Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Domain growth in binary mixtures at low temperatures

We have studied domain growth during spinodal decomposition at low temperatures. We have performed a numerical integration of the deterministic time-dependent Ginzburg-Landau equation with a variable, concentration-dependent diffusion coefficient. The form of the pair-correlation function and the structure function are independent of temperature but the dynamics is slower at low temperature. A crossover between interfacial diffusion and bulk diffusion mechanisms is observed in the behavior of the characteristic domain size. This effect is explained theoretically in terms of an equation of motion for the interface.

Effects of domain morphology in phase-separation dynamics at low temperature

We present numerical results of the deterministic Ginzburg-Landau equation with a concentration-dependent diffusion coefficient, for different values of the volume fraction phi of the minority component. The morphology of the domains affects the dynamics of phase separation. The effective growth exponents, but not the scaled functions, are found to be temperature dependent.

Fluctuations in domain growth: Ginzburg-Landau equations with multiplicative noise

Ginzburg-Landau equations with multiplicative noise are considered, to study the effects of fluctuations in domain growth. The equations are derived from a coarse-grained methodology and expressions for the resulting concentration-dependent diffusion coefficients are proposed. The multiplicative noise gives contributions to the Cahn-Hilliard linear-stability analysis. In particular, it introduces a delay in the domain-growth dynamics.

Numerical algorithm for Ginzburg-Landau equations with multiplicative noise: Application to domain growth

We consider stochastic partial differential equations with multiplicative noise. We derive an algorithm for the computer simulation of these equations. The algorithm is applied to study domain growth of a model with a conserved order parameter. The numerical results corroborate previous analytical predictions obtained by linear analysis.

Front and domain growth in the presence of gravity

Front and domain growth of a binary mixture in the presence of a gravitational field is studied. The interplay of bulk- and surface-diffusion mechanisms is analyzed. An equation for the evolution of interfaces is derived from a time-dependent Ginzburg-Landau equation with a concentration-dependent diffusion coefficient. Scaling arguments on this equation give the exponents of a power-law growth. Numerical integrations of the Ginzburg-Landau equation corroborate the theoretical analysis.

Characterization of gravitational rock slope deformations at different spatial scales based on field, remote sensing and numerical approaches

Rock slope instabilities such as rock slides, rock avalanche or deep-seated gravitational slope deformations are widespread in Alpine valleys. These phenomena represent at the same time a main factor that control the mountain belts erosion and also a significant natural hazard that creates important losses to the mountain communities. However, the potential geometrical and dynamic connections linking outcrop and slope-scale instabilities are often unknown. A more detailed definition of the potential links will be essential to improve the comprehension of the destabilization processes and to dispose of a more complete hazard characterization of the rock instabilities at different spatial scales. In order to propose an integrated approach in the study of the rock slope instabilities, three main themes were analysed in this PhD thesis: (1) the inventory and the spatial distribution of rock slope deformations at regional scale and their influence on the landscape evolution, (2) the influence of brittle and ductile tectonic structures on rock slope instabilities development and (3) the characterization of hazard posed by potential rock slope instabilities through the development of conceptual instability models. To prose and integrated approach for the analyses of these topics, several techniques were adopted. In particular, high resolution digital elevation models revealed to be fundamental tools that were employed during the different stages of the rock slope instability assessment. A special attention was spent in the application of digital elevation model for detailed geometrical modelling of past and potential instabilities and for the rock slope monitoring at different spatial scales. Detailed field analyses and numerical models were performed to complete and verify the remote sensing approach. In the first part of this thesis, large slope instabilities in Rhone valley (Switzerland) were mapped in order to dispose of a first overview of tectonic and climatic factors influencing their distribution and their characteristics. Our analyses demonstrate the key influence of neotectonic activity and the glacial conditioning on the spatial distribution of the rock slope deformations. Besides, the volumes of rock instabilities identified along the main Rhone valley, were then used to propose the first estimate of the postglacial denudation and filling of the Rhone valley associated to large gravitational movements. In the second part of the thesis, detailed structural analyses of the Frank slide and the Sierre rock avalanche were performed to characterize the influence of brittle and ductile tectonic structures on the geometry and on the failure mechanism of large instabilities. Our observations indicated that the geometric characteristics and the variation of the rock mass quality associated to ductile tectonic structures, that are often ignored landslide study, represent important factors that can drastically influence the extension and the failure mechanism of rock slope instabilities. In the last part of the thesis, the failure mechanisms and the hazard associated to five potential instabilities were analysed in detail. These case studies clearly highlighted the importance to incorporate different analyses and monitoring techniques to dispose of reliable and hazard scenarios. This information associated to the development of a conceptual instability model represents the primary data for an integrated risk management of rock slope instabilities. - Les mouvements de versant tels que les chutes de blocs, les éboulements ou encore les phénomènes plus lents comme les déformations gravitaires profondes de versant représentent des manifestations courantes en régions montagneuses. Les mouvements de versant sont à la fois un des facteurs principaux contrôlant la destruction progressive des chaines orogéniques mais aussi un danger naturel concret qui peut provoquer des dommages importants. Pourtant, les phénomènes gravitaires sont rarement analysés dans leur globalité et les rapports géométriques et mécaniques qui lient les instabilités à l'échelle du versant aux instabilités locales restent encore mal définis. Une meilleure caractérisation de ces liens pourrait pourtant représenter un apport substantiel dans la compréhension des processus de déstabilisation des versants et améliorer la caractérisation des dangers gravitaires à toutes les échelles spatiales. Dans le but de proposer un approche plus globale à la problématique des mouvements gravitaires, ce travail de thèse propose trois axes de recherche principaux: (1) l'inventaire et l'analyse de la distribution spatiale des grandes instabilités rocheuses à l'échelle régionale, (2) l'analyse des structures tectoniques cassantes et ductiles en relation avec les mécanismes de rupture des grandes instabilités rocheuses et (3) la caractérisation des aléas rocheux par une approche multidisciplinaire visant à développer un modèle conceptuel de l'instabilité et une meilleure appréciation du danger . Pour analyser les différentes problématiques traitées dans cette thèse, différentes techniques ont été utilisées. En particulier, le modèle numérique de terrain s'est révélé être un outil indispensable pour la majorité des analyses effectuées, en partant de l'identification de l'instabilité jusqu'au suivi des mouvements. Les analyses de terrain et des modélisations numériques ont ensuite permis de compléter les informations issues du modèle numérique de terrain. Dans la première partie de cette thèse, les mouvements gravitaires rocheux dans la vallée du Rhône (Suisse) ont été cartographiés pour étudier leur répartition en fonction des variables géologiques et morphologiques régionales. En particulier, les analyses ont mis en évidence l'influence de l'activité néotectonique et des phases glaciaires sur la distribution des zones à forte densité d'instabilités rocheuses. Les volumes des instabilités rocheuses identifiées le long de la vallée principale ont été ensuite utilisés pour estimer le taux de dénudations postglaciaire et le remplissage de la vallée du Rhône lié aux grands mouvements gravitaires. Dans la deuxième partie, l'étude de l'agencement structural des avalanches rocheuses de Sierre (Suisse) et de Frank (Canada) a permis de mieux caractériser l'influence passive des structures tectoniques sur la géométrie des instabilités. En particulier, les structures issues d'une tectonique ductile, souvent ignorées dans l'étude des instabilités gravitaires, ont été identifiées comme des structures très importantes qui contrôlent les mécanismes de rupture des instabilités à différentes échelles. Dans la dernière partie de la thèse, cinq instabilités rocheuses différentes ont été étudiées par une approche multidisciplinaire visant à mieux caractériser l'aléa et à développer un modèle conceptuel trois dimensionnel de ces instabilités. A l'aide de ces analyses on a pu mettre en évidence la nécessité d'incorporer différentes techniques d'analyses et de surveillance pour une gestion plus objective du risque associée aux grandes instabilités rocheuses.

Monte Carlo study of the relation between vacancy diffusion and domain growth in two-dimensional binary alloys

Domain growth in a two-dimensional binary alloy is studied by means of Monte Carlo simulation of an ABV model. The dynamics consists of exchanges of particles with a small concentration of vacancies. The influence of changing the vacancy concentration and finite-size effects has been analyzed. Features of the vacancy diffusion during domain growth are also studied. The anomalous character of the diffusion due to its correlation with local order is responsible for the obtained fast-growth behavior.

Electrical conductivity of soil irrigated with swine wastewater estimated by time-domain reflectometry¹

Wastewater application to soil is an alternative for fertilization and water reuse. However, particular care must be taken with this practice, since successive wastewater applications can cause soil salinization. Time-domain reflectometry (TDR) allows for the simultaneous and continuous monitoring of both soil water content and apparent electrical conductivity and thus for the indirect measurement of the electrical conductivity of the soil solution. This study aimed to evaluate the suitability of TDR for the indirect determination of the electrical conductivity (ECse) of the saturated soil extract by using an empirical equation for the apparatus TDR Trase 6050X1. Disturbed soil samples saturated with swine wastewater were used, at soil proportions of 0, 0.45, 0.90, 1.80, 2.70, and 3.60 m³ m-3. The probes were equipped with three handmade 0.20 cm long rods. The fit of the empirical model that associated the TDR measured values of electrical conductivity (EC TDR) to ECse was excellent, indicating this approach as suitable for the determination of electrical conductivity of the soil solution.

The emerging importance of the SPX domain-containing proteins in phosphate homeostasis

Plant growth and development are strongly influenced by the availability of nutrients in the soil solution. Among them, phosphorus (P) is one of the most essential and most limiting macro-elements for plants. In the environment, plants are often confronted with P starvation as a result of extremely low concentrations of soluble inorganic phosphate (Pi) in the soil. To cope with these conditions, plants have developed a wide spectrum of mechanisms aimed at increasing P use efficiency. At the molecular level, recent studies have shown that several proteins carrying the SPX domain are essential for maintaining Pi homeostasis in plants. The SPX domain is found in numerous eukaryotic proteins, including several proteins from the yeast PHO regulon, involved in maintaining Pi homeostasis. In plants, proteins harboring the SPX domain are classified into four families based on the presence of additional domains in their structure, namely the SPX, SPX-EXS, SPX-MFS and SPX-RING families. In this review, we highlight the recent findings regarding the key roles of the proteins containing the SPX domain in phosphate signaling, as well as providing further research directions in order to improve our knowledge on P nutrition in plants, thus enabling the generation of plants with better P use efficiency.

Quorum-sensing-negative (lasR) mutants of Pseudomonas aeruginosa avoid cell lysis and death.

In Pseudomonas aeruginosa, N-acylhomoserine lactone signals regulate the expression of several hundreds of genes, via the transcriptional regulator LasR and, in part, also via the subordinate regulator RhlR. This regulatory network termed quorum sensing contributes to the virulence of P. aeruginosa as a pathogen. The fact that two supposed PAO1 wild-type strains from strain collections were found to be defective for LasR function because of independent point mutations in the lasR gene led to the hypothesis that loss of quorum sensing might confer a selective advantage on P. aeruginosa under certain environmental conditions. A convenient plate assay for LasR function was devised, based on the observation that lasR mutants did not grow on adenosine as the sole carbon source because a key degradative enzyme, nucleoside hydrolase (Nuh), is positively controlled by LasR. The wild-type PAO1 and lasR mutants showed similar growth rates when incubated in nutrient yeast broth at pH 6.8 and 37 degrees C with good aeration. However, after termination of growth during 30 to 54 h of incubation, when the pH rose to > or = 9, the lasR mutants were significantly more resistant to cell lysis and death than was the wild type. As a consequence, the lasR mutant-to-wild-type ratio increased about 10-fold in mixed cultures incubated for 54 h. In a PAO1 culture, five consecutive cycles of 48 h of incubation sufficed to enrich for about 10% of spontaneous mutants with a Nuh(-) phenotype, and five of these mutants, which were functionally complemented by lasR(+), had mutations in lasR. The observation that, in buffered nutrient yeast broth, the wild type and lasR mutants exhibited similar low tendencies to undergo cell lysis and death suggests that alkaline stress may be a critical factor providing a selective survival advantage to lasR mutants.

Dynamics of domain walls in pattern formation under traveling-wave forcing

We study dynamics of domain walls in pattern forming systems that are externally forced by a moving space-periodic modulation close to 2:1 spatial resonance. The motion of the forcing induces nongradient dynamics, while the wave number mismatch breaks explicitly the chiral symmetry of the domain walls. The combination of both effects yields an imperfect nonequilibrium Ising-Bloch bifurcation, where all kinks (including the Ising-like one) drift. Kink velocities and interactions are studied within the generic amplitude equation. For nonzero mismatch, a transition to traveling bound kink-antikink pairs and chaotic wave trains occurs.

Monitoring and predicting crop growth and analysing agricultural ecosystems by remote sensing

Selostus: Maatalousekosysteemien analysointi ja sadon ennustaminen kaukokartoituksen avulla