Intersection Pairing and intersection motive of surfaces

We construct the Chow motive modelling intersection co-homology of a proper surface. We then study its functoriality properties. Using Murre's decompositions of the motive of a desingularization into KÄunneth components [Mr1], we show that such decompositions exist also for the intersection motive.

Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

Memoria – beca BE2005

Report for the scientific sojourn at the Centre for Interdisciplinary studies in Environment and Development (CISED), located in Bangalore (Southern India), from September to December 2005. A field-work in the South Indian city of Chennai (former Madras) was developed to analyse the mounting urban (and peri-urban) water crisis. In view of tackling this matter, the state government has done a deal to construct a 100 million litres per day seawater desalination plant. Due to its relative energy-intensiveness (compared to conventional water supply means), the fact that such a large capacity plant will be located in poor country such as India, constitutes somewhat of a surprising novelty, as most desalination facilities in the world are to be found in the oil-rich Persian Gulf countries. This work faces the environmental impact, the energy-intensive technology required, the cost and the missed water management options

Generating trees for permutations avoiding generalized patterns

We construct generating trees with with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation, which allows us to incorporate the adjacency condition about some entries in an occurrence of a generalized pattern. We use these trees to find functional equations for the generating functions enumerating these classes of permutations with respect to different parameters. In several cases we solve them using the kernel method and some ideas of Bousquet-Mélou [2]. We obtain refinements of known enumerative results and find new ones.

Pure motives, mixed motives and extensions of motives associated to singular surfaces

We first recall the construction of the Chow motive modelling intersection cohomology of a proper surface X and study its fundamental properties. Using Voevodsky's category of effective geometrical motives, we then study the motive of the exceptional divisor D in a non-singular blow-up of X. If all geometric irreducible components of D are of genus zero, then Voevodsky's formalism allows us to construct certain one-extensions of Chow motives, as canonical subquotients of the motive with compact support of the smooth part of X. Specializing to Hilbert-Blumenthal surfaces, we recover a motivic interpretation of a recent construction of A. Caspar.

Orthogonal systems in finite grahps

To a finite graph there corresponds a free partially commutative group: with the given graph as commutation graph. In this paper we construct an orthogonality theory for graphs and their corresponding free partially commutative groups. The theory developed here provides tools for the study of the structure of partially commutative groups, their universal theory and automorphism groups. In particular the theory is applied in this paper to the centraliser lattice of such groups.

Model analític de les característiques DC de transistors de doble porta

En aquest treball s’implementa un model analític de les característiques DC del MOSFET de doble porta (DG-MOSFET), basat en la solució de l’equació de Poisson i en la teoria de deriva-difussió[1]. El MOSFET de doble porta asimètric presenta una gran flexibilitat en el disseny de la tensió llindar i del corrent OFF. El model analític reprodueix les característiques DC del DG-MOSFET de canal llarg i és la base per construir models circuitals tipus SPICE.

Invariants de matrius Hadamard en MAGMA

L'objectiu d'aquest projecte ha estat generalitzar i integrar la funcionalitat de dos projectes anteriors que ampliaven el tractament que oferia el Magma respecte a les matrius de Hadamard. Hem implementat funcions genèriques que permeten construir noves matrius Hadamard de qualsevol mida per a cada rang i dimensió de nucli, i així ampliar la seva base de dades. També hem optimitzat la funció que calcula el nucli, i hem desenvolupat funcions que calculen la invariant Symmetric Hamming Distance Enumerator (SH-DE) proposada per Kai-Tai Fang i Gennian Gei que és més sensible per a la detecció de la no equivalència de les matrius Hadamard.

Redirecció de l'especificitat de les cél·lules T contra epítops del VIH restringit per la HLA-A2 mitjaçant transferència genética

Existeixen creixents evidències què la resposta dels limfòcits T CD8+ alpha beta citotòxics (CTLs) és un element fonamental en la infecció produïda pel VIH. Les CTLs VIH especifiques es consideren molt importants en la reducció de la càrrega viral i en la contenció de la infecció. Encara que la combinació dels antiretrovirals (HAART) ha suposat una millora considerable en la lluita contra el VIH induint una important reducció de la càrrega viral i augmentant el nombre de cèl•lules T CD4+, diverses complicacions han fet ressaltar la necessitat de noves alternatives terapèutiques. Les complicacions inclouen: manca de recuperació d’una resposta immune sòlida contra el VIH, toxicitat a llarg termini de la teràpia i el descobriment que les cèl•lules T CD4+ constitueixen un reservori pel virus. Les noves alternatives controlaran la replicació viral i reconstituiran la immunitat. L’eficàcia de la immunoteràpia cel•lular amb transferència adoptiva de CTLs virals específics s’ha provat en diferents infeccions virals humanes, incloent el VIH. Proposem una modificació de la immunoteràpia adoptiva redirigint l’especificitat de les cèl•lules T contra el VIH mitjançant la transfecció dels gens del TCR. En aquest assaig preclínic, ens aprofitarem de la tecnologia dels animals transgènics per les molècules de HLA, amb la finalitat de generar TCRs d’alta afinitat dirigits contra epitops del VIH restringits per la molècula HLA. Aquests TCRs seran induïts in vivo i seleccionats in vitro. Les cadenes alpha i beta dels TCRs VIH específics procedents de les CTLs seran clonades mitjançant tècniques de biologia molecular. Aquests TCRs VIH específics seran transferits a cèl•lules T CD8+ humanes i la seva especificitat i capacitat citolítica contra cèl•lules diana que presentin antígens de VIH-1 s’estudiaran mitjançant la combinació de diverses tècniques noves (FCC, transfecció mitjançant Nucleoefector). Finalment, una construcció retroviral adient per la seva transducció en cèl•lules T humanes s’establirà amb un TCR òptim seleccionat.

The Private and fiscal returns to schooling and the effect of public policies on private incentives to invest in education: a general framework and some results for the EU

This paper develops a comprehensive framework for the quantitative analysis of the private and fiscal returns to schooling and of the effect of public policies on private incentives to invest in education. This framework is applied to 14 member states of the European Union. For each of these countries, we construct estimates of the private return to an additional year of schooling for an individual of average attainment, taking into account the effects of education on wages and employment probabilities after allowing for academic failure rates, the direct and opportunity costs of schooling, and the impact of personal taxes, social security contributions and unemployment and pension benefits on net incomes. We also construct a set of effective tax and subsidy rates that measure the effects of different public policies on the private returns to education, and measures of the fiscal returns to schooling that capture the long-term effects of a marginal increase in attainment on public finances under conditions that approximate general equilibrium.

Note on homology of expanding foliations

This note contains some remarks about the homologies that can be associated to a foliation which is invariant and uniformly expanded by a diffeomorphism. We construct a family of 'dynamical' closed currents supported on the foliation which help us relate the geometric volume growth of the leaves under the diffeomorphism with the map induced on homology in the case when these currents have nonzero homology.

Diagnosi i pla de gestió ambiental del casal de joves de Haër (Senegal)

Per tal de fer front al deteriorament i la destrucció de l’única infraestructura comuna per a joves existent al barri de Haër (M’lomp), l’associació de joves “Les Criquets de Haër” ha dut a terme un projecte de construcció d’un Casal de Joves, el qual pretén fer front no només a la manca d’infraestructures sinó també a la falta de tallers en condicions, de llocs de treball i d’espai agrícola. Amb l’objectiu de construir un centre integrat en el medi i amb capacitat per atendre les necessitats tant dels joves de Haër com d’altres poblacions properes, s’ha optat per realitzar una diagnosi ambiental del terreny on es construirà el complex. La informació obtinguda en aquesta diagnosi ha permès determinar els possibles impactes que la construcció del casal pot suposar per al medi i, a partir d’aquí, elaborar un pla de gestió ambiental dissenyant les mesures correctores més adequades per a la mitigació dels impactes detectats. Les actuacions plantejades en el Pla de gestió ambiental s’han dissenyat tenint en compte el context social i econòmic en el qual es desenvolupen les obres, així com també la predisposició de la població per a dur-les a terme i garantir-ne la continuïtat.

Dividends and weighted values in games with externalities

We consider cooperative environments with externalities (games in partition function form) and provide a recursive definition of dividends for each coalition and any partition of the players it belongs to. We show that with this definition and equal sharing of these dividends the averaged sum of dividends for each player, over all the coalitions that contain the player, coincides with the corresponding average value of the player. We then construct weighted Shapley values by departing from equal division of dividends and finally, for each such value, provide a bidding mechanism implementing it.

Evaluating the impact of public subsidies on a firm's performance: A quasi-experimental approach

Many regional governments in developed countries design programs to improve the competitiveness of local firms. In this paper, we evaluate the effectiveness of public programs whose aim is to enhance the performance of firms located in Catalonia (Spain). We compare the performance of publicly subsidised companies (treated) with that of similar, but unsubsidised companies (non-treated). We use the Propensity Score Matching (PSM) methodology to construct a control group which, with respect to its observable characteristics, is as similar as possible to the treated group, and that allows us to identify firms which retain the same propensity to receive public subsidies. Once a valid comparison group has been established, we compare the respective performance of each firm. As a result, we find that recipient firms, on average, change their business practices, improve their performance, and increase their value added as a direct result of public subsidy programs.

A Thomason model structure on the category of small n-fold categories

We construct a cofibrantly generated Thomason model structure on the category of small n-fold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An n-fold functor is a weak equivalence if and only if the diagonal of its n-fold nerve is a weak equivalence of simplicial sets. We introduce an n-fold Grothendieck construction for multisimplicial sets, and prove that it is a homotopy inverse to the n-fold nerve. As a consequence, the unit and counit of the adjunction between simplicial sets and n-fold categories are natural weak equivalences.