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.

Predicting the potential for lightning activity in mediterranean storms based on the WRF model dynamic and microphysical fields

A new parameter is introduced: the lightning potential index (LPI), which is a measure of the potential for charge generation and separation that leads to lightning flashes in convective thunderstorms. The LPI is calculated within the charge separation region of clouds between 0 C and 20 C, where the noninductive mechanism involving collisions of ice and graupel particles in the presence of supercooled water is most effective. As shown in several case studies using the Weather Research and Forecasting (WRF) model with explicit microphysics, the LPI is highly correlated with observed lightning. It is suggested that the LPI may be a useful parameter for predicting lightning as well as a tool for improving weather forecasting of convective storms and heavy rainfall.

Use of human MAR elements to improve retroviral vector production.

Retroviral vectors have many favorable properties for gene therapies, but their use remains limited by safety concerns and/or by relatively lower titers for some of the safer self-inactivating (SIN) derivatives. In this study, we evaluated whether increased production of SIN retroviral vectors can be achieved from the use of matrix attachment region (MAR) epigenetic regulators. Two MAR elements of human origin were found to increase and to stabilize the expression of the green fluorescent protein transgene in stably transfected HEK-293 packaging cells. Introduction of one of these MAR elements in retroviral vector-producing plasmids yielded higher expression of the viral vector RNA. Consistently, viral titers obtained from transient transfection of MAR-containing plasmids were increased up to sixfold as compared with the parental construct, when evaluated in different packaging cell systems and transfection conditions. Thus, use of MAR elements opens new perspectives for the efficient generation of gene therapy vectors.

An adenovirus-based fluorescent reporter vector to identify and isolate HIV-infected cells.

A procedure is described that allows the simple identification and sorting of live human cells that transcribe actively the HIV virus, based on the detection of GFP fluorescence in cells. Using adenoviral vectors for gene transfer, an expression cassette including the HIV-1 LTR driving the reporter gene GFP was introduced into cells that expressed stably either the Tat transcriptional activator, or an inactive mutant of Tat. Both northern and fluorescence-activated cell sorting (FACS) analysis indicate that cells containing the functional Tat protein presented levels of GFP mRNA and GFP fluorescence several orders of magnitude higher than control cells. Correspondingly, cells infected with HIV-1 showed similar enhanced reporter gene activation. HIV-1-infected cells of the lymphocytic line Jurkat were easily identified by fluorescence-activated cell sorting (FACS) as they displayed a much higher green fluorescence after transduction with the reporter adenoviral vector. This procedure could also be applied on primary human cells as blood monocyte-derived macrophages exposed to the adenoviral LTR-GFP reporter presented a much higher fluorescence when infected with HIV-1 compared with HIV-uninfected cells. The vector described has the advantages of labelling cells independently of their proliferation status and that analysis can be carried on intact cells which can be isolated subsequently by fluorescence-activated cell sorting (FACS) for further culture. This work suggests that adenoviral vectors carrying a virus-specific transcriptional control element controlling the expressions of a fluorescent protein will be useful in the identification and isolation of cells transcribing actively the viral template, and to be of use for drug screening and susceptibility assays.

Geomodelling of a fluvial system with semi-supervised support vector regression

Fluvial deposits are a challenge for modelling flow in sub-surface reservoirs. Connectivity and continuity of permeable bodies have a major impact on fluid flow in porous media. Contemporary object-based and multipoint statistics methods face a problem of robust representation of connected structures. An alternative approach to model petrophysical properties is based on machine learning algorithm ? Support Vector Regression (SVR). Semi-supervised SVR is able to establish spatial connectivity taking into account the prior knowledge on natural similarities. SVR as a learning algorithm is robust to noise and captures dependencies from all available data. Semi-supervised SVR applied to a synthetic fluvial reservoir demonstrated robust results, which are well matched to the flow performance

Example-based support vector machine for drug concentration analysis

Machine learning has been largely applied to analyze data in various domains, but it is still new to personalized medicine, especially dose individualization. In this paper, we focus on the prediction of drug concentrations using Support Vector Machines (S VM) and the analysis of the influence of each feature to the prediction results. Our study shows that SVM-based approaches achieve similar prediction results compared with pharmacokinetic model. The two proposed example-based SVM methods demonstrate that the individual features help to increase the accuracy in the predictions of drug concentration with a reduced library of training data.

Current-density-functional approach to large quantum dots in intense magnetic fields

Within current-density-functional theory, we have studied a quantum dot made of 210 electrons confined in a disk geometry. The ground state of this large dot exhibits some features as a function of the magnetic field (Beta) that can be attributed in a clear way to the formation of compressible and incompressible states of the system. The orbital and spin angular momenta, the total energy, ionization and electron chemical potentials of the ground state, as well as the frequencies of far-infrared edge modes are calculated as a function of Beta, and compared with available experimental and theoretical results.

Wave-vector dependence of spin and density multipole excitations in quantum dots

We have employed time-dependent local-spin density-functional theory to analyze the multipole spin and charge density excitations in GaAs-AlxGa1-xAs quantum dots. The on-plane transferred momentum degree of freedom has been taken into account, and the wave-vector dependence of the excitations is discussed. In agreement with previous experiments, we have found that the energies of these modes do not depend on the transferred wave vector, although their intensities do. Comparison with a recent resonant Raman scattering experiment [C. Schüller et al., Phys. Rev. Lett. 80, 2673 (1998)] is made. This allows us to identify the angular momentum of several of the observed modes as well as to reproduce their energies

Ground-state self-consistent calculation of quantum dots under magnetic fields: Addition spectrum

A density-functional self-consistent calculation of the ground-state electronic density of quantum dots under an arbitrary magnetic field is performed. We consider a parabolic lateral confining potential. The addition energy, E(N+1)-E(N), where N is the number of electrons, is compared with experimental data and the different contributions to the energy are analyzed. The Hamiltonian is modeled by a density functional, which includes the exchange and correlation interactions and the local formation of Landau levels for different equilibrium spin populations. We obtain an analytical expression for the critical density under which spontaneous polarization, induced by the exchange interaction, takes place.

Exchange-correlation effects on quantum wires with spin-orbit interactions under the influence of in-plane magnetic fields.

Within the noncollinear local spin-density approximation, we have studied the ground state structure of a parabolically confined quantum wire submitted to an in-plane magnetic field, including both Rashba and Dresselhaus spin-orbit interactions. We have explored a wide range of linear electronic densities in the weak (strong) coupling regimes that appear when the ratio of spin-orbit to confining energy is small (large). These results are used to obtain the conductance of the wire. In the strong coupling limit, the interplay between the applied magnetic field¿irrespective of the in-plane direction, the exchange-correlation energy, and the spin-orbit energy-produces anomalous plateaus in the conductance vs linear density plots that are otherwise absent, or washes out plateaus that appear when the exchange-correlation energy is not taken into account.