With a prospect of creating a new generation of cellular networks using IP based communication, service providers, operators and developers have created the IP Multimedia Subsystem (IMS). Which with a more open architecture than older cellular networks will make it more like the internet in terms of service creation. This thesis creates an example service that uses subscriber data in the Home Subscriber Server (HSS) to deliver a service to the network’s users. The service is created to extend the functionality of the IMS test environment at Attentec AB to assist them in their efforts of learning and experimenting with the IMS core network. In this thesis the FoHSS used in the test environment is evaluated in order to measure its performance. This thesis gives examples of the implementation overhead of creating services in the IMS network and shows some of the functionality that is available to IMS services compared to service creation on the internet. Load tests of the FoHSS are made and shows that it uses polling to maintain subscription updates and that it has a negative impact on performance under heavy load. This thesis suggests that it is good for IMS test environments but not commercial use. / Med ambitionen att skapa nästa generations mobilnätverk med IP-baserad kommunikation, har tjänsteleverantörer, operatörer och utvecklare skapat IMS. IMS som med en mer öppen arkitektur än dess föregångare försöker närma sig internet när det gäller skapande av nya tjänster. Det ska vara enklare och ta mindre tid än i ett äldre mobilnät. Detta examensarbete skapar en exempeltjänst som använder användaruppgifter i IMS användardatabas för att leverera en tjänst till nätets användare. Tjänsten har skapats för att utöka funktionerna i den IMS testmiljö som Attentec AB har satt upp för att underlätta för sina anställda att lära sig mer om med IMS-kärnan genom att experimentera med den. I denna avhandling utvärderas även den HSS som finns i testmiljön. Examensarbetet ger exempel på det extraarbete som behöver göras för att skapa tjänster i ett IMS-nätverk och visar på en del av den funktionalitet som finns tillgänglig för tjänster i IMS jämfört med skapande av nya tjänster på Internet. De lasttester som utfördes på användardatabasen visar att den använder pollning för att upptäcka ändringar i användardata och skicka ut uppdateringar till prenumeranter samt att dessa har en negativ inverkan på prestandan under tung belastning. Denna avhandling visar att den passar bra i IMS testmiljöer men för inte kommersiellt bruk.

With the increasing shift to the Internet Protocol [3] for all networks and the desire of telecommunications service providers to offer new value to their customers, the need exists to coordinate the delivery of end-to-end quality of service so that providers may offer new services to support their customer’s applications. The key objective of the EuQoS project is to research, integrate, test, validate, and demonstrate end-to-end QoS technologies to support advanced QoS-aware applications over multiple, heterogeneous research, scientific, and industrial network domains. End-to-end quality of service support for multiple applications is a great added value and could become the next major growth spurt in the telecommunications industry. A crucial requirement for the QoS model is that it must not add significant complexity to the existing mechanisms and must be compatible with legacy applications and equipment. Proxy signaling handlers will be used to satisfy the latter constraint. This thesis analyzes possible roaming scenarios and how Authentication, Authorization, and Accounting should be tackled. I seek to provide reasonable solutions and to consider the current environment, always trying to re-use, when possible, the existing architecture and components. / De huvudsakliga målen med EuQoS projektet är att integrera, testa, utvärdera och demonstrera QoS från en ende av kommunikationen till en annan för att stödja avancerade QoS tillämpningar inom multipla nätverksdomäner industrioch forskningsverksamhet. Denna nya teknik är av stort värde och kan komma att bli nästa stora steg i utvecklingen av telekommunikation. Användandet av IPnätverk ökar och i samma takt ökar även efterfrågan av nya och bättre kommunikationstjänster. Därför finns det ett stort behov av QoS hos Internetleverantörerna som ständigt måste tillgodose kundernas önskemål. Det är viktigt att QoS modellen inte komplicerar den redan existerande tekniken. Därför måste den vara kompatibel med befintliga tekniker och utrustning. För att uppfylla dessa krav kommer Proxy signalbehandlare att användas. Den här rapporten behandlar möjliga roaming scenarier och hur AAA bör hanteras. Jag har som mål att presentera rimliga lösningar som tar hänsyn till miljön. För detta används i största möjliga mån redan existerande infrastruktur. / Con la continua evolución de las aplicaciones basadas en el protocolo IP en todas las redes, y el deseo de los proveedores de servicios de telecomunicaciones de ofrecer un valor añadido a sus clientes, cohabita la necesidad de coordinar la entrega de calidad de servicio (QoS) extremo a extremo. De esta forma los proveedores pueden aumentar la oferta de servicios mediante nuevas aplicaciones. El principal objetivo del proyecto EuQoS es investigar, desarrollar, integrar y probar una tecnología independiente de la red de acceso que garantice QoS extremo a extremo. El sistema esta pensado inicialmente para dar soporte a las aplicaciones: VoIP, VoD, video conferencia, y a una aplicación médica llamada MEDIGRAF, sobre múltiples y heterogéneas redes de acceso. Los parámetros que EuQoS tiene en cuenta para la reserva de la calidad de servicio son el ancho de banda, el retardo, la variación del retardo (jitter), y las pérdidas permitidas. Un requisito fundamental para el modelo de QoS es que debe añadir la mínima complejidad posible al existe funcionamiento del sistema y debe ser compatible con el legado de aplicaciones y equipo. Esto se solucionará mediante el uso de señalización a nivel de Proxy. Este proyecto analiza los posibles escenarios de roaming y cómo se debería afrontar la Autenticación, Autorización, y Accounting (AAA) en estas condiciones de itinerancia. En los capítulos iniciales hacen una descripción general del sistema EuQoS, para tener una visión global del proceso de reserva de recursos. Es necesario conocer la estructura completa para lograr una integración mayor y con el menor coste posible. El proyecto EuQoS propone y desarrolla un nuevo mecanismo de QoS que se construye sobre un estado del arte que incorpora los siguientes mecanismos: Monitorización y Medición, Control de Admisión, Gestión de Fallos, Señalización y Negociación de Servicio, Seguridad y AAA, Charging, Ingeniería de Tráfico y Optimización de Recursos. Con el fin de conocer lo que anteriormente otros habían hecho en este campo, antes de escribir una sola línea de este proyecto, llevé a cabo una extensa búsqueda de documentación. Parte de la información utilizada en este documento ha sido extraída de las entregas públicas del proyecto EuQoS hechas a la Comisión Europea. Además de la bibliografía mostrada en las referencias, Ericsson tiene sus propios informes técnicos e implementaciones de protocolos como el protocolo de iniciación de sesión (SIP) y DIAMETER, que se han consultado en varias ocasiones y han contribuido a lo largo de la investigación. Existe una enorme similitud entre la arquitectura del sistema y la de IMS. De esta manera, algunos de los conceptos aplicados a la hora de desarrollar una solución para el caso de roaming para EuQoS se basan en los flujos de señalización utilizados en IMS y en los anteproyectos de nuevos RFCs.

The total domination number γt(G) of a graph G is the minimum cardinality of a set S of vertices, so that every vertex of G is adjacent to a vertex in S. In this article, we determine an optimal upper bound on the total domination number of a graph with diameter 2. We show that for every graph G on n vertices with diameter 2, γt(G)≤1+nln(n). This bound is optimal in the sense that given any ε>0, there exist graphs G with diameter 2 of all sufficiently large even orders n such that γt(G)>(14+ε)nln(n).

A graph G is diameter 2-critical if its diameter is two, and the deletion of any edge increases the diameter. Murty and Simon conjectured that the number of edges in a diameter 2-critical graph of order n is at most n2/4 and that the extremal graphs are complete bipartite graphs with equal size partite sets. We use an association with total domination to prove the conjecture for the graphs whose complements have diameter three.

A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γt(G). The graph G is 3t-critical if γt(G)=3 and γt(G+e)=2 for every edge e in the complement of G. We show that no bipartite graph is 3t-critical. The tripartite 3 t-critical graphs are characterized. For every k<3, we prove that there are only a finite number of 3t-critical k-partite graphs. We show that the 5-cycle is the only 3t-critical K3-free graph and that there are only a finite number of 3t-critical K4-free graphs.

A graph G is diameter 2-critical if its diameter is 2, and the deletion of any edge increases the diameter. Murty and Simon conjectured that the number of edges in a diameter 2-critical graph of order n is at most n24 and that the extremal graphs are complete bipartite graphs with equal size partite sets. We use an important association with total domination to prove the conjecture for the graphs whose complements are claw-free.

A total dominating set of a graph G with no isolated vertex is a set 5 of vertices of G such that every vertex is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set in G. In this paper, we present several upper bounds on the total domination number in terms of the minimum degree, diameter, girth and order.

A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G - v is less than the total domination number of G. These graphs we call γt-critical. If such a graph G has total domination number k, we call it k-γt-critical. We characterize the connected graphs with minimum degree one that are γ t-critical and we obtain sharp bounds on their maximum diameter. We calculate the maximum diameter of a k-γt-critical graph for k≤8 and provide an example which shows that the maximum diameter is in general at least 5k/3 - O(1).

The primary objective of this study was to evaluate the relationship between milk-fat intake and obesity, particularly abdominal obesity, in 13,544 U.S. adults. A secondary objective was to determine the extent to which the association was influenced by multiple potential confounding variables. This cross-sectional study used data from the 2011–2016 National Health and Nutrition Examination Survey (NHANES). Level of milk-fat content regularly consumed was the exposure variable. Body mass index (BMI) and sagittal abdominal diameter (SAD), a measure of abdominal obesity, were the outcome variables. SAD correlates strongly with visceral fat, when measured by computed tomography, and has been shown to predict cardiometabolic disorders better than BMI. After controlling for age, gender, race, physical activity, sedentary behavior, alcohol habits, and cigarette use, significantly lower BMIs were associated with regular nonfat and full-fat milk consumption (F = 4.1, P = 0.0063). A significantly lower SAD was associated only with regular consumption of nonfat milk (F = 5.0, P = 0.0019). No significant differences were found between the other milk-fat groups or milk abstainers. In this nationally representative sample, only 19.6% of adults regularly consumed low-fat milk. In conclusion, regular nonfat milk intake was associated with lower levels of abdominal adiposity compared to consumption of higher levels of milk-fat.

Linear optimization is concerned with maximizing, or minimizing, a linear objective function over a feasible region defined as the intersection of a finite number of hyperplanes. Pivot-based simplex methods and central-path following interior point methods are the computationally most efficient algorithms to solve linear optimization instances. Discrete optimization further assumes that some of the variables are integer-valued. This dissertation focuses on the geometric properties of the feasible region under some structural assumptions. In the first part, we consider lattice (d,k)-polytopes; that is, the convex hull of a set of points drawn from {0,1,...,k}^d, and study the largest possible diameter, delta(d,k), that a lattice (d,k)- polytope can achieve. We present novel properties and an enumeration algorithm to determine previously unknown values of delta(d,k). In particular, we determine the values for delta(3,6) and delta(5,3), and enumerate all the lattice (3,3)-polytopes achieving delta(3,3). In the second part, we consider the convex hull of all the 2^(2^d - 1) subsums of the 2^d - 1 nonzero {0,1}-valued vectors of length d, and denote by a(d) the number of its vertices. The value of a(d) has been determined until d =8 as well as asymptotically tight lower and upper bounds for loga(d). This convex hull forms a so-called primitive zonotope that is dual to the resonance hyperplane arrangement and belongs to a family that is conjectured to include lattice polytopes achieving the largest possible diameter over all lattice (d,k)-polytopes. We propose an algorithm exploiting the combinatorial and geometric properties of the input and present preliminary computational results. / Thesis / Doctor of Philosophy (PhD)