Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Extreme times for volatility processes

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.

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.

Parrondo-like behavior in continuous-time random walks with memory

The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.

Time consistent Pareto solutions in common access resource gameswith asymmetric players

In the analysis of equilibrium policies in a di erential game, if agents have different time preference rates, the cooperative (Pareto optimum) solution obtained by applying the Pontryagin's Maximum Principle becomes time inconsistent. In this work we derive a set of dynamic programming equations (in discrete and continuous time) whose solutions are time consistent equilibrium rules for N-player cooperative di erential games in which agents di er in their instantaneous utility functions and also in their discount rates of time preference. The results are applied to the study of a cake-eating problem describing the management of a common property exhaustible natural resource. The extension of the results to a simple common property renewable natural resource model in in nite horizon is also discussed.

Géopatrimoines des trois Chablais. Identification et valorisation des témoins glaciaires

Cette recherche s'applique aux témoins glaciaires des Chablais dans quatre de leurs dimensions : géopatrimoine, connaissance objective, inventaire de géosites et valorisation. Elle est organisée sur le canevas d'un processus de patrimonialisation auquel elle participe et qu'elle interroge à la fois. En 2009, débutait le projet 123 Chablais, pour une durée de quatre ans. Il concernait l'ensemble du territoire chablaisien, réparti sur deux pays (France et Suisse) et trois entités administratives (département de la Haute-Savoie, cantons de Vaud et du Valais). Ce projet, élaboré dans le cadre du programme Interreg IV France-Suisse, avait pour but de dynamiser le développement économique local en s'appuyant sur les patrimoines régionaux. Le géopatrimoine, identifié comme une de ces ressources, faisait donc l'objet de plusieurs actions, dont cette recherche. En parallèle, le Chablais haut-savoyard préparait sa candidature pour rejoindre l'European Geopark Network (EGN). Son intégration, effective dès 2012, a fait de ce territoire le cinquième géoparc français du réseau. Le Geopark du Chablais fonde son identité géologique sur l'eau et la glace, deux thématiques intimement liées aux témoins glaciaires. Dans ce contexte d'intérêt pour le géopatrimoine local et en particulier pour le patrimoine glaciaire, plusieurs missions ont été assignées à cette recherche qui devait à la fois améliorer la connaissance objective des témoins glaciaires, inventorier les géosites glaciaires et valoriser le patrimoine glaciaire. Le premier objectif de ce travail était d'acquérir une vision synthétique des témoins glaciaires. Il a nécessité une étape de synthèse bibliographique ainsi que sa spatialisation, afin d'identifier les lacunes de connaissance et la façon dont ce travail pouvait contribuer à les combler. Sur cette base, plusieurs méthodes ont été mises en oeuvre : cartographie géomorphologique, reconstitution des lignes d'équilibre glaciaires et datations de blocs erratiques à l'aide des isotopes cosmogéniques produits in situ. Les cartes géomorphologiques ont été élaborées en particulier dans les cirques et vallons glaciaires. Les datations cosmogéniques ont été concentrées sur deux stades du glacier du Rhône : le Last Local Glacial Maximum (LLGM) et le stade de Monthey. Au terme de cette étape, les spécificités du patrimoine glaciaire régional se sont révélées être 1) une grande diversité de formes et des liens étroits avec différents autres processus géomorphologiques ; 2) une appartenance des témoins glaciaires à dix grandes étapes de la déglaciation du bassin lémanique. Le second objectif était centré sur le processus d'inventaire des géosites glaciaires. Nous avons mis l'accent sur la sélection du géopatrimoine en développant une approche basée sur deux axes (temps et espace) identifiés dans le volet précédent et avons ainsi réalisé un inventaire à thèmes, composé de 32 géosites. La structure de l'inventaire a également été explorée de façon à intégrer des critères d'usage de ces géosites. Cette démarche, soutenue par une réflexion sur les valeurs attribuées au géopatrimoine et sur la façon d'évaluer ces valeurs, nous a permis de mettre en évidence le point de vue anthropo - et scientifico - centré qui prévaut nettement dans la recherche européenne sur le géopatrimoine. L'analyse des résultats de l'inventaire a fait apparaître quelques caractéristiques du patrimoine glaciaire chablaisien, discret, diversifié, et comportant deux spécificités exploitables dans le cadre d'une médiation scientifique : son statut de « berceau de la théorie glaciaire » et ses liens étroits avec des activités de la vie quotidienne, en tant que matière première, support de loisir ou facteur de risque. Cette recherche a débouché sur l'élaboration d'une exposition itinérante sur le patrimoine glaciaire des Chablais. Ce produit de valorisation géotouristique a été conçu pour sensibiliser la population locale à l'impact des glaciers sur son territoire. Il présente une série de sept cartes de stades glaciaires, encadrées par les deux mêmes thématiques, l'histoire de la connaissance glaciaire d'une part, les témoins glaciaires et la société, d'autre part. -- This research focuses on glacial witnesses in the Chablais area according to four dimensions : geoheritage, objective knowledge, inventory and promotion of geosites. It is organized on the model of an heritage's process which it participates and that it questions both. In 2009, the project 123 Chablais started for a period of four years. It covered the entire chablaisien territory spread over two countries and three administrative entities (département of Haute-Savoie, canton of Vaud, canton of Valais). This project, developed in the framework of the Interreg IV France-Switzerland program, aimed to boost the local development through regional heritage. The geoheritage identified as one of these resources, was therefore the subject of several actions, including this research. In parallel, the French Chablais was preparing its application to join the European Geopark Network (EGN). Its integration, effective since 2012, made of this area the fifth French Geopark of the network. The Chablais Geopark geological identity was based on water and ice, two themes closely linked to the glacial witnesses. In this context of interest for the regional geoheritage and especially for the glacial heritage, several missions have been assigned to this research which should improve objective knowledge of glacial witnesses, inventory and assess glacial geosites. The objective knowledge's component was to acquire a synthetic vision of the glacial witnesses. It required a first bibliography synthesis step in order to identify gaps in knowledge and how this work could help to fill them. On this basis, several methods have been implemented: geomorphological mapping, reconstruction of the equilibrium-line altitude and dating of glacial erratic blocks using cosmogenic isotopes produced in situ. Geomorphological maps have been developed especially in glacial cirques and valleys. Cosmogenic datings were concentrated on two stages of the Rhone glacier: the Last Local Glacial Maximum (LLGM) and « the stage of Monthey ». After this step, the specificities of the regional glacial heritage have emerged to us as 1) a wide variety of forms and links to various other geomorphological processes; 2) belonging of glacial witnesses to ten major glacial stages of Léman Lake's deglaciation. In the inventory of glacial geosites component we focused on the selection of geoheritage. We developed an approach based on two axes (time and space) identified in the preceding components. We obtained a thematic inventory, consisting of 32 geosites. The structure of the inventory was also explored in the aim to integrate use criteria of geosites. This approach, supported by a thought on the values attributed to the geoheritage and how to assess these values allowed us to highlight the point of view much anthropological - and scientific -centered prevailing in the European research on geoheritage. The analysis of the inventory's results revealed some characteristics of chablaisien glacial heritage, discrete, diverse, and with two features exploitable in the context of a scientific mediation: its status as « cradle of the glacial theory » and its close links with activities of daily life, as raw material, leisure support and risk factor. This research leads to the development of a traveling exhibition on the glacial heritage of the Chablais area. It presents a series of seven glacial stage's cards, framed by the two themes mentioned above: « history of glacial knowledge » and « glacial witnesses and society ».

Unravelling the interaction between tectonic and sedimentary processes during lithospheric thinning in the Alpine Tethys margins

The discovery of exhumed continental mantle and hyper-extended crust in present-day magma-poor rifted margins is at the origin of a paradigm shift within the research field of deep-water rifted margins. It opened new questions about the strain history of rifted margins and the nature and composition of sedimentary, crustal and mantle rocks in rifted margins. Thanks to the benefit of more than one century of work in the Alps and access to world-class outcrops preserving the primary relationships between sediments and crustal and mantle rocks from the fossil Alpine Tethys margins, it is possible to link the subsidence history and syn-rift sedimentary evolution with the strain distribution observed in the crust and mantle rocks exposed in the distal rifted margins. In this paper, we will focus on the transition from early to late rifting that is associated with considerable crustal thinning and a reorganization of the rift system. Crustal thinning is at the origin of a major change in the style of deformation from high-angle to low-angle normal faulting which controls basin-architecture, sedimentary sources and processes and the nature of basement rocks exhumed along the detachment faults in the distal margin. Stratigraphic and isotopic ages indicate that this major change occurred in late Sinemurian time, involving a shift of the syn-rift sedimentation toward the distal domain associated with a major reorganization of the crustal structure with exhumation of lower and middle crust. These changes may be triggered by mantle processes, as indicated by the infiltration of MOR-type magmas in the lithospheric mantle, and the uplift of the Brianconnais domain. Thinning and exhumation of the crust and lithosphere also resulted in the creation of new paleogeographic domains, the Proto Valais and Liguria-Piemonte domains. These basins show a complex, 3D temporal and spatial evolution that might have evolved, at least in the case of the Liguria-Piemonte basin, in the formation of an embryonic oceanic crust. The re-interpretation of the rift evolution and the architecture of the distal rifted margins in the Alps have important implications for the understanding of rifted margins worldwide, but also for the paleogeographic reconstruction of the Alpine domain and its subsequent Alpine compressional overprint.

Multiple processes regulate long-term population dynamics of sea urchins on Mediterranean rocky reefs

We annually monitored the abundance and size structure of herbivorous sea urchin populations (Paracentrotus lividus and Arbacia lixula) inside and outside a marine reserve in the Northwestern Mediterranean on two distinct habitats (boulders and vertical walls) over a period of 20 years, with the aim of analyzing changes at different temporal scales in relation to biotic and abiotic drivers. P. lividus exhibited significant variability in density over time on boulder bottoms but not on vertical walls, and temporal trends were not significantly different between the protection levels. Differences in densities were caused primarily by variance in recruitment, which was less pronounced inside the MPA and was correlated with adult density, indicating density-dependent recruitment under high predation pressure, as well as some positive feedback mechanisms that may facilitate higher urchin abundances despite higher predator abundance. Populations within the reserve were less variable in abundance and did not exhibit the hyper-abundances observed outside the reserve, suggesting that predation effects maybe more subtle than simply lowering the numbers of urchins in reserves. A. lixula densities were an order of magnitude lower than P. lividus densities and varied within sites and over time on boulder bottoms but did not differ between protection levels. In December 2008, an exceptionally violent storm reduced sea urchin densities drastically (by 50% to 80%) on boulder substrates, resulting in the lowest values observed over the entire study period, which remained at that level for at least two years (up to the present). Our results also showed great variability in the biological and physical processes acting at different temporal scales. This study highlights the need for appropriate temporal scales for studies to fully understand ecosystem functioning, the concepts of which are fundamental to successful conservation and management.

On Ito's formula for elliptic diffusion processes

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Ito's formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303-328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x.

Using Scanning Lasers for Real-Time Pavement Thickness Measurement, TR-538, 2006

Due to limited budgets and reduced inspection staff, state departments of transportation (DOTs) are in need of innovative approaches for providing more efficient quality assurance on concrete paving projects. The goal of this research was to investigate and test new methods that can determine pavement thickness in real time. Three methods were evaluated: laser scanning, ultrasonic sensors, and eddy current sensors. Laser scanning, which scans the surface of the base prior to paving and then scans the surface after paving, can determine the thickness at any point. Also, scanning lasers provide thorough data coverage that can be used to calculate thickness variance accurately and identify any areas where the thickness is below tolerance. Ultrasonic and eddy current sensors also have the potential to measure thickness nondestructively at discrete points and may result in an easier method of obtaining thickness. There appear to be two viable approaches for measuring concrete pavement thickness during the paving operation: laser scanning and eddy current sensors. Laser scanning has proved to be a reliable technique in terms of its ability to provide virtual core thickness with low variability. Research is still required to develop a prototype system that integrates point cloud data from two scanners. Eddy current sensors have also proved to be a suitable alternative, and are probably closer to field implementation than the laser scanning approach. As a next step for this research project, it is suggested that a pavement thickness measuring device using eddy current sensors be created, which would involve both a handheld and paver-mounted version of the device.

Astrocytic αVβ3 integrin inhibits neurite outgrowth and promotes retraction of neuronal processes by clustering Thy-1.

Thy-1 is a membrane glycoprotein suggested to stabilize or inhibit growth of neuronal processes. However, its precise function has remained obscure, because its endogenous ligand is unknown. We previously showed that Thy-1 binds directly to α(V)β(3) integrin in trans eliciting responses in astrocytes. Nonetheless, whether α(V)β(3) integrin might also serve as a Thy-1-ligand triggering a neuronal response has not been explored. Thus, utilizing primary neurons and a neuron-derived cell line CAD, Thy-1-mediated effects of α(V)β(3) integrin on growth and retraction of neuronal processes were tested. In astrocyte-neuron co-cultures, endogenous α(V)β(3) integrin restricted neurite outgrowth. Likewise, α(V)β(3)-Fc was sufficient to suppress neurite extension in Thy-1(+), but not in Thy-1(-) CAD cells. In differentiating primary neurons exposed to α(V)β(3)-Fc, fewer and shorter dendrites were detected. This effect was abolished by cleavage of Thy-1 from the neuronal surface using phosphoinositide-specific phospholipase C (PI-PLC). Moreover, α(V)β(3)-Fc also induced retraction of already extended Thy-1(+)-axon-like neurites in differentiated CAD cells as well as of axonal terminals in differentiated primary neurons. Axonal retraction occurred when redistribution and clustering of Thy-1 molecules in the plasma membrane was induced by α(V)β(3) integrin. Binding of α(V)β(3)-Fc was detected in Thy-1 clusters during axon retraction of primary neurons. Moreover, α(V)β(3)-Fc-induced Thy-1 clustering correlated in time and space with redistribution and inactivation of Src kinase. Thus, our data indicates that α(V)β(3) integrin is a ligand for Thy-1 that upon binding not only restricts the growth of neurites, but also induces retraction of already existing processes by inducing Thy-1 clustering. We propose that these events participate in bi-directional astrocyte-neuron communication relevant to axonal repair after neuronal damage.

Real-time monitoring of the silicidation process of tungsten filaments at high temperature used as catalysers for silane decomposition

The scope of this work is the systematic study of the silicidation process affecting tungsten filaments at high temperature (1900ºC) used for silane decomposition in the hot-wire chemical vapour deposition technique (HWCVD). The correlation between the electrical resistance evolution of the filaments, Rfil(t), and the different stages of the their silicidation process is exposed. Said stages correspond to: the rapid formation of two WSi2 fronts at the cold ends of the filaments and their further propagation towards the middle of the filaments; and, regarding the hot central portion of the filaments: a initial stage of silicon dissolution into the tungsten bulk, with a random duration for as-manufactured filaments, followed by the inhomogeneous nucleation of W5Si3 (which is later replaced by WSi2) and its further growth towards the filaments core. An electrical model is used to obtain real-time information about the current status of the filaments silicidation process by simply monitoring their Rfil(t) evolution during the HWCVD process. It is shown that implementing an annealing pre-treatment to the filaments leads to a clearly repetitive trend in the monitored Rfil(t) signatures. The influence of hydrogen dilution of silane on the filaments silicidation process is also discussed.

Els manlleus en la revista “Time Out Barcelona”

El present treball constitueix un estudi i una anàlisi sobre les dades obtingudes del buidatge dels manlleus recollits en dos números de la revista catalana Time Out Barcelona. L’objectiu és aprofundir en el tema dels préstecs i extreure algunes conclusions sobre els tipus d’unitats manllevades i el seu tractament.

On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management

The choice network revenue management (RM) model incorporates customer purchase behavioras customers purchasing products with certain probabilities that are a function of the offeredassortment of products, and is the appropriate model for airline and hotel network revenuemanagement, dynamic sales of bundles, and dynamic assortment optimization. The underlyingstochastic dynamic program is intractable and even its certainty-equivalence approximation, inthe form of a linear program called Choice Deterministic Linear Program (CDLP) is difficultto solve in most cases. The separation problem for CDLP is NP-complete for MNL with justtwo segments when their consideration sets overlap; the affine approximation of the dynamicprogram is NP-complete for even a single-segment MNL. This is in contrast to the independentclass(perfect-segmentation) case where even the piecewise-linear approximation has been shownto be tractable. In this paper we investigate the piecewise-linear approximation for network RMunder a general discrete-choice model of demand. We show that the gap between the CDLP andthe piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinearapproximation is polynomially-time solvable for a fixed consideration set size, bringing itinto the realm of tractability for small consideration sets; small consideration sets are a reasonablemodeling tradeoff in many practical applications. Our solution relies on showing that forany discrete-choice model the separation problem for the linear program of the piecewise-linearapproximation can be solved exactly by a Lagrangian relaxation. We give modeling extensionsand show by numerical experiments the improvements from using piecewise-linear approximationfunctions.

Estimating traveltimes and groundwater flow patterns using 3D time-lapse crosshole ERT imaging of electrical resistivity fluctuations induced by infiltrating river water

The infiltration of river water into aquifers is of high relevance to drinking-water production and is a key driver of biogeochemical processes in the hyporheic and riparian zone, but the distribution and quantification of the infiltrating water are difficult to determine using conventional hydrological methods (e.g., borehole logging and tracer tests). By time-lapse inverting crosshole ERT (electrical resistivity tomography) monitoring data, we imaged groundwater flow patterns driven by river water infiltrating a perialpine gravel aquifer in northeastern Switzerland. This was possible because the electrical resistivity of the infiltrating water changed during rainfall-runoff events. Our time-lapse resistivity models indicated rather complex flow patterns as a result of spatially heterogeneous bank filtration and aquifer heterogeneity. The upper part of the aquifer was most affected by the river infiltrate, and the highest groundwater velocities and possible preferential flow occurred at shallow to intermediate depths. Time series of the reconstructed resistivity models matched groundwater electrical resistivity data recorded on borehole loggers in the upper and middle parts of the aquifer, whereas the resistivity models displayed smaller variations and delayed responses with respect to the logging data. in the lower part. This study demonstrated that crosshole ERT monitoring of natural electrical resistivity variations of river infiltrate could be used to image and quantify 3D bank filtration and aquifer dynamics at a high spatial resolution.