Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable con gurations are generated with positive probability Lundh calls this percolation di usion. An integral condition for percolation di ffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

A continuous strain-space model of viral evolution within a host

Viruses rapidly evolve, and HIV in particular is known to be one of the fastest evolving human viruses. It is now commonly accepted that viral evolution is the cause of the intriguing dynamics exhibited during HIV infections and the ultimate success of the virus in its struggle with the immune system. To study viral evolution, we use a simple mathematical model of the within-host dynamics of HIV which incorporates random mutations. In this model, we assume a continuous distribution of viral strains in a one-dimensional phenotype space where random mutations are modelled by di ffusion. Numerical simulations show that random mutations combined with competition result in evolution towards higher Darwinian fitness: a stable traveling wave of evolution, moving towards higher levels of fi tness, is formed in the phenoty space.

Oxidation of biogenic and water-soluble compounds in aqueous and organic aerosol droplets by ozone: a kinetic and product analysis approach using laser Raman tweezers

The results of an experimental study into the oxidative degradation of proxies for atmospheric aerosol are presented. We demonstrate that the laser Raman tweezers method can be used successfully to obtain uptake coeffcients for gaseous oxidants on individual aqueous and organic droplets, whilst the size and composition of the droplets is simultaneously followed. A laser tweezers system was used to trap individual droplets containing an unsaturated organic compound in either an aqueous or organic ( alkane) solvent. The droplet was exposed to gas- phase ozone and the reaction kinetics and products followed using Raman spectroscopy. The reactions of three different organic compounds with ozone were studied: fumarate anions, benzoate anions and alpha pinene. The fumarate and benzoate anions in aqueous solution were used to represent components of humic- like substances, HULIS; a alpha- pinene in an alkane solvent was studied as a proxy for biogenic aerosol. The kinetic analysis shows that for these systems the diffusive transport and mass accommodation of ozone is relatively fast, and that liquid- phase di. ffusion and reaction are the rate determining steps. Uptake coe. ffcients, g, were found to be ( 1.1 +/- 0.7) x 10(-5), ( 1.5 +/- 0.7) x 10 (-5) and ( 3.0 - 7.5) x 10 (-3) for the reactions of ozone with the fumarate, benzoate and a- pinene containing droplets, respectively. Liquid- phase bimolecular rate coe. cients for reactions of dissolved ozone molecules with fumarate, benzoate and a- pinene were also obtained: k(fumarate) = ( 2.7 +/- 2) x 10 (5), k(benzoate) = ( 3.5 +/- 3) x 10 (5) and k(alpha-pinene) = ( 1-3) x 10(7) dm(3) mol (-1) s (- 1). The droplet size was found to remain stable over the course of the oxidation process for the HULIS- proxies and for the oxidation of a- pinene in pentadecane. The study of the alpha- pinene/ ozone system is the first using organic seed particles to show that the hygroscopicity of the particle does not increase dramatically over the course of the oxidation. No products were detected by Raman spectroscopy for the reaction of benzoate ions with ozone. One product peak, consistent with aqueous carbonate anions, was observed when following the oxidation of fumarate ions by ozone. Product peaks observed in the reaction of ozone with alpha- pinene suggest the formation of new species containing carbonyl groups.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Ground state correlation energy of the Be-sequence for Z = 4-20 in MCDF approximation

The ground state (J = 0) electronic correlation energy of the 4-electron Be-sequence is calculated in the Multi-Configuration Dirac-Fock approximation for Z = 4-20. The 4 electrons were distributed over the configurations arising from the 1s, 2s, 2p, 3s, 3p and 3d orbitals. Theoretical values obtained here are in good agreement with experimental correlation energies.

Applicazione ed integrazione di metodi di prospezione geofisica: studio idrogeofisico della Zona Insatura in condizioni idriche controllate

Il lavoro è incentrato sull’applicazione ed integrazione di differenti tecniche di indagine geofisica in campo ambientale e ingegneristico/archeologico. Alcuni esempi sono stati descritti al fine di dimostrare l’utilità delle metodologie geofisiche nella risoluzione di svariate problematiche. Nello specifico l’attenzione è stata rivolta all’utilizzo delle tecniche del Ground Penetrating Radar e del Time Domain Reflectometry in misure condotte su un corpo sabbioso simulante una Zona Insatura. L’esperimento è stato realizzato all’interno di un’area test costruita presso l’azienda agricola dell’Università La Tuscia di Viterbo. Hanno partecipato al progetto le Università di Roma Tre, Roma La Sapienza, La Tuscia, con il supporto tecnico della Sensore&Software. Nello studio è stato condotto un approccio definito idrogeofisico al fine di ottenere informazioni da misure dei parametri fisici relativi alla Zona Insatura simulata nell’area test. Il confronto e l’integrazione delle due differenti tecniche di indagine ha offerto la possibilità di estendere la profondità di indagine all’interno del corpo sabbioso e di verificare l’utilità della tecnica GPR nello studio degli effetti legati alle variazioni del contenuto d’acqua nel suolo, oltre a determinare la posizione della superficie piezometrica per i differenti scenari di saturazione. Uno specifico studio è stato realizzato sul segnale radar al fine di stabilire i fattori di influenza sulla sua propagazione all’interno del suolo. Il comportamento dei parametri dielettrici nelle condizioni di drenaggio e di imbibizione del corpo sabbioso è stato riprodotto attraverso una modellizzazione delle proprietà dielettriche ed idrologiche sulla base della dimensione, forma e distribuzione dei granuli di roccia e pori, nonché sulla base della storia relativa alla distribuzione dei fluidi di saturazione all’interno del mezzo. La modellizzazione è stata operata sulle basi concettuali del Differential Effective Medium Approximation.

Modelizzazione spazio-temporale delle dinamiche di uso del suolo ed analisi comparativa di differenti approcci predittivi. Uso integrato di SIG e telerilevamento nello studio dei processi di deforestazione nella regione La Joyanca in Peten, Guatemala

L’uso frequente dei modelli predittivi per l’analisi di sistemi complessi, naturali o artificiali, sta cambiando il tradizionale approccio alle problematiche ambientali e di rischio. Il continuo miglioramento delle capacità di elaborazione dei computer facilita l’utilizzo e la risoluzione di metodi numerici basati su una discretizzazione spazio-temporale che permette una modellizzazione predittiva di sistemi reali complessi, riproducendo l’evoluzione dei loro patterns spaziali ed calcolando il grado di precisione della simulazione. In questa tesi presentiamo una applicazione di differenti metodi predittivi (Geomatico, Reti Neurali, Land Cover Modeler e Dinamica EGO) in un’area test del Petén, Guatemala. Durante gli ultimi decenni questa regione, inclusa nella Riserva di Biosfera Maya, ha conosciuto una rapida crescita demografica ed un’incontrollata pressione sulle sue risorse naturali. L’area test puó essere suddivisa in sotto-regioni caratterizzate da differenti dinamiche di uso del suolo. Comprendere e quantificare queste differenze permette una migliore approssimazione del sistema reale; é inoltre necessario integrare tutti i parametri fisici e socio-economici, per una rappresentazione più completa della complessità dell’impatto antropico. Data l’assenza di informazioni dettagliate sull’area di studio, quasi tutti i dati sono stati ricavati dall’elaborazione di 11 immagini ETM+, TM e SPOT; abbiamo poi realizzato un’analisi multitemporale dei cambi uso del suolo passati e costruito l’input per alimentare i modelli predittivi. I dati del 1998 e 2000 sono stati usati per la fase di calibrazione per simulare i cambiamenti nella copertura terrestre del 2003, scelta come data di riferimento per la validazione dei risultati. Quest’ultima permette di evidenziare le qualità ed i limiti per ogni modello nelle differenti sub-regioni.

Tecniche avanzate per l'analisi di sensitività globale: applicazione alla contaminazione delle acque sotterranee.

The thesis is framed within the field of the stochastic approach to flow and transport themes of solutes in natural porous materials. The methodology used to characterise the uncertainty associated with the modular predictions is completely general and can be reproduced in various contexts. The theme of the research includes the following among its main objectives: (a) the development of a Global Sensitivity Analysis on contaminant transport models in the subsoil to research the effects of the uncertainty of the most important parameters; (b) the application of advanced techniques, such as Polynomial Chaos Expansion (PCE), for obtaining surrogate models starting from those which conduct traditionally developed analyses in the context of Monte Carlo simulations, characterised by an often not negligible computational burden; (c) the analyses and the understanding of the key processes at the basis of the transport of solutes in natural porous materials using the aforementioned technical and analysis resources. In the complete picture, the thesis looks at the application of a Continuous Injection transport model of contaminants, of the PCE technique which has already been developed and applied by the thesis supervisors, by way of numerical code, to a Slug Injection model. The methodology was applied to the aforementioned model with original contribution deriving from surrogate models with various degrees of approximation and developing a Global Sensitivity Analysis aimed at the determination of Sobol’ indices.

In defence of modeling simultaneity for a correct approximation of cultural aspects: implications for food consumers studies with latent variables

Dealing with latent constructs (loaded by reflective and congeneric measures) cross-culturally compared means studying how these unobserved variables vary, and/or covary each other, after controlling for possibly disturbing cultural forces. This yields to the so-called ‘measurement invariance’ matter that refers to the extent to which data collected by the same multi-item measurement instrument (i.e., self-reported questionnaire of items underlying common latent constructs) are comparable across different cultural environments. As a matter of fact, it would be unthinkable exploring latent variables heterogeneity (e.g., latent means; latent levels of deviations from the means (i.e., latent variances), latent levels of shared variation from the respective means (i.e., latent covariances), levels of magnitude of structural path coefficients with regard to causal relations among latent variables) across different populations without controlling for cultural bias in the underlying measures. Furthermore, it would be unrealistic to assess this latter correction without using a framework that is able to take into account all these potential cultural biases across populations simultaneously. Since the real world ‘acts’ in a simultaneous way as well. As a consequence, I, as researcher, may want to control for cultural forces hypothesizing they are all acting at the same time throughout groups of comparison and therefore examining if they are inflating or suppressing my new estimations with hierarchical nested constraints on the original estimated parameters. Multi Sample Structural Equation Modeling-based Confirmatory Factor Analysis (MS-SEM-based CFA) still represents a dominant and flexible statistical framework to work out this potential cultural bias in a simultaneous way. With this dissertation I wanted to make an attempt to introduce new viewpoints on measurement invariance handled under covariance-based SEM framework by means of a consumer behavior modeling application on functional food choices.

Crystal Structure Of (3e)-3-(2,4-di-nitro-phen-oxy-meth-yl)-4-phenyl-but-3-en-2-one.

In the title compound, C17H14N2O6, the conformation about the C=C double bond [1.345 (2) Å] is E, with the ketone moiety almost coplanar [C-C-C-C torsion angle = 9.5 (2)°] along with the phenyl ring [C-C-C-C = 5.9 (2)°]. The aromatic rings are almost perpendicular to each other [dihedral angle = 86.66 (7)°]. The 4-nitro moiety is approximately coplanar with the benzene ring to which it is attached [O-N-C-C = 4.2 (2)°], whereas the one in the ortho position is twisted [O-N-C-C = 138.28 (13)°]. The mol-ecules associate via C-H⋯O inter-actions, involving both O atoms from the 2-nitro group, to form a helical supra-molecular chain along [010]. Nitro-nitro N⋯O inter-actions [2.8461 (19) Å] connect the chains into layers that stack along [001].

Histopathological Alterations In The Prostates Of Mongolian Gerbils Exposed To A High-fat Diet And Di-n-butyl Phthalate Individually Or In Combination.

Both high-fat diet and exposure to endocrine-disrupting chemicals have been implicated in susceptibility to pathological prostate lesions, but the consequences of combining the two have not yet been examined. We evaluated the effects of gestational and postnatal exposure to a high-fat diet (20% fat) and low doses of di-n-butyl phthalate (DBP; 5mg/kg/day), individually or in combination, on the tissue response and incidence of pathological lesions in the ventral prostate of adult gerbils. Continuous intake of a high-fat diet caused dyslipidemia, hypertrophy, and promoted the development of inflammatory, premalignant and malignant prostate lesions, even in the absence of obesity. Life-time DBP exposure was obesogenic and dyslipidemic and increased the incidence of premalignant prostate lesions. Combined exposure to DBP and a high-fat diet also caused prostate hypertrophy, but the effects were less severe than those of individual treatments; combined exposure neither induced an inflammatory response nor altered serum lipid content.

Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.