Unsteady supersonic aerodynamic theory for interfering surfaces by the method of potential gradient

A generalized solution of the hyperbolic wave equation was further developed to relate the velocity components at a field point to the potential gradient distribution in the dependence domain. Singular integrals were evaluated in closed form, with numerical integration methods for more complex but analytic functions. Idealization of the lifting surfaces by trapezoidal elements with two sides parallel to the streamlines is computationally efficient. Streamwise integrals were performed analytically, and spanwise integrals were neccessary only on element leading and trailing sides. All integrands vanish on the Mach cone. Pressure distribution on a double delta wing and generalized aerodynamic coefficients for three AGARD planforms were calculated and compared with available results

Modeling the Dependency Structure of Stock Index Returns using a Copula Function Approach

In the present study we assess the dependency structure between stock indexes by econometrically estimating the empirical copula function and the parameters of various parametric copula functions. The main finding is that the t-copula and the Gumbel-Clayton mixture copula are the most appropriate copula functions to capture the dependency structure of two financial return series. With the dependency structure given by the estimated copula functions we quantify the efficient portfolio frontier using as a risk measure CVaR (Conditional VaR) computed by Monte Carlo simulation. We find that in the case of using normal distributions for modeling individual returns the market risk is underestimated no mater what copula function is employed to capture the dependency structure.copula functions, copula mixtures, the efficient portfolio frontier, Conditional VAR, Monte Carlo simulation

Predictive Inference for Spatio-temporal Precipitation Data and Its Extremes

Modelling of precipitation and its extremes is important for urban and agriculture planning purposes. We present a method for producing spatial predictions and measures of uncertainty for spatio-temporal data that is heavy-tailed and subject to substaintial skewness which often arise in measurements of many environmental processes, and we apply the method to precipitation data in south-west Western Australia. A generalised hyperbolic Bayesian hierarchical model is constructed for the intensity, frequency and duration of daily precipitation, including the extremes. Unlike models based on extreme value theory, which only model maxima of finite-sized blocks or exceedances above a large threshold, the proposed model uses all the data available efficiently, and hence not only fits the extremes but also models the entire rainfall distribution. It captures spatial and temporal clustering, as well as spatially and temporally varying volatility and skewness. The model assumes that the regional precipitation is driven by a latent process characterised by geographical and climatological covariates. Effects not fully described by the covariates are captured by spatial and temporal structure in the hierarchies. Inference is provided by MCMC using a Metropolis-Hastings algorithm and spatial interpolation method, which provide a natural approach for estimating uncertainty. Similarly both spatial and temporal predictions with uncertainty can be produced with the model.Comment: Under review at Journal of the American Statistical Association. 27 pages, 10 figure

Numerical convergence of the block-maxima approach to the Generalized Extreme Value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. [2006] have found analytical results.Comment: 34 pages, 7 figures; Journal of Statistical Physics 201

Modeling a Distribution of Mortgage Credit Losses

One of the biggest risks arising from financial operations is the risk of counterparty default, commonly known as a “credit risk”. Leaving unmanaged, the credit risk would, with a high probability, result in a crash of a bank. In our paper, we will focus on the credit risk quantification methodology. We will demonstrate that the current regulatory standards for credit risk management are at least not perfect, despite the fact that the regulatory framework for credit risk measurement is more developed than systems for measuring other risks, e.g. market risks or operational risk. Generalizing the well known KMV model, standing behind Basel II, we build a model of a loan portfolio involving a dynamics of the common factor, influencing the borrowers’ assets, which we allow to be non-normal. We show how the parameters of our model may be estimated by means of past mortgage deliquency rates. We give a statistical evidence that the non-normal model is much more suitable than the one assuming the normal distribution of the risk factors. We point out how the assumption that risk factors follow a normal distribution can be dangerous. Especially during volatile periods comparable to the current crisis, the normal distribution based methodology can underestimate the impact of change in tail losses caused by underlying risk factors.Credit Risk, Mortgage, Delinquency Rate, Generalized Hyperbolic Distribution, Normal Distribution

Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models

Global sensitivity analysis aims at quantifying the impact of input variability onto the variation of the response of a computational model. It has been widely applied to deterministic simulators, for which a set of input parameters has a unique corresponding output value. Stochastic simulators, however, have intrinsic randomness due to their use of (pseudo)random numbers, so they give different results when run twice with the same input parameters but non-common random numbers. Due to this random nature, conventional Sobol' indices, used in global sensitivity analysis, can be extended to stochastic simulators in different ways. In this paper, we discuss three possible extensions and focus on those that depend only on the statistical dependence between input and output. This choice ignores the detailed data generating process involving the internal randomness, and can thus be applied to a wider class of problems. We propose to use the generalized lambda model to emulate the response distribution of stochastic simulators. Such a surrogate can be constructed without the need for replications. The proposed method is applied to three examples including two case studies in finance and epidemiology. The results confirm the convergence of the approach for estimating the sensitivity indices even with the presence of strong heteroskedasticity and small signal-to-noise ratio

Coupling of cytoplasm and adhesion dynamics determines cell polarization and locomotion

Observations of single epidermal cells on flat adhesive substrates have revealed two distinct morphological and functional states, namely a non-migrating symmetric unpolarized state and a migrating asymmetric polarized state. These states are characterized by different spatial distributions and dynamics of important biochemical cell components: F-actin and myosin-II form the contractile part of the cytoskeleton, and integrin receptors in the plasma membrane connect F-actin filaments to the substratum. In this way, focal adhesion complexes are assembled, which determine cytoskeletal force transduction and subsequent cell locomotion. So far, physical models have reduced this phenomenon either to gradients in regulatory control molecules or to different mechanics of the actin filament system in different regions of the cell. Here we offer an alternative and self-organizational model incorporating polymerization, pushing and sliding of filaments, as well as formation of adhesion sites and their force dependent kinetics. All these phenomena can be combined into a non-linearly coupled system of hyperbolic, parabolic and elliptic differential equations. Aim of this article is to show how relatively simple relations for the small-scale mechanics and kinetics of participating molecules may reproduce the emergent behavior of polarization and migration on the large-scale cell level.Comment: v2 (updates from proof): add TOC, clarify Fig. 4, fix several typo