Some special Kahler metrics on SL(2,C) and their holomorphic quantization

The group SU(2)*SU(2) acts naturally on SL(2,C) by simultaneous right and left multiplication. We study the Kahler metrics invariant under this action using global Kahler potentials. The volume growth and various curvature quantities are then explicitly computable. Examples include metrics of positive, negative and zero Ricci curvature, and the 1-lump metric of the CP^1-model on a sphere. We then look at the holomorphic quantization of these metrics, where some physically satisfactory results on the dimension of the Hilbert space can be obtained. These give rise to an interesting geometrical conjecture, regarding the dimension of this space for general Stein manifolds in the semi-classical limit.Comment: 28 pages, no figure

Moduli of vortices and Grassmann manifolds

We use the framework of Quot schemes to give a novel description of the moduli spaces of stable n-pairs, also interpreted as gauged vortices on a closed Riemann surface with target Mat(r x n, C), where n >= r. We then show that these moduli spaces embed canonically into certain Grassmann manifolds, and thus obtain natural Kaehler metrics of Fubini-Study type; these spaces are smooth at least in the local case r=n. For abelian local vortices we prove that, if a certain "quantization" condition is satisfied, the embedding can be chosen in such a way that the induced Fubini-Study structure realizes the Kaehler class of the usual L^2 metric of gauged vortices.Comment: 22 pages, LaTeX. Final version: last section removed, typos corrected, two references added; to appear in Commun. Math. Phy

Editorial: Cancer Nanotheranostics: What Have We Learned So Far?

According to the National Cancer Institute, in 2015 an estimated of 1.7 million new cases of cancer will be diagnosed only in the United States and around 600, 000 people will die from the disease. The most common type of cancer is breast cancer, with more than 234, 000 new cases expected in the United States in 2015. The next most common cancers are prostate cancer and lung cancer.After a quarter of century of rapid technological advances, research has revealed the complexity of cancer, a disease intimately related to the dynamic transformation of the genome. These transformations trigger a range of modification to cell processes and molecular events that initiate and promote tumor genesis and progression, then local invasion and metastasis, i.e., the hallmarks of cancer development. These alterations may cause a wide scope of “diseases” that share similar molecular patterns that cause transformation and malignancy. Each of this stepwise evolution of the initial molecular event drives abnormal growth and loss of differentiation that ultimately causes tissue and organ failure. The initial molecular event may lay within the erroneous expression of a given gene, epigenetic modification and/or sporadic mutations occurring on genomic DNA during the life span of organisms. Each and every one of these molecular events may be evaluated and used as diagnostics biomarker and therapeutic target. For example, therapy action may target a mutated gene and silence its expression so as to avoid erroneous protein expression that mutates cell function. However, the full understanding of the molecular onset of this disease is still far from achieved and the search for mechanisms of treatment will follow closely..

Um modelo de caracterização e avaliação ecológica para o planeamento e gestão

Decorrem actualmente na Universidade de Évora diversos projectos de investigação visando o desenvolvimento de metodologias de caracterização e avaliação ecológica com vista ao planeamento e gestão do território. Tais projectos, desenvolvidos a escalas complementares (1:10 000; 1:25 000 e 1:100 000), pretendem via a constituir um quadro metodológico inovador integrando num único plano de caracterização e avaliação, o plano dos sistemas de uso e o plano dos sistemas ecológicos espaciais. A necessidade de um tal sistema integrado justifica-se pela carência de um referencial de caracterização e avaliação do território com vista à articulação od sprocesos de gestão e à promoção dos objectivos de Conservação da Natureza. Com efeito, a necessidade de assegurar a preservação da biodiversidade da globalidade do território impõe uma abordagem à gestaõ do uso deste que assegure que o nível de fragmentação, de conectividade residual, e de complementaridade funcional asseguram as condições para a sustentação viável de meta-populações das espécie-objectivo. Para atingir tal objectivo importa conhecer e conseguir articular nos processos de simulação e gestão, as necessidades, processos e funções dos diferentes usos antrópicos de uma dada região e as necessidades processos, funções e condicionantes espaciais dos diferentes sistemas ecológicos susceptiveis de ocorrerem nessa região ou locais. Interessa igualmente identificat a forma como essa articulação se processa e a sua hierarquização escalar e funcional

Quantum lump dynamics on the two-sphere

It is well known that the low-energy classical dynamics of solitons of Bogomol'nyi type is well approximated by geodesic motion in M_n, the moduli space of static n-solitons. There is an obvious quantization of this dynamics wherein the wavefunction evolves according to the Hamiltonian H_0 equal to (half) the Laplacian on M_n. Born-Oppenheimer reduction of analogous mechanical systems suggests, however, that this simple Hamiltonian should receive corrections including k, the scalar curvature of M_n, and C, the n-soliton Casimir energy, which are usually difficult to compute, and whose effect on the energy spectrum is unknown. This paper analyzes the spectra of H_0 and two corrections to it suggested by work of Moss and Shiiki, namely H_1=H_0+k/4 and H_2=H_1+C, in the simple but nontrivial case of a single CP^1 lump moving on the two-sphere. Here M_1=TSO(3), a noncompact kaehler 6-manifold invariant under an SO(3)xSO(3) action, whose geometry is well understood. The symmetry gives rise to two conserved angular momenta, spin and isospin. A hidden isometry of M_1 is found which implies that all three energy spectra are symmetric under spin-isospin interchange. The Casimir energy is found exactly on the zero section of TSO(3), and approximated numerically on the rest of M_1. The lowest 19 eigenvalues of H_i are found for i=0,1,2, and their spin-isospin and parity compared. The curvature corrections in H_1 lead to a qualitatively unchanged low-level spectrum while the Casimir energy in H_2 leads to significant changes. The scaling behaviour of the spectra under changes in the radii of the domain and target spheres is analyzed, and it is found that the disparity between the spectra of H_1 and H_2 is reduced when the target sphere is made smaller.Comment: 35 pages, 3 figure

Non-abelian vortices on compact Riemann surfaces

We consider the vortex equations for a U(n) gauge field coupled to a Higgs field with values on the n times n square matrices. It is known that when these equations are defined on a compact Riemann surface, their moduli space of solutions is closely related to a moduli space of tau-stable holomorphic n-pairs on that surface. Using this fact and a local factorization result for the Higgs matrix, we show that the vortex solutions are entirely characterized by (1) the location in the surface of the zeros of the determinant of the Higgs matrix and (2) by the choice of a vortex internal structure at each of these zeros. We describe explicitly the vortex internal spaces and show that they are compact and connected spaces.Comment: 17 pages; v2: typos corrected, as will appear in CM

Density Perturbations in the Brans-Dicke Theory

We analyse the fate of density perturbation in the Brans-Dicke Theory, giving a general classification of the solutions of the perturbed equations when the scale factor of the background evolves as a power law. We study with details the cases of vacuum, inflation, radiation and incoherent matter. We find, for the a negative Brans-Dicke parameter, a significant amplification of perturbations.Comment: 26 pages, latex fil

A regional survey of emerging hot climate conditions in Portugal and the new challenge to animal housing

Portugal, located in the South-western Europe, is characterised by a Mediterranean climate with hot and dry summer. According to data from Portuguese IM (Instituto de Meteorologia) during the last decade, summer temperatures tend to be higher, and several heat waves have occurred, with temperatures above 40 oC. During summer, days with high temperatures and heat waves are becoming more and more common in Portugal. The past four summers have been among the hottest ever registered. These frequently high temperatures can cause problems in intensive animal production. In most cases, the livestock buildings are not prepared for animal production under high temperatures and most of them do not have environmental control equipments adequate to control indoor environment under such conditions. From a geographical point of view, and examining climatic data, we find two regions (Alentejo and Trás-os-Montes) where high temperatures are more usual and summer tend to be hot. In these two regions, livestock is quite relevant and have a great significance to the regional economy. Two locations were chosen in these regions to register and analyse air temperature in order to identify the occurrence of hot climate conditions; and to evaluate its influence on the inside animal housing climate

Twisting gauged non-linear sigma-models

We consider gauged sigma-models from a Riemann surface into a Kaehler and hamiltonian G-manifold X. The supersymmetric N=2 theory can always be twisted to produce a gauged A-model. This model localizes to the moduli space of solutions of the vortex equations and computes the Hamiltonian Gromov-Witten invariants. When the target is equivariantly Calabi-Yau, i.e. when its first G-equivariant Chern class vanishes, the supersymmetric theory can also be twisted into a gauged B-model. This model localizes to the Kaehler quotient X//G.Comment: 33 pages; v2: small additions, published versio

VINHOS QUE PENSAM - parte I/III GESTÃO DO VIGOR VEGETATIVO DA VINHA A PARTIR DE SENSORES ATIVOS MUTIESPECTRAIS PRÓXIMOS

Costumo dizer que o projeto “Vinhos que pensam” nasceu de um aperto de mão entre a equipa de Agricultura de Precisão da Universidade de Évora e a Fundação Eugénio de Almeida, nasceu sem financiamento próprio mas com uma visão muito clara de criar valor social na área da vitivinicultura Alentejana. Passados 6 anos, julgamos que o conhecimento produzido é relevante para a atividade e gestão vitivinícola Alentejana, no entanto, novas perguntas surgem todos os anos e dessa forma somos alimentados na motivação de prosseguir com este projeto, ao qual, outras entidades e vontades se vão agora também associando. A Agrobótica, muito recentemente, desafiou-nos a apresentar os resultados mais relevantes do projeto “Vinhos que pensam” e com o maior prazer lhe dissemos que sim, no entanto, colocou-se-nos um problema, os resultados mais relevantes, muito dificilmente caberiam num único artigo, como tal, decidimos dividir tais resultados em três artigos, este primeiro mais virado para os aspetos da gestão do vigor da vegetação da vinha; o segundo mais virado para os sensores geoelétricos do solo e sua aplicação na gestão e estudo do solo; e por fim, um terceiro mais virado para aspetos da nutrição das plantas considerando a interação solo/planta e a utilização dos sensores multiespectrais