This thesis evaluates the viability of a data cube as a basis for visualization of unbounded data. A cube designed for use with visualization of static data was adapted to allow for point-by-point insertions. The new cube was evaluated by measuring the time it took to insert different numbers of data points. The results indicate that the cube can keep up with data streams with a velocity of up to approximately 100 000 data points per second. The conclusion is that the cube is useful if the velocity of the data stream is within this bound, and if the granularity of the represented dimensions is sufficiently low. / Det här exjobbet utvärderar dugligheten av en datakub som bas för visualisering av obegränsad data. En kub designad för användning till visualisering av statisk data anpassades till att medge insättning punkt för punkt. Den nya kuben evaluerades genom att mäta tiden det tog att sätta in olika antal datapunkter. Resultaten indikerade att kuben kan hantera dataströmmar med en hastighet på upp till 100 000 punkter per sekund. Slutsatsen är att kuben är användbar om hastigheten av dataströmmen är inom denna gräns, och om grovheten av de representerade dimensionerna är tillräckligt hög.

Cubical complexes are defined in a manner analogous to that for simplicial complexes, the chief difference being that cubical complexes are unions of cubes rather than of simplices. A very natural cubical complex to consider is the complex C(k_1,...,k_n) where k_1,...,k_n are nonnegative integers. This complex has as its underlying space [0,k_1]x...x[0,k_n] subset of R^n with vertices at all points having integer coordinates and higher dimensional cubes formed by the vertices in the natural way. The genus of a cubical complex is defined to be the maximum genus of all surfaces that are subcomplexes of the cubical complex. A formula is given for determining the genus of the cubical complex C(k_1,...,k_n) when at least three of the k_i are odd integers. For the remaining cases a general solution is not known. When k_1=...=k_n=1 the genus of C(k_1,...,k_n) is shown to be (n-4)2^{n-3}+1 which is equivalent to the genus of the graph of the n-cube. Indeed, the genus of the complex and the genus of the graph of the 1-skeleton of the complex, are shown to be equal when at least three of the k_i are odd, but not equal in general.

The poetics of an architecture of a moment is explored through design of a contemplative room (wherin the geometric transformation of a cubic base to a cone) demonstrates the rhythmn and proportion of the construction of the room and the relative motion of the sun in the space. The relationship of the sun rays on the walls of the room passing through a reflecting pool are shown using demonstrative and constructive means of descriptive geometry as both the design generator and poetic expression.The composition of the buildings reveals the play of light on form. / Master of Architecture / An exploration to understand the relationship of architecture and the material sensible world. The work seeks to reveal that through the tangible architectural strategies of form, structure, material and light, the intangible qualities of architecture are defined.

Archeological research embracing complex Information Technology techniques can result in vast quantities of heterogeneous information from different sites in different formats. ETANA-DL is an Archeological Digital Library (DL), providing services suited for the archeological domain. With a growing collection of records in the DL, it is a challenge to present them in an organized and meaningful way. We have designed a new visual browsing interface called ETANA-CMV that aims to provide users a richer and more insightful browsing experience. ETANA-CMV allows users to navigate through the records in ETANA-DL that are multidimensional, hierarchical, and categorical in nature. ETANA-CMV was designed to be scalable, flexible, and easy to learn. This interface employs a data cube based browsing index to counter performance issues that usually limit the interactivity of visual browsing interfaces to DLs. The interface has been integrated with the existing Browse Interface and the search service in ETANA-DL. Formative evaluation of the new visual interface led to several improvements in the interface. It appears that users were able to detect trends in the DL collections more accurately using visualization based strategies than with the existing textual browse interface. / Master of Science

This thesis inquires into the nature of economy and its connection with the architecture of the house. Economy is a slippery term. In its original sense, the word had more to do with philosophy than finance. It raised issues of necessity, hierarchy, government, and happiness. Aristotle distinguished chrematistics, the art of getting wealth, from economy, the art of household management.Vitruvius, the first architectural theorist, offered a differing interpretation of the word, and included it as one of his six principles of architecture. Henry David Thoreau revisited Aristotleâ s ideas and invented a new, solitary economy. Both he and Aristotle emphasized that the purpose of economy is to meet material needs with sufficiency rather than surfeit. Economie House explores these ideas architecturally. On an imaginary site a perfect red cube sits on a concrete platform. Steel frames support a translucent, gabled roof. The cube opens in various ways to reveal the machines that serve manâ s biological needs. Closed, the cube suggests the limits of material goods as contributions to the good life. / Master of Architecture

Initial formal studies of three dimensional cubic objects and their affects on space and light lead to the design of complex living arrangements that take the form of apartments. Rooms within the building volumes develop interdependent relationships that blur the distinction between inside and outside space and emphasis the private and public aspects of a clustered arrangement of buildings. / Master of Architecture

This thesis began with the goal of designing a bold house cantilevered over the edge of a cliff 120 feet above the water, and evolved into the study of how to design when starting with the primary form of a cube. The cube was chosen as representing the crystalline form of the rock upon which the house sits. The outside shell of the house is horizontal, board formed concrete, also in reference to the layered rock of the cliff face. There are two primary forces cutting away the mass of the cube to produce the final form of the house. The first force is of the site, and is generated by two spectacular views. These two views are used to cut through the house, forming an â Xâ shaped atrium eight feet wide and four storeys high, in the center of the house. The second force is generated by the desire to bring daylight into two opposite corners of the house. The southern corner of the house faces the lake. The bottom of that corner is cut out more than the top to admit direct sun in the winter, indirect sun in the summer, and reflected sun off the lake year round. The northern corner of the house faces the woods. The top of that corner is cut out more than the bottom to allow northern light into the top floors and maintain privacy on the lower floor, where the driveway approaches the house. / Master of Architecture

Cette thèse est consacrée à l'étude des différents problèmes liés aux structures des cubes , en théorie ergodique et en dynamique topologique. Elle est composée de six chapitres. La présentation générale nous permet de présenter certains résultats généraux en théorie ergodique et dynamique topologique. Ces résultats, qui sont associés d'une certaine façon aux structures des cubes, sont la motivation principale de cette thèse. Nous commençons par les structures de cube introduites en théorie ergodique par Host et Kra (2005) pour prouver la convergence dans $L^2 $ de moyennes ergodiques multiples. Ensuite, nous présentons la notion correspondante en dynamique topologique. Cette théorie, développée par Host, Kra et Maass (2010), offre des outils pour comprendre la structure topologique des systèmes dynamiques topologiques. En dernier lieu, nous présentons les principales implications et extensions dérivées de l'étude de ces structures. Ceci nous permet de motiver les nouveaux objets introduits dans la présente thèse, afin d'expliquer l'objet de notre contribution. Dans le Chapitre 1, nous nous attachons au contexte général en théorie ergodique et dynamique topologique, en mettant l'accent sur l'étude de certains facteurs spéciaux. Les Chapitres 2, 3, 4 et 5 nous permettent de développer les contributions de cette thèse. Chaque chapitre est consacré à un thème particulier et aux questions qui s'y rapportent, en théorie ergodique ou en dynamique topologique, et est associé à un article scientifique. Les structures de cube mentionnées plus haut sont toutes définies pour un espace muni d'une unique transformation. Dans le Chapitre 2, nous introduisons une nouvelle structure de cube liée à l'action de deux transformations S et T qui commutent sur un espace métrique compact X. Nous étudions les propriétés topologiques et dynamiques de cette structure et nous l'utilisons pour caractériser les systèmes qui sont des produits ou des facteurs de produits. Nous présentons également plusieurs applications, comme la construction des facteurs spéciaux. Le Chapitre 3 utilise la nouvelle structure de cube définie dans le Chapitre 2 dans une question de théorie ergodique mesurée. Nous montrons la convergence ponctuelle d'une moyenne cubique dans un système muni deux transformations qui commutent. Dans le Chapitre 4, nous étudions le semigroupe enveloppant d'une classe très importante des systèmes dynamiques, les nilsystèmes. Nous utilisons les structures des cubes pour montrer des liens entre propriétés algébriques du semigroupe enveloppant et les propriétés topologiques et dynamiques du système. En particulier, nous caractérisons les nilsystèmes d'ordre 2 par une propriété portant sur leur semigroupe enveloppant. Dans le Chapitre 5, nous étudions les groupes d'automorphismes des espaces symboliques unidimensionnels et bidimensionnels. Nous considérons en premier lieu des systèmes symboliques de faible complexité et utilisons des facteurs spéciaux, dont certains liés aux structures de cube, pour étudier le groupe de leurs automorphismes. Notre résultat principal indique que, pour un système minimal de complexité sous-linéaire, le groupe d'automorphismes est engendré par l'action du shift et un ensemble fini. Par ailleurs, en utilisant les facteurs associés aux structures de cube introduites dans le Chapitre 2, nous étudions le groupe d'automorphismes d'un système de pavages représentatif. La bibliographie, commune à l'ensemble de la thèse, se trouve en fin document / This thesis is devoted to the study of different problems in ergodic theory and topological dynamics related to og cube structures fg. It consists of six chapters. In the General Presentation we review some general results in ergodic theory and topological dynamics associated in some way to cubes structures which motivates this thesis. We start by the cube structures introduced in ergodic theory by Host and Kra (2005) to prove the convergence in $L^2$ of multiple ergodic averages. Then we present its extension to topological dynamics developed by Host, Kra and Maass (2010), which gives tools to understand the topological structure of topological dynamical systems. Finally we present the main implications and extensions derived of studying these structures, we motivate the new objects introduced in the thesis and sketch out our contributions. In Chapter 1 we give a general background in ergodic theory and topological dynamics given emphasis to the treatment of special factors. % We give basic definitions and describe special factors associated to a From Chapter 2 to Chapter 5 we develop the contributions of this thesis. Each one is devoted to a different topic and related questions, both in ergodic theory and topological dynamics. Each one is associated to a scientific article. In Chapter 2 we introduce a novel cube structure to study the actions of two commuting transformations $S$ and $T$ on a compact metric space $X$. In the same chapter we study the topological and dynamical properties of such structure and we use it to characterize products systems and their factors. We also provide some applications, like the construction of special factors. In the same topic, in Chapter 3 we use the new cube structure to prove the pointwise convergence of a cubic average in a system with two commuting transformations. In Chapter 4, we study the enveloping semigroup of a very important class of dynamical systems, the nilsystems. We use cube structures to show connexions between algebraic properties of the enveloping semigroup and the geometry and dynamics of the system. In particular, we characterize nilsystems of order 2 by its enveloping semigroup. In Chapter 5 we study automorphism groups of one-dimensional and two-dimensional symbolic spaces. First, we consider low complexity symbolic systems and use special factors, some related to the introduced cube structures, to study the group of automorphisms. Our main result states that for minimal systems with sublinear complexity such groups are spanned by the shift action and a finite set. Also, using factors associated to the cube structures introduced in Chapter 2 we study the automorphism group of a representative tiling system. The bibliography is defer to the end of this document

Duomenų kubo konstravimas yra laikui ir kompiuteriniams resursams imlus procesas. Nepaisant to, šis darbas turi būti atliktas norint pasinaudoti greitų užklausų iš ypatingai didelių OLAP kubų teikiamais privalumais . Telekomunikacijų bendrovės surenka didelius duomenų kiekius apie įvykius telekomunikaciniuose tinkluose. Kiekviena duomenų porcija aprašo daug informacijos (pavyzdžiui: paslaugos tipą, iniciatorių, gavėją, pradžios laiką, trukmę, perduotų duomenų kiekį, skambučio kryptį, kainą, tinklo sąsajos adresą ir t.t.). Mobiliojo ryšio rinkoje yra įprasta apdovanoti kiekvieną abonentą tam tikru prizu (pinigais, nuolaidomis ar nauju mobiliuoju telefonu) mainais į 24 mėnesių sutartį naudotis konkretaus operatoriaus paslaugomis. Taigi kas 24 mėnesius abonentas turi galimybę pakeisti paslaugos teikėją. Tam, kad ryšio operatorius išlaikytų savo klientus, už sutarties pratęsimą taip pat turi pasiūlyti dovaną. Kad būtų galima tai atlikti nepatiriant finansinių nuostolių – mobiliojo ryšio operatorius privalo žinoti kiekvieno abonento naudojimosi paslaugomis statistiką. Šiame dokumente aprašoma pora būtų kaip pakeisti duomenų pirminį vaizdą (struktūrą ir sudėtį) siekiant pagreitinti duomenų kubų konstravimo procesą. Vienas šių metodų – duomenų agregavimas iki didžiausio, vis dar tinkamo analizei, lygio. Kitas metodas – tai lėtai kintančių kubo dimensijų sintezavimas taip sumažinant kubo dydį ir pagreitinant jo kūrimą. / Data cube pre computing is time and computer resources consuming task. In spite of this it needs to be done in order to construct an OLAP cube to take advantage of fast querying in data sets enormous in its sizes. Telecommunication industries collect huge amount of data about events in its networks. Every data portion holds a lot of information (i.e. service type, originator, receiver, time for start, duration, data volume, calling direction, cost, network interface address, etc.). In mobile telecommunication industries it is common to award each customer / subscriber by some prize (money, cell phone, discount to services and so on) in return of 24 month obligation to use one’s services. So, every 24 months subscriber gains ability to choose another telecommunication network. In order to maintain stable amount of subscribers’ service provider must offer something in return. In order to do that correctly, without financial loses, one must know exact usage statistics of each subscriber. This paper covers couple tips to arrange data in data warehouses (data marts) in order to achieve greater data cube pre processing speed. One of these methods covers partial data aggregation to highest degree, still sufficient to answer specific queries. Another method shows the ability to synthesize data cube dimensions in order to lower data volumes, that data cube pre calculation could take less time.

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.