We design and analyze algorithms for the following two robot navigation problems: 1. TARGET SEARCH. Given a robot located at a point s in the plane, how will a robot navigate to a goal t in the presence of unknown obstacles ? 2. LOCALIZATION. A robot is "lost" in an environment with a map of its surroundings. How will it find its true location by traveling the minimum distance ? Since efficient algorithms for these two problems will make a robot completely autonomous, they have held the interest of both robotics and computer science communities. Previous work has focussed mainly on designing competitive algorithms where the robot's performance is compared to that of an omniscient adversary. For example, a competitive algorithm for target search will compare the distance traveled by the robot with the shortest path from s to t. We analyze these problems from the worst-case perspective, which, in our view, is a more appropriate measure. Our results are : 1. For target search, we analyze an algorithm called Dynamic A*. The robot continuously moves to the goal on the shortest path which it recomputes on the discovery of obstacles. A variant of this algorithm has been employed in Mars Rover prototypes. We show that D* takes O(n log n) time on planar graphs and also show a comparable bound on arbitrary graphs. Thus, our results show that D* combines the optimistic possibility of reaching the goal very soon while competing with depth-first search within a logarithmic factor. 2. For the localization problem, worst-case analysis compares the performance of the robot with the optimal decision tree over the set of possible locations. No approximation algorithm has been known. We give a polylogarithmic approximation algorithm and also show a near-tight lower bound for the grid graphs commonly used in practice. The key idea is to plan travel on a "majority-rule map" which eliminates uncertainty and permits a link to the half-Group Steiner problem. We also extend the problem to polygonal maps by discretizing the domain using novel geometric techniques.

The popularity of the great variety of Internet usage brings about a significant growth of the data traffic in telecommunication network. Data transmission efficiency will be challenged under the premise of current network capacity and data flow control mechanisms. In addition to increasing financial investment to expand the network capacity, improving the existing techniques are more rational and economical. Various cutting-edge researches to cope with future network requirement have emerged, and one of them is called network coding. As a natural extension in coding theory, it allows mixing different network flows on the intermediate nodes, which changes the way of avoiding collisions of data flows. It has been applied to achieve better throughput and reliability, security, and robustness in various network environments and applications. This dissertation focuses on the use of network coding for multicast in fixed mesh networks and distributed storage systems. We first model various multicast routing strategies within an optimization framework, including tree-based multicast and network coding; we solve the models with efficient algorithms, and compare the coding advantage, in terms of throughput gain in medium size randomly generated graphs. Based on the numerical analysis obtained from previous experiments, we propose a revised multicast routing framework, called strategic network coding, which combines standard multicast forwarding and network coding features in order to obtain the most benefit from network coding at lowest cost where such costs depend both on the number of nodes performing coding and the volume of traffic that is coded. Finally, we investigate a revised transportation problem which is capable of calculating a static routing scheme between servers and clients in distributed storage systems where we apply coding to support the storage of contents. We extend the application to a general optimization problem, named transportation problem with degree constraints, which can be widely used in different industrial fields, including telecommunication, but has not been studied very often. For this problem, we derive some preliminary theoretical results and propose a reasonable Lagrangian decomposition approach

La modélisation 3d automatique d'un environnement à partir d'images est un sujet toujours d'actualité en vision par ordinateur. Ce problème se résout en général en trois temps : déplacer une caméra dans la scène pour prendre la séquence d'images, reconstruire la géométrie, et utiliser une méthode de stéréo dense pour obtenir une surface de la scène. La seconde étape met en correspondances des points d'intérêts dans les images puis estime simultanément les poses de la caméra et un nuage épars de points 3d de la scène correspondant aux points d'intérêts. La troisième étape utilise l'information sur l'ensemble des pixels pour reconstruire une surface de la scène, par exemple en estimant un nuage de points dense.Ici nous proposons de traiter le problème en calculant directement une surface à partir du nuage épars de points et de son information de visibilité fournis par l'estimation de la géométrie. Les avantages sont des faibles complexités en temps et en espace, ce qui est utile par exemple pour obtenir des modèles compacts de grands environnements comme une ville. Pour cela, nous présentons une méthode de reconstruction de surface du type sculpture dans une triangulation de Delaunay 3d des points reconstruits. L'information de visibilité est utilisée pour classer les tétraèdres en espace vide ou matière. Puis une surface est extraite de sorte à séparer au mieux ces tétraèdres à l'aide d'une méthode gloutonne et d'une minorité de points de Steiner. On impose sur la surface la contrainte de 2-variété pour permettre des traitements ultérieurs classiques tels que lissage, raffinement par optimisation de photo-consistance ... Cette méthode a ensuite été étendue au cas incrémental : à chaque nouvelle image clef sélectionnée dans une vidéo, de nouveaux points 3d et une nouvelle pose sont estimés, puis la surface est mise à jour. La complexité en temps est étudiée dans les deux cas (incrémental ou non). Dans les expériences, nous utilisons une caméra catadioptrique bas coût et obtenons des modèles 3d texturés pour des environnements complets incluant bâtiments, sol, végétation ... Un inconvénient de nos méthodes est que la reconstruction des éléments fins de la scène n'est pas correcte, par exemple les branches des arbres et les pylônes électriques.

Consider distinct latin squares, L and M, of order n. Then the pair (T1, T2) where T1 = L \M and T2 = M \ L is called a latin bitrade. Furthermore T1 and T2 are referred to as latin trades, in which T2 is said to be a disjoint mate of T1 (and vice versa). Drápal (1991) showed that, under certain conditions, a partition of an equilateral triangle of side length n, where n is some integer, into smaller, integer length sided equilateral triangles gives rise to a latin trade within the latin square based on the addition table for the integers modulo n. A partial latin square P of order n is said to be completable if there exists a latin square L of order n such that P ⊆ L. If there is only one such possible latin square, L, of order n then P is said to be uniquely completable and P is called a defining set of L. Furthermore, if C is a uniquely completable partial latin square such that no proper subset of C is uniquely completable, C is said to be a critical set or a minimal defining set. These concepts, namely latin trades and defining sets in latin squares, are intimately connected by the following observation. If L is a latin square and D ⊆ L is a defining set, then D intersects all latin bitrades for which one mate is contained in L. In Part I of this thesis Dr´apal’s result is applied to investigate the structure of certain defining sets in latin squares. The results that are obtained are interesting in themselves; furthermore, the geometric approach to the problem yields additional appealing results. These geometric results are discussed in Chapters 3, 4, 5 and 6. They pertain to partitioning regions (polygons in R2 that satisfy certain obvious conditions) into equilateral, integer length sided, triangles, such that no point, in the region, is a corner of more than three distinct triangles. In Chapter 2 one of the main two theorems on defining sets is established, as is a method for using the above geometric results to prove the nonexistence of certain types of defining sets. In Part II of this thesis, intersection problems, for latin squares and Steiner triple systems, are considered. The seminal works, for problems of these types, are due to Lindner and Rosa (1975) and Fu (1980). A natural progression, from the established literature, for intersection problems between elements in a pair of latin squares or Steiner triple systems is to problems in which the intersection is composed of a number of disjoint configurations (isomorphic copies of some specified partial triple system). In this thesis solutions to two intersection problems for disjoint configurations are detailed. An m-flower, (F,F), is a partial triple system/configuration, such that: F = {{x, yi, zi} | {yi, zi} ∩ {yj , zj} = ∅, for 0 ≤ i, j ≤ m − 1, i 6= j}; and F = UX∈FX. The first such problem considered in this thesis asks for necessary and sufficient conditions for integers k and m ≥ 2 such that a pair of latin squares of order n exists that intersect precisely in k disjoint m-flowers. The necessary terminology, constructions, lemmas and proof for this result are contained in Chapters 7, 8 and 9. The second such problem considered in this thesis asks for necessary and sufficient conditions for integers k such that a pair of Steiner triple systems of order u exists that intersect precisely in k disjoint 2-flowers. This result relies on the solution to the latin square problem and an additional result from Chapter 9. The further constructions and lemmas used to prove this result are detailed in Chapter 10.

Consider distinct latin squares, L and M, of order n. Then the pair (T1, T2) where T1 = L \M and T2 = M \ L is called a latin bitrade. Furthermore T1 and T2 are referred to as latin trades, in which T2 is said to be a disjoint mate of T1 (and vice versa). Drápal (1991) showed that, under certain conditions, a partition of an equilateral triangle of side length n, where n is some integer, into smaller, integer length sided equilateral triangles gives rise to a latin trade within the latin square based on the addition table for the integers modulo n. A partial latin square P of order n is said to be completable if there exists a latin square L of order n such that P ⊆ L. If there is only one such possible latin square, L, of order n then P is said to be uniquely completable and P is called a defining set of L. Furthermore, if C is a uniquely completable partial latin square such that no proper subset of C is uniquely completable, C is said to be a critical set or a minimal defining set. These concepts, namely latin trades and defining sets in latin squares, are intimately connected by the following observation. If L is a latin square and D ⊆ L is a defining set, then D intersects all latin bitrades for which one mate is contained in L. In Part I of this thesis Dr´apal’s result is applied to investigate the structure of certain defining sets in latin squares. The results that are obtained are interesting in themselves; furthermore, the geometric approach to the problem yields additional appealing results. These geometric results are discussed in Chapters 3, 4, 5 and 6. They pertain to partitioning regions (polygons in R2 that satisfy certain obvious conditions) into equilateral, integer length sided, triangles, such that no point, in the region, is a corner of more than three distinct triangles. In Chapter 2 one of the main two theorems on defining sets is established, as is a method for using the above geometric results to prove the nonexistence of certain types of defining sets. In Part II of this thesis, intersection problems, for latin squares and Steiner triple systems, are considered. The seminal works, for problems of these types, are due to Lindner and Rosa (1975) and Fu (1980). A natural progression, from the established literature, for intersection problems between elements in a pair of latin squares or Steiner triple systems is to problems in which the intersection is composed of a number of disjoint configurations (isomorphic copies of some specified partial triple system). In this thesis solutions to two intersection problems for disjoint configurations are detailed. An m-flower, (F,F), is a partial triple system/configuration, such that: F = {{x, yi, zi} | {yi, zi} ∩ {yj , zj} = ∅, for 0 ≤ i, j ≤ m − 1, i 6= j}; and F = UX∈FX. The first such problem considered in this thesis asks for necessary and sufficient conditions for integers k and m ≥ 2 such that a pair of latin squares of order n exists that intersect precisely in k disjoint m-flowers. The necessary terminology, constructions, lemmas and proof for this result are contained in Chapters 7, 8 and 9. The second such problem considered in this thesis asks for necessary and sufficient conditions for integers k such that a pair of Steiner triple systems of order u exists that intersect precisely in k disjoint 2-flowers. This result relies on the solution to the latin square problem and an additional result from Chapter 9. The further constructions and lemmas used to prove this result are detailed in Chapter 10.

Consider distinct latin squares, L and M, of order n. Then the pair (T1, T2) where T1 = L \M and T2 = M \ L is called a latin bitrade. Furthermore T1 and T2 are referred to as latin trades, in which T2 is said to be a disjoint mate of T1 (and vice versa). Drápal (1991) showed that, under certain conditions, a partition of an equilateral triangle of side length n, where n is some integer, into smaller, integer length sided equilateral triangles gives rise to a latin trade within the latin square based on the addition table for the integers modulo n. A partial latin square P of order n is said to be completable if there exists a latin square L of order n such that P ⊆ L. If there is only one such possible latin square, L, of order n then P is said to be uniquely completable and P is called a defining set of L. Furthermore, if C is a uniquely completable partial latin square such that no proper subset of C is uniquely completable, C is said to be a critical set or a minimal defining set. These concepts, namely latin trades and defining sets in latin squares, are intimately connected by the following observation. If L is a latin square and D ⊆ L is a defining set, then D intersects all latin bitrades for which one mate is contained in L. In Part I of this thesis Dr´apal’s result is applied to investigate the structure of certain defining sets in latin squares. The results that are obtained are interesting in themselves; furthermore, the geometric approach to the problem yields additional appealing results. These geometric results are discussed in Chapters 3, 4, 5 and 6. They pertain to partitioning regions (polygons in R2 that satisfy certain obvious conditions) into equilateral, integer length sided, triangles, such that no point, in the region, is a corner of more than three distinct triangles. In Chapter 2 one of the main two theorems on defining sets is established, as is a method for using the above geometric results to prove the nonexistence of certain types of defining sets. In Part II of this thesis, intersection problems, for latin squares and Steiner triple systems, are considered. The seminal works, for problems of these types, are due to Lindner and Rosa (1975) and Fu (1980). A natural progression, from the established literature, for intersection problems between elements in a pair of latin squares or Steiner triple systems is to problems in which the intersection is composed of a number of disjoint configurations (isomorphic copies of some specified partial triple system). In this thesis solutions to two intersection problems for disjoint configurations are detailed. An m-flower, (F,F), is a partial triple system/configuration, such that: F = {{x, yi, zi} | {yi, zi} ∩ {yj , zj} = ∅, for 0 ≤ i, j ≤ m − 1, i 6= j}; and F = UX∈FX. The first such problem considered in this thesis asks for necessary and sufficient conditions for integers k and m ≥ 2 such that a pair of latin squares of order n exists that intersect precisely in k disjoint m-flowers. The necessary terminology, constructions, lemmas and proof for this result are contained in Chapters 7, 8 and 9. The second such problem considered in this thesis asks for necessary and sufficient conditions for integers k such that a pair of Steiner triple systems of order u exists that intersect precisely in k disjoint 2-flowers. This result relies on the solution to the latin square problem and an additional result from Chapter 9. The further constructions and lemmas used to prove this result are detailed in Chapter 10.

Consider distinct latin squares, L and M, of order n. Then the pair (T1, T2) where T1 = L \M and T2 = M \ L is called a latin bitrade. Furthermore T1 and T2 are referred to as latin trades, in which T2 is said to be a disjoint mate of T1 (and vice versa). Drápal (1991) showed that, under certain conditions, a partition of an equilateral triangle of side length n, where n is some integer, into smaller, integer length sided equilateral triangles gives rise to a latin trade within the latin square based on the addition table for the integers modulo n. A partial latin square P of order n is said to be completable if there exists a latin square L of order n such that P ⊆ L. If there is only one such possible latin square, L, of order n then P is said to be uniquely completable and P is called a defining set of L. Furthermore, if C is a uniquely completable partial latin square such that no proper subset of C is uniquely completable, C is said to be a critical set or a minimal defining set. These concepts, namely latin trades and defining sets in latin squares, are intimately connected by the following observation. If L is a latin square and D ⊆ L is a defining set, then D intersects all latin bitrades for which one mate is contained in L. In Part I of this thesis Dr´apal’s result is applied to investigate the structure of certain defining sets in latin squares. The results that are obtained are interesting in themselves; furthermore, the geometric approach to the problem yields additional appealing results. These geometric results are discussed in Chapters 3, 4, 5 and 6. They pertain to partitioning regions (polygons in R2 that satisfy certain obvious conditions) into equilateral, integer length sided, triangles, such that no point, in the region, is a corner of more than three distinct triangles. In Chapter 2 one of the main two theorems on defining sets is established, as is a method for using the above geometric results to prove the nonexistence of certain types of defining sets. In Part II of this thesis, intersection problems, for latin squares and Steiner triple systems, are considered. The seminal works, for problems of these types, are due to Lindner and Rosa (1975) and Fu (1980). A natural progression, from the established literature, for intersection problems between elements in a pair of latin squares or Steiner triple systems is to problems in which the intersection is composed of a number of disjoint configurations (isomorphic copies of some specified partial triple system). In this thesis solutions to two intersection problems for disjoint configurations are detailed. An m-flower, (F,F), is a partial triple system/configuration, such that: F = {{x, yi, zi} | {yi, zi} ∩ {yj , zj} = ∅, for 0 ≤ i, j ≤ m − 1, i 6= j}; and F = UX∈FX. The first such problem considered in this thesis asks for necessary and sufficient conditions for integers k and m ≥ 2 such that a pair of latin squares of order n exists that intersect precisely in k disjoint m-flowers. The necessary terminology, constructions, lemmas and proof for this result are contained in Chapters 7, 8 and 9. The second such problem considered in this thesis asks for necessary and sufficient conditions for integers k such that a pair of Steiner triple systems of order u exists that intersect precisely in k disjoint 2-flowers. This result relies on the solution to the latin square problem and an additional result from Chapter 9. The further constructions and lemmas used to prove this result are detailed in Chapter 10.

It is well known that for any Steiner triple system (STS) one can define a binary operation · upon its base set by assigning x·x = x for all x and x·y = z, where z is the third point in the block containing the pair {x, y}. The same can be done for Mendelsohn triple systems (MTS), directed triple systems (DTS) as well as hybrid triple systems (HTS), where (x, y) is considered to be ordered. In the case of STSs and MTSs the operation yields a quasigroup, however this is not necessarily the case for DTSs and HTSs. A DTS or an HTS which induces a quasigroup is said to be Latin. The quasigroups associated with STSs and MTSs satisfy the flexible law x · (y · x) = (x · y) · x but those associated with Latin DTSs and Latin HTSs need not. A DTS or an HTS is said to be pure if when considered as a twofold triple system it contains no repeated blocks. This thesis focuses on the study of Latin DTSs and Latin HTSs, in particular it aims to examine flexibility, purity and other related properties in these systems. Latin DTSs and Latin HTSs which admit a cyclic or a rotational automorphism are also studied. The existence spectra of these systems are proved and enumeration results are presented. A smaller part of the thesis is then devoted to examining the size of the centre of a Steiner loop and the connection to...

From Introduction: In his influential treatise, Concerning the Spiritual in Art, Wassily Kandinsky refers to Goethe's "prophetic remark" made in connection with the relationship between the arts in which Goethe had asserted that "painting must count this relationship her main foundation". Kandinsky went on to say that Painting in his day stood "at the first stage of a road by which she abstraction of composition". I will, according to her thought and arrive own possibilities, make art an finally at purely artistic What he seems to have been suggesting is that form, colour and sound are differentiated expressions of a unifying spiritual content, that this spiritual content lives also somehow in the human soul and that it is the new task of the artist to awaken original creativity from out of this spirit by working consciously in creative empathy with the laws implicit in form, colour and sound. The extent to which this view of creativity is indebted to Goethe is only fully realised when it is discovered how closely Kandinsky's writings on colour recapitulate his. In an unpublished essay: Goethe's Theory of Colours : Its relation to some aspects in . the history of Art, Michael Grimly argues that not only Kandinsky in Germany but also Chevreul, the colour-theoretician who was, in France, the leading light, in a technical sense, both of Delacroix and of the Impressionists simply repeats in his writings on Colour many of the ideas that Goethe had already formulated.

Made available in DSpace on 2016-02-05T18:30:02Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-07-13. Added 1 bitstream(s) on 2016-02-05T18:34:08Z : No. of bitstreams: 1 000857699.pdf: 993960 bytes, checksum: 4b11dbb813ff41cc61fc48f7120fc224 (MD5) / Este trabalho investiga os princípios pedagógicos de Paulo Freire e Rudolf Steiner para dialogar com a realidade discente, influenciada pelos meios eletrônicos - televisão, videogame e computador. A abordagem é qualitativa e utiliza para a coleta de dados análise documental e entrevista semiestruturada. As equipes gestoras e três professores de cada escola, uma waldorf e outra freireana, ambas do interior de São Paulo, foram entrevistados. Para análise dos dados utilizou-se o paradigma indiciário proposto por Carlo Ginzburg. A partir desses dados, concluiu-se que as duas pedagogias apresentam em comum a não utilização de apostilas e o incentivo à autonomia dos professores. Em complementação, a waldorf prioriza o desenvolvimento individual dos alunos para beneficiar o social e a freireana, o contexto social como base formativa para a construção do indivíduo. Ao abordar os meios eletrônicos identificou-se cautela: a pedagogia waldorf defende as vivências artísticas e um ritmo diferenciado de condução dos conteúdos, como alimento que supre as necessidades dos alunos; a pedagogia freireana acredita na interdisciplinaridade dos conteúdos, praticados em forma de projetos que se modificam ano a ano, despertando o interesse dos alunos. Steiner e Freire não viveram a tecnologia do século XXI, mas suas contribuições alertam para que os meios eletrônicos não constituam o âmbito mais fundamental no contexto escolar; pois, a educação humanística, defendida por ambos, luta pela valorização de um Homem historicamente situado no mundo de forma crítica e autônoma. O ser docente deve educar-se permanentemente, ao considerar o discente num agir a partir do ser e reconhecer / This paper investigates the pedagogical principles of Paulo Freire and Rudolf Steiner in how they approach the student reality, as influenced by electronic media - television, videogame and computer. The methodology is qualitative and data were collected in the pedagogic projects and semi-structured interviews. The management teams and three teachers from each school, one Waldorf and one Freire, both in the interior of São Paulo State, were interviewed. Data analysis used the evidentiary paradigm proposed by Carlo Ginzburg. It was concluded that the two pedagogies have in common not using handouts and encouragement of the teacher‟s autonomy. In addition, the Waldorf prioritizes the individual development of students towards the social, and Freire, the social context as a formative basis for the construction of the individual. In addressing the electronic media, it was identified care: the Waldorf pedagogy defends the artistic experience and an individual pace of driving of the contents, as impulse to meet the needs of students; Freire's pedagogy believes in the interdisciplinary content, practiced in the form of projects that change every year, attracting the interest of students. Steiner and Freire did not live with twenty-first century technology, but their contributions warn that electronic media are not the most important part in the school context; therefore, humanistic education, advocated by both, seeks to educate the individuals critically and independently, historically situated in the world. To be a teacher imply educate himself/herself permanently, and consider the student action from student‟s being and recognizing