On restricted families of projections in ℝ3

We study projections onto non-degenerate one-dimensional families of lines and planes in R 3 . Using the classical potential theoretic approach of R. Kaufman, one can show that the Hausdorff dimension of at most 12 -dimensional sets [Math Processing Error] is typically preserved under one-dimensional families of projections onto lines. We improve the result by an ε , proving that if [Math Processing Error], then the packing dimension of the projections is almost surely at least [Math Processing Error]. For projections onto planes, we obtain a similar bound, with the threshold 12 replaced by 1 . In the special case of self-similar sets [Math Processing Error] without rotations, we obtain a full Marstrand-type projection theorem for 1-parameter families of projections onto lines. The [Math Processing Error] case of the result follows from recent work of M. Hochman, but the [Math Processing Error] part is new: with this assumption, we prove that the projections have positive length almost surely.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

Isotone Recursive Methods for Overlapping Generation Models with Stochastic Nonclassical Production

Based on an order-theoretic approach, we derive sufficient conditions for the existence, characterization, and computation of Markovian equilibrium decision processes and stationary Markov equilibrium on minimal state spaces for a large class of stochastic overlapping generations models. In contrast to all previous work, we consider reduced-form stochastic production technologies that allow for a broad set of equilibrium distortions such as public policy distortions, social security, monetary equilibrium, and production nonconvexities. Our order-based methods are constructive, and we provide monotone iterative algorithms for computing extremal stationary Markov equilibrium decision processes and equilibrium invariant distributions, while avoiding many of the problems associated with the existence of indeterminacies that have been well-documented in previous work. We provide important results for existence of Markov equilibria for the case where capital income is not increasing in the aggregate stock. Finally, we conclude with examples common in macroeconomics such as models with fiat money and social security. We also show how some of our results extend to settings with unbounded state spaces.

Toward reduction of artifacts in fused images

Most fusion satellite image methodologies at pixel-level introduce false spatial details, i.e.artifacts, in the resulting fusedimages. In many cases, these artifacts appears because image fusion methods do not consider the differences in roughness or textural characteristics between different land covers. They only consider the digital values associated with single pixels. This effect increases as the spatial resolution image increases. To minimize this problem, we propose a new paradigm based on local measurements of the fractal dimension (FD). Fractal dimension maps (FDMs) are generated for each of the source images (panchromatic and each band of the multi-spectral images) with the box-counting algorithm and by applying a windowing process. The average of source image FDMs, previously indexed between 0 and 1, has been used for discrimination of different land covers present in satellite images. This paradigm has been applied through the fusion methodology based on the discrete wavelet transform (DWT), using the à trous algorithm (WAT). Two different scenes registered by optical sensors on board FORMOSAT-2 and IKONOS satellites were used to study the behaviour of the proposed methodology. The implementation of this approach, using the WAT method, allows adapting the fusion process to the roughness and shape of the regions present in the image to be fused. This improves the quality of the fusedimages and their classification results when compared with the original WAT method

Theoretical analysis and numerical verification of the consistency of viscous smoothed-particle-hydrodynamics formulations in simulating free-surface flows

The theoretical formulation of the smoothed particle hydrodynamics (SPH) method deserves great care because of some inconsistencies occurring when considering free-surface inviscid flows. Actually, in SPH formulations one usually assumes that (i) surface integral terms on the boundary of the interpolation kernel support are neglected, (ii) free-surface conditions are implicitly verified. These assumptions are studied in detail in the present work for free-surface Newtonian viscous flow. The consistency of classical viscous weakly compressible SPH formulations is investigated. In particular, the principle of virtual work is used to study the verification of the free-surface boundary conditions in a weak sense. The latter can be related to the global energy dissipation induced by the viscous term formulations and their consistency. Numerical verification of this theoretical analysis is provided on three free-surface test cases including a standing wave, with the three viscous term formulations investigated.

The ionized gas in the CALIFA early-type galaxies I. Mapping two representative cases: NGC 6762 and NGC 5966

As part of the ongoing CALIFA survey, we have conducted a thorough bidimensional analysis of the ionized gas in two E/S0 galaxies, NGC 6762 and NGC 5966, aiming to shed light on the nature of their warm ionized ISM. Specifically, we present optical (3745–7300 Å) integral field spectroscopy obtained with the PMAS/PPAK integral field spectrophotometer. Its wide field-of-view (1′ × 1′) covers the entire optical extent of each galaxy down to faint continuum surface brightnesses. To recover the nebular lines, we modeled and subtracted the underlying stellar continuum from the observed spectra using the STARLIGHT spectral synthesis code. The pure emission-line spectra were used to investigate the gas properties and determine the possible sources of ionization. We show the advantages of IFU data in interpreting the complex nature of the ionized gas in NGC 6762 and NGC 5966. In NGC 6762, the ionized gas and stellar emission display similar morphologies, while the emission line morphology is elongated in NGC 5966, spanning ~6 kpc, and is oriented roughly orthogonal to the major axis of the stellar continuum ellipsoid. Whereas gas and stars are kinematically aligned in NGC 6762, the gas is kinematically decoupled from the stars in NGC 5966. A decoupled rotating disk or an “ionization cone” are two possible interpretations of the elongated ionized gas structure in NGC 5966. The latter would be the first “ionization cone” of such a dimension detected within a weak emission-line galaxy. Both galaxies have weak emission-lines relative to the continuum[EW(Hα) ≲ 3 Å] and have very low excitation, log([OIII]λ5007/Hβ) ≲ 0.5. Based on optical diagnostic ratios ([OIII]λ5007/Hβ, [NII]λ6584/Hα, [SII]λ6717, 6731/Hα, [OI]λ6300/Hα), both objects contain a LINER nucleus and an extended LINER-like gas emission. The emission line ratios do not vary significantly with radius or aperture, which indicates that the nebular properties are spatially homogeneous. The gas emission in NGC 6762 can be best explained by photoionization by pAGB stars without the need of invoking any other excitation mechanism. In the case of NGC 5966, the presence of a nuclear ionizing source seems to be required to shape the elongated gas emission feature in the “ionization cone” scenario, although ionization by pAGB stars cannot be ruled out. Further study of this object is needed to clarify the nature of its elongated gas structure.

Regularity and relaxed problems of minimizing biharmonic maps into spheres

For n >= 5 and k >= 4, we show that any minimizing biharmonic map from Omega subset of R-n to S-k is smooth off a closed set whose Hausdorff dimension is at most n - 5. When n = 5 and k = 4, for a parameter lambda is an element of [0, 1] we introduce lambda-relaxed energy H-lambda of the Hessian energy for maps in W-2,W-2 (Omega; S-4) so that each minimizer u(lambda) of H-lambda is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of H-lambda for lambda is an element of [0, 1).

Identifying and correcting non-Markov states in peptide conformational dynamics

Conformational transitions in proteins define their biological activity and can be investigated in detail using the Markov state model. The fundamental assumption on the transitions between the states, their Markov property, is critical in this framework. We test this assumption by analyzing the transitions obtained directly from the dynamics of a molecular dynamics simulated peptide valine-proline-alanine-leucine and states defined phenomenologically using clustering in dihedral space. We find that the transitions are Markovian at the time scale of ˜ 50 ps and longer. However, at the time scale of 30–40 ps the dynamics loses its Markov property. Our methodology reveals the mechanism that leads to non-Markov behavior. It also provides a way of regrouping the conformations into new states that now possess the required Markov property of their dynamics.

Modelling data and voice traffic over IP networks using continuous-time Markov models

Common approaches to IP-traffic modelling have featured the use of stochastic models, based on the Markov property, which can be classified into black box and white box models based on the approach used for modelling traffic. White box models, are simple to understand, transparent and have a physical meaning attributed to each of the associated parameters. To exploit this key advantage, this thesis explores the use of simple classic continuous-time Markov models based on a white box approach, to model, not only the network traffic statistics but also the source behaviour with respect to the network and application. The thesis is divided into two parts: The first part focuses on the use of simple Markov and Semi-Markov traffic models, starting from the simplest two-state model moving upwards to n-state models with Poisson and non-Poisson statistics. The thesis then introduces the convenient to use, mathematically derived, Gaussian Markov models which are used to model the measured network IP traffic statistics. As one of the most significant contributions, the thesis establishes the significance of the second-order density statistics as it reveals that, in contrast to first-order density, they carry much more unique information on traffic sources and behaviour. The thesis then exploits the use of Gaussian Markov models to model these unique features and finally shows how the use of simple classic Markov models coupled with use of second-order density statistics provides an excellent tool for capturing maximum traffic detail, which in itself is the essence of good traffic modelling. The second part of the thesis, studies the ON-OFF characteristics of VoIP traffic with reference to accurate measurements of the ON and OFF periods, made from a large multi-lingual database of over 100 hours worth of VoIP call recordings. The impact of the language, prosodic structure and speech rate of the speaker on the statistics of the ON-OFF periods is analysed and relevant conclusions are presented. Finally, an ON-OFF VoIP source model with log-normal transitions is contributed as an ideal candidate to model VoIP traffic and the results of this model are compared with those of previously published work.

Performing Irishness: translations of Irish drama for the Galician stage (1921-2011)

This PhD thesis provides a detailed analysis of the role and significance of Irish drama in the Galician cultural context, from the early twentieth century onwards, through scrutiny of key works translated, adapted and mediated for the Galician stage. Drawing primarily on the theoretical framework of Descriptive Translation Studies, informed by Polysystems theory (Toury), Post-colonial Translation, research on processes of cultural translation (Bassnett, Lefevere, Venuti, Aaltonen), as well as careful comparative attention to the specificities of literary, theatrical and cultural context, I examine the factors governing the incorporation, reshaping and reception of twentieth century Irish plays in Galicia in order to produce a cultural history of the representation of Ireland on the Galician stage. Focusing on the five key periods I have identified in the translation/reception of Irish drama in Galicia, as represented in specific versions of plays by Yeats, Synge, O’Casey and McDonagh, my thesis examines in detail the particular linguistic, sociopolitical, theatrical and cultural dimensions of each rewriting and/or restaging in order to uncover the ways in which Irish identity is perceived, constructed and performed in a Galician context. Moving beyond the literary, historical and philological focus of existing studies of the reception of Irish literature and foreign dramatic texts in the Galician system, my own approach draws on Theatre and Performance Studies to attend also to the performative dimension of these processes of cultural adaptation and reception, giving full account of the different agents involved in theatre translation as a rich and complex process of multivalent cultural mediation.

Empowering development: capabilities and Latin American critical traditions

This thesis theoretically and critically examines the move towards people-centred approaches to development. It offers a critical examination of the work of Amartya Sen using theoretical resources emerging from Latin American traditions. Amartya Sen’s calls to understand Development as Freedom (1999) have significantly influenced mainstream development thinking and practice, constituting the clearest example of people-centred approaches to development today. Overcoming the limitations of previous state-centred notions of development articulated around ideas of economic growth, in Sen’s Capability Approach (CA) development is seen as a process of expanding the real freedoms that people enjoy. In this understanding, the agency of development shifts from the state to individuals and the analytic focus moves from economic growth to individual capabilities. In this manner, this framework is structured towards the central goal of empowerment, wherein the expansion of capabilities is seen both as the means and end of development. Since its inception, the widespread support for the CA has allowed for the expansion of ethical considerations within mainstream development thinking. Even while the remarkable advances offered by Sen’s work should be praised, this thesis argues that these have come with new limitations. These limitations stem from, what is termed here, a “Paradox of Empowerment” that effectively encloses Sen’s approach within Western notions of development. While Sen’s approach is poised to provide a theoretical framework that is built on the expansion of freedom and individual agency, there is little agency here to move beyond the ideas of development fundamentally linked to liberal democracies and market economies. This thesis engages with several critical traditions from Latin America, recovering their often undervalued insights for development thinking. Crucially, this engagement provides the critical framework to illustrate the aforementioned paradox and explore multiple dimensions of empowerment central for contemporary development thinking and practice. In this, the thesis engages Sen’s work with the Liberation Theology of Gustavo Gutierrez, with Paulo Freire’s Critical Pedagogy and with the contemporary discussions of ‘Buen Vivir’ associated with Indigenous philosophies of the Andean region. Throughout its chapters,it uncovers the conceptual baggage within the Paradox of Empowerment in Sen’s work and examines the ethical challenges and boundaries of this approach in relation to the collective dimension of development processes, the possibilities for structural transformation and concerns for sustainability. Progressively engaging the different dimensions of this paradox, this thesis advances the recovery of the transformative potential of the ideas of empowerment for development.

Bridging Perspectives

People’s ability to change their social and economic circumstances may be constrained by various forms of social, cultural and political domination. Thus to consider a social actor’s particular lifeworld in which the research is embedded assists in the understanding of how and why different trajectories of change occur or are hindered and how those changes fundamentally affect livelihood opportunities and constraints. In seeking to fulfill this condition this thesis adopted an actor-oriented approach to the study of rural livelihoods. A comprehensive livelihoods study requires grasping how social reality is being historically constituted. That means to understand how the interaction of modes of production and symbolical reproduction produces the socio-space. Research is here integrated to action through the facilitation of farmer groups. The overall aim of the groups was to prompt agency, as essential conditions to build more resilient livelihoods. The smallholder farmers in the Mabalane District of Mozambique are located in a remote semi-arid area. Their livelihoods customarily depend at least as much on livestock as on (mostly) rain-fed food crops. Increased climate variability exerts pressure on the already vulnerable production system. An extensive 10-month duration of participant observation divided into 3 periods of fieldwork structured the situated multi-method approach that drew on a set of interview categories. The actor-oriented appraisal of livelihoods worked in building a mutually shared definition of the situation. This reflection process was taken up by the facilitation of the farmer groups, one in Mabomo and one in Mungazi, which used an inquiry iteratively combining individual interviews and facilitated group meetings. Integration of action and reflection was fundamental for group constitution as spaces for communicative action. They needed to be self-organized and to achieve understanding intersubjectively, as well as to base action on cooperation and coordination. Results from this approach focus on how learning as collaboratively generated was enabled, or at times hindered, in (a) selecting meaningful options to test; (b) in developing mechanisms for group functioning; and (c) in learning from steering the testing of options. The study of livelihoods looked at how the different assets composing livelihoods are intertwined and how the increased severity of dry spells is contributing to escalated food insecurity. The reorganization of the social space, as households moved from scattered homesteads to form settlements, further exerts pressure on the already scarce natural resource-based livelihoods. Moreover, this process disrupted a normative base substantiating the way that the use of resources is governed. Hence, actual livelihood strategies and response mechanisms turn to diversification through income-generating activities that further increase pressure on the resource-base in a rather unsustainable way. These response mechanisms are, for example, the increase in small-livestock keeping, which has easier conversion to cash, and charcoal production. The latter results in ever more precarious living and working conditions. In the majority of the cases such responses are short-term and reduce future opportunities in a downward spiral of continuously decreasing assets. Thus, by indicating the failure of institutions in the mediation of smallholders’ adaptive capabilities, the livelihood assessment in Mabomo and Mungazi sheds light on the complex underlying structure of present day social vulnerability, linking the macro-context to the actual situation. To assist in breaking this state of “subordination”, shaped by historical processes, weak institutions and food insecurity, the chosen approach to facilitation of farmer groups puts farmer knowledge at the center of an evolving process of intersubjective co-construction of knowledge towards emancipation.

Geometric properties of 2-dimensional minimal surfaces in a sub-Riemannian manifold which models the Visual Cortex

In this paper we study the notion of degree forsubmanifolds embedded in an equiregular sub-Riemannian manifold and we provide the definition of their associated area functional. In this setting we prove that the Hausdorff dimension of a submanifold coincides with its degree, as stated by Gromov. Using these general definitions we compute the first variation for surfaces embedded in low dimensional manifolds and we obtain the partial differential equation associated to minimal surfaces. These minimal surfaces have several applications in the neurogeometry of the visual cortex.

Sociocultural context as a facilitator of student learning of function concepts in mathematics

In Costa Rica, many secondary students have serious difficulties to establish relationships between mathematics and real-life contexts. They question the utilitarian role of the school mathematics. This fact motivated the research object of this report which evidences the need to overcome methodologies unrelated to students’ reality, toward new didactical options that help students to value mathematics, reasoning and its  applications, connecting it with their socio-cultural context. The research used a case study as a qualitative methodology and the social constructivism as an educational paradigm in which the knowledge is built by the student; as a product of his social interactions. A collection of learning situations was designed, validated, and implemented. It allowed establishing relationships between mathematical concepts and the socio-cultural context of participants. It analyzed the impact of students’socio-cultural context in their mathematics learning of basic concepts of real variable functions, consistent with the Ministry of Education (MEP) Official Program.  Among the results, it was found that using students’sociocultural context improved their motivational processes, mathematics sense making, and promoted cooperative social interactions. It was evidenced that contextualized learning situations favored concepts comprehension that allow students to see mathematics as a discipline closely related with their every-day life.

Primeira intervenção da GNR no local do crime

Este trabalho aborda a questão dos atos preparatórios no local do crime, isto é, as medidas cautelares e de polícia que o primeiro interveniente policial que chega ao local deve aplicar. As diligências efetuadas pelo primeiro militar que assume uma ocorrência e que, normalmente, não é especialista na área da Investigação Criminal ou forense, revelam-se de elevada importância para o sucesso da investigação pois repercutem-se ao longo de toda a investigação. Essa abordagem caracteriza-se por não visar uma intervenção investigatória e inspetiva, mas sim de prevenção e proteção do local. O objetivo geral do trabalho consiste numa contribuição para uma exploração mais determinada do local onde foi cometido um crime, através do melhor desempenho possível do primeiro interveniente policial. Os objetivos específicos passam por definir os procedimentos a tomar pelo primeiro interveniente (tendo em conta a sua especialidade, materiais e particularidades da fase da investigação) e definir o que é, para ele, um crime de cenário, identificando as possíveis repercussões de uma má gestão do local do crime para o sucesso da investigação. Utilizamos o método comparativo, estudando os diferentes Manuais de procedimentos (nacionais e internacionais). O quadro de referência é o materialismo histórico pois enfatizamos a dimensão histórica dos processos sociais, a legislação vigente e os problemas atuais para interpretar o nosso estudo. Este trabalho assume contornos exploratório-explicativos. Seguimos um método dedutivo, pois pretende-se chegar a um caso particular da lei geral, ou seja, aos procedimentos específicos do primeiro interveniente policial entre toda a gestão do local do crime. Os resultados mais significativos são a justificação da importância do local do crime para a Investigação Criminal e da complexidade que pode advir para o trabalho do primeiro interveniente. É possível concluir um conjunto padrão de ações que devem ser tomadas (guia prático) e como se pode melhorar a intervenção através de formação e cooperação entre os elementos.