The bogomolov conjecture for totally degenerate Abelian varieties

We prove the Bogomolov conjecture for a totally degenerate abelian variety A over a function field. We adapt Zhang's proof of the number field case replacing the complex analytic tools by tropical analytic geometry. A key step is the tropical equidistribution theorem for A at the totally degenerate place.

Tropical varieties for non-archimedean analytic spaces

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Diophantine approximation on projective varieties I: algebraic distance and metric Bézout theorem

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Strong exceptional sequences of vector bundles on certain Fano varieties

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Evaluation of susceptibility of pear and plum varieties and rootstocks to Ca. P. pyri and Ca. P. prunorum using Real-Time PCR

Real-time PCR was used to quantify phytoplasma concentration in fifty inoculated trees from five Prunus rootstocks and in forty-eight symptomatic pear and Japanese plum trees from orchards. Seasonal fluctuation of Ca. P. prunorum in different Prunus rootstocks, over three years, showed that the highest percentage detected by nested-PCR was in the ‘Garnem’ rootstock on nearly all sampling dates. Intra-varietal differences were also observed. Phytoplasma titer could be estimated by real time PCR in some trees of the rootstocks ‘Garnem’, ‘Barrier’, ‘GF-677’ and ‘Marianna’, and ranged from 4.7x105 to 3.18x109 phytoplasmas per gram of tissue. Quantification by real-time PCR was not possible in the ‘Cadaman’ trees analyzed, probably due to a lower phytoplasma titer in this variety. Samples from infected trees from commercial plots had different phytoplasma concentration and detection percentage depending on the variety, both being lower in ‘Fortune’ and ‘606’ Japanese plum and in ‘Blanquilla’ pear trees.

Digital beamforming and moving target indication for future spaceborne synthetic aperture radar

During the last decade the interest on space-borne Synthetic Aperture Radars (SAR) for remote sensing applications has grown as testified by the number of recent and forthcoming missions as TerraSAR-X, RADARSAT-2, COSMO-kyMed, TanDEM-X and the Spanish SEOSAR/PAZ. In this sense, this thesis proposes to study and analyze the performance of the state-of-the-Art space-borne SAR systems, with modes able to provide Moving Target Indication capabilities (MTI), i.e. moving object detection and estimation. The research will focus on the MTI processing techniques as well as the architecture and/ or configuration of the SAR instrument, setting the limitations of the current systems with MTI capabilities, and proposing efficient solutions for the future missions. Two European projects, to which the Universitat Politècnica de Catalunya provides support, are an excellent framework for the research activities suggested in this thesis. NEWA project proposes a potential European space-borne radar system with MTI capabilities in order to fulfill the upcoming European security policies. This thesis will critically review the state-of-the-Art MTI processing techniques as well as the readiness and maturity level of the developed capabilities. For each one of the techniques a performance analysis will be carried out based on the available technologies, deriving a roadmap and identifying the different technological gaps. In line with this study a simulator tool will be developed in order to validate and evaluate different MTI techniques in the basis of a flexible space-borne radar configuration. The calibration of a SAR system is mandatory for the accurate formation of the SAR images and turns to be critical in the advanced operation modes as MTI. In this sense, the SEOSAR/PAZ project proposes the study and estimation of the radiometric budget. This thesis will also focus on an exhaustive analysis of the radiometric budget considering the current calibration concepts and their possible limitations. In the framework of this project a key point will be the study of the Dual Receive Antenna (DRA) mode, which provides MTI capabilities to the mission. An additional aspect under study is the applicability of the Digital Beamforming on multichannel and/or multistatic radar platforms, which conform potential solutions for the NEWA project with the aim to fully exploit its capability jointly with MTI techniques.

Human synthetic lethal inference as potential anti-cancer target gene detection

Background: Two genes are called synthetic lethal (SL) if mutation of either alone is not lethal, but mutation of both leads to death or a significant decrease in organism's fitness. The detection of SL gene pairs constitutes a promising alternative for anti-cancer therapy. As cancer cells exhibit a large number of mutations, the identification of these mutated genes' SL partners may provide specific anti-cancer drug candidates, with minor perturbations to the healthy cells. Since existent SL data is mainly restricted to yeast screenings, the road towards human SL candidates is limited to inference methods. Results: In the present work, we use phylogenetic analysis and database manipulation (BioGRID for interactions, Ensembl and NCBI for homology, Gene Ontology for GO attributes) in order to reconstruct the phylogenetically-inferred SL gene network for human. In addition, available data on cancer mutated genes (COSMIC and Cancer Gene Census databases) as well as on existent approved drugs (DrugBank database) supports our selection of cancer-therapy candidates.Conclusions: Our work provides a complementary alternative to the current methods for drug discovering and gene target identification in anti-cancer research. Novel SL screening analysis and the use of highly curated databases would contribute to improve the results of this methodology.

The varieties of regional change

Many metropolitan areas have experienced extreme boom-bust cycles over the past century. Some places, like Detroit, grew enormously as industrial powerhouses and then declined, while other older cities, like Boston, seem quite resilient. Education does a reasonable job of explaining urban resilience. In this paper, we present a simple model where education increases the level of entrepreneurship. In this model, human capital spillovers occur at the city level because skilled workers produce more product varieties and thereby increase labor demand. We decompose empirically the causes of the connection between skills and urban success and find that skills are associated with growth in productivity or entrepreneurship, not with growth in quality of life, at least outside of the West. We also find that skills seem to have depressed housing supply growth in the West, but not in other regions, which supports the view that educated residents in that region have fought for tougher land-use controls. We also present evidence that skills have had a disproportionately large impact on unemployment during the current recession.

The Brauer group and the second Abel-Jacobi map for 0-cycles on algebraic varieties

This paper focuses on the connection between the Brauer group and the 0-cycles of an algebraic variety. We give an alternative construction of the second l-adic Abel-Jacobi map for such cycles, linked to the algebraic geometry of Severi-Brauer varieties on X. This allows us then to relate this Abel-Jacobi map to the standard pairing between 0-cycles and Brauer groups (see [M], [L]), completing results from [M] in this direction. Second, for surfaces, it allows us to present this map according to the more geometrical approach devised by M. Green in the framework of (arithmetic) mixed Hodge structures (see [G]). Needless to say, this paper owes much to the work of U. Jannsen and, especially, to his recently published older letter [J4] to B. Gross.

Arithmetical problems in number fields, abelian varieties and modular forms

Number theory, a fascinating area in mathematics and one of the oldest, has experienced spectacular progress in recent years. The development of a deep theoretical background and the implementation of algorithms have led to new and interesting interrelations with mathematics in general which have paved the way for the emergence of major theorems in the area. This report summarizes the contribution to number theory made by the members of the Seminari de Teoria de Nombres (UB-UAB-UPC) in Barcelona. These results are presented in connection with the state of certain arithmetical problems, and so this monograph seeks to provide readers with a glimpse of some specific lines of current mathematical research.

Particle dispersion in synthetic turbulent flows

We study particle dispersion advected by a synthetic turbulent flow from a Lagrangian perspective and focus on the two-particle and cluster dispersion by the flow. It has been recently reported that Richardson¿s law for the two-particle dispersion can stem from different dispersion mechanisms, and can be dominated by either diffusive or ballistic events. The nature of the Richardson dispersion depends on the parameters of our flow and is discussed in terms of the values of a persistence parameter expressing the relative importance of the two above-mentioned mechanisms. We support this analysis by studying the distribution of interparticle distances, the relative velocity correlation functions, as well as the relative trajectories.

Langevin approach to generate synthetic turbulent flows

We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian turbulent flows by using a linear Langevin equation, where the noise term acts as a stochastic stirring force. The characteristic parameters of the velocity field are well introduced, in particular the kinematic viscosity and the spectrum of energy. As an application, the diffusion of a passive scalar is studied for two different energy spectra. Numerical results are compared favorably with analytical calculations.

Computation of arbitrarily constrained synthetic discriminant functions

An algorithm for computing correlation filters based on synthetic discriminant functions that can be displayed on current spatial light modulators is presented. The procedure is nondivergent, computationally feasible, and capable of producing multiple solutions, thus overcoming some of the pitfalls of previous methods.