Geometry and physics of knots

KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).

Lack of directed V alpha 14-J alpha 281 rearrangements in NK1+ T cells.

NK1.1+ T cells are an unusual subset of TCR alpha beta cells distinguished by their highly restricted V beta repertoire and predominant usage of an invariant V alpha 14-J alpha 281 chain. To assess whether a directed rearrangement mechanism could be responsible for this invariant alpha chain, we have analyzed V alpha 14 rearrangements by polymerase chain reaction and Southern blot in a panel of cloned T-T hybrids derived from thymic NK1.1+ T cells. As expected a high proportion (17/20) of the hybrids had rearranged V alpha 14 to J alpha 281. However, V alpha 14-J alpha 281 rearrangements always occurred on only one chromosome and were accompanied by other V alpha-J alpha rearrangements (not involving V alpha 14) on the homologous chromosome. These data argue that rigorous ligand selection rather than directed rearrangement is responsible for the high frequency of V alpha 14-J alpha 281 rearrangements in NK1.1+ T cells.

Absolute requirement for the pre-T cell receptor alpha chain during NK1.1+ TCRalphabeta cell development.

Most natural killer T (NKT) cells express a highly skewed alphabeta TCR repertoire, consisting of an invariant V alpha14-J alpha281 chain paired preferentially with a polyclonal Vbeta8.2 chain. This repertoire is positively selected by the monomorphic CD1d molecule expressed on cells of hematopoietic origin. The origin of NKT cells and their lineage relationship to conventional T cells is controversial. We show here that the development of NKT cells is absolutely dependent on expression of the pre-TCRalpha chain, in marked contrast to conventional T cells which arise in significant numbers even in the absence of a functional pre-TCR. Distinct developmental requirements for pre-TCR expression in the NKT and T cell lineages may reflect differences in the ability of the TCRalphabeta to substitute functionally for the pre-TCR in immature precursor cells.

Exponentially small splitting of separatrices in the perturbed McMillan map

The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. We consider a perturbation of the McMillan map for which we show that the loop breaks in two invariant curves which are exponentially close one to the other and which intersect transversely along two primary homoclinic orbits. We compute the asymptotic expansion of several quantities related to the splitting, namely the Lazutkin invariant and the area of the lobe between two consecutive primary homoclinic points. Complex matching techniques are in the core of this work. The coefficients involved in the expansion have a resurgent origin, as shown in [MSS08].

Selective induction of NK cell proliferation and cytotoxicity by activated NKT cells.

NK T cells produce cytokines when their semi-invariant TCR engages glycolipids associated with CD1d. The physiological consequences of NKT cell activation remain controversial, although they have been implicated in control of autoimmunity, parasites and tumors. We show here that specific activation of NKT cells in liver and spleen leads to a rapid induction of extensive NK cell proliferation and cytotoxicity. This NK cell activation is dependent, at least in part, on IFN-gamma production by NKT cells and IL-12 production by antigen-presenting cells. Remarkably, activation of NK cells by NKT cells is highly selective, since bystander T and B lymphocytes show transient expression of activation markers but almost no proliferation. Collectively our data suggest that CD1d-dependent NKT cells regulate innate immunity by sampling blood-borne glycolipid antigens and rapidly activating NK cells.

Estudio sobre la extracción de puntos característicos en imágenes y sus aplicaciones

En aquest treball realitzem un estudi sobre la detecció y la descripció de punts característics, una tecnologia que permet extreure informació continguda en les imatges. Primerament presentem l'estat de l'art juntament amb una avaluació dels mètodes més rellevants. A continuació proposem els nous mètodes que hem creat de detecció i descripció, juntament amb l'algorisme òptim anomenat DART, el qual supera l'estat de l'art. Finalment mostrem algunes aplicacions on s'utilitzen els punts DART. Basant-se en l'aproximació de l'espai d'escales Gaussià, el detector proposat pot extreure punts de distint tamany invariants davant canvis en el punt de vista, la rotació i la iluminació. La reutilització de l'espai d'escales durant el procés de descripció, així com l'ús d'estructures simplificades i optimitzades, permeten realitzar tot el procediment en un temps computacional menor a l'obtingut fins al moment. Així s'aconsegueixen punts invariants i distingibles de forma ràpida, el qual permet la seva utilització en aplicacions com el seguiment d'objectes, la reconstrucció d'escenaris 3D i en motors de cerca visual.

Estudi de la reformació amb vapor de biocombustibles per a l'obtenció d'hidrogen utilitzant suports estructurats ceràmics funcionalitzats

Donada una aplicació racional en una varietat complexa, Bellon i Viallet van definit l’entropia algebraica d’aquesta aplicació i van provar que aquest valor és un invariant biracional. Un invariant biracional equivalent és el grau asimptòtic, grau dinàmic o complexitat, definit per Boukraa i Maillard. Aquesta noció és propera a la complexitat definida per Arnold. Conjecturalment, el grau asimptòtic satisfà una recurrència lineal amb coeficients enters. Aquesta conjectura ha estat provada en el cas polinòmic en el pla afí complex per Favre i Jonsson i resta oberta en per al cas projectiu global i per al cas local. L’estudi de l’arbre valoratiu de Favre i Jonsson ha resultat clau per resoldre la conjectura en el cas polinòmic en el pla afí complex. El beneficiari ha estudiat l’arbre valoratiu global de Favre i Jonsson i ha reinterpretat algunes nocions i resultats des d’un punt de vista més geomètric. Així mateix, ha estudiat la demostració de la conjectura de Bellon – Viallet en el cas polinòmic en el pla afí complex com a primer pas per trobar una demostració en el cas local i projectiu global en estudis futurs. El projecte inclou un estudi detallat de l'arbre valoratiu global des d'un punt de vista geomètric i els primers passos de la demostració de la conjectura de Bellon - Viallet en el cas polinòmic en el pla afí complex que van efectuar Favre i Jonsson.

Aspectes geomètrics i dinàmics de transformacions racionals planes

Donada una aplicació racional en una varietat complexa, Bellon i Viallet van definit l’entropia algebraica d’aquesta aplicació i van provar que aquest valor és un invariant biracional. Un invariant biracional equivalent és el grau asimptòtic, grau dinàmic o complexitat, definit per Boukraa i Maillard. Aquesta noció és propera a la complexitat definida per Arnold. Conjecturalment, el grau asimptòtic satisfà una recurrència lineal amb coeficients enters. Aquesta conjectura ha estat provada en el cas polinòmic en el pla afí complex per Favre i Jonsson i resta oberta en per al cas projectiu global i per al cas local. L’estudi de l’arbre valoratiu de Favre i Jonsson ha resultat clau per resoldre la conjectura en el cas polinòmic en el pla afí complex. El beneficiari ha estudiat l’arbre valoratiu global de Favre i Jonsson i ha reinterpretat algunes nocions i resultats des d’un punt de vista més geomètric. Així mateix, ha estudiat la demostració de la conjectura de Bellon – Viallet en el cas polinòmic en el pla afí complex com a primer pas per trobar una demostració en el cas local i projectiu global en estudis futurs. El projecte inclou un estudi detallat de l'arbre valoratiu global des d'un punt de vista geomètric i els primers passos de la demostració de la conjectura de Bellon - Viallet en el cas polinòmic en el pla afí complex que van efectuar Favre i Jonsson.

Biased V beta usage in immature thymocytes is independent of DJ beta proximity and pT alpha pairing.

During thymus development, the TCR beta locus rearranges before the TCR alpha locus. Pairing of productively rearranged TCR beta-chains with an invariant pT alpha chain leads to the formation of a pre-TCR and subsequent expansion of immature pre-T cells. Essentially nothing is known about the TCR V beta repertoire in pre-T cells before or after the expression of a pre-TCR. Using intracellular staining, we show here that the TCR V beta repertoire is significantly biased at the earliest developmental stage in which VDJ beta rearrangement has occurred. Moreover (and in contrast to the V(H) repertoire in immature B cells), V beta repertoire biases in immature T cells do not reflect proximity of V beta gene segments to the DJ beta cluster, nor do they depend upon preferential V beta pairing with the pT alpha chain. We conclude that V gene repertoires in developing T and B cells are controlled by partially distinct mechanisms.

Sistema de reconeixement de cares basat en múltiples vistes

En aquest projecte es proposa un algorisme de detecció de pell que introdueix el veïnatge a l’hora de classificar píxels. Partim d’un espai de color invariant après a partir de múltiples vistes i introduïm la influència del veïnatge mitjançant camps aleatoris de Markov. A partir dels experiments realitzats podem concloure que la inclusió del veïnatge en el procés de classificació de píxels millora significativament els resultats de detecció.

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

How does monetary policy change? evidence on inflation targeting countries

We examine the evolution of monetary policy rules in a group of inflation targeting countries (Australia, Canada, New Zealand, Sweden and the United Kingdom) applying moment- based estimator at time-varying parameter model with endogenous regressors. Using this novel flexible framework, our main findings are threefold. First, monetary policy rules change gradually pointing to the importance of applying time-varying estimation framework. Second, the interest rate smoothing parameter is much lower that what previous time-invariant estimates of policy rules typically report. External factors matter for all countries, albeit the importance of exchange rate diminishes after the adoption of inflation targeting. Third, the response of interest rates on inflation is particularly strong during the periods, when central bankers want to break the record of high inflation such as in the U.K. or in Australia at the beginning of 1980s. Contrary to common wisdom, the response becomes less aggressive after the adoption of inflation targeting suggesting the positive effect of this regime on anchoring inflation expectations. This result is supported by our finding that inflation persistence as well as policy neutral rate typically decreased after the adoption of inflation targeting.

Age effects, unobserved characteristics and hedonic price indexes: The Spanish car market in the 1990s

This paper computes and compares alternative quality-adjusted price indexes for new cars in Spain in the period 1990-2000. The proposed hedonic approach simultaneously controls for time-invariant unobserved product e¤ects and time-variant unobserved quality changes, that are assumed to be captured by model age effects. The results show that the non-adjusted price index largely overstates the increase in the cost of living induced by changes in car prices and that previous evidence for this market have not measured the real extent of that bias, probably due to the omission of controls for unobservables. It is also shown that omitting age effects can also lead to misleading conclusions. The estimated price indexes give also some insights on what could have been the determinants of price evolution in the Spanish car market.

Age effects, unobserved characteristics and hedonic price indexes: The Spanish car market in the 1990's

This paper computes and compares alternative quality-adjusted price indexes for new cars in Spain in the period 1990-2000. The proposed hedonic approach simultaneously controls for time-invariant unobserved product effects and time-variant unobserved quality changes, that are assumed to be captured by model age effects. The results show that the non-adjusted price index largely overstates the increase in the cost of living induced by changes in car prices and that previous evidence for this market have not measured the real extent of that bias, probably due to the omission of controls for unobservables. It is also shown that omitting age effects can also lead to misleading conclusions. The estimated price indexes give also some insights on what could have been the determinants of price evolution in the Spanish car market. JEL classi…fication numbers: C43, E31, L11, L13, Keywords: Hedonic price indexes, Spanish car market, car prices, CPI, Cost of living

Immune Response of Cattle Infected with African Trypanosomes

Trypanosomosis is the most economically important disease constraint to livestock productivity in sub-Saharan Africa and has significant negative impact in other parts of the world. Livestock are an integral component of farming systems and thus contribute significantly to food and economic security in developing countries. Current methods of control for trypanosomosis are inadequate to prevent the enormous socioeconomic losses resulting from this disease. A vaccine has been viewed as the most desirable control option. However, the complexity of the parasite's antigenic repertoire made development of a vaccine based on the variable surface glycoprotein coat unlikely. As a result, research is now focused on identifying invariant trypanosome components as potential targets for interrupting infection or infection-mediated disease. Immunosuppression appears to be a nearly universal feature of infection with African trypanosomes and thus may represent an essential element of the host-parasite relationship, possibly by reducing the host's ability to mount a protective immune response. Antibody, T cell and macrophage/monocyte responses of infected cattle are depressed in both trypanosusceptible and trypanotolerant breeds of cattle. This review describes the specific T cell and monocyte/macrophage functions that are altered in trypanosome-infected cattle and compares these disorders with those that have been described in the murine model of trypanosomosis. The identification of parasite factors that induce immunosuppression and the mechanisms that mediate depressed immune responses might suggest novel disease intervention strategies.