A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

Recerca versus docència en una experiència d'internalització dels estudis de Geografia a la Universitat de Girona: The faces of landscape, Catalonia and North Karelia = Research versus teaching in one experience of internationalization of the Geography degree studies in the University of Girona: The faces of landscape, Catalonia and North Karelia

Un dels reptes cabdals de la Universitat és enllaçar l’experiència de recerca amb la docència, així com promoure la internacionalització dels estudis, especialment a escala europea, tenint present que ambdues poden actuar com a catalitzadores de la millora de la qualitat docent. Una de les fórmules d’internacionalització és la realització d’assignatures compartides entre universitats de diferents països, fet que suposa l’oportunitat d’implementar noves metodologies docents. En aquesta comunicació es presenta una experiència en aquesta línia desenvolupada entre la Universitat de Girona i la Universitat de Joensuu (Finlàndia) en el marc dels estudis de Geografia amb la realització de l’assignatura 'The faces of landscape: Catalonia and North Karelia'. Aquesta es desenvolupa al llarg de dues setmanes intensives, una en cadascuna de les Universitats. L’objectiu és presentar i analitzar diferents significats del concepte paisatge aportant també metodologies d’estudi tant dels aspectes físics i ecològics com culturals que s’hi poden vincular i que són les que empren els grups de recerca dels professors responsables de l’assignatura. Aquesta part teòrica es completa amb una presentació de les característiques i dinàmiques pròpies dels paisatges finlandesos i catalans i una sortida de camp. Per a la part pràctica es constitueixen grups d’estudi multinacionals que treballen a escala local algun dels aspectes en els dos països, es comparen i es realitza una presentació i defensa davant del conjunt d’estudiants i professorat. La llengua vehicular de l’assignatura és l’anglès.

Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation

To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consuming method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computational effort in the approximation while, at the same time, the accuracy increases.

Forces de Casimir i les seves aplicacions

Report for the scientific sojourn carried out at the Darmouth College, from august 2007 until february 2008. It has been very successful, from different viewpoints: scientific, philosophical, human. We have definitely advanced, during the past six months, towards the comprehension of the behaviour of the fluctuations of the quantum vacuum in the presence of boundaries, moving and non-moving, and also in situations where the topology of space-time changes: the dynamical Casimir effect, regularization problems, particle creation statistics, according to different BC, etc. We have solved some longstanding problems and got in this subject quite remarkable results (as we will explain in more detail below). We also pursued a general approach towards a viable modified f(R) gravity in both the Jordan and the Einstein frames (which are known to be mathematically equivalent, but physically not so). A class of exponential, realistic modified gravities has been introduced by us and investigated with care. Special focus was made on step-class models, most promising from the phenomenological viewpoint and which provide a natural way to classify all viable modified gravities. One- and two-steps models were considered, but the analysis is extensible to N-step models. Both inflation in the early universe and the onset of recent accelerated expansion arise in these models in a natural, unified way, what makes them very promising. Moreover, it is monstrated in our work that models in this category easily pass all local tests, including stability of spherical body solution, non-violation of Newton's law, and generation of a very heavy positive mass for the additional scalar degree of freedom.

El préstec de documents en un campus virtual : generant un nou concepte

El préstec de documents és un dels pilars fonamentals de la biblioteca per donar suport a l'estudi, docència i recerca. A la Biblioteca de la Universitat Oberta de Catalunya, la diferència principal respecte a altres biblioteques universitàries, és el nou concepte virtual sense parets, i aquest concepte s'estén també a aquest servei de préstec. Els usuaris no han d'accedir necessàriament a un espai físic per consultar les fonts d'informació disponibles, ni per endur-se documents en préstec. Des de casa, i de manera remota, poden demanar els documents en els que estiguin interessats, des del mateix catàleg i sense cap tipus d'intermediari gràcies al desenvolupament d'un nou servei de préstec de documents, que genera alhora un nou model dins d'un campus virtual.

La Biblioteca Virtual de la Universitat Oberta de Catalunya : un nuevo concepto de biblioteca

The Virtual Library of the UOC not only contains its own bibliographic resources distributed in small physical libraries in the Support Centres of the University spread throughout the main cities of Catalonia, it also allows online access from one's place of residence to all the information registered and stored anywhere in the world. Because of this, we can define the Virtual Library of the UOC as a "library without walls". Currently, services offered by the library are available through a website interface within the Virtual Campus of the University.

Aplicación de un estudio de usabilidad en bibliotecas digitales : la Biblioteca Virtual de la UOC

The Open University of Catalonia (UOC) has conducted a study of operability of its user interfaces, creating for this purpose different work groups that have analyzed different casuistries. One of these groups focused on the study and analysis of the usability of the Virtual Library's website, with the objective of obtaining benefits for our users. As a result of this analysis, an important qualitative jump is occurring in the new implementation of the website of the UOC's Virtual Library, prioritizing the role of users from different points of view: ease of navigation, management of profiles and the services associated to these and the restructuring of the information architecture, with the final aim of facilitating access to the resources and the services offered from the Library, advocating in this way for their quality and improvement.

La gestió dels recursos documentals a les aules de la UOC

La gestió dels recursos documentals a les aules de la UOC es fa de manera compartida entre el professorat i la Biblioteca de la Universitat. La responsabilitat dels continguts que trobem com a 'recursos de l'aula' i de l'actualització d'aquests recau en el professor/a responsable de l'assignatura que és qui decideix quins recursos electrònics han de tenir les aules de les seves assignatures i comunica a la Biblioteca aquests recursos i les possibles actualitzacions i/o modificacions que cal fer-hi. La gestió d'aquests recursos que es fa des de la biblioteca és un element clau perquè, a través d'aquest procés, la biblioteca esdevingui un element realment facilitador de l'aprenentatge i la docència, i situa la biblioteca com un element central en el model d'aprenentatge de la UOC. S'inclou al final de la presentació un seguit de recomanacions per a l'èxit dels recursos documentals a les aules virtuals.

Solució mental i solució motriu en la iniciació als esports col·lectius en l'Educació Primària

The adjustment of the teaching learning contents in Physical Education, requires of a rigorous analysis that permits to adjust them to the maximum with the educational needs of the student body. It has been approached an investigation study in the one which have intervened pupils, boys and girls, of two different populations, Girona and Madrid in order to prove and analyse the motor and mental components of the student body in the real situation of the game. The hypothesis that we have treated are:if it exists differences between the boys and girls of the educational levels studied in the motor and mental solution in the sports initiation, additionally, the differences that they can exist between the courses and what distance is verified between the study ages to approach a physical activity that implies an initial step to the hour of teaching the collective sports in the classes of Physical education. They have been employed three measure instruments: the first permits to analyse the mental solution without need of practice employing situation photographs of the real game with those which the pupils must choose to who to happen; the second is a pass test that permits to prove the technical dominance to use in a collective sport and the third is a real game situation that permits to put in manifesto the relationship between the mental behaviour and the motor of the pupil. This real game situation is ‘the game of ten pass’ (Blázquez,1986; Torres,1993). The results demonstrate that it do not exist differences between the two sexes in the study ages. In the case of the technical execution level, there is a considerable increase with the age and it is slightly greater in the kids that in the girls. In the case of the real game, we find ourselves with a great variability in the results and we cannot conclude that there are relative differences to the sex in none of the three courses. Respect at participation level during the game is confirmed that the pupils that more participate are not the pupils than more balls lose, what permits to guarantee the idea of the fact that it is convenient to use the real game practice as direct learning element. Finally, there is no a high correlation between the execution level measured in the test of technical execution and the decision execution during the game

Study and implementation of some quantitative trading models

Quantitative or algorithmic trading is the automatization of investments decisions obeying a fixed or dynamic sets of rules to determine trading orders. It has increasingly made its way up to 70% of the trading volume of one of the biggest financial markets such as the New York Stock Exchange (NYSE). However, there is not a signi cant amount of academic literature devoted to it due to the private nature of investment banks and hedge funds. This projects aims to review the literature and discuss the models available in a subject that publications are scarce and infrequently. We review the basic and fundamental mathematical concepts needed for modeling financial markets such as: stochastic processes, stochastic integration and basic models for prices and spreads dynamics necessary for building quantitative strategies. We also contrast these models with real market data with minutely sampling frequency from the Dow Jones Industrial Average (DJIA). Quantitative strategies try to exploit two types of behavior: trend following or mean reversion. The former is grouped in the so-called technical models and the later in the so-called pairs trading. Technical models have been discarded by financial theoreticians but we show that they can be properly cast into a well defined scientific predictor if the signal generated by them pass the test of being a Markov time. That is, we can tell if the signal has occurred or not by examining the information up to the current time; or more technically, if the event is F_t-measurable. On the other hand the concept of pairs trading or market neutral strategy is fairly simple. However it can be cast in a variety of mathematical models ranging from a method based on a simple euclidean distance, in a co-integration framework or involving stochastic differential equations such as the well-known Ornstein-Uhlenbeck mean reversal ODE and its variations. A model for forecasting any economic or financial magnitude could be properly defined with scientific rigor but it could also lack of any economical value and be considered useless from a practical point of view. This is why this project could not be complete without a backtesting of the mentioned strategies. Conducting a useful and realistic backtesting is by no means a trivial exercise since the \laws" that govern financial markets are constantly evolving in time. This is the reason because we make emphasis in the calibration process of the strategies' parameters to adapt the given market conditions. We find out that the parameters from technical models are more volatile than their counterpart form market neutral strategies and calibration must be done in a high-frequency sampling manner to constantly track the currently market situation. As a whole, the goal of this project is to provide an overview of a quantitative approach to investment reviewing basic strategies and illustrating them by means of a back-testing with real financial market data. The sources of the data used in this project are Bloomberg for intraday time series and Yahoo! for daily prices. All numeric computations and graphics used and shown in this project were implemented in MATLAB^R scratch from scratch as a part of this thesis. No other mathematical or statistical software was used.

One kind of lawlessness: estimating the welfare cost of Somali piracy

This paper estimates the effect of piracy attacks on shipping costs using a unique data set on shipping contracts in the dry bulk market. We look at shipping routes whose shortest path exposes them to piracy attacks and find that the increase in attacks in 2008 lead to around a ten percent increase in shipping costs. We use this estimate to get a sense of the welfare loss imposed by piracy. Our intermediate estimate suggests that the creation of $120 million of revenue for pirates in the Somalia area led to a welfare loss of over $1.5 billion.

One-dimensional solidification of supercooled melts

In this paper a one-phase supercooled Stefan problem, with a nonlinear relation between the phase change temperature and front velocity, is analysed. The model with the standard linear approximation, valid for small supercooling, is first examined asymptotically. The nonlinear case is more difficult to analyse and only two simple asymptotic results are found. Then, we apply an accurate heat balance integral method to make further progress. Finally, we compare the results found against numerical solutions. The results show that for large supercooling the linear model may be highly inaccurate and even qualitatively incorrect. Similarly as the Stefan number β → 1&sup&+&/sup& the classic Neumann solution which exists down to β =1 is far from the linear and nonlinear supercooled solutions and can significantly overpredict the solidification rate.

A chemical Hamiltonian approach study of the basis set superposition error changes on electron densities and one- and two-center energy components

A comparision of the local effects of the basis set superposition error (BSSE) on the electron densities and energy components of three representative H-bonded complexes was carried out. The electron densities were obtained with Hartee-Fock and density functional theory versions of the chemical Hamiltonian approach (CHA) methodology. It was shown that the effects of the BSSE were common for all complexes studied. The electron density difference maps and the chemical energy component analysis (CECA) analysis confirmed that the local effects of the BSSE were different when diffuse functions were present in the calculations

Density functional energy decomposition into one- and two-atom contributions

The present work provides a generalization of Mayer's energy decomposition for the density-functional theory (DFT) case. It is shown that one- and two-atom Hartree-Fock energy components in Mayer's approach can be represented as an action of a one-atom potential VA on a one-atom density ρ A or ρ B. To treat the exchange-correlation term in the DFT energy expression in a similar way, the exchange-correlation energy density per electron is expanded into a linear combination of basis functions. Calculations carried out for a number of density functionals demonstrate that the DFT and Hartree-Fock two-atom energies agree to a reasonable extent with each other. The two-atom energies for strong covalent bonds are within the range of typical bond dissociation energies and are therefore a convenient computational tool for assessment of individual bond strength in polyatomic molecules. For nonspecific nonbonding interactions, the two-atom energies are low. They can be either repulsive or slightly attractive, but the DFT results more frequently yield small attractive values compared to the Hartree-Fock case. The hydrogen bond in the water dimer is calculated to be between the strong covalent and nonbonding interactions on the energy scale

One- and two-center physical space partitioning of the energy in the density functional theory

A conceptually new approach is introduced for the decomposition of the molecular energy calculated at the density functional theory level of theory into sum of one- and two-atomic energy components, and is realized in the "fuzzy atoms" framework. (Fuzzy atoms mean that the three-dimensional physical space is divided into atomic regions having no sharp boundaries but exhibiting a continuous transition from one to another.) The new scheme uses the new concept of "bond order density" to calculate the diatomic exchange energy components and gives them unexpectedly close to the values calculated by the exact (Hartree-Fock) exchange for the same Kohn-Sham orbitals