Construction of signal sets from quotient rings of the quaternion orders associated with arithmetic fuchsian groups

This paper aims to construct signal sets from quotient rings of the quaternion over a real number field associated with the arithmetic Fuchsian group Γ 4g , where g is the genus of the associated surface. These Fuchsian groups consist of the edge-pairing isometries of the regular hyperbolic polygons (fundamental region) P 4g , which tessellate the hyperbolic plane D 2 . The corresponding tessellations are the self-dual tessellations {4g, 4g}. Knowing the generators of the quaternion orders which realize the edge-pairings of the polygons, the signal points of the signal sets derived from the quotient rings of the quaternion orders are determined. It is shown by examples the relevance of adequately selecting the ideal in the maximal order to construct the signal sets satisfying the property of geometrical uniformity. The labeling of such signals is realized by using the mapping by set partitioning concept to solve the corresponding Diophantine equations (extreme quadratic forms). Trellis coded modulation and multilevel codes whose signal sets are derived from quotient rings of quaternion orders are considered possible applications8196050196061CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP305656/2015-52013/25977-

Improving Sampling-Based Motion Planning Using Library of Trajectories

Plánování pohybu je jedním z podstatných problémů robotiky. Tato práce kombinuje pokroky v plánování pohybu a hodnocení podobnosti objektů za účelem zrychlení plánování ve statických prostředích. První část této práce pojednává o současných metodách používaných pro hodnocení podobnosti objektů a plánování pohybu. Prostřední část popisuje, jak jsou tyto metody použity pro zrychlení plánování s využitím získaných znalostí o prostředí. V poslední části jsou navržené metody porovnány s ostatními plánovači v nezávislém testu. Námi navržené algoritmy se v experimentech ukázaly být často rychlejší v porovnání s ostatními plánovači. Také často nacházely cesty v prostředích, kde ostatní plánovače nebyly schopny cestu nalézt.Motion planning is one of the fundamental problems in robotics. This thesis combines the advances in motion planning and shape matching to improve planning speeds in static environments. The first part of this thesis covers current methods used in object similarity evaluation and motion planning. The middle part describes how these methods are used together to improve planning speeds by utilizing prior knowledge about the environment, along with additional modifications. In the last part, the proposed methods are tested against other state-of-the-art planners in an independent benchmarking facility. The proposed algorithms are shown to be faster than other planners in many cases, often finding paths in environments where the other planners are unable to

Strategies for image visualisation and browsing

PhDThe exploration of large information spaces has remained a challenging task even though the proliferation of database management systems and the state-of-the art retrieval algorithms is becoming pervasive. Signi cant research attention in the multimedia domain is focused on nding automatic algorithms for organising digital image collections into meaningful structures and providing high-semantic image indices. On the other hand, utilisation of graphical and interactive methods from information visualisation domain, provide promising direction for creating e cient user-oriented systems for image management. Methods such as exploratory browsing and query, as well as intuitive visual overviews of image collection, can assist the users in nding patterns and developing the understanding of structures and content in complex image data-sets. The focus of the thesis is combining the features of automatic data processing algorithms with information visualisation. The rst part of this thesis focuses on the layout method for displaying the collection of images indexed by low-level visual descriptors. The proposed solution generates graphical overview of the data-set as a combination of similarity based visualisation and random layout approach. Second part of the thesis deals with problem of visualisation and exploration for hierarchical organisation of images. Due to the absence of the semantic information, images are considered the only source of high-level information. The content preview and display of hierarchical structure are combined in order to support image retrieval. In addition to this, novel exploration and navigation methods are proposed to enable the user to nd the way through database structure and retrieve the content. On the other hand, semantic information is available in cases where automatic or semi-automatic image classi ers are employed. The automatic annotation of image items provides what is referred to as higher-level information. This type of information is a cornerstone of multi-concept visualisation framework which is developed as a third part of this thesis. This solution enables dynamic generation of user-queries by combining semantic concepts, supported by content overview and information ltering. Comparative analysis and user tests, performed for the evaluation of the proposed solutions, focus on the ways information visualisation a ects the image content exploration and retrieval; how e cient and comfortable are the users when using di erent interaction methods and the ways users seek for information through di erent types of database organisation

An algorithmic framework for visualising and exploring multidimensional data

To help understand multidimensional data, information visualisation techniques are often applied to take advantage of human visual perception in exposing latent structure. A popular means of presenting such data is via two-dimensional scatterplots where the inter-point proximities reflect some notion of similarity between the entities represented. This can result in potentially interesting structure becoming almost immediately apparent. Traditional algorithms for carrying out this dimension reduction tend to have different strengths and weaknesses in terms of run times and layout quality. However, it has been found that the combination of algorithms can produce hybrid variants that exhibit significantly lower run times while maintaining accurate depictions of high-dimensional structure. The author's initial contribution in the creation of such algorithms led to the design and implementation of a software system (HIVE) for the development and investigation of new hybrid variants and the subsequent analysis of the data they transform. This development was motivated by the fact that there are potentially many hybrid algorithmic combinations to explore and therefore an environment that is conductive to their development, analysis and use is beneficial not only in exploring the data they transform but also in exploring the growing number of visualisation tools that these algorithms beget. This thesis descries three areas of the author's contribution to the field of information visualisation. Firstly, work on hybrid algorithms for dimension reduction is presented and their analysis shows their effectiveness. Secondly, the development of a framework for the creation of tailored hybrid algorithms is illustrated. Thirdly, a system embodying the framework, providing an environment conductive to the development, evaluation and use of the algorithms is described. Case studies are provided to demonstrate how the author and others have used and found value in the system across areas as diverse as environmental science, social science and investigative psychology, where multidimensional data are in abundance

Greedy routing and virtual coordinates for future networks

At the core of the Internet, routers are continuously struggling with ever-growing routing and forwarding tables. Although hardware advances do accommodate such a growth, we anticipate new requirements e.g. in data-oriented networking where each content piece has to be referenced instead of hosts, such that current approaches relying on global information will not be viable anymore, no matter the hardware progress. In this thesis, we investigate greedy routing methods that can achieve similar routing performance as today but use much less resources and which rely on local information only. To this end, we add specially crafted name spaces to the network in which virtual coordinates represent the addressable entities. Our scheme enables participating routers to make forwarding decisions using only neighbourhood information, as the overarching pseudo-geometric name space structure already organizes and incorporates "vicinity" at a global level. A first challenge to the application of greedy routing on virtual coordinates to future networks is that of "routing dead-ends" that are local minima due to the difficulty of consistent coordinates attribution. In this context, we propose a routing recovery scheme based on a multi-resolution embedding of the network in low-dimensional Euclidean spaces. The recovery is performed by routing greedily on a blurrier view of the network. The different network detail-levels are obtained though the embedding of clustering-levels of the graph. When compared with higher-dimensional embeddings of a given network, our method shows a significant diminution of routing failures for similar header and control-state sizes. A second challenge to the application of virtual coordinates and greedy routing to future networks is the support of "customer-provider" as well as "peering" relationships between participants, resulting in a differentiated services environment. Although an application of greedy routing within such a setting would combine two very common fields of today's networking literature, such a scenario has, surprisingly, not been studied so far. In this context we propose two approaches to address this scenario. In a first approach we implement a path-vector protocol similar to that of BGP on top of a greedy embedding of the network. This allows each node to build a spatial map associated with each of its neighbours indicating the accessible regions. Routing is then performed through the use of a decision-tree classifier taking the destination coordinates as input. When applied on a real-world dataset (the CAIDA 2004 AS graph) we demonstrate an up to 40% compression ratio of the routing control information at the network's core as well as a computationally efficient decision process comparable to methods such as binary trees and tries. In a second approach, we take inspiration from consensus-finding in social sciences and transform the three-dimensional distance data structure (where the third dimension encodes the service differentiation) into a two-dimensional matrix on which classical embedding tools can be used. This transformation is achieved by agreeing on a set of constraints on the inter-node distances guaranteeing an administratively-correct greedy routing. The computed distances are also enhanced to encode multipath support. We demonstrate a good greedy routing performance as well as an above 90% satisfaction of multipath constraints when relying on the non-embedded obtained distances on synthetic datasets. As various embeddings of the consensus distances do not fully exploit their multipath potential, the use of compression techniques such as transform coding to approximate the obtained distance allows for better routing performances