Twisted Reidemeister torsion for twist knots

The aim of this paper is to give an explicit formula for the SL2(C)-twisted Reidemeister torsion as defined in [6] in the case of twist knots. For hyperbolic twist knots, we also prove that the twisted Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape of the knot. Tables given approximations of the twisted Reidemeister torsion for twist knots on some concrete examples are also enclosed.

Hemispheric competence for auditory spatial representation.

Sound localization relies on the analysis of interaural time and intensity differences, as well as attenuation patterns by the outer ear. We investigated the relative contributions of interaural time and intensity difference cues to sound localization by testing 60 healthy subjects: 25 with focal left and 25 with focal right hemispheric brain damage. Group and single-case behavioural analyses, as well as anatomo-clinical correlations, confirmed that deficits were more frequent and much more severe after right than left hemispheric lesions and for the processing of interaural time than intensity difference cues. For spatial processing based on interaural time difference cues, different error types were evident in the individual data. Deficits in discriminating between neighbouring positions occurred in both hemispaces after focal right hemispheric brain damage, but were restricted to the contralesional hemispace after focal left hemispheric brain damage. Alloacusis (perceptual shifts across the midline) occurred only after focal right hemispheric brain damage and was associated with minor or severe deficits in position discrimination. During spatial processing based on interaural intensity cues, deficits were less severe in the right hemispheric brain damage than left hemispheric brain damage group and no alloacusis occurred. These results, matched to anatomical data, suggest the existence of a binaural sound localization system predominantly based on interaural time difference cues and primarily supported by the right hemisphere. More generally, our data suggest that two distinct mechanisms contribute to: (i) the precise computation of spatial coordinates allowing spatial comparison within the contralateral hemispace for the left hemisphere and the whole space for the right hemisphere; and (ii) the building up of global auditory spatial representations in right temporo-parietal cortices.

Geometria integral i convexitat en espais de curvatura holomorfa constant

En aquest treball es tracten qüestions de la geometria integral clàssica a l'espai hiperbòlic i projectiu complex i a l'espai hermític estàndard, els anomenats espais de curvatura holomorfa constant. La geometria integral clàssica estudia, entre d'altres, l'expressió en termes geomètrics de la mesura de plans que tallen un domini convex fixat de l'espai euclidià. Aquesta expressió es dóna en termes de les integrals de curvatura mitja. Un dels resultats principals d'aquest treball expressa la mesura de plans complexos que tallen un domini fixat a l'espai hiperbòlic complex, en termes del que definim com volums intrínsecs hermítics, que generalitzen les integrals de curvatura mitja. Una altra de les preguntes que tracta la geometria integral clàssica és: donat un domini convex i l'espai de plans, com s'expressa la integral de la s-èssima integral de curvatura mitja del convex intersecció entre un pla i el convex fixat? A l'espai euclidià, a l'espai projectiu i hiperbòlic reals, aquesta integral correspon amb la s-èssima integral de curvatura mitja del convex inicial: se satisfà una propietat de reproductibitat, que no es té en els espais de curvatura holomorfa constant. En el treball donem l'expressió explícita de la integral de la curvatura mitja quan integrem sobre l'espai de plans complexos. L'expressem en termes de la integral de curvatura mitja del domini inicial i de la integral de la curvatura normal en una direcció especial: l'obtinguda en aplicar l'estructura complexa al vector normal. La motivació per estudiar els espais de curvatura holomorfa constant i, en particular, l'espai hiperbòlic complex, es troba en l'estudi del següent problema clàssic en geometria. Quin valor pren el quocient entre l'àrea i el perímetre per a successions de figures convexes del pla que creixen tendint a omplir-lo? Fins ara es coneixia el comportament d'aquest quocient en els espais de curvatura seccional negativa i que a l'espai hiperbòlic real les fites obtingudes són òptimes. Aquí provem que a l'espai hiperbòlic complex, les cotes generals no són òptimes i optimitzem la superior.

Modeling Dependence Structure and Forecasting Market Risk with Dynamic Asymmetric Copula

We investigate the dynamic and asymmetric dependence structure between equity portfolios from the US and UK. We demonstrate the statistical significance of dynamic asymmetric copula models in modelling and forecasting market risk. First, we construct “high-minus-low" equity portfolios sorted on beta, coskewness, and cokurtosis. We find substantial evidence of dynamic and asymmetric dependence between characteristic-sorted portfolios. Second, we consider a dynamic asymmetric copula model by combining the generalized hyperbolic skewed t copula with the generalized autoregressive score (GAS) model to capture both the multivariate non-normality and the dynamic and asymmetric dependence between equity portfolios. We demonstrate its usefulness by evaluating the forecasting performance of Value-at-Risk and Expected Shortfall for the high-minus-low portfolios. From back-testing, e find consistent and robust evidence that our dynamic asymmetric copula model provides the most accurate forecasts, indicating the importance of incorporating the dynamic and asymmetric dependence structure in risk management.

Semigroup analysis of structured populations with distributed states-at-birth arising in mathematical aquaculture

Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.

Some Considerations Concerning Regulation and Competition in the Port Sector

The aim of this paper is to discuss the circumstances in which the process of competition between ports takes place in Spain − circumstances arising from the way the port system is currently set up and from the regulations governing it. The importance of this matter lies both in the fact that intensified competition between ports is the way to set about boosting the efficiency of the Spanish port sector and in the relevance of this business to the economies of the regions in which the ports are located. It is precisely for this reason that the reform instituted in 1992 aimed to combine balanced development of the national port system with the defence of the interests of autonomous regions. To this end the current regulatory framework provides for the possibility of port authorities drawing up their own competitive strategies, but makes their implementation conditional upon approval of their business plan by the Spanish state port authority. The latter body coordinates the national port system to ensure the guidelines set by the central government authorities are followed in the field of transport. However, the scale of the differences which exist among both the size of facilities and their relevant markets on the one hand, and the financial and economic circumstances of each of them on the other, suggest that each port authority's needs must be very different. Consequently, their competitive strategies must also be very different. It is therefore valid to ask whether coping with this diversity calls for different guidelines to regulate their freedom of action. Key words: Competition, regulation, port sector JEL classification numbers: L1, L5, L9

Desarrollo de una aplicación web para representación de datos de posicionamiento

En aquesta memòria s’explica el desenvolupament d’una eina útil que permet a l’usuari visualitzar en l’aplicació Google Maps les dades de posicionament captats en una sessió GPS. En aquest projecte, hem dissenyat una aplicació Web en la qual recollim les dades ingressades per l’usuari mitjançant un formulari. Un cop emmagatzemades aquestes dades en el servidor, la nostra eina hi executa l’aplicació encarregada del càlcul de les posicions. Aquesta és un script desenvolupat en MATLAB, que s’encarrega d’interpretar les dades subministrades per l’usuari, amb les quals es poden calcular les coordenades captades pel receptor GPS. Una vegada calculades, el software les emmagatzema en el servidor, en un arxiu .xml, que serà el que posteriorment interpretarà Google Maps gràcies al seu API. D’aquesta manera, l’usuari obtindrà el resultat visual de la sessió GPS que hagi decidit carregar sense necessitat des disposar de cap software específic per a la interpretació i el càlcul de les dades que hi ha capturat.

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].

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the raph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group.

Evaluating the influence of spatial uncertainty in locality points for species distributional modeling

1. Species distribution modelling is used increasingly in both applied and theoretical research to predict how species are distributed and to understand attributes of species' environmental requirements. In species distribution modelling, various statistical methods are used that combine species occurrence data with environmental spatial data layers to predict the suitability of any site for that species. While the number of data sharing initiatives involving species' occurrences in the scientific community has increased dramatically over the past few years, various data quality and methodological concerns related to using these data for species distribution modelling have not been addressed adequately. 2. We evaluated how uncertainty in georeferences and associated locational error in occurrences influence species distribution modelling using two treatments: (1) a control treatment where models were calibrated with original, accurate data and (2) an error treatment where data were first degraded spatially to simulate locational error. To incorporate error into the coordinates, we moved each coordinate with a random number drawn from the normal distribution with a mean of zero and a standard deviation of 5 km. We evaluated the influence of error on the performance of 10 commonly used distributional modelling techniques applied to 40 species in four distinct geographical regions. 3. Locational error in occurrences reduced model performance in three of these regions; relatively accurate predictions of species distributions were possible for most species, even with degraded occurrences. Two species distribution modelling techniques, boosted regression trees and maximum entropy, were the best performing models in the face of locational errors. The results obtained with boosted regression trees were only slightly degraded by errors in location, and the results obtained with the maximum entropy approach were not affected by such errors. 4. Synthesis and applications. To use the vast array of occurrence data that exists currently for research and management relating to the geographical ranges of species, modellers need to know the influence of locational error on model quality and whether some modelling techniques are particularly robust to error. We show that certain modelling techniques are particularly robust to a moderate level of locational error and that useful predictions of species distributions can be made even when occurrence data include some error.

Mucosal immunology and models of mucosal HIV infection

The mucosa associated lymphoid tissue regulates and coordinates immune responses against mucosal pathogens. Mucosal tissues are the major targets exposed to HIV during transmission. In this paper we describe in vitro models of HIV mucosal infection using human explants to investigate target cells within this tissue.

The carbohydrate-binding specificity and molecular modelling of Canavalia maritima and Dioclea grandiflora lectins

The carbohydrate-binding specificity of lectins from the seeds of Canavalia maritima and Dioclea grandiflora was studied by hapten-inhibition of haemagglutination using various sugars and sugar derivatives as inhibitors, including N-acetylneuraminic acid and N-acetylmuramic acid. Despite some discrepancies, both lectins exhibited a very similar carbohydrate-binding specificity as previously reported for other lectins from Diocleinae (tribe Phaseoleae, sub-tribe Diocleinae). Accordingly, both lectins exhibited almost identical hydropathic profiles and their three-dimensional models built up from the atomic coordinates of ConA looked very similar. However, docking experiments of glucose and mannose in their monosaccharide-binding sites, by comparison with the ConA-mannose complex used as a model, revealed conformational changes in side chains of the amino acid residues involved in the binding of monosaccharides. These results fully agree with crystallographic data showing that binding of specific ligands to ConA requires conformational chances of its monosaccharide-binding site.

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.

Catabolic ornithine carbamoyltransferase of Pseudomonas aeruginosa. Importance of the N-terminal region for dodecameric structure and homotropic carbamoylphosphate cooperativity.

Pseudomonas aeruginosa has an anabolic (ArgF) and a catabolic (ArcB) ornithine carbamoyltransferase (OTCase). Despite extensive sequence similarities, these enzymes function unidirectionally in vivo. In the dodecameric catabolic OTCase, homotropic cooperativity for carbamoylphosphate strongly depresses the anabolic reaction; the residue Glu1O5 and the C-terminus are known to be essential for this cooperativity. When Glu1O5 and nine C-terminal amino acids of the catabolic OTCase were introduced, by in vitro genetic manipulation, into the closely related, trimeric, anabolic (ArgF) OTCase of Escherichia coli, the enzyme displayed Michaelis-Menten kinetics and no cooperativity was observed. This indicates that additional amino acid residues are required to produce homotropic cooperativity and a dodecameric assembly. To localize these residues, we constructed several hybrid enzymes by fusing, in vivo or in vitro, the E. coli argF gene to the P. aeruginosa arcB gene. A hybrid enzyme consisting of 101 N-terminal ArgF amino acids fused to 233 C-terminal ArcB residues and the reciprocal ArcB-ArgF hybrid were both trimers with little or no cooperativity. Replacing the seven N-terminal residues of the ArcB enzyme by the corresponding six residues of E. coli ArgF enzyme produced a dodecameric enzyme which showed a reduced affinity for carbamoylphosphate and an increase in homotropic cooperativity. Thus, the N-terminal amino acids of catabolic OTCase are important for interaction with carbamoylphosphate, but do not alone determine dodecameric assembly. Hybrid enzymes consisting of either 26 or 42 N-terminal ArgF amino acids and the corresponding C-terminal ArcB residues were both trimeric, yet they retained some homotropic cooperativity. Within the N-terminal ArcB region, a replacement of motif 28-33 by the corresponding ArgF segment destabilized the dodecameric structure and the enzyme existed in trimeric and dodecameric states, indicating that this region is important for dodecameric assembly. These findings were interpreted in the light of the three-dimensional structure of catabolic OTCase, which allows predictions about trimer-trimer interactions. Dodecameric assembly appears to require at least three regions: the N- and C-termini (which are close to each other in a monomer), residues 28-33 and residues 147-154. Dodecameric structure correlates with high carbamoylphosphate cooperativity and thermal stability, but some trimeric hybrid enzymes retain cooperativity, and the dodecameric Glu1O5-->Ala mutant gives hyperbolic carbamoylphosphate saturation, indicating that dodecameric structure is neither necessary nor sufficient to ensure cooperativity.

Identifying genetic signatures of selection in a non-model species, alpine gentian (Gentiana nivalis L.), using a landscape genetic approach

It is generally accepted that most plant populations are locally adapted. Yet, understanding how environmental forces give rise to adaptive genetic variation is a challenge in conservation genetics and crucial to the preservation of species under rapidly changing climatic conditions. Environmental variation, phylogeographic history, and population demographic processes all contribute to spatially structured genetic variation, however few current models attempt to separate these confounding effects. To illustrate the benefits of using a spatially-explicit model for identifying potentially adaptive loci, we compared outlier locus detection methods with a recently-developed landscape genetic approach. We analyzed 157 loci from samples of the alpine herb Gentiana nivalis collected across the European Alps. Principle coordinates of neighbor matrices (PCNM), eigenvectors that quantify multi-scale spatial variation present in a data set, were incorporated into a landscape genetic approach relating AFLP frequencies with 23 environmental variables. Four major findings emerged. 1) Fifteen loci were significantly correlated with at least one predictor variable (R (adj) (2) > 0.5). 2) Models including PCNM variables identified eight more potentially adaptive loci than models run without spatial variables. 3) When compared to outlier detection methods, the landscape genetic approach detected four of the same loci plus 11 additional loci. 4) Temperature, precipitation, and solar radiation were the three major environmental factors driving potentially adaptive genetic variation in G. nivalis. Techniques presented in this paper offer an efficient method for identifying potentially adaptive genetic variation and associated environmental forces of selection, providing an important step forward for the conservation of non-model species under global change.