985 resultados para Twisted Algebra


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The large biodiversity of cyanobacteria together with the increasing genomics and proteomics metadata provide novel information for finding new commercially valuable metabolites. With the advent of global warming, there is growing interest in the processes that results in efficient CO2 capture through the use of photosynthetic microorganisms such as cyanobacteria. This requires a detailed knowledge of how cyanobacteria respond to the ambient CO2. My study was aimed at understanding the changes in the protein profile of the model organism, Synechocystis PCC 6803 towards the varying CO2 level. In order to achieve this goal I have employed modern proteomics tools such as iTRAQ and DIGE, recombinant DNA techniques to construct different mutants in cyanobacteria and biophysical methods to study the photosynthetic properties. The proteomics study revealed several novel proteins, apart from the well characterized proteins involved in carbon concentrating mechanisms (CCMs), that were upregulated upon shift of the cells from high CO2 concentration (3%) to that in air level (0.039%). The unknown proteins, Slr0006 and flavodiiron proteins (FDPs) Sll0217-Flv4 and Sll0219-Flv2, were selected for further characterization. Although slr0006 was substantially upregulated under Ci limiting conditions, inactivation of the gene did not result in any visual phenotype under various environmental conditions indicating that this protein is not essential for cell survival. However, quantitative proteomics showed the induction of novel plasmid and chromosome encoded proteins in deltaslr0006 under air level CO2 conditions. The expression of the slr0006 gene was found to be strictly dependent on active photosynthetic electron transfer. Slr0006 contains conserved dsRNA binding domain that belongs to the Sua5/YrdC/YciO protein family. Structural modelling of Slr0006 showed an alpha/beta twisted open-sheet structure and a positively charged cavity, indicating a possible binding site for RNA. The 3D model and the co-localization of Slr0006 with ribosomal subunits suggest that it might play a role in translation or ribosome biogenesis. On the other hand, deletions in the sll0217-sll218- sll0219 operon resulted in enhanced photodamage of PSII and distorted energy transfer from phycobilisome (PBS) to PSII, suggesting a dynamic photoprotection role of the operon. Constructed homology models also suggest efficient electron transfer in heterodimeric Flv2/Flv4, apparently involved in PSII photoprotection. Both Slr0006 and FDPs exhibited several common features, including negative regulation by NdhR and ambiguous cellular localization when subjected to different concentrations of divalent ions. This strong association with the membranes remained undisturbed even in the presence of detergent or high salt. My finding brings ample information on three novel proteins and their functions towards carbon limitation. Nevertheless, many pathways and related proteins remain unexplored. The comprehensive understanding of the acclimation processes in cyanobacteria towards varying environmental CO2 levels will help to uncover adaptive mechanisms in other organisms, including higher plants.

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Machine learning provides tools for automated construction of predictive models in data intensive areas of engineering and science. The family of regularized kernel methods have in the recent years become one of the mainstream approaches to machine learning, due to a number of advantages the methods share. The approach provides theoretically well-founded solutions to the problems of under- and overfitting, allows learning from structured data, and has been empirically demonstrated to yield high predictive performance on a wide range of application domains. Historically, the problems of classification and regression have gained the majority of attention in the field. In this thesis we focus on another type of learning problem, that of learning to rank. In learning to rank, the aim is from a set of past observations to learn a ranking function that can order new objects according to how well they match some underlying criterion of goodness. As an important special case of the setting, we can recover the bipartite ranking problem, corresponding to maximizing the area under the ROC curve (AUC) in binary classification. Ranking applications appear in a large variety of settings, examples encountered in this thesis include document retrieval in web search, recommender systems, information extraction and automated parsing of natural language. We consider the pairwise approach to learning to rank, where ranking models are learned by minimizing the expected probability of ranking any two randomly drawn test examples incorrectly. The development of computationally efficient kernel methods, based on this approach, has in the past proven to be challenging. Moreover, it is not clear what techniques for estimating the predictive performance of learned models are the most reliable in the ranking setting, and how the techniques can be implemented efficiently. The contributions of this thesis are as follows. First, we develop RankRLS, a computationally efficient kernel method for learning to rank, that is based on minimizing a regularized pairwise least-squares loss. In addition to training methods, we introduce a variety of algorithms for tasks such as model selection, multi-output learning, and cross-validation, based on computational shortcuts from matrix algebra. Second, we improve the fastest known training method for the linear version of the RankSVM algorithm, which is one of the most well established methods for learning to rank. Third, we study the combination of the empirical kernel map and reduced set approximation, which allows the large-scale training of kernel machines using linear solvers, and propose computationally efficient solutions to cross-validation when using the approach. Next, we explore the problem of reliable cross-validation when using AUC as a performance criterion, through an extensive simulation study. We demonstrate that the proposed leave-pair-out cross-validation approach leads to more reliable performance estimation than commonly used alternative approaches. Finally, we present a case study on applying machine learning to information extraction from biomedical literature, which combines several of the approaches considered in the thesis. The thesis is divided into two parts. Part I provides the background for the research work and summarizes the most central results, Part II consists of the five original research articles that are the main contribution of this thesis.

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Production and generation of electrical power is evolving to more environmental friendly technologies and schemes. Pushed by the increasing cost of fossil fuels, the operational costs of producing electrical power with fossil fuels and the effect in the environment, like pollution and global warming, renewable energy sources gain con-stant impulse into the global energy economy. In consequence, the introduction of distributed energy sources has brought a new complexity to the electrical networks. In the new concept of smart grids and decen-tralized power generation; control, protection and measurement are also distributed and requiring, among other things, a new scheme of communication to operate with each other in balance and improve performance. In this research, an analysis of different communication technologies (power line communication, Ethernet over unshielded twisted pair (UTP), optic fiber, Wi-Fi, Wi-MAX, and Long Term Evolution) and their respective characteristics will be carried out. With the objective of pointing out strengths and weaknesses from different points of view (technical, economical, deployment, etc.) to establish a richer context on which a decision for communication approach can be done depending on the specific application scenario of a new smart grid deployment. As a result, a description of possible optimal deployment solutions for communication will be shown considering different options for technologies, and a mention of different important considerations to be taken into account will be made for some of the possible network implementation scenarios.

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Active Magnetic Bearings offer many advantages that have brought new applications to the industry. However, similarly to all new technology, active magnetic bearings also have downsides and one of those is the low standardization level. This thesis is studying mainly the ISO 14839 standard and more specifically the system verification methods. These verifying methods are conducted using a practical test with an existing active magnetic bearing system. The system is simulated with Matlab using rotor-bearing dynamics toolbox, but this study does not include the exact simulation code or a direct algebra calculation. However, this study provides the proof that standardized simulation methods can be applied in practical problems.

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Tässä työssä esitetään venäläisen matemaatikon A.I. Shirshovin teorioita ja tuloksia sanojen kombinatoriikasta. Lisäksi näytetään miten ne soveltuvat PI-algebrojen maailmaan. Shirshovin tuloksia tarkasteltaessa käsitellään sanoja erillisinä kombinatorisina objekteina ja todistetaan Shirshovin Lemma, joka on tämän työn perusta. Lemmanmukaan tarpeeksi pitkille sanoille saadaan tiettyä säännönmukaisuutta ja se todistetaan kolme kertaa. Ensimmäisestä saadaan tarpeeksi pitkän sanan olemassaolo.Toinen todistus mukailee Shirshovin alkuperäistä todistusta. Kolmannessa todistuksessa annetaan tarpeeksi pitkälle sanalle paremmin käytäntöön soveltuva raja. Tämän jälkeen käsitellään sanoja algebrallisina objekteina. Työn päätuloksena todistetaan Shirshovin Korkeuslause, jonka mukaan jokainen äärellisesti generoidunPI-algebran alkio on sanojen ω1k1 ···ωdkd lineaarikombinaatio, missä sanojen ωi pi-tuudet sekä indeksi i ovat rajatut. Shirshovin Korkeuslauseesta seuraa suoraan positiivinen ratkaisu Kurochin ongelmaan PI-algebroilla sekä saadaan raja alkioiden lukumäärälle, jolla algebra generoituu moduliksi. Lisäksi esitetään toisena sovelluksena ilman todistuksia Shirshovin soveltuvuus Jacobsonin radikaalin nilpotenttisuuteen. Pääsääntöisenä lähteenä käytetään A. Kanel-Belowin ja L. H. Rowenin kirjaa: Computational aspects of polynomial identities.

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As classificações dos signos de C.S.Peirce começam a ser desenvolvidas em 1865 e se estendem a até, pelo menos, 1909. Vou apresentar o período que tem início em 1865, e possui dois momentos de intensa produção - "On a New List of Categories" e "On the Algebra of Logic: a contribution to the philosophy of notation". Em seguida apresento as dez classes de signos, uma morfologia que aparece no "Syllabus of Certain Topics of Logic", e é desenvolvida a partir de 1903. Meu propósito aqui é familiarizar o leitor com as intrincadas classificações sígnicas de Peirce.

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A fluorescence excitation spectrum of formic acid monomer (HCOOH) , has been recorded in the 278-246 nm region and has been attributed to an n >7r* electron promotion in the anti conformer. The S^< S^ electronic origins of the HCOOH/HCOOD/DCOOH/DCOOD isotopomers were assigned to weak bands observed at 37431.5/37461.5/37445.5/37479.3 cm'''. From a band contour analysis of the 0°^ band of HCOOH, the rotational constants for the excited state were estimated: A'=1.8619, B'=0.4073, and C'=0.3730 cm'\ Four vibrational modes, 1/3(0=0), j/^(0-C=0) , J/g(C-H^^^) and i/,(0-H^yJ were observed in the spectrum. The activity of the antisymmetric aldehyde wagging and hydroxyl torsional modes in forming progressions is central to the analysis, leading to the conclusion that the two hydrogens are distorted from the molecular plane, 0-C=0, in the upper S. state. Ab initio calculations were performed at the 6-3 IG* SCF level using the Gaussian 86 system of programs to aid in the vibrational assignments. The computations show that the potential surface which describes the low frequency OH torsion (twisting motion) and the CH wagging (molecular inversion) motions is complex in the S^ excited electronic state. The OH and CH bonds were calculated to be twisted with respect to the 0-C=0 molecular frame by 63.66 and 4 5.76 degrees, respectively. The calculations predicted the existence of the second (syn) rotamer which is 338 cm'^ above the equilibrium configuration with OH and CH angles displaced from the plane by 47.91 and 41.32 degrees.

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Given a heterogeneous relation algebra R, it is well known that the algebra of matrices with coefficient from R is relation algebra with relational sums that is not necessarily finite. When a relational product exists or the point axiom is given, we can represent the relation algebra by concrete binary relations between sets, which means the algebra may be seen as an algebra of Boolean matrices. However, it is not possible to represent every relation algebra. It is well known that the smallest relation algebra that is not representable has only 16 elements. Such an algebra can not be put in a Boolean matrix form.[15] In [15, 16] it was shown that every relation algebra R with relational sums and sub-objects is equivalent to an algebra of matrices over a suitable basis. This basis is given by the integral objects of R, and is, compared to R, much smaller. Aim of my thesis is to develop a system called ReAlM - Relation Algebra Manipulator - that is capable of visualizing computations in arbitrary relation algebras using the matrix approach.

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Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

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Relation algebras is one of the state-of-the-art means used by mathematicians and computer scientists for solving very complex problems. As a result, a computer algebra system for relation algebras called RelView has been developed at Kiel University. RelView works within the standard model of relation algebras. On the other hand, relation algebras do have other models which may have different properties. For example, in the standard model we always have L;L=L (the composition of two (heterogeneous) universal relations yields a universal relation). This is not true in some non-standard models. Therefore, any example in RelView will always satisfy this property even though it is not true in general. On the other hand, it has been shown that every relation algebra with relational sums and subobjects can be seen as matrix algebra similar to the correspondence of binary relations between sets and Boolean matrices. The aim of my research is to develop a new system that works with both standard and non-standard models for arbitrary relations using multiple-valued decision diagrams (MDDs). This system will implement relations as matrix algebras. The proposed structure is a library written in C which can be imported by other languages such as Java or Haskell.

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Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

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University of Toronto exams. These are in and envelope which is marked “Arts 1st year”. Included in this package are some text book pages [Latin] with the name Ham K. Woodruff written on them. The exams include: Anatomy, Arithmetic and Algebra, Medicine Chemistry, English, Euclid, French, Greek, Latin, Latin Grammar, Latin Prose (2 copies), Materia Medica and Therapeutics and Physiology for 1879. The exams for 1880 include Arithmetic and Algebra, Greek and Trigonometry. The 1881 Greek exam is also included. There is writing on some of the exams and some are worn and stained. The envelope is torn and stained and the textbook pages are slightly burned. This does not affect the text, 1879-1881.

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Associée à d'autres techniques observationnelles, la polarimétrie dans le visible ou dans le proche infrarouge permet d'étudier la morphologie des champs magnétiques à la périphérie de nombreuses régions de formation stellaire. A l'intérieur des nuages molécualires la morphologie des champs est connue par polarimétrie submillimétrique, mais rarement pour les mêmes régions. Habituellement, il manque une échelle spatiale intermédiaire pour pouvoir comparer correctement la morphologie du champ magnétique galactique avec celle située à l'intérieur des nuages moléculaires. -- Cette thèse propose les moyens nécessaires pour réaliser ce type d'analyse multi-échelle afin de mieux comprendre le rôle que peuvent jouer les champs magnétiques dans les processus de formation stellaire. La première analyse traite de la région GF 9. Vient ensuite une étude de la morphologie du champ magnétique dans les filaments OMC-2 et OMC-3 suivie d'une analyse multi-échelle dans le complexe de nuages moléculaires Orion A dont OMC-2 et OMC-3 font partie. -- La synthèse des résultats couvrant GF 9 et Orion A est la suivante. Les approches statistiques employées montrent qu'aux grandes échelles spatiales la morphologie des champs magnétiques est poloïdale dans la région GF 9, et probablement hélicoïdale dans la région Orion A. A l'échelle spatiale des enveloppes des nuages moléculaires, les champs magnétiques apparaissent alignés avec les champs situés à leur périphérie. A l'échelle spatiale des coeurs, le champ magnétique poloïdal environnant la région GF 9 est apparemment entraîné par le coeur en rotation, et la diffusion ambipolaire n'y semble pas effective actuellement. Dans Orion A, la morphologie des champs est difficilement détectable dans les sites actifs de formation d'OMC-2, ou bien très fortement contrainte par les effets de la gravité dans OMC-1. Des effets probables de la turbulence ne seont détectés dans aucune des régions observées. -- Les analyses multi-échelles suggèrent donc qu'indépendamment du stade évolutif et de la gamme de masse des régions de formation stellaires, le champ magnétique galactique subit des modifications de sa morphologie aux échelles spatiales comparables à celles des coeurs protostellaires, de la même façon que les propriétés structurelles des nuages moléculaires suivent des lois d'autosimilarité jusqu'à des échelles comparables à celles des coeurs.

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Soit G un groupe algébrique semi-simple sur un corps de caractéristique 0. Ce mémoire discute d'un théorème d'annulation de la cohomologie supérieure du faisceau D des opérateurs différentiels sur une variété de drapeaux de G. On démontre que si P est un sous-groupe parabolique de G, alors H^i(G/P,D)=0 pour tout i>0. On donne en fait trois preuves indépendantes de ce théorème. La première preuve est de Hesselink et n'est valide que dans le cas où le sous-groupe parabolique est un sous-groupe de Borel. Elle utilise un argument de suites spectrales et le théorème de Borel-Weil-Bott. La seconde preuve est de Kempf et n'est valide que dans le cas où le radical unipotent de P agit trivialement sur son algèbre de Lie. Elle n'utilise que le théorème de Borel-Weil-Bott. Enfin, la troisième preuve est attribuée à Elkik. Elle est valide pour tout sous-groupe parabolique mais utilise le théorème de Grauert-Riemenschneider. On présente aussi une construction détaillée du faisceau des opérateurs différentiels sur une variété.

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La construction d'un quotient, en topologie, est relativement simple; si $G$ est un groupe topologique agissant sur un espace topologique $X$, on peut considérer l'application naturelle de $X$ dans $X/G$, l'espace d'orbites muni de la topologie quotient. En géométrie algébrique, malheureusement, il n'est généralement pas possible de munir l'espace d'orbites d'une structure de variété. Dans le cas de l'action d'un groupe linéairement réductif $G$ sur une variété projective $X$, la théorie géométrique des invariants nous permet toutefois de construire un morphisme de variété d'un ouvert $U$ de $X$ vers une variété projective $X//U$, se rapprochant autant que possible d'une application quotient, au sens topologique du terme. Considérons par exemple $X\subseteq P^{n}$, une $k$-variété projective sur laquelle agit un groupe linéairement réductif $G$ et supposons que cette action soit induite par une action linéaire de $G$ sur $A^{n+1}$. Soit $\widehat{X}\subseteq A^{n+1}$, le cône affine au dessus de $\X$. Par un théorème de la théorie classique des invariants, il existe alors des invariants homogènes $f_{1},...,f_{r}\in C[\widehat{X}]^{G}$ tels que $$C[\widehat{X}]^{G}= C[f_{1},...,f_{r}].$$ On appellera le nilcone, que l'on notera $N$, la sous-variété de $\X$ définie par le locus des invariants $f_{1},...,f_{r}$. Soit $Proj(C[\widehat{X}]^{G})$, le spectre projectif de l'anneau des invariants. L'application rationnelle $$\pi:X\dashrightarrow Proj(C[f_{1},...,f_{r}])$$ induite par l'inclusion de $C[\widehat{X}]^{G}$ dans $C[\widehat{X}]$ est alors surjective, constante sur les orbites et sépare les orbites autant qu'il est possible de le faire; plus précisément, chaque fibre contient exactement une orbite fermée. Pour obtenir une application régulière satisfaisant les mêmes propriétés, il est nécessaire de jeter les points du nilcone. On obtient alors l'application quotient $$\pi:X\backslash N\rightarrow Proj(C[f_{1},...,f_{r}]).$$ Le critère de Hilbert-Mumford, dû à Hilbert et repris par Mumford près d'un demi-siècle plus tard, permet de décrire $N$ sans connaître les $f_{1},...,f_{r}$. Ce critère est d'autant plus utile que les générateurs de l'anneau des invariants ne sont connus que dans certains cas particuliers. Malgré les applications concrètes de ce théorème en géométrie algébrique classique, les démonstrations que l'on en trouve dans la littérature sont généralement données dans le cadre peu accessible des schémas. L'objectif de ce mémoire sera, entre autres, de donner une démonstration de ce critère en utilisant autant que possible les outils de la géométrie algébrique classique et de l'algèbre commutative. La version que nous démontrerons est un peu plus générale que la version originale de Hilbert \cite{hilbert} et se retrouve, par exemple, dans \cite{kempf}. Notre preuve est valide sur $C$ mais pourrait être généralisée à un corps $k$ de caractéristique nulle, pas nécessairement algébriquement clos. Dans la seconde partie de ce mémoire, nous étudierons la relation entre la construction précédente et celle obtenue en incluant les covariants en plus des invariants. Nous démontrerons dans ce cas un critère analogue au critère de Hilbert-Mumford (Théorème 6.3.2). C'est un théorème de Brion pour lequel nous donnerons une version un peu plus générale. Cette version, de même qu'une preuve simplifiée d'un théorème de Grosshans (Théorème 6.1.7), sont les éléments de ce mémoire que l'on ne retrouve pas dans la littérature.