functionality of each object in the network focused on providing a service to the user. Although the proposed system includes artificial intelligence processing, it follows the same technical aspects as its predecessors since its operation and communication is still based on the application and transport layer of the TCP/IP protocol stack. However, in order to take advantage of IoT-Protocols without modifying their operation, an additional protocol is created that encapsulates and adapts to its payload. This protocol discovers the features of an object (DFSP) divided into functions, services, capabilities, and resources, and extracts them to be centralised in the network manager (IoT-Gateway). With this information, the IoT-Gateway can make decisions such as creating autonomous workgroups that provide a service to the user and routing the objects in this group that provide the service. It also measures the quality of experience (QoE) of the service. Moreover, manages internet access and integrates with other IoT-Networks, using artificial intelligence in the cloud. This proposal is based on a new hierarchical system for interconnecting objects of different types controlled by AI with centralised management, reducing the fault tolerance and security, and improving data processing. Data is preprocessed on three levels depending on the type of service and sent through an interface. However, if it is data about its features, it does not require much processing, so each object preprocesses it independently, structures it and sends it to the central administration. The IoT-Network based on this architecture can classify a new object arriving on the network in a workgroup without user intervention. It also can provide a service that requires high processing (e.g., multimedia), and user tracking in other IoT-Networks through the cloud. / González Ramírez, PL. (2022). Interconnection Architecture of Proximity Smart IoE-Networks with Centralised Management [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/181892

Indiana University-Purdue University Indianapolis (IUPUI) / Magnetic resonance (MR) spectroscopy is a neuroimaging technique. It is widely used to quantify the concentration of important metabolites in a brain tissue. Imbalance in concentration of brain metabolites has been found to be associated with development of neurological impairment. There has been increasing trend of using MR spectroscopy as a diagnosis tool for neurological disorders. We established statistical methodology to analyze data obtained from the MR spectroscopy in the context of the HIV associated neurological disorder. First, we have developed novel methodology to study the association of marker of neurological disorder with MR spectrum from brain and how this association evolves with time. The entire problem fits into the framework of scalar-on-function regression model with individual spectrum being the functional predictor. We have extended one of the existing cross-sectional scalar-on-function regression techniques to longitudinal set-up. Advantage of proposed method includes: 1) ability to model flexible time-varying association between response and functional predictor and (2) ability to incorporate prior information. Second part of research attempts to study the influence of the clinical and demographic factors on the progression of brain metabolites over time. In order to understand the influence of these factors in fully non-parametric way, we proposed LongCART algorithm to construct regression tree with longitudinal data. Such a regression tree helps to identify smaller subpopulations (characterized by baseline factors) with differential longitudinal profile and hence helps us to identify influence of baseline factors. Advantage of LongCART algorithm includes: (1) it maintains of type-I error in determining best split, (2) substantially reduces computation time and (2) applicable even observations are taken at subject-specific time-points. Finally, we carried out an in-depth analysis of longitudinal changes in the brain metabolite concentrations in three brain regions, namely, white matter, gray matter and basal ganglia in chronically infected HIV patients enrolled in HIV Neuroimaging Consortium study. We studied the influence of important baseline factors (clinical and demographic) on these longitudinal profiles of brain metabolites using LongCART algorithm in order to identify subgroup of patients at higher risk of neurological impairment. / Partial research support was provided by the National Institutes of Health grants U01-MH083545, R01-CA126205 and U01-CA086368