Geometric spin foams, Yang-Mills theory and background-independent models

We review the dual transformation from pure lattice gauge theory to spin foam models with an emphasis on a geometric viewpoint. This allows us to give a simple dual formulation of SU(N) Yang-Mills theory, where spin foam surfaces are weighted with the exponentiated area. In the case of gravity, we introduce a symmetry condition which demands that the amplitude of an individual spin foam depends only on its geometric properties and not on the lattice on which it is defined. For models that have this property, we define a new sum over abstract spin foams that is independent of any choice of lattice or triangulation. We show that a version of the Barrett-Crane model satisfies our symmetry requirement.Comment: 28 pages, 27 diagrams, typos correcte

Sampled data systems passivity and discrete port-Hamiltonian systems

In this paper, we present a novel way to approach the interconnection of a continuous and a discrete time physical system first presented in [1][2] [3]. This is done in a way which preserves passivity of the coupled system independently of the sampling time T. This strategy can be used both in the field of telemanipulation, for the implementation of a passive master/slave system on a digital transmission line with varying time delays and possible loss of packets (e.g., the Internet), and in the field of haptics, where the virtual environment should `feel¿ like a physical equivalent system

Sequence-based protein classification: binary Profile Hidden Markov Models and propositionalisation

Detecting similarity in biological sequences is a key element to understanding the mechanisms of life. Researchers infer potential structural, functional or evolutionary relationships from similarity. However, the concept of similarity is complex in biology. Sequences consist of different molecules with different chemical properties, have short and long distance interactions, form 3D structures and change through evolutionary processes. Amino acids are one of the key molecules of life. Most importantly, a sequence of amino acids constitutes the building block for proteins which play an essential role in cellular processes. This thesis investigates similarity amongst proteins. In this area of research there are two important and closely related classification tasks – the detection of similar proteins and the discrimination amongst them. Hidden Markov Models (HMMs) have been successfully applied to the detection task as they model sequence similarity very well. From a Machine Learning point of view these HMMs are essentially one-class classifiers trained solely on a small number of similar proteins neglecting the vast number of dissimilar ones. Our basic assumption is that integrating this neglected information will be highly beneficial to the classification task. Thus, we transform the problem representation from a one-class to a binary one. Equipped with the necessary sound understanding of Machine Learning, especially concerning problem representation and statistically significant evaluation, our work pursues and combines two different avenues on this aforementioned transformation. First, we introduce a binary HMM that discriminates significantly better than the standard one, even when only a fraction of the negative information is used. Second, we interpret the HMM as a structured graph of information. This information cannot be accessed by highly optimised standard Machine Learning classifiers as they expect a fixed length feature vector representation. Propositionalisation is a technique to transform the former representation into the latter. This thesis introduces new propositionalisation techniques. The change in representation changes the learning problem from a one-class, generative to a propositional, discriminative one. It is a common assumption that discriminative techniques are better suited for classification tasks, and our results validate this assumption. We suggest a new way to significantly improve on discriminative power and runtime by means of terminating the time-intense training of HMMs early, subsequently applying propositionalisation and classifying with a discriminative, binary learner

Study and application of motion measurement methods by means of opto-electronics systems - Studio e applicazione di metodi di misura del moto mediante sistemi opto-elettronici

This thesis addresses the problem of localizing a vehicle in unstructured environments through on-board instrumentation that does not require infrastructure modifications. Two widely used opto-electronic systems which allow for non-contact measurements have been chosen: camera and laser range finder. Particular attention is paid to the definition of a set of procedures for processing the environment information acquired with the instruments in order to provide both accuracy and robustness to measurement noise. An important contribute of this work is the development of a robust and reliable algorithm for associating data that has been integrated in a graph based SLAM framework also taking into account uncertainty thus leading to an optimal vehicle motion estimation. Moreover, the localization of the vehicle can be achieved in a generic environment since the developed global localization solution does not necessarily require the identification of landmarks in the environment, neither natural nor artificial. Part of the work is dedicated to a thorough comparative analysis of the state-of-the-art scan matching methods in order to choose the best one to be employed in the solution pipeline. In particular this investigation has highlighted that a dense scan matching approach can ensure good performances in many typical environments. Several experiments in different environments, also with large scales, denote the effectiveness of the global localization system developed. While the laser range data have been exploited for the global localization, a robust visual odometry has been investigated. The results suggest that the use of camera can overcome the situations in which the solution achieved by the laser scanner has a low accuracy. In particular the global localization framework can be applied also to the camera sensor, in order to perform a sensor fusion between two complementary instrumentations and so obtain a more reliable localization system. The algorithms have been tested for 2D indoor environments, nevertheless it is expected that they are well suited also for 3D and outdoors

Four Lessons in Versatility or How Query Languages Adapt to the Web

Exposing not only human-centered information, but machine-processable data on the Web is one of the commonalities of recent Web trends. It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers. Yet this exposition has fractured the Web into islands of data, each in different Web formats: Some providers choose XML, others RDF, again others JSON or OWL, for their data, even in similar domains. This fracturing stifles innovation as application builders have to cope not only with one Web stack (e.g., XML technology) but with several ones, each of considerable complexity. With Xcerpt we have developed a rule- and pattern based query language that aims to give shield application builders from much of this complexity: In a single query language XML and RDF data can be accessed, processed, combined, and re-published. Though the need for combined access to XML and RDF data has been recognized in previous work (including the W3C’s GRDDL), our approach differs in four main aspects: (1) We provide a single language (rather than two separate or embedded languages), thus minimizing the conceptual overhead of dealing with disparate data formats. (2) Both the declarative (logic-based) and the operational semantics are unified in that they apply for querying XML and RDF in the same way. (3) We show that the resulting query language can be implemented reusing traditional database technology, if desirable. Nevertheless, we also give a unified evaluation approach based on interval labelings of graphs that is at least as fast as existing approaches for tree-shaped XML data, yet provides linear time and space querying also for many RDF graphs. We believe that Web query languages are the right tool for declarative data access in Web applications and that Xcerpt is a significant step towards a more convenient, yet highly efficient data access in a “Web of Data”

A Polynomial transformation from vertex cover problem to exact inference problem in bayesian belief networks

Exact Inference problem in Belief Networks has been well studied in the literature and has various application areas. In this thesis, a polynomial time transformation from Vertex Cover Problem to Exact Inference problem in Belief Networks is proposed and proved. To understand and see the development of the transformation, some well-known transformations about Vertex Cover Problem and Exact Inference, are introduced. By using the transformation proposed, some Vertex Cover problems are converted to Exact Inference Problems and solved by softwares using the algorithms of Exact Inference

Semiclassical Mechanics of the Wigner 6j-Symbol

The semiclassical mechanics of the Wigner 6j-symbol is examined from the standpoint of WKB theory for multidimensional, integrable systems, to explore the geometrical issues surrounding the Ponzano-Regge formula. The relations among the methods of Roberts and others for deriving the Ponzano-Regge formula are discussed, and a new approach, based on the recoupling of four angular momenta, is presented. A generalization of the Yutsis-type of spin network is developed for this purpose. Special attention is devoted to symplectic reduction, the reduced phase space of the 6j-symbol (the 2-sphere of Kapovich and Millson), and the reduction of Poisson bracket expressions for semiclassical amplitudes. General principles for the semiclassical study of arbitrary spin networks are laid down; some of these were used in our recent derivation of the asymptotic formula for the Wigner 9j-symbol.Comment: 64 pages, 50 figure