The proof of Kontsevich's periodicity conjecture on noncommutative birational transformations

For an arbitrary associative unital ring RR, let J1J1 and J2J2 be the following noncommutative, birational, partly defined involutions on the set M3(R)M3(R) of 3×33×3 matrices over RR: J1(M)=M−1J1(M)=M−1 (the usual matrix inverse) and J2(M)jk=(Mkj)−1J2(M)jk=(Mkj)−1 (the transpose of the Hadamard inverse).

We prove the surprising conjecture by Kontsevich that (J2∘J1)3(J2∘J1)3 is the identity map modulo the DiagL×DiagRDiagL×DiagR action (D1,D2)(M)=D−11MD2(D1,D2)(M)=D1−1MD2 of pairs of invertible diagonal matrices. That is, we show that, for each MM in the domain where (J2∘J1)3(J2∘J1)3 is defined, there are invertible diagonal 3×33×3 matrices D1=D1(M)D1=D1(M) and D2=D2(M)D2=D2(M) such that (J2∘J1)3(M)=D−11MD2(J2∘J1)3(M)=D1−1MD2.

Epistemic Modality in Linguistic and Literature Essays in English : A comparative corpus-based study of modal verbs in student claims

This study is a corpus-based comparison between student essays written in the subject areas of English linguistics and literature at undergraduate level. They are 200 Bachelor degree theses submitted at a variety of university departments (such as English, Language and Literature, Humanities, Social and Intercultural Studies) in Sweden. The comparison concerns frequencies of core modal verbs and how often they occur together with the I, we and it subject pronouns and in the structures this/the [essay, study, project, thesis] when students attempt to communicate their personal claims. Quantitative and qualitative analyses of the essays show few similarities in the ways that core modal verbs appear in both disciplines. The results indicate mainly distinct differences, especially in relation to clusters and variation of performative verbs. Specific patterns in the ways that students use core modal verbs as hedges have also been identified.

Numerical analysis of the modal coupling at low resonances in a Colombian Andean Bandola in C using the finite element method

The work presented in this thesis is concerned with the dynamical behavior of a CBandola's acoustical box at low resonances -- Two models consisting of two and three coupled oscillators are proposed in order to analyse the response at the first two and three resonances, respectively -- These models describe the first resonances in a bandola as a combination of the lowest modes of vibration of enclosed air, top and back plates -- Physically, the coupling between these elements is caused by the fluid-structure interaction that gives rise to coupled modes of vibration for the assembled resonance box -- In this sense, the coupling in the models is expressed in terms of the ratio of effective areas and masses of the elements which is an useful parameter to control the coupling -- Numerical models are developed for the analysis of modal coupling which is performed using the Finite Element Method -- First, it is analysed the modal behavior of separate elements: enclosed air, top plate and back plate -- This step is important to identify participating modes in the coupling -- Then, a numerical model of the resonance box is used to compute the coupled modes -- The computation of normal modes of vibration was executed in the frequency range of 0-800Hz -- Although the introduced models of coupled oscillators only predict maximum the first three resonances, they also allow to study qualitatively the coupling between the rest of the computed modes in the range -- Considering that dynamic response of a structure can be described in terms of the modal parameters, this work represents, in a good approach, the basic behavior of a CBandola, although experimental measurements are suggested as further work to verify the obtained results and get more information about some characteristics of the coupled modes, for instance, the phase of vibration of the air mode and the radiation e ciency

Human traces in urban places.

Over the last two centuries many major cities have undergone large-scale modernisation that has led to the growing sense of homogenisation associated with such locales across the globe. The fractal logic that is at the heart of so many urban settings, where the whole system is made up of parts that are identical to the whole, seems to serve in making anonymous everyday experiences. Public transport and its corresponding street furniture, if thoughtfully designed and planned, has the potential to form an integral element in the promotion of a sense of identity, interconnectedness and flow within a city. Furthermore, bus stops, benches, litter bins, curb-sides, posts and pavements, to mention a few, offer interesting cases to consider how people truly engage with contemporary urban spaces. These objects—part of routine and made familiar—are elements of daily lives that are ingredients towards visual and multi-modal experiences. In addition, these are places where individuals encounter sociality and materiality in ordinary and sometimes extraordinary ways. This paper uses a visual ethnographic approach towards exploring the human traces of routine activities that have an impact on the cityscape. An Investigation of these details found within the urban landscape lead us towards understanding how we engage with and navigate cities. This is essentially an urban archaeological study that looks to reveal how non-designed phenomenon in urban places can contribute to our image of a city, providing a reflection on homogeneity within the built environment. Our visual ethnography focuses on six major cities: two each in Britain, Europe and North America. The findings of this work illustrate through visual analyses three key characteristics: first, how urban spaces are transformed intentionally and unintentionally; second, how transformations are practical, functional, beautiful and sometimes ridiculous; third, how transformations reveal values around visual and multi-modal experiences inherent to people.

Mapping and Displaying Structural Transformations between XML and PDF

Documents are often marked up in XML-based tagsets to delineate major structural components such as headings, paragraphs, figure captions and so on, without much regard to their eventual displayed appearance. And yet these same abstract documents, after many transformations and 'typesetting' processes, often emerge in the popular format of Adobe PDF, either for dissemination or archiving. Until recently PDF has been a totally display-based document representation, relying on the underlying PostScript semantics of PDF. Early versions of PDF had no mechanism for retaining any form of abstract document structure but recent releases have now introduced an internal structure tree to create the so called 'Tagged PDF'. This paper describes the development of a plugin for Adobe Acrobat which creates a two-window display. In one window is shown an XML document original and in the other its Tagged PDF counterpart is seen, with an internal structure tree that, in some sense, matches the one seen in XML. If a component is highlighted in either window then the corresponding structured item, with any attendant text, is also highlighted in the other window. Important applications of correctly Tagged PDF include making PDF documents reflow intelligently on small screen devices and enabling them to be read out in correct reading order, via speech synthesiser software, for the visually impaired. By tracing structure transformation from source document to destination one can implement the repair of damaged PDF structure or the adaptation of an existing structure tree to an incrementally updated document.

Structure, transports and transformations of the water masses in the Atlantic Subpolar Gyre

We discuss the distributions and transports of the main water masses in the North Atlantic Subpolar Gyre (NASPG) for the mean of the period 2002–2010 (OVIDE sections 2002–2010 every other year), as well as the inter-annual variability of the water mass structure from 1997 (4x and METEOR sections) to 2010. The water mass structure of the NASPG, quantitatively assessed by means of an Optimum MultiParameter analysis (with 14 water masses), was combined with the velocity fields resulting from previous studies using inverse models to obtain the water mass volume transports. We also evaluate the relative contribution to the Atlantic Meridional Overturning Circulation (AMOC) of the main water masses characterizing the NASPG, identifying the water masses that contribute to the AMOC variability. The reduction of the magnitude of the upper limb of the AMOC between 1997 and the 2000s is associated with the reduction in the northward transport of the Central Waters. This reduction of the northward flow of the AMOC is partially compensated by the reduction of the southward flow of the lower limb of the AMOC, associated with the decrease in the transports of Polar Intermediate Water and Subpolar Mode Water (SPMW) in the Irminger Basin. We also decompose the flow over the Reykjanes Ridge from the East North Atlantic Basin to the Irminger Basin (9.4 ± 4.7 Sv) into the contributions of the Central Waters (2.1 ± 1.8 Sv), Labrador Sea Water (LSW, 2.4 ± 2.0 Sv), Subarctic Intermediate Water (SAIW, 4.0 ± 0.5 Sv) and Iceland–Scotland Overflow Water (ISOW, 0.9 ± 0.9 Sv). Once LSW and ISOW cross over the Reykjanes Ridge, favoured by the strong mixing around it, they leave the Irminger Basin through the deep-to-bottom levels. The results also give insights into the water mass transformations within the NASPG, such as the contribution of the Central Waters and SAIW to the formation of the different varieties of SPMW due to air–sea interaction.

Modal Control of Vibration in Rotating Machines and Other Generally Damped Systems

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual o-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper a method to utilise modal control using the decoupled second order matrix equations involving nonclassical damping is proposed. An example of modal control sucessfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components.

Modal Control of Vibration in Rotating Machines and Other Generally Damped Systems

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual off-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper a method to utilise modal control using the decoupled second order matrix equations involving non-classical damping is proposed. An example of modal control successfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components.

In vitro studies of drug transformations: application to forensic toxicology

The forensic toxicologist faces challenges in the detection of drugs and poisons in biological samples due to transformations which occur both during life and after death. For example, changes can result from drug metabolism during life or from the use of formalin solution for post mortem embalming purposes. The former requires the identification of drug metabolites and the latter the identification of chemical reaction products in order to know which substances had been administered. The work described in this thesis was aimed at providing ways of tackling these challenges and was divided into two parts. Part 1 investigated the use of in vitro drug metabolism by human liver microsomes (HLM) to obtain information on drug metabolites and Part 2 investigated the chemical reactions of drugs and a carbamate pesticide with formalin solution and formalin-blood. The initial aim of part I was to develop an in vitro metabolism method using HLM, based on a literature review of previous studies of this type. MDMA was chosen as a model compound to develop the HLM method because its metabolism was known and standards of its metabolites were commercially available. In addition, a sensitive and selective method was developed for the identification and quantitation of hydrophilic phase I drug metabolites using LC/MS/MS with a conventional reverse-phase (C18) column. In order to obtain suitable retention factors for polar drug metabolites on this column, acetyl derivatives were evaluated for converting the metabolites to more lipophilic compounds and an optimal separation system was developed. Acetate derivatives were found to be stable in the HPLC mobile phase and to provide good chromatographic separation of the target analytes. In vitro metabolism of MDMA and, subsequently, of other drugs involved incubation of 4 µg drug substance in pH 7.4 buffer with an NADPH generating system (NGS) at 37oC for 90 min with addition of more NGS after 30 min. The reaction was stopped at 90 min by the addition of acetonitrile before extraction of the metabolites. Acetate derivatives of MDMA metabolites were identified by LC/MS/MS using multiple reaction monitoring (MRM). Three phase I metabolites (both major and minor metabolites) of MDMA were detected in HLM samples. 3,4-dihydroxy-methamphetamine and 4-hydroxy-3-methoxymethamphetamine were found to be major metabolites of MDMA whereas 3,4-methylenedioxyamphetamine was found to be a minor metabolite. Subsequently, ten MDMA positive urines were analysed to compare the metabolite patterns with those produced by HLM. An LC/MS method for MDMA and its metabolites in urine samples was developed and validated. The method demonstrated good linearity, accuracy and precision and insignificant matrix effects, with limits of quantitation of 0.025 µg/ml. Moreover, derivatives of MDMA and its metabolites were quantified in all 10 positive human urine samples. The urine metabolite pattern was found to be similar to that from HLM. The second aim of Part 1 was to use the HLM system to study the metabolism of some new psychoactive substances, whose misuse worldwide has necessitated the development of analytical methods for these drugs in biological specimens. Methylone and butylone were selected as representative cathinones and para-methoxyamphetamine (PMA) was chosen as a representative ring-substituted amphetamine, because of the involvement of these drugs in recent drug-related deaths, because of a relative lack of information on their metabolism, and because reference standards of their metabolites were not commercially available. An LC/MS/MS method for the analysis of methylone, butylone, PMA and their metabolites was developed. Three phase I metabolites of methylone and butylone were detected in HLM samples. Ketone reduction to β-OH metabolites and demethylenation to dihydroxy-metabolites were found to be major phase I metabolic pathways of butylone and methylone whereas N-demethylation to nor-methylone and nor-butylone were found to be minor pathways. Also, demethylation to para-hydroxyamphetamine was found to be a major phase I metabolic pathway of PMA whereas β-hydroxylation to β-OH-PMA was found to be a minor pathway. Formaldehyde is used for embalming, to reduce decomposition and preserve cadavers, especially in tropical countries such as Thailand. Drugs present in the body can be exposed to formaldehyde resulting in decreasing concentrations of the original compounds and production of new substances. The aim of part II of the study was to evaluate the in vitro reactions of formaldehyde with selected drug groups including amphetamines (amphetamine, methamphetamine and MDMA), benzodiazepines (alprazolam and diazepam), opiates (morphine, hydromorphone, codeine and hydrocodone) and with a carbamate insecticide (carbosulfan). The study would identify degradation products to serve as markers for the parent compounds when these were no longer detectable. Drugs standards were spiked in 10% formalin solution and 10% formalin blood. Water and whole blood without formalin were used for controls. Samples were analysed by LC/MS/MS at different times from the start, over periods of up to 30 days. Amphetamine, methamphetamine and MDMA were found to rapidly convert to methamphetamine, DMA and MDDMA respectively, in both formalin solution and formalin blood, confirming the Eschweiler-Clarke reaction between amine-containing compounds and formaldehyde. Alprazolam was found to be unstable whereas diazepam was found to be stable in both formalin solution and water. Both were found to hydrolyse in formalin solution and to give open-ring alprazolam and open-ring diazepam. Other alprazolam conversion products attached to paraformaldehyde were detected in both formalin solution and formalin blood. Morphine and codeine were found to be more stable than hydromorphone and hydrocodone in formalin solution. Conversion products of hydromorphone and hydrocodone attached to paraformaldehyde were tentatively identified in formalin solution. Moreover, hydrocodone and hydromorphone rapidly decreased within 24 h in formalin blood and could not be detected after 7 days. Carbosulfan was found to be unstable in formalin solution and was rapidly hydrolysed within 24 h, whereas in water it was stable up to 48 h. Carbofuran was the major degradation product, plus smaller amounts of other products, 3-ketocarbofuran and 3-hydrocarbofuran. By contrast, carbosulfan slowly hydrolysed in formalin-blood and was still detected after 15 days. It was concluded that HLM provide a useful tool for human drug metabolism studies when ethical considerations preclude their controlled administration to humans. The use of chemical derivatisation for hydrophilic compounds such as polar drug metabolites for analysis by LC/MS/MS with a conventional C18 column is effective and inexpensive, and suitable for routine use in the identification and quantitation of drugs and their metabolites. The detection of parent drugs and their metabolites or conversion and decomposition products is potentially very useful for the interpretation of cases in forensic toxicology, especially when the original compounds cannot be observed.

Wondrous transformations: rereading and rewriting wonder in contemporary anglophone and francophone fairy tales

This thesis compares contemporary anglophone and francophone rewritings of traditional fairy tales for adults. Examining material dating from the 1990s to the present, including novels, novellas, short stories, comics, televisual and filmic adaptations, this thesis argues that while the revisions studied share similar themes and have comparable aims, the methods for inducing wonder (where wonder is defined as the effect produced by the text rather than simply its magical contents) are diametrically opposed, and it is this opposition that characterises the difference between the two types of rewriting. While they all engage with the hybridity of the fairy-tale genre, the anglophone works studied tend to question traditional narratives by keeping the fantasy setting, while francophone works debunk the tales not only in relation to questions of content, but also aesthetics. Through theoretical, historical, and cultural contextualisation, along with close readings of the texts, this thesis aims to demonstrate the existence of this francophone/anglophone divide and to explain how and why the authors in each tradition tend to adopt such different views while rewriting similar material. This division is the guiding thread of the thesis and also functions as a springboard to explore other concepts such as genre hybridity, reader-response, and feminism. The thesis is divided into two parts; the first three chapters work as an in-depth literature review: after examining, in chapters one and two, the historical and contemporary cultural field in which these works were created, chapter three examines theories of fantasy and genre hybridity. The second part of the thesis consists of textual studies and comparisons between francophone and anglophone material and is built on three different approaches. The first (chapter four) looks at selected texts in relation to questions of form, studying the process of world building and world creation enacted when authors combine and rewrite several fairy tales in a single narrative world. The second (chapter five) is a thematic approach which investigates the interactions between femininity, the monstrous, and the wondrous in contemporary tales of animal brides. Finally, chapter six compares rewritings of the tale of ‘Bluebeard’ with a comparison hinged on the representation of the forbidden room and its contents: Bluebeard’s cabinet of wonder is one that he holds sacred, one where he sublimates his wives’ corpses, and it is the catalyst of wonder, terror, and awe. The three contextual chapters and the three text-based studies work towards tracing the tangible existence of the division postulated between francophone and anglophone texts, but also the similarities that exist between the two cultural fields and their roles in the renewal of the fairy-tale genre.

Recyclage et transformations du religieux dans le roman québécois contemporain (Maleficium de Martine Desjardins et L’âge de Pierre de Pierre Gariépy)

L'influence de l'Église catholique sur la vie des Québécois, autrefois dominante, s'est beaucoup amenuisée au cours des dernières décennies. Si tel est le cas, les signes, les motifs, les images et les mots de la religion n’ont pas, quant à eux, déserté l’espace symbolique. Ils sont les traces d’un héritage et squattent l'imaginaire social (Pierre Popovic) du Québec contemporain. À ce titre, ils peuvent être mobilisés, maniés, détournés, resémantisés par la littérature. Ce mémoire a pour but d’étudier ces reliques imaginaires de la religion chrétienne, laquelle est considérée en tant qu'Église et en tant que mythologie, dans deux romans québécois publiés en 2011 : L'âge de Pierre de Pierre Gariépy et Maleficium de Martine Desjardins. Dans une perspective sociocritique, il analyse les rapports à l'autorité, à l'érotisme, à la morale, aux étrangers et à l'écriture tels qu'ils sont travaillés par les « mises en texte » (Claude Duchet) dans ces œuvres. L’étude démontre que les deux romans thématisent la religion et la tiennent pour un matériau familier et malléable à merci, non pour entretenir un patrimoine ni par nostalgie, mais afin de porter un regard critique sur la société québécoise contemporaine. D’une certaine manière, ils disent que celle-ci est toujours pieuse, mais que les croyances qui la traversent sont à chercher désormais du côté de la politique, des médias et du commerce.

Introducción al análisis modal operacional

Es frecuente que las estructuras, una vez realizadas, muestren diferencias, respecto de su concepción original que, en ocasiones, pueden hacer necesaria una intervención posterior con el objetivo de corregir su comportamiento estructural. En otras ocasiones estas actuaciones se hacen necesarias como consecuencias de deterioros sufridos durante la vida útil de la estructura (daño estructural) o como consecuencia de cambios en el propio uso de la estructura. En cualquier caso, tanto en las situaciones descritas, como en muchas otras, la estructura ha de someterse a un proceso de monitorización que nos permita obtener información experimental de ciertos parámetros estructurales con los que afinar los modelos numéricos que de ellas se realizan. Esta jornada se ha estructurado en cuatro conferencias en las que investigadores de las universidades de Sevilla y Córdoba nos darán una visión divulgativa del problema, nos acercarán a alguna de sus técnicas y nos mostrarán algún caso práctico de gran interés. En la segunda conferencia, el profesor de la Universidad de Córdoba Dr. D. Rafael Castro Triguero, Ingeniero de Caminos, Canales y Puertos y con una amplia experiencia en monitorización de estructuras, mostrará las bases de alguna de estas técnicas y cómo, de la información obtenida, pueden inferirse parámetros estructurales para mejorar los modelos y/o detectar daños estructurales.

Identificación de daño en estructuras históricas mediante análisis modal operacional (OMA)

Es frecuente que las estructuras, una vez realizadas, muestren diferencias, respecto de su concepción original que, en ocasiones, pueden hacer necesaria una intervención posterior con el objetivo de corregir su comportamiento estructural. En otras ocasiones estas actuaciones se hacen necesarias como consecuencias de deterioros sufridos durante la vida útil de la estructura (daño estructural) o como consecuencia de cambios en el propio uso de la estructura. En cualquier caso, tanto en las situaciones descritas, como en muchas otras, la estructura ha de someterse a un proceso de monitorización que nos permita obtener información experimental de ciertos parámetros estructurales con los que afinar los modelos numéricos que de ellas se realizan. Esta jornada se ha estructurado en cuatro conferencias en las que investigadores de las universidades de Sevilla y Córdoba nos darán una visión divulgativa del problema, nos acercarán a alguna de sus técnicas y nos mostrarán algún caso práctico de gran interés. En la tercera conferencia, el profesor de la Universidad de Sevilla Dr. D. Víctor Jesús Compán Cardiel, Arquitecto, mostró cómo la técnica de monitorización conocida pos sus siglas en inglés OMA puede ser aplicada a estructuras antiguas, que forman parte del patrimonio, para aprender de estas estructuras y, llegado el caso, detectar daño en las mismas y poder tomar las medidas necesarias para mejorar su capacidad portante y, con ello, incrementar el tiempo por el que podremos disfrutar de estos singulares edificios.

Multi-modal ultrasound imaging for breast cancer detection

This work describes preliminary results of a two-modality imaging system aimed at the early detection of breast cancer. The first technique is based on compounding conventional echographic images taken at regular angular intervals around the imaged breast. The other modality obtains tomographic images of propagation velocity using the same circular geometry. For this study, a low-cost prototype has been built. It is based on a pair of opposed 128-element, 3.2 MHz array transducers that are mechanically moved around tissue mimicking phantoms. Compounded images around 360 degrees provide improved resolution, clutter reduction, artifact suppression and reinforce the visualization of internal structures. However, refraction at the skin interface must be corrected for an accurate image compounding process. This is achieved by estimation of the interface geometry followed by computing the internal ray paths. On the other hand, sound velocity tomographic images from time of flight projections have been also obtained. Two reconstruction methods, Filtered Back Projection (FBP) and 2D Ordered Subset Expectation Maximization (2D OSEM), were used as a first attempt towards tomographic reconstruction. These methods yield useable images in short computational times that can be considered as initial estimates in subsequent more complex methods of ultrasound image reconstruction. These images may be effective to differentiate malignant and benign masses and are very promising for breast cancer screening. (C) 2015 The Authors. Published by Elsevier B.V.