Ground-state clusters of two-, three- and four-dimensional +-J Ising spin glasses

A huge number of independent true ground-state configurations is calculated for two-, three- and four-dimensional +- J spin-glass models. Using the genetic cluster-exact approximation method, system sizes up to N=20^2,8^3,6^4 spins are treated. A ``ballistic-search'' algorithm is applied which allows even for large system sizes to identify clusters of ground states which are connected by chains of zero-energy flips of spins. The number of clusters n_C diverges with N going to infinity. For all dimensions considered here, an exponential increase of n_C appears to be more likely than a growth with a power of N. The number of different ground states is found to grow clearly exponentially with N. A zero-temperature entropy per spin of s_0=0.078(5)k_B (2d), s_0=0.051(3)k_B (3d) respectively s_0=0.027(5)k_B (4d) is obtained.Comment: large extensions, now 12 pages, 9 figures, 27 reference

Parallel Deterministic and Stochastic Global Minimization of Functions with Very Many Minima

The optimization of three problems with high dimensionality and many local minima are investigated under five different optimization algorithms: DIRECT, simulated annealing, Spall’s SPSA algorithm, the KNITRO package, and QNSTOP, a new algorithm developed at Indiana University

A new method for analyzing ground-state landscapes: ballistic search

A ``ballistic-search'' algorithm is presented which allows the identification of clusters (or funnels) of ground states in Ising spin glasses even for moderate system sizes. The clusters are defined to be sets of states, which are connected in state-space by chains of zero-energy flips of spins. The technique can also be used to estimate the sizes of such clusters. The performance of the method is tested with respect to different system sizes and choices of parameters. As an application the ground-state funnel structure of two-dimensional +or- J spin glasses of systems up to size L=20 is analyzed by calculating a huge number of ground states per realization. A T=0 entropy per spin of s_0=0.086(4)k_B is obtained.Comment: 10 pages, 11 figures, 35 references, revte

Simulated evaluation of faceted browsing based on feature selection

In this paper we explore the limitations of facet based browsing which uses sub-needs of an information need for querying and organising the search process in video retrieval. The underlying assumption of this approach is that the search effectiveness will be enhanced if such an approach is employed for interactive video retrieval using textual and visual features. We explore the performance bounds of a faceted system by carrying out a simulated user evaluation on TRECVid data sets, and also on the logs of a prior user experiment with the system. We first present a methodology to reduce the dimensionality of features by selecting the most important ones. Then, we discuss the simulated evaluation strategies employed in our evaluation and the effect on the use of both textual and visual features. Facets created by users are simulated by clustering video shots using textual and visual features. The experimental results of our study demonstrate that the faceted browser can potentially improve the search effectiveness

Navigace mobilních robotů v neznámém prostředí s využitím měření vzdáleností

The ability of a robot to navigate itself in the environment is a crucial step towards its autonomy. Navigation as a subtask of the development of autonomous robots is the subject of this thesis, focusing on the development of a method for simultaneous localization an mapping (SLAM) of mobile robots in six degrees of freedom (DOF). As a part of this research, a platform for 3D range data acquisition based on a continuously inclined laser rangefinder was developed. This platform is presented, evaluating the measurements and also presenting the robotic equipment on which the platform can be fitted. The localization and mapping task is equal to the registration of multiple 3D images into a common frame of reference. For this purpose, a method based on the Iterative Closest Point (ICP) algorithm was developed. First, the originally implemented SLAM method is presented, focusing on the time-wise performance and the registration quality issues introduced by the implemented algorithms. In order to accelerate and improve the quality of the time-demanding 6DOF image registration, an extended method was developed. The major extension is the introduction of a factorized registration, extracting 2D representations of vertical objects called leveled maps from the 3D point sets, ensuring these representations are 3DOF invariant. The extracted representations are registered in 3DOF using ICP algorithm, allowing pre-alignment of the 3D data for the subsequent robust 6DOF ICP based registration. The extended method is presented, showing all important modifications to the original method. The developed registration method was evaluated using real 3D data acquired in different indoor environments, examining the benefits of the factorization and other extensions as well as the performance of the original ICP based method. The factorization gives promising results compared to a single phase 6DOF registration in vertically structured environments. Also, the disadvantages of the method are discussed, proposing possible solutions. Finally, the future prospects of the research are presented.Schopnost lokalizace a navigace je podmínkou autonomního provozu mobilních robotů. Předmětem této disertační práce jsou navigační metody se zaměřením na metodu pro simultánní lokalizaci a mapování (SLAM) mobilních robotů v šesti stupních volnosti (6DOF). Nedílnou součástí tohoto výzkumu byl vývoj platformy pro sběr 3D vzdálenostních dat s využitím kontinuálně naklápěného laserového řádkového scanneru. Tato platforma byla vyvinuta jako samostatný modul, aby mohla být umístěna na různé šasi mobilních robotů. Úkol lokalizace a mapování je ekvivalentní registraci více 3D obrazů do společného souřadného systému. Pro tyto účely byla vyvinuta metoda založená na algoritmu Iterative Closest Point Algorithm (ICP). Původně implementovaná verze navigační metody využívá ICP s akcelerací pomocí kd-stromů přičemž jsou zhodnoceny její kvalitativní a výkonnostní aspekty. Na základě této analýzy byly vyvinuty rozšíření původní metody založené na ICP. Jednou z hlavních modifikací je faktorizace registračního procesu, kdy tato faktorizace je založena na redukci dat: vytvoření 2D „leveled“ map (ve smyslu jednoúrovňových map) ze 3D vzdálenostních obrazů. Pro tuto redukci je technologicky i algoritmicky zajištěna invariantnost těchto map vůči třem stupňům volnosti. Tyto redukované mapy jsou registrovány pomocí ICP ve zbylých třech stupních volnosti, přičemž získaná transformace je aplikována na 3D data za účelem před-registrace 3D obrazů. Následně je provedena robustní 6DOF registrace. Rozšířená metoda je v disertační práci v popsána spolu se všemi podstatnými modifikacemi. Vyvinutá metoda byla otestována a zhodnocena s využitím skutečných 3D vzdálenostních dat naměřených v různých vnitřních prostředích. Jsou zhodnoceny přínosy faktorizace a jiných modifikací ve srovnání s původní jednofázovou 6DOF registrací, také jsou zmíněny nevýhody implementované metody a navrženy způsoby jejich řešení. Nakonec následuje návrh budoucího výzkumu a diskuse o možnostech dalšího rozvoje.

Particle-based and Meshless Methods with Aboria

Aboria is a powerful and flexible C++ library for the implementation of particle-based numerical methods. The particles in such methods can represent actual particles (e.g. Molecular Dynamics) or abstract particles used to discretise a continuous function over a domain (e.g. Radial Basis Functions). Aboria provides a particle container, compatible with the Standard Template Library, spatial search data structures, and a Domain Specific Language to specify non-linear operators on the particle set. This paper gives an overview of Aboria's design, an example of use, and a performance benchmark