Meanders and the Temperley-Lieb algebra

The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weight $q$ per connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram determinant as a function of $q$, and make use of the orthogonalization process to derive alternative expressions for meander numbers as sums over correlated random walks.Comment: 85p, uuencoded, uses harvmac (l mode) and epsf, 88 figure

Modelling stochastic bivariate mortality

Stochastic mortality, i.e. modelling death arrival via a jump process with stochastic intensity, is gaining increasing reputation as a way to represent mortality risk. This paper represents a first attempt to model the mortality risk of couples of individuals, according to the stochastic intensity approach. On the theoretical side, we extend to couples the Cox processes set up, i.e. the idea that mortality is driven by a jump process whose intensity is itself a stochastic process, proper of a particular generation within each gender. Dependence between the survival times of the members of a couple is captured by an Archimedean copula. On the calibration side, we fit the joint survival function by calibrating separately the (analytical) copula and the (analytical) margins. First, we select the best fit copula according to the methodology of Wang and Wells (2000) for censored data. Then, we provide a sample-based calibration for the intensity, using a time-homogeneous, non mean-reverting, affine process: this gives the analytical marginal survival functions. Coupling the best fit copula with the calibrated margins we obtain, on a sample generation, a joint survival function which incorporates the stochastic nature of mortality improvements and is far from representing independency.On the contrary, since the best fit copula turns out to be a Nelsen one, dependency is increasing with age and long-term dependence exists

Reticular pseudodrusen in late-onset retinal degeneration

PURPOSE: To characterize the association of reticular pseudodrusen (RPD) with late-onset retinal degeneration (L-ORD) using multimodal imaging. DESIGN: Prospective, two-center, longitudinal case series. SUBJECTS: Twenty-nine cases with L-ORD. METHODS: All subjects were evaluated within a three-year interval with near-infrared reflectance, fundus autofluorescence, and spectral-domain optical coherence tomography. In addition, a subset of patients also underwent indocyanine green angiography, fundus fluorescein angiography, mesopic microperimetry, and multifocal electroretinography. Main outcome measures: Prevalence, topographic distribution, and temporal phenotypic changes of RPD in L-ORD. RESULTS: A total of 29 molecularly confirmed L-ORD cases were included in this prospective study. RPD was detected in 18 cases (62%) at baseline, of which 10 were male. The prevalence of RPD varied with age. The mean age of RPD patients was 57.3±7.2 years. RPD was not seen in cases below the fifth decade (n=3 patients) or in the eighth decade (n=5 patients). RPD were found commonly in the macula with relative sparing of the fovea and were also identified in the peripheral retina. The morphology of RPD changed with follow-up. Two cases (3 eyes) demonstrated RPD regression. CONCLUSIONS: RPD is found frequently in cases with L-ORD and at a younger age than in individuals with AMD. RPD exhibits quick formation and collapse, change in type and morphology with time, relative foveal-sparing, and also has a peripheral retinal location in L-ORD

Derivatives and Credit Contagion in Interconnected Networks

The importance of adequately modeling credit risk has once again been highlighted in the recent financial crisis. Defaults tend to cluster around times of economic stress due to poor macro-economic conditions, {\em but also} by directly triggering each other through contagion. Although credit default swaps have radically altered the dynamics of contagion for more than a decade, models quantifying their impact on systemic risk are still missing. Here, we examine contagion through credit default swaps in a stylized economic network of corporates and financial institutions. We analyse such a system using a stochastic setting, which allows us to exploit limit theorems to exactly solve the contagion dynamics for the entire system. Our analysis shows that, by creating additional contagion channels, CDS can actually lead to greater instability of the entire network in times of economic stress. This is particularly pronounced when CDS are used by banks to expand their loan books (arguing that CDS would offload the additional risks from their balance sheets). Thus, even with complete hedging through CDS, a significant loan book expansion can lead to considerably enhanced probabilities for the occurrence of very large losses and very high default rates in the system. Our approach adds a new dimension to research on credit contagion, and could feed into a rational underpinning of an improved regulatory framework for credit derivatives.Comment: 26 pages, 7 multi-part figure

Hypoxia activates IKK-NF-κB and the immune response in <em>Drosophila melanogaster</em>

Hypoxia, or low oxygen availability, is an important physiological and pathological stimulus for multicellular organisms. Molecularly, hypoxia activates a transcriptional programme directed at restoration of oxygen homoeostasis and cellular survival. In mammalian cells, hypoxia not only activates the HIF (hypoxia-inducible factor) family, but also additional transcription factors such as NF-κB (nuclear factor κB). Here we show that hypoxia activates the IKK–NF-κB [IκB (inhibitor of nuclear factor κB)–NF-κB] pathway and the immune response in Drosophila melanogaster. We show that NF-κB activation is required for organism survival in hypoxia. Finally, we identify a role for the tumour suppressor Cyld, as a negative regulator of NF-κB in response to hypoxia in Drosophila. The results indicate that hypoxia activation of the IKK–NF-κB pathway and the immune response is an important and evolutionary conserved response

Adsorption Isotherms of Hydrogen: The Role of Thermal Fluctuations

It is shown that experimentally obtained isotherms of adsorption on solid substrates may be completely reconciled with Lifshitz theory when thermal fluctuations are taken into account. This is achieved within the framework of a solid-on-solid model which is solved numerically. Analysis of the fluctuation contributions observed for hydrogen adsorption onto gold substrates allows to determine the surface tension of the free hydrogen film as a function of film thickness. It is found to decrease sharply for film thicknesses below seven atomic layers.Comment: RevTeX manuscript (3 pages output), 3 figure

Scope for Credit Risk Diversification

This paper considers a simple model of credit risk and derives the limit distribution of losses under different assumptions regarding the structure of systematic risk and the nature of exposure or firm heterogeneity. We derive fat-tailed correlated loss distributions arising from Gaussian risk factors and explore the potential for risk diversification. Where possible the results are generalised to non-Gaussian distributions. The theoretical results indicate that if the firm parameters are heterogeneous but come from a common distribution, for sufficiently large portfolios there is no scope for further risk reduction through active portfolio management. However, if the firm parameters come from different distributions, then further risk reduction is possible by changing the portfolio weights. In either case, neglecting parameter heterogeneity can lead to underestimation of expected losses. But, once expected losses are controlled for, neglecting parameter heterogeneity can lead to overestimation of risk, whether measured by unexpected loss or value-at-risk

Hamiltonian dynamics of the two-dimensional lattice phi^4 model

The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the presence of the continuous phase transition at a finite energy density and are consistent both qualitatively and quantitatively with the predictions of equilibrium statistical mechanics. The Hamiltonian microscopic dynamics also exhibits critical slowing down close to the transition. Moreover, the relationship between chaos and the phase transition is considered, and interpreted in the light of a geometrization of dynamics.Comment: REVTeX, 24 pages with 20 PostScript figure