En 1949, C. Loewner a demontré dans un travail non publié l'inégalité systolique optimale du tore T reliant l'aire au carré de la systole. Par la systole on désigne la longueur du plus court lacet non contractile de T. De plus, l' égalité est atteinte si et seulement si le tore est plat hexagonal. Ce résultat a donné naissance à la géométrie systolique. Dans cette thèse, nous étudions des inégalités de type systolique portant sur les longueurs minimales de différentes courbes et pas seulement la systole.Dans un premier temps, nous démontrons trois inégalités géométriques optimales conformes sur la bouteille de Klein reliant l'aire au produit des longueurs des plus courts lacets noncontractiles dans des classes d'homotopie libres différentes. Pour chaque classe conforme, nous décrivons la métrique extrémale réalisant le cas d'égalité.Nous établissons ensuite des inégalités géométriques optimales sur le ruban deMobius muni d'une métrique de Finsler. Ces inégalités géométriques relient la systole et la hauteur du ruban de Mobius à son volume de Holmes-Thompson. Nous en déduisons une inégalité systolique optimale sur la bouteille de Klein munie d'une métrique de Finsler avec des symétries. Nous décrivons également une famille de métriques extrémales dans les deux cas.Dans le troisième travail, nous démontrons une inégalité systolique critique sur la surface de genre deux. Plus précisément, il est connu que la surface de genre deux admet une métrique Riemannienne plate à singularités coniques qui est extrémale parmi les métriques à courbure nonpositive pour l' inégalité systolique. Nous montrons que cette métrique est en fait critique pour des variations lentes de métriques, cette fois-ci sans hypothèse de courbure, pour un autre problème systolique portant sur les longueurs des plus courts lacets non contractiles dans certaines classes d'homotopie libres données. Ces classes d'homotopie correspondent aux lacets systoliques et deux-systoliques de la surface extrémale / In 1949, C. Loewner proved in an unpublished work that the two-torus T satisfies an optimal systolic inequality relating the area of the torus to the square of its systole. By a systole here we mean the smallest length of a noncontractible loop in T. Furthermore, the equality is attained if and only if the torus is flat hexagonal. This result led to whatwas called later systolic geometry. In this thesis, we study several systolic-like inequalities. These inequalities involve the minimal length of various curves and not merely the systole.First we obtain three optimal conformal geometric inequalities on Riemannian Klein bottles relating the area to the product of the lengths of the shortest noncontractible loops in different free homotopy classes. We describe the extremal metrics in each conformal class.Then we prove optimal systolic inequalities on Finsler Mobius bands relating the systoleand the height of the Mobius band to its Holmes-Thompson volume. We also establish an optimalsystolic inequality for Finsler Klein bottles with symmetries. We describe extremal metric families in both cases.Finally, we prove a critical systolic inequality on genus two surface. More precisely, it is known that the genus two surface admits a piecewise flat metric with conical singularities which is extremal for the systolic inequality among all nonpositively curved Riemannian metrics. We show that this piecewise flat metric is also critical for slow metric variations, this time without curvature restrictions, for another type of systolic inequality involving the lengths of the shortest noncontractible loops in different free homotopy classes. The free homotopy classes considered correspond to those of the systolic loops and the second-systolic loops of the extremal surface

This thesis concerns of benchmarking $\mu$C/OS-II systems on different microcontroller architectures. The thesis describes COS-II microcontroller core and possible series of benchmark tests which can be used. Selected tests are implemented and measured properties of microcontrollers with different architecture are compared.

Shotgun proteomics is a widely known technique for identification of protein and peptide sequences from an "in vitro" sample. A tandem mass spectrometer generates tens of thousands of mass spectra which must be annotated with peptide sequences. For this purpose, the similarity search in a database of theoretical spectra generated from a database of known protein sequences can be utilized. Since the sizes of databases grow rapidly in recent years, there is a demand for utilization of various database indexing techniques. We investigate the capabilities of (non)metric access methods as the database indexing techniques for fast and approximate similarity retrieval in mass spectra databases. We show that the method for peptide sequences identification is more than 100x faster than a sequential scan over the entire database while more than 90% of spectra are correctly annotated with peptide sequences. Since the method is currently suitable for small mixtures of proteins, we also utilize a precursor mass filter as the database indexing technique for complex mixtures of proteins. The precursor mass filter followed by ranking of spectra by a modification of the parametrized Hausdorff distance outperforms state-of-the-art tools in the number of identified peptide sequences and the speed of search. The...

The characteristics of vehicle steering perception are decisive factors concerning vehicle safety and overall pleasure behind the wheel. It is a challenge for vehicle manufacturers to achieve these features and qualities, because usually vehicle tuning almost only relies on subjective evaluation of test drivers, which is costly and time consuming. In order to optimize suspension design and develop a tool that can be used to evaluate steering with objective metrics instead of subjective assessment, links between them must be confirmed. In this master thesis, both objective and subjective testing data of over 20 vehicles across four different segments are introduced in linear and nonlinear analysis. Linear regression analysis is applied to investigate simply positive or negative correlation between a pair of subjective-objective parameters. However, even if certain linear correlations are obtained, it is still hard to define the optimal value for objective metrics. Considering that the general shape of a correlation function can reveal which objective range give higher subjective rating, it is possible to define these preferred ranges with Neural Network (NN). The best data available is adopted from three drivers who tested 15 sedans, and some interesting results are found. The initial results demonstrate that NN is a powerful tool to uncover and graphically illustrate the links between objective metrics and subjective assessments, i.e., the specific range leading to better steering feel. Given a larger sample size, more reliable and optimal links can be defined by following the same method. These confirmed links would enable vehicle dynamics engineers to more effectively develop new vehicles with nearly perfect steering feel.

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In this thesis we build on the theory concerning the metric geometry of relatively hyperbolic and mapping class groups, especially with respect to the difficulty of embedding such groups into Banach spaces. In Chapter 3 (joint with Alessandro Sisto) we construct simple embeddings of closed graph manifold groups into a product of three metric trees, answering positively a conjecture of Smirnov concerning the Assouad-Nagata dimension of such spaces. Consequently, we obtain optimal embeddings of such spaces into certain Banach spaces. The ideas here have been extended to other closed three-manifolds and to higher dimensional analogues of graph manifolds. In Chapter 4 we give an explicit method of embedding relatively hyperbolic groups into certain Banach spaces, which yields optimal bounds on the compression exponent of such groups relative to their peripheral subgroups. From this we deduce that the fundamental group of every closed three-manifold has Hilbert compression exponent one. In Chapter 5 we prove that relatively hyperbolic spaces with a tree-graded quasi-isometry representative can be characterised by a relative version of Manning's bottleneck property. This applies to the Bestvina-Bromberg-Fujiwara quasi-trees of spaces, yielding an embedding of each mapping class group of a closed surface into a finite product of simplicial trees. From this we obtain explicit embeddings of mapping class groups into certain Banach spaces and deduce that these groups have finite Assouad-Nagata dimension. It also applies to relatively hyperbolic groups, proving that such groups have finite Assouad-Nagata dimension if and only if each peripheral subgroup does.

A quantum channel is a mapping which sends density matrices to density matrices. The estimation of quantum channels is of great importance to the field of quantum information. In this thesis two topics related to estimation of quantum channels are investigated. The first of these is the upper bound of Sarovar and Milburn (2006) on the Fisher information obtainable by measuring the output of a channel. Two questions raised by Sarovar and Milburn about their bound are answered. A Riemannian metric on the space of quantum states is introduced, related to the construction of the Sarovar and Milburn bound. Its properties are characterized. The second topic investigated is the estimation of unitary channels. The situation is considered in which an experimenter has several non-identical unitary channels that have the same parameter. It is shown that it is possible to improve estimation using the channels together, analogous to the case of identical unitary channels. Also, a new method of phase estimation is given based on a method sketched by Kitaev (1996). Unlike other phase estimation procedures which perform similarly, this procedure requires only very basic experimental resources.

A large number of machine learning algorithms are critically dependent on the underlying distance/metric/similarity function. Learning an appropriate distance function is therefore crucial to the success of many methods. The class of distance functions that can be learned accurately is characterized by the amount and type of supervision available to the particular application. In this thesis, we explore a variety of such distance learning problems using different amounts/types of supervision and provide efficient and scalable algorithms to learn appropriate distance functions for each of these problems. First, we propose a generic regularized framework for Mahalanobis metric learning and prove that for a wide variety of regularization functions, metric learning can be used for efficiently learning a kernel function incorporating the available side-information. Furthermore, we provide a method for fast nearest neighbor search using the learned distance/kernel function. We show that a variety of existing metric learning methods are special cases of our general framework. Hence, our framework also provides a kernelization scheme and fast similarity search scheme for such methods. Second, we consider a variation of our standard metric learning framework where the side-information is incremental, streaming and cannot be stored. For this problem, we provide an efficient online metric learning algorithm that compares favorably to existing methods both theoretically and empirically. Next, we consider a contrasting scenario where the amount of supervision being provided is extremely small compared to the number of training points. For this problem, we consider two different modeling assumptions: 1) data lies on a low-dimensional linear subspace, 2) data lies on a low-dimensional non-linear manifold. The first assumption, in particular, leads to the problem of matrix rank minimization over polyhedral sets, which is a problem of immense interest in numerous fields including optimization, machine learning, computer vision, and control theory. We propose a novel online learning based optimization method for the rank minimization problem and provide provable approximation guarantees for it. The second assumption leads to our geometry-aware metric/kernel learning formulation, where we jointly model the metric/kernel over the data along with the underlying manifold. We provide an efficient alternating minimization algorithm for this problem and demonstrate its wide applicability and effectiveness by applying it to various machine learning tasks such as semi-supervised classification, colored dimensionality reduction, manifold alignment etc. Finally, we consider the task of learning distance functions under no supervision, which we cast as a problem of learning disparate clusterings of the data. To this end, we propose a discriminative approach and a generative model based approach and we provide efficient algorithms with convergence guarantees for both the approaches. / text

Darbas skirtas hiperbolinio tipo I rūšies beveik kontaktinėms metrinėms struktūroms, arba -struktūroms, egzistuojančioms hiperbolinio tipo A-erdvės hiperpaviršiuose. / Working for the hyperbolic type of class I almost contact metric structures existing in the hypersurfaces of hyperbolic type A-space.