Epireflections and supercompact cardinals

We prove that, under suitable assumptions on a category C, the existence of supercompact cardinals implies that every absolute epireflective class of objects of C is a small-orthogonality class. More precisely, if L is a localization functor on an accessible category C such that the unit morphism X→LX is an extremal epimorphism for all X, and the class of L-local objects is defined by an absolute formula with parameters, then the existence of a supercompact cardinal above the cardinalities of the parameters implies that L is a localization with respect to some set of morphisms.

On extending Pollard's theorem for t-representable sums

"Vegeu el resum a l'inici del document del fitxer adjunt."

The role of the right parietal cortex in sound localization: a chronometric single pulse transcranial magnetic stimulation study.

Auditory spatial functions, including the ability to discriminate between the positions of nearby sound sources, are subserved by a large temporo-parieto-frontal network. With the aim of determining whether and when the parietal contribution is critical for auditory spatial discrimination, we applied single pulse transcranial magnetic stimulation on the right parietal cortex 20, 80, 90 and 150 ms post-stimulus onset while participants completed a two-alternative forced choice auditory spatial discrimination task in the left or right hemispace. Our results reveal that transient TMS disruption of right parietal activity impairs spatial discrimination when applied at 20 ms post-stimulus onset for sounds presented in the left (controlateral) hemispace and at 80 ms for sounds presented in the right hemispace. We interpret our finding in terms of a critical role for controlateral temporo-parietal cortices over initial stages of the building-up of auditory spatial representation and for a right hemispheric specialization in integrating the whole auditory space over subsequent, higher-order processing stages.

Manual de preparació per a olimpíades i competicions matemàtiques

Treball de recerca realitzat per un alumne d’ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l’any 2008. Es presenta als interessats en les competicions de matemàtiques un manual sòlid, compacte, però sintetitzat, que els permeti, complementar i ampliar els seus coneixements matemàtics dirigits a aquestes competicions. En la primera part, es tracten les olimpíades matemàtiques més importants estatals i arreu del món per tal de donar-les a conèixer al lector. A continuació s'expliquen les tècniques generals més utilitzades per construir una demostració determinada. Finalment, es tanca la secció parlant de la creació de problemes, un apartat que permet estimular i potenciar la pròpia creativitat. En la segona part, es troba el propi cos del manual, amb una gran quantitat de problemas solucionats. Per tal de facilitar-ne l'ús, s'ha dividit en quatre grans temes, corresponents als que es treballen a les Olimpíades Matemàtiques: teoria de nombres o aritmètica, geometria, àlgebra i combinatòria. Cada un d'aquests temes es troba, a la vegada, dividit en dues seccions: la de teoremes i conceptes, en què s'enuncien els principals teoremes i fórmules que el lector necessita conéixer, i la d'exercicis i problemes on s’han recollit multitud de problemes provinents de diferents competicions, indicant el grau de dificultat - cal remarcar però, que el present document és una reducció del treball original, per això s'ha decidit només incloure-hi l'apartat d'aritmètica i ometre els altres tres -.

Sex biased spatial strategies relying on the integration of multimodal cues in a rat model of schizophrenia: impairment in predicting future context?

Male and female Wistar rats were treated postnatally (PND 5-16) with BSO (l-buthionine-(S,R)-sulfoximine) to provide a rat model of schizophrenia based on transient glutathione deficit. In the watermaze, BSO-treated male rats perform very efficiently in conditions where a diversity of visual information is continuously available during orientation trajectories [1]. Our hypothesis is that the treatment impairs proactive strategies anticipating future sensory information, while supporting a tight visual adjustment on memorized snapshots, i.e. compensatory reactive strategies. To test this hypothesis, BSO rats' performance was assessed in two conditions using an 8-arm radial maze task: a semi-transparent maze with no available view on the environment from maze centre [2], and a modified 2-parallel maze known to induce a neglect of the parallel pair in normal rats [3-5]. Male rats, but not females, were affected by the BSO treatment. In the semi-transparent maze, BSO males expressed a higher error rate, especially in completing the maze after an interruption. In the 2-parallel maze shape, BSO males, unlike controls, expressed no neglect of the parallel arms. This second result was in accord with a reactive strategy using accurate memory images of the contextual environment instead of a representation based on integrating relative directions. These results are coherent with a treatment-induced deficit in proactive decision strategy based on multimodal cognitive maps, compensated by accurate reactive adaptations based on the memory of local configurations. Control females did not express an efficient proactive capacity in the semi-transparent maze, neither did they show the significant neglect of the parallel arms, which might have masked the BSO induced effect. Their reduced sensitivity to BSO treatment is discussed with regard to a sex biased basal cognitive style.

Computation of an integral basis of a quartic number field

"Vegeu el resum a l'inici del document del fitxer adjunt."

Computation of an integral basis of quartic number field

"Vegeu el resum a l'inici del document del fitxer ajunt."

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

Catabolite repression in Pseudomonas aeruginosa PAO1 regulates the uptake of C4 -dicarboxylates depending on succinate concentration.

In Pseudomonas aeruginosa carbon catabolite repression (CCR) is exerted by the CbrA/B-CrcZ-Crc global regulatory system. Crc is a translational repressor that, in the presence of preferred carbon sources, such as C4 -dicarboxylates, impairs the utilization of less preferred substrates. When non-preferred substrates are present, the CrcZ sRNA levels increase leading to Crc capture, thereby allowing growth of the bacterium at the expense of the non-preferred substrates. The C4 -dicarboxylate transport (Dct) system in P. aeruginosa is composed of two main transporters: DctA, more efficient at mM succinate concentrations, and DctPQM, more important at μM. In this study, we demonstrate that the Dct transporters are differentially regulated by Crc, depending on the concentration of succinate. At high concentrations, Crc positively regulates the expression of the dctA transporter gene and negatively regulates dctPQM post-transcriptionally. The activation of dctA is explained by a Crc-mediated repression of dctR, encoding a transcriptional repressor of dctA. At low succinate concentrations, Crc regulation is impaired. In this condition, CrcZ levels are higher and therefore more Crc proteins are sequestered, decreasing the amount of Crc available to perform CCR on dctR and dctPQM. As a result, expression of dctA is reduced and that of dctPQM is increased.

La programació al servei de la matemàtica

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit cientí­fic del Jovent l'any 2009. La programació al servei de la matemàtica és un programa informàtic fet amb Excel i Visual Basic. Resol equacions de primer grau, equacions de segon grau, sistemes d'equacions lineals de dues equacions i dues incògnites, sistemes d'equacions lineals compatibles determinats de tres equacions i tres incògnites i troba zeros de funcions amb el teorema de Bolzano. En cadascun dels casos, representa les solucions gràficament. Per a això, en el treball s'ha hagut de treballar, en matemàtiques, amb equacions, nombres complexos, la regla de Cramer per a la resolució de sistemes, i buscar la manera de programar un mètode iteratiu pel teorema de Bolzano. En la part gràfica, s'ha resolt com fer taules de valors amb dues i tres variables i treballar amb rectes i plans. Per la part informàtica, s'ha emprat un llenguatge nou per l'alumne i, sobretot, ha calgut saber decidir on posar una determinada instrucció, ja que el fet de variar-ne la posició una sola lí­nea ho pot canviar tot. A més d'això, s'han resolt altres problemes de programació i també s'ha realitzat el disseny de pantalles.

Jugant amb l'atzar i la probabilitat

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit cientí­fic del Jovent l'any 2009. Quins científics van interessar-se per la probabilitat en els seus inicis?, quins altres van fer-la evolucionar? i quins conceptes coneixem i apliquem a l'actualitat? són preguntes que el treball teòric es proposa respondre. Pel que fa a la part pràctica del treball, el seu objectiu és el de crear un mecanisme capaç de generar nombres aleatoris a partir d'un taulell condicionat per paràmetres. El treball s'estructura en 4 blocs que aborden diversos camps de la probabilitat: la història de la probabilitat, els conceptes bàsics de la probabilitat, una introducció pràctica al mecanisme aleatori i el treball de camp. Els resultats finals rebel·len la possibilitat de generar nombres aleatoris a partir d'aparells senzills.

ICR a partir de traços d'escriptura natural captats amb un bolígraf digital

Aquest projecte consisteix en la realització d’una anàlisi de diferents reconeixedors de caracters manuscrits, concretament de nombres, per a una possible implantació en la digitalització de formularis en la industria. Al llarg del document s’estudien dos reconeixedors diferents, concretament l’incorporat al paquet "Tablet PC and Recognition Pack" de Microsoft i el Heloise Hse, proporcionat per la Universitat de Berkeley a Califòrnia.

Effects of sodium arsenite on neurite outgrowth and glutamate AMPA receptor expression in mouse cortical neurons.

There has been broad concern that arsenic in the environment exerts neurotoxicity. To determine the mechanism by which arsenic disrupts neuronal development, primary cultured neurons obtained from the cerebral cortex of mouse embryos were exposed to sodium arsenite (NaAsO2) at concentrations between 0 and 2μM from days 2 to 4 in vitro and cell survival, neurite outgrowth and expression of glutamate AMPA receptor subunits were assessed at day 4 in vitro. Cell survival was significantly decreased by exposure to 2μM NaAsO2, whereas 0.5μM NaAsO2 increased cell survival instead. The assessment of neurite outgrowth showed that total neurite length was significantly suppressed by 1μM and 2μM NaAsO2, indicating that the lower concentration of NaAsO2 impairs neuritogenesis before inducing cell death. Immunoblot analysis of AMPA receptor subunit expression showed that the protein level of GluA1, a specific subunit of the AMPA receptor, was significantly decreased by 1μM and 2μM NaAsO2. When immunocytochemistry was used to confirm this effect by staining for GluA1 expression in neuropeptide Y neurons, most of which contain GluA1, GluA1 expression in neuropeptide Y neurons was found to be significantly suppressed by 1μM and 2μM NaAsO2 but to be increased at the concentration of 0.5μM. Finally, to determine whether neurons could be rescued from the NaAsO2-induced impairment of neuritogenesis by compensatory overexpression of GluA1, we used primary cultures of neurons transfected with a plasmid vector to overexpress either GluA1 or GluA2, and the results showed that GluA1/2 overexpression protected against the deleterious effects of NaAsO2 on neurite outgrowth. These results suggest that the NaAsO2 concentration inducing neurite suppression is lower than the concentration that induces cell death and is the same as the concentration that suppresses GluA1 expression. Consequently, the suppression of GluA1 expression by NaAsO2 seems at least partly responsible for neurite suppression induced by NaAsO2.