The growing acceptance of B-ISDN (Broadband Integrated Services Digital Network) requires entirely new switching support a wide range of service demands including voice, video and data. At the same time, advances in the field of VLSI have enabled new principles to the design and architecture high-performance switching fabrics. Direct binary switch fabrics are a suitable candidate for future B- switches. Binary hypercubes have regular topology, are highly fault and have multiple paths for routing cells which help avoid performance penalties due to congestion and faults. In addition, these switches can adopt the novel, distributed, and adaptive routing scheme called 'deflection routing'. In normal routing, cells are routed along shortest paths to their destinations; in case of multiple cells contending for a single outgoing channel, the rest of the contending cells are either buffered or dropped to avoid congestion. In the case of deflection routing, cells can be routed along non-shortest paths. As a result, deflection routing helps avoid dropping cells. The scheme may be implemented with and without queuing buffers at the routers. In order to properly provision, control, and design these hypercube switches, it is essential that their performance capabilities be completely understood. Researchers have used both analytical model and simulations to evaluate performance of hypercube switches. The presence of distributed logic, multi-path routing, deflection routing, and queuing buffers make modeling tasks highly challenging. Building a reasonably accurate model of a hypercube switch with queuing buffers and deflection routing and using that model to gain practical insights into some of the important design parameters of the switch has been the major motivation of this thesis. An approximate Markov model of a single switching element is built to capture the behavior of a d-dimension switch. The numerical model is solved iteratively. Accuracy of the model is established by validating against simulation results. One disadvantage of having multiple paths, queuing buffers, and deflection motion of cells in hypercube switches is that the cells belonging to a particular traffic stream may not be delivered at their destinations in sequence. This phenomenon is known as 'out-of-orderness' of cells. An additional goal of this thesis has been development of a model to capture out-of-orderness phenomenon. The model is validated by comparing model results against simulation. Results show that the model is accurate and reveals significant insight into switch's behavior that can be used to design and engineer d-dimension hypercube switches.

Le cube de Fibonacci est un sous-graphe isométrique de l'hyper- cube ayant un nombre de Fibonacci de sommets. Le cube de Fibonacci a été initialement introduit par W-J. Hsu comme un réseau d'interconnexion et, comme l'hypercube, il a des propriétés topologiques très attractives, mais avec une croissance plus modérée. Parmi ces propriétés, nous discutons de l'hamiltonicité dans le cube de Fibonacci et aussi dans le cube de Lucas qui est obtenu à partir du cube de Fibonacci en supprimant toutes les chaînes qui commencent et nissent avec 1. Nous trouvons également le nombre de som- mets des cubes de Fibonacci et Lucas ayant une certaine excentricité. En n, nous présentons une étude de deux cubes du point de vue de la domination et du 2-packing.

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-09-28T13:05:06Z No. of bitstreams: 2 Dissertação - Tatiane Nunes da Costa - 2016.pdf: 5111300 bytes, checksum: 82d5b13d4c4d57e1f4850a62f149025c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-09-30T13:03:40Z (GMT) No. of bitstreams: 2 Dissertação - Tatiane Nunes da Costa - 2016.pdf: 5111300 bytes, checksum: 82d5b13d4c4d57e1f4850a62f149025c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-09-30T13:03:41Z (GMT). No. of bitstreams: 2 Dissertação - Tatiane Nunes da Costa - 2016.pdf: 5111300 bytes, checksum: 82d5b13d4c4d57e1f4850a62f149025c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-08-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Most of the time, modern problems of engineering are nonlinear and, may also be subject to certain types of uncertainty that can directly influence in the answers of a particular system. In this sense, the stochastic methods have been thoroughly studied in order to get the best settings for a given project. Out of the stochastic techniques, the Method of Monte Carlo stands out and, especially the Latin Hypercube Sampling (LHS) which is a simpler version of the same. For this type of modeling, the Stochastic Finite Elements Method (SFEM) is becoming more frequently used, given that, an important tool for the discretization of stochastic fields can be given by the Karhunèn-Loève (KL) expansion. In this work, the following three case studies will be used: A discrete system of 2 g.d.l., a continuous system of a coupled beam type both in linear and nonlinear springs and a rotor consisting of axis, bearings and disks. In this sense, the influence of uncertainties in the systems studied will be checked, using for this, the LHS, SFEM and the KL expansion. The stochastic study in question will be used in the construction of the great project for the rotor problem already presented. / Problemas modernos de engenharia, na maioria das vezes são não lineares e, podem também estar sujeitos a certos tipos de incertezas que podem influenciar diretamente nas respostas de um dado sistema. Nesse sentido, os métodos estocásticos têm sido exaustivamente estudados com o intuito de se obter as melhores configurações para um dado projeto. Dentre as técnicas estocásticas, destacam-se o Método de Monte Carlo e, principalmente o Método Hipercubo Latino (HCL) que é uma versão mais simples do mesmo. Para este tipo de modelagem, é cada vez mais utilizado o Método dos Elementos Finitos Estocásticos (MEFE), sendo que uma importante ferramenta para a discretização dos campos estocásticos pode ser dada pela expansão de Karhunèn-Loève (KL). Neste trabalho serão utilizados três estudos de casos, quais sejam: Um sistema discreto de 2 g.d.l., um sistema contínuo do tipo viga acoplada tanto em molas lineares quanto não lineares e um rotor composto por eixo, mancais e discos. Nesse sentido, será verificada a influência de incertezas nos sistemas estudados, utilizando para isto, o método HCL, MEFE e a expansão de KL. O estudo estocástico em questão será empregado na construção do projeto ótimo robusto para o problema do rotor já apresentado.

Cette thèse a pour objectif l"établissement de méthodes numériques pour l'optimisation multi-objectif de structures soumises à des facteurs incertains. Au cœur de ce travail, nous nous sommes focalisés sur l'adaptation du chaos polynomial pour l'évaluation non intrusive de la part de l'incertain. Pour atteindre l'objectif fixé, nous sommes confrontés à deux verrous : l'un concerne les coûts élevés de calcul d'une simulation unitaire par éléments finis, l'autre sa précision limitée. Afin de limiter la charge de calcul pour la construction du chaos polynomial, nous nous sommes concentrés sur la construction d'un chaos polynomial creux. Nous avons également développé un programme d’échantillonnage basé sur l’hypercube latin personnalisé prenant en compte la précision limitée de la simulation. Du point de vue de la modélisation nous avons proposé une approche multi-fidèle impliquant une hiérarchie de modèles allant des simulations par éléments finis complètes jusqu'aux surfaces de réponses en passant par la réduction de modèles basés sur la physique. Enfin, nous avons étudié l'optimisation multi-objectif de structures sous incertitudes. Nous avons étendu le modèle PCE des fonctions objectif à la prise en compte des variables déterministes de conception. Nous avons illustré notre travail sur des exemples d'emboutissage et sur la conception optimale des structures en treillis. / This thesis aims at Multi-Objective Optimization under Uncertainty in structural design. We investigate Polynomial Chaos Expansion (PCE) surrogates which require extensive training sets. We then face two issues: high computational costs of an individual Finite Element simulation and its limited precision. From numerical point of view and in order to limit the computational expense of the PCE construction we particularly focus on sparse PCE schemes. We also develop a custom Latin Hypercube Sampling scheme taking into account the finite precision of the simulation. From the modeling point of view,we propose a multifidelity approach involving a hierarchy of models ranging from full scale simulations through reduced order physics up to response surfaces. Finally, we investigate multiobjective optimization of structures under uncertainty. We extend the PCE model of design objectives by taking into account the design variables. We illustrate our work with examples in sheet metal forming and optimal design of truss structures.

Approved for public release; distribution is unlimited / The US Department of Defense is currently pursuing the most comprehensive transformation of its forces since the early years of WWII. This transformation is a holistic approach to update both the equipment that the forces will fight its conflicts with and the way in which they will fight. This transformation relies heavily on fully networked air, ground and space based platforms. While many experts agree that in the course of the next 10 years communications equipment will emerge to support the networking of these systems, there remains much uncertainty on how operations will be effected if the technology does not mature enough to meet expectations. This research shows that even a 25 percent degradation in communications range could pose significant challenges for this Future Force. Additionally, even small delays (latencies greater than one minute) and constraints on network throughput can increase the Future Force casualties and the duration of battle. While the end result in all analysis shows that the Future Force is a superior element with the same battle end state-victory, the cost of that victory depends significantly on effective communications. / Captain, United States Army

Approved for public release, distribution is unlimited / Recent insurgent tactics during Operation Iraqi Freedom (OIF) have demonstrated that coalition logistical convoys are vulnerable targets. This thesis examines the tactics, techniques and procedures (TTPs) used in convoy operations in an attempt to identify the critical factors that lead to mission success. A ground convoy operation scenario is created in the agentbased model (ABM) Map Aware Non-uniform Automata (MANA). The scenario models a generic logistical convoy consisting of security vehicles, logistical vehicles, an unmanned aerial vehicle (UAV) and an enemy ambushing force. The convoy travels along a main supply route (MSR) where it is ambushed by a small insurgent force. We use military experience, judgment and exploratory simulation runs to identify 11 critical factors within the created scenario. The data farming process and Latin Hypercube (LHC) experimental design technique are used to thoroughly examine the 11 factors. Using the 11 factors 516 design points are created and data farmed over to produce 25,800 observations. Additive multiple linear regression is used to fit a model to the 25,800 observations. From the created scenario it is concluded that: convoy mission success may be determined by only a few factors; the actions of logistical vehicles are more critical than those of security vehicles; UAVs provide a statistically significant advantage; and ABMs coupled with LHCs and data farming are valuable tools for understanding complex problems. / Captain, United States Marine Corps

Approved for public release, distribution is unlimited / This thesis examines a 2015 Marine Expeditionary Brigade scheme of maneuver as the baseline scenario for a commercial logistics support software program called SEAWAY. Modifications to this scenario are conducted using a designed experiment in order to explore how the plan characteristics relate to eleven specified input factors. Multiple regression analysis is used to fit models to the resulting data for three different measures of performance: Total Aircraft Sorties, Total Aircraft Sortie Time and Total Aircraft Tons. The results suggest the plan performance is predicted well by a small subset of the factors and their interactions. One implication of this work is a better understanding of which factors are key determinants of the plan characteristics for variations on this specific base scenario. By using these fitted models, the number of SEAWAY runs needed to identify acceptable plans should decrease dramatically. The approach in this thesis provides a blueprint for similar analyses of other scenarios by demonstrating how information gained from models fit during an exploration phase might allow the logistician to quickly determine factor settings that yield an acceptable plan once details of an operation become available. Finally, working with the SEAWAY developers provided them with some new insights. / Lieutenant Commandeer, United States Navy

Approved for public release; distribution is unlimited / To ensure sufficient capacity to handle unexpected demands for electric power, decision makers often over-estimate expeditionary power requirements. Therefore, we often use limited resources inefficiently by purchasing more generators and investing in more renewable energy sources than needed to run power systems on the battlefield. Improvement of the efficiency of expeditionary power units requires better managing of load requirements on the power grids and, where possible, shifting those loads to a more economical time of day. We analyze the performance of a previously developed optimization model for scheduling time-shiftable electrical loads in an expeditionary power grids model in two experiments. One experiment uses model data similar to the original baseline data, in which expected demand and expected renewable production remain constant throughout the day. The second experiment introduces unscheduled demand and realistic fluctuations in the power production and the demand distributions data that more closely reflect actual data. Our major findings show energy grid power production composition affects which uncertain factor(s) influence fuel con-sumption, and uncertainty in the energy grid system does not always increase fuel consumption by a large amount. We also discover that the generators running the most do not always have the best load factor on the grid, even when optimally scheduled. / Lieutenant Commander, United States Navy

本論文對線性三對角方程組之解法提出平行演算法於超立方體網路 ( hypercube network), 並且此平行演算法能達到最佳費用 (optimal cost ) O(N). 討論的解法包含 (1)循環消減法 (cyclic reduction method)及 (2)高斯消去法 (Gaussian elimination method), 基於 (1)法之平行演算法當使用處理器個數為 O(N/logN)時, 其執行時間為 O( logN); 基於 (2) 法之平行演算法當使用處理器個數為 O(N/(logN)^2) 時, 其執行時間為 O((logN)^2); 費用 (cost) 等於處理器個數乘以執行 時間.

L'hypercube a suscité de nombreuses études engendrant une littérature très dense aussi bien en mathématiques discrètes qu'en informatique. Cet intérêt sans cesse croissant est largement motivé par l'utilisation de sa structure dans de nombreux domaines (architectures parallèles, transfert de l'information, décision multicritère,...). Chacun peut s'étonner des raisons qui font que le cube soit le cube?. Sa simple définition peut déjà apporter une réponse quoique partielle à une telle question. Plusieurs propriétés spécifiques à l'hypercube ont, soit, défini de nouvelles classes de graphes, soit, fait ressortir le rôle remarquable joué par celui-ci dans plusieurs classes déjà existantes. Les (0, 2)-graphes sont une généralisation naturelle de l'hypercube. Il est maximal dans cette classe. Le thème de cette thèse consiste en la définition et la caractérisation de quelques classes de (0, 2)-graphes obtenues à partir de l'hypercube par rajout d'arêtes ou identification de sommets. Nous caractérisons au chapitre II, le graphe de l'hyperoctaèdre comme un {2(n-2), 2(n-1)}-graphe d'ordre 2n, et nous prouvons l'unicité de son cycle hamiltonien et cela à une équivalence naturelle près. Nous donnons, au chapitre III, une caractérisation de l'hypercube en tant que graphe distance-régulier de vecteur d'intersection {d, d-1, ..., 1; 1, 2, ..., d}. Une classe de (0, 2)-graphes minimaux -les graphes de Shrikhande généralisés- y est étudiée et une caractérisation des graphes de Laborde-Mulder comme (0, 2)-graphes de diamètre minimum [d/2] parmi ceux d'ordre 2d-1 et de degré d impair est donnée. Au chapitre IV, nous caractérisons parmi les hypercubes généralisés ceux qui sont des (0, 2)-graphes. Nous présentons une construction de (0, 2)-graphes non sommet-transitifs. On montre enfin que les graphes de Laborde-Mulder et du demi-cube sont plongeables dans le carré de l'hypercube. Dans un dernier chapitre, nous nous intéressons au problème d'existence de (0, 2)-graphe d'un ordre donné. Nous donnons une condition nécessaire d'existence de tels graphes pour un ordre impair. Nous montrons ensuite qu'à l'ordre 18 et 20, il n'existe pas de (0, 2)-graphes, en utilisant à cette fin un algorithme de construction de (0, 2)-graphes. Nous présentons enfin quelques résultats sur la structure locale des (0, 2)-graphes