Mutigrid preconditioner for nonconforming discretization of elliptic problems with jump coefficients

In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic problems with jump coe fficients. The preconditioner uses the standard conforming subspaces as coarse spaces. Numerical tests show both robustness with respect to the jump in the coe fficient and near-optimality with respect to the number of degrees of freedom.

Influence of initial foot dorsal flexion on vertical jump and running performance.

Several studies (on an inclined platform or with special shoes) have reported improved jump performance when the ankle was in a dorsiflexion (DF) position. The present study aims to test whether shoes inducing moderate DF modify vertical jump performance and energy cost. Twenty-one young, healthy female subjects (30 +/- 6 yr, 58 +/- 6 kg, O2max 45 +/- 3 mLxkg-1xmin-1, mean +/- SD) participated in the study. Jump performance was tested with subjects either wearing 4 degrees DF or standard (S) shoes. The jump tests (performed on a force platform) consisted of squat jump (SJ), countermovement jump (CMJ), and continuous jumps (CJ) during 15 seconds. Measured parameters were jump height, speed at take off, and maximal and average power. Oxygen uptake was measured on a treadmill while subjects ran at 95% of the anaerobic threshold during a 7-minute steady-state period. As compared with S shoes, DF shoes significantly improved the height of SJ (31 +/- 4 cm vs. 34 +/- 4 cm, p = 0.0001), CMJ (32 +/- 4 cm vs. 34 +/- 4 cm, p = 0.0004), and CJ (17.5 +/- 4.2 cm vs. 22.0 +/- 6.0 cm, p = 0.0001). Speed at take off was also significantly higher. Mean power significantly increased in SJ and CJ but not in CMJ. Oxygen uptake was not different between conditions (p = 0.40). Dorsiflexion shoes induce a significant increase in jump performance. These results are in accordance with the concept that a DF of the ankle may induce an increase of the length and strength of the triceps surae (higher torque). However, wearing DF shoes did not require more energy during running. Dorsiflexion shoes could be used to increase jump performance in several sports such as volleyball in which jump height is essential.

On the term structure of Interbank interest rates: Jump-diffusion processes and option pricing

In this paper we study the dynamic behavior of the term structureof Interbank interest rates and the pricing of options on interest ratesensitive securities. We posit a generalized single factor model withjumps to take into account external influences in the market. Daily datais used to test for jump effects. Qualitative examination of the linkagebetween Monetary Authorities' interventions and jumps are studied. Pricingresults suggests a systematic underpricing in bonds and call options ifthe jumps component is not included. However, the pricing of put optionson bonds presents indeterminacies.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

A system to measure the kinematics during the entire ski jump sequence using inertial sensors.

Three-dimensional analysis of the entire sequence in ski jumping is recommended when studying the kinematics or evaluating performance. Camera-based systems which allow three-dimensional kinematics measurement are complex to set-up and require extensive post-processing, usually limiting ski jumping analyses to small numbers of jumps. In this study, a simple method using a wearable inertial sensors-based system is described to measure the orientation of the lower-body segments (sacrum, thighs, shanks) and skis during the entire jump sequence. This new method combines the fusion of inertial signals and biomechanical constraints of ski jumping. Its performance was evaluated in terms of validity and sensitivity to different performances based on 22 athletes monitored during daily training. The validity of the method was assessed by comparing the inclination of the ski and the slope at landing point and reported an error of -0.2±4.8°. The validity was also assessed by comparison of characteristic angles obtained with the proposed system and reference values in the literature; the differences were smaller than 6° for 75% of the angles and smaller than 15° for 90% of the angles. The sensitivity to different performances was evaluated by comparing the angles between two groups of athletes with different jump lengths and by assessing the association between angles and jump lengths. The differences of technique observed between athletes and the associations with jumps length agreed with the literature. In conclusion, these results suggest that this system is a promising tool for a generalization of three-dimensional kinematics analysis in ski jumping.

Anomalous specific-heat jump in a two-component ultracold Fermi gas

The thermodynamic functions of a Fermi gas with spin population imbalance are studied in the temperature-asymmetry plane in the BCS limit. The low-temperature domain is characterized by an anomalous enhancement of the entropy and the specific heat above their values in the unpaired state, decrease of the gap and eventual unpairing phase transition as the temperature is lowered. The unpairing phase transition induces a second jump in the specific heat, which can be measured in calorimetric experiments. While the superfluid is unstable against a supercurrent carrying state, it may sustain a metastable state if cooled adiabatically down from the stable high-temperature domain. In the latter domain the temperature dependence of the gap and related functions is analogous to the predictions of the BCS theory.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Velocity-jump instabilities in Hele-Shaw flow of associating polymer solutions

We study fracturelike flow instabilities that arise when water is injected into a Hele-Shaw cell filled with aqueous solutions of associating polymers. We explore various polymer architectures, molecular weights, and solution concentrations. Simultaneous measurements of the finger tip velocity and of the pressure at the injection point allow us to describe the dynamics of the finger in terms of the finger mobility, which relates the velocity to the pressure gradient. The flow discontinuities, characterized by jumps in the finger tip velocity, which are observed in experiments with some of the polymer solutions, can be modeled by using a nonmonotonic dependence between a characteristic shear stress and the shear rate at the tip of the finger. A simple model, which is based on a viscosity function containing both a Newtonian and a non-Newtonian component, and which predicts nonmonotonic regions when the non-Newtonian component of the viscosity dominates, is shown to agree with the experimental data.

Human-to-bovine jump of Staphylococcus aureus CC8 is associated with the loss of a β-hemolysin converting prophage and the acquisition of a new staphylococcal cassette chromosome.

Staphylococcus aureus can colonize and infect both humans and animals, but isolates from both hosts tend to belong to different lineages. Our recent finding of bovine-adapted S. aureus showing close genetic relationship to the human S. aureus clonal complex 8 (CC8) allowed us to examine the genetic basis of host adaptation in this particular CC. Using total chromosome microarrays, we compared the genetic makeup of 14 CC8 isolates obtained from cows suffering subclinical mastitis, with nine CC8 isolates from colonized or infected human patients, and nine S. aureus isolates belonging to typical bovine CCs. CC8 isolates were found to segregate in a unique group, different from the typical bovine CCs. Within this CC8 group, human and bovine isolates further segregated into three subgroups, among which two contained a mix of human and bovine isolates, and one contained only bovine isolates. This distribution into specific clusters and subclusters reflected major differences in the S. aureus content of mobile genetic elements (MGEs). Indeed, while the mixed human-bovine clusters carried commonly human-associated β-hemolysin converting prophages, the bovine-only isolates were devoid of such prophages but harbored an additional new non-mec staphylococcal cassette chromosome (SCC) unique to bovine CC8 isolates. This composite cassette carried a gene coding for a new LPXTG-surface protein sharing homologies with a protein found in the environmental bacterium Geobacillus thermoglucosidans. Thus, in contrast to human CC8 isolates, the bovine-only CC8 group was associated with the combined loss of β-hemolysin converting prophages and gain of a new SCC probably acquired in the animal environment. Remaining questions are whether the new LPXTG-protein plays a role in bovine colonization or infection, and whether the new SCC could further acquire antibiotic-resistance genes and carry them back to human.

Valuing equity-linked death benefits in jump diffusion models

The paper is motivated by the valuation problem of guaranteed minimum death benefits in various equity-linked products. At the time of death, a benefit payment is due. It may depend not only on the price of a stock or stock fund at that time, but also on prior prices. The problem is to calculate the expected discounted value of the benefit payment. Because the distribution of the time of death can be approximated by a combination of exponential distributions, it suffices to solve the problem for an exponentially distributed time of death. The stock price process is assumed to be the exponential of a Brownian motion plus an independent compound Poisson process whose upward and downward jumps are modeled by combinations (or mixtures) of exponential distributions. Results for exponential stopping of a Lévy process are used to derive a series of closed-form formulas for call, put, lookback, and barrier options, dynamic fund protection, and dynamic withdrawal benefit with guarantee. We also discuss how barrier options can be used to model lapses and surrenders.

The practical examination and how it correlates with the triple jump, tutorial, and written examination

This study explored the relationship between the practical examination and other course evaluation methods~ specifically, the triple jump, tutorial, and written examination. Studies correlating academic and clinical grades tended to indicate that they may not be highly correlated because each evaluation process contributes different kinds of information regarding student knowledge, skills, and attitudes. Six hypotheses were generated stating a positive relationship between the four evaluation methods. A correlation matrix was produced of the Pearson Product Moment correlation co-efficients on the four evaluation methods in the second and third year Occupational Therapy Technique and Clinical Problem Solving courses of the 1988 and 1989 graduates (n~45). The results showed that the highest correlations existed between the triple jump and the tutorial grades and the lowest correlations existed between the practical examination and written examination grades. Not all of the correlations~ however~ reached levels of significance. The correlations overall. though, were only low to moderate at best which indicates that the evaluation methods may be measuring different aspects of student learning. This conclusion supports the studies researched. The implications and significance of this study is that it will assist the faculty in defining what the various evaluation methods measure which will in turn promote more critical input into curriculum development for the remaining years of the program.