Black-scholes type equations

In this work we are concerned with the analysis and numerical solution of Black-Scholes type equations arising in the modeling of incomplete financial markets and an inverse problem of determining the local volatility function in a generalized Black-Scholes model from observed option prices. In the first chapter a fully nonlinear Black-Scholes equation which models transaction costs arising in option pricing is discretized by a new high order compact scheme. The compact scheme is proved to be unconditionally stable and non-oscillatory and is very efficient compared to classical schemes. Moreover, it is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. In the next chapter we turn to the calibration problem of computing local volatility functions from market data in a generalized Black-Scholes setting. We follow an optimal control approach in a Lagrangian framework. We show the existence of a global solution and study first- and second-order optimality conditions. Furthermore, we propose an algorithm that is based on a globalized sequential quadratic programming method and a primal-dual active set strategy, and present numerical results. In the last chapter we consider a quasilinear parabolic equation with quadratic gradient terms, which arises in the modeling of an optimal portfolio in incomplete markets. The existence of weak solutions is shown by considering a sequence of approximate solutions. The main difficulty of the proof is to infer the strong convergence of the sequence. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution, but without additional regularity assumptions on the solution. The results are illustrated by a numerical example.

Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

Longitudinal evolution of cognitive functions in patients with multiple system atrophy: a prospective study

Introduction and Background: Multiple system atrophy (MSA) is a sporadic, adult-onset, progressive neurodegenerative disease characterized clinically by parkinsonism, cerebellar ataxia, and autonomic failure. We investigated cognitive functions longitudinally in a group of probable MSA patients, matching data with sleep parameters. Patients and Methods: 10 patients (7m/3f) underwent a detailed interview, a general and neurological examination, laboratory exams, MRI scans, a cardiovascular reflexes study, a battery of neuropsychological tests, and video-polysomnographic recording (VPSG). Patients were revaluated (T1) a mean of 16±5 (range: 12-28) months after the initial evaluation (T0). At T1, the neuropsychological assessment and VPSG were repeated. Results: The mean patient age was 57.8±6.4 years (range: 47-64) with a mean age at disease onset of 53.2±7.1 years (range: 43-61) and symptoms duration at T0 of 60±48 months (range: 12-144). At T0, 7 patients showed no cognitive deficits while 3 patients showed isolated cognitive deficits. At T1, 1 patient worsened developing multiple cognitive deficits from a normal condition. At T0 and T1, sleep efficiency was reduced, REM latency increased, NREM sleep stages 1-2 slightly increased. Comparisons between T1 and T0 showed a significant worsening in two tests of attention and no significant differences of VPSG parameters. No correlation was found between neuropsychological results and VPSG findings or RBD duration. Discussion and Conclusions: The majority of our patients do not show any cognitive deficits at T0 and T1, while isolated cognitive deficits are present in the remaining patients. Attention is the cognitive function which significantly worsened. Our data confirm the previous findings concerning the prevalence, type and the evolution of cognitive deficits in MSA. Regarding the developing of a condition of dementia, our data did not show a clear-cut diagnosis of dementia. We confirm a mild alteration of sleep structure. RBD duration does not correlate with neuropsychological findings.

Modellazione Tridimensionale del Processo di Combustione di un Razzo a Propellente Solido

La regolazione dei sistemi di propulsione a razzo a propellente solido (Solid Rocket Motors) ha da sempre rappresentato una delle principali problematiche legate a questa tipologia di motori. L’assenza di un qualsiasi genere di controllo diretto del processo di combustione del grano solido, fa si che la previsione della balistica interna rappresenti da sempre il principale strumento utilizzato sia per definire in fase di progetto la configurazione ottimale del motore, sia per analizzare le eventuali anomalie riscontrate in ambito sperimentale. Variazioni locali nella struttura del propellente, difettosità interne o eterogeneità nelle condizioni di camera posso dare origine ad alterazioni del rateo locale di combustione del propellente e conseguentemente a profili di pressione e di spinta sperimentali differenti da quelli previsti per via teorica. Molti dei codici attualmente in uso offrono un approccio piuttosto semplificato al problema, facendo per lo più ricorso a fattori correttivi (fattori HUMP) semi-empirici, senza tuttavia andare a ricostruire in maniera più realistica le eterogeneità di prestazione del propellente. Questo lavoro di tesi vuole dunque proporre un nuovo approccio alla previsione numerica delle prestazioni dei sistemi a propellente solido, attraverso la realizzazione di un nuovo codice di simulazione, denominato ROBOOST (ROcket BOOst Simulation Tool). Richiamando concetti e techiche proprie della Computer Grafica, questo nuovo codice è in grado di ricostruire in processo di regressione superficiale del grano in maniera puntuale, attraverso l’utilizzo di una mesh triangolare mobile. Variazioni locali del rateo di combustione posso quindi essere facilmente riprodotte ed il calcolo della balistica interna avviene mediante l’accoppiamento di un modello 0D non-stazionario e di uno 1D quasi-stazionario. L’attività è stata svolta in collaborazione con l’azienda Avio Space Division e il nuovo codice è stato implementato con successo sul motore Zefiro 9.

Hydrodynamical simulations of early-type galaxies: effects of galaxy shape and stellar dynamics on hot coronae

Early-Type galaxies (ETGs) are embedded in hot (10^6-10^7 K), X-ray emitting gaseous haloes, produced mainly by stellar winds and heated by Type Ia supernovae explosions, by the thermalization of stellar motions and occasionally by the central super-massive black hole (SMBH). In particular, the thermalization of the stellar motions is due to the interaction between the stellar and the SNIa ejecta and the hot interstellar medium (ISM) already residing in the ETG. A number of different astrophysical phenomena determine the X-ray properties of the hot ISM, such as stellar population formation and evolution, galaxy structure and internal kinematics, Active Galactic Nuclei (AGN) presence, and environmental effects. With the aid of high-resolution hydrodynamical simulations performed on state-of-the-art galaxy models, in this Thesis we focus on the effects of galaxy shape, stellar kinematics and star formation on the evolution of the X-ray coronae of ETGs. Numerical simulations show that the relative importance of flattening and rotation are functions of the galaxy mass: at low galaxy masses, adding flattening and rotation induces a galactic wind, thus lowering the X-ray luminosity; at high galaxy masses the angular momentum conservation keeps the central regions of rotating galaxies at low density, whereas in non-rotating models a denser and brighter atmosphere is formed. The same dependence from the galaxy mass is present in the effects of star formation (SF): in light galaxies SF contributes to increase the spread in Lx, while at high galaxy masses the halo X-ray properties are marginally sensitive to SF effects. In every case, the star formation rate at the present epoch quite agrees with observations, and the massive, cold gaseous discs are partially or completely consumed by SF on a time-scale of few Gyr, excluding the presence of young stellar discs at the present epoch.

3D-ultrastructure, functions and stress responses of rhogocytes from the freshwater gastropods Biomphalaria glabrata and Lymnaea stagnalis

Rhogocytes, also termed ‘pore cells’, exist free in the hemolymph or embedded in the connective tissue of different body parts of molluscs, notably gastropods. These unique cells can be round, elongated or irregularly shaped, and up to 30 μm in diameter. Their hallmark is the so-called slit apparatus: i.e. pocket-like invaginations of the plasma membrane creating extracellular lacunae, bridged by cytoplasmic bars. These bars form distinctive slits of ca. 20 nm width. A slit diaphragm composed of proteins establishes a molecular sieve with holes of 20 x 20 nm. Different functions have been assigned to this special molluscan cell type, notably biosynthesis of the hemolymph respiratory protein hemocyanin. It has further been proposed, but not proven, that in the case of red-blooded snail species rhogocytes might synthesize the hemoglobin. However, the secretion pathway of these hemolymph proteins, and the functional role of the enigmatic slit apparatus remained unclear. Additionally proposed functions of rhogocytes, such as heavy metal detoxification or hemolymph protein degradation, are also not well studied. This work provides more detailed electron microscopical, histological and immunobiochemical information on the structure and function of rhogocytes of the freshwater snails Biomphalaria glabrata and Lymnaea stagnalis. By in situ hybridization on mantle tissues, it proves that B. glabrata rhogocytes synthesize hemoglobin and L. stagnalis rhogocytes synthesize hemocyanin. Hemocyanin is present, in endoplasmic reticulum lacunae and in vesicles, as individual molecules or pseudo-crystalline arrays. The first 3D reconstructions of rhogocytes are provided by means of electron tomography and show unprecedented details of the slit apparatus. A highly dense material in the cytoplasmic bars close to the diaphragmatic slits was shown, by immunogold labeling, to contain actin. By immunofluorescence microscopy, the protein nephrin was localized at the periphery of rhogocytes. The presence of both proteins in the slit apparatus supports the previous hypothesis, hitherto solely based on similarities of the ultrastructure, that the molluscan rhogocytes are phylogenetically related to mammalian podocytes and insect nephrocytes. A possible secretion pathway of respiratory proteins that includes a transfer mechanism of vesicles through the diaphragmatic slits is proposed and discussed. We also studied, by electron microscopy, the reaction of rhogocytes in situ to two forms of animal stress: deprivation of food and cadmium contamination of the tank water. Significant cellular reactions to both stressors were observed and documented. Notably, the slit apparatus surface and the number of electron-dense cytoplasmic vesicles increased in response to cadmium stress. Food deprivation led to an increase in hemocyanin production. These observations are also discussed in the framework of using such animals as potential environmental biomarkers.

Fic domain-catalyzed adenylylation: insight provided by the structural analysis of the type IV secretion system effector BepA

Numerous bacterial pathogens subvert cellular functions of eukaryotic host cells by the injection of effector proteins via dedicated secretion systems. The type IV secretion system (T4SS) effector protein BepA from Bartonella henselae is composed of an N-terminal Fic domain and a C-terminal Bartonella intracellular delivery domain, the latter being responsible for T4SS-mediated translocation into host cells. A proteolysis resistant fragment (residues 10-302) that includes the Fic domain shows autoadenylylation activity and adenylyl transfer onto Hela cell extract proteins as demonstrated by autoradiography on incubation with α-[(32)P]-ATP. Its crystal structure, determined to 2.9-Å resolution by the SeMet-SAD method, exhibits the canonical Fic fold including the HPFxxGNGRxxR signature motif with several elaborations in loop regions and an additional β-rich domain at the C-terminus. On crystal soaking with ATP/Mg(2+), additional electron density indicated the presence of a PP(i) /Mg(2+) moiety, the side product of the adenylylation reaction, in the anion binding nest of the signature motif. On the basis of this information and that of the recent structure of IbpA(Fic2) in complex with the eukaryotic target protein Cdc42, we present a detailed model for the ternary complex of Fic with the two substrates, ATP/Mg(2+) and target tyrosine. The model is consistent with an in-line nucleophilic attack of the deprotonated side-chain hydroxyl group onto the α-phosphorus of the nucleotide to accomplish AMP transfer. Furthermore, a general, sequence-independent mechanism of target positioning through antiparallel β-strand interactions between enzyme and target is suggested.

Putative functions of extracellular matrix glycoproteins in secondary palate morphogenesis

Cleft palate is a common birth defect in humans. Elevation and fusion of paired palatal shelves are coordinated by growth and transcription factors, and mutations in these can cause malformations. Among the effector genes for growth factor signaling are extracellular matrix (ECM) glycoproteins. These provide substrates for cell adhesion (e.g., fibronectin, tenascins), but also regulate growth factor availability (e.g., fibrillins). Cleft palate in Bmp7 null mouse embryos is caused by a delay in palatal shelf elevation. In contrast, palatal shelves of Tgf-β3 knockout mice elevate normally, but a cleft develops due to their failure to fuse. However, nothing is known about a possible functional interaction between specific ECM proteins and Tgf-β/Bmp family members in palatogenesis. To start addressing this question, we studied the mRNA and protein distribution of relevant ECM components during secondary palate development, and compared it to growth factor expression in wildtypewild type and mutant mice. We found that fibrillin-2 (but not fibrillin-1) mRNA appeared in the mesenchyme of elevated palatal shelves adjacent to the midline epithelial cells, which were positive for Tgf-β3 mRNA. Moreover, midline epithelial cells started expressing fibronectin upon contact of the two palatal shelves. These findings support the hypothesis that fibrillin-2 and fibronectin are involved in regulating the activity of Tgf-β3 at the fusing midline. In addition, we observed that tenascin-W (but not tenascin-C) was misexpressed in palatal shelves of Bmp7-deficient mouse embryos. In contrast to tenascin-C, tenascin-W secretion was strongly induced by Bmp7 in embryonic cranial fibroblasts in vitro. These results are consistent with a putative function for tenascin-W as a target of Bmp7 signaling during palate elevation. Our results indicate that distinct ECM proteins are important for morphogenesis of the secondary palate, both as downstream effectors and as regulators of Tgf-β/Bmp activity.

Comparing skew Schur functions: a quasisymmetric perspective

Reiner, Shaw and van Willigenburg showed that if two skew Schur functions sA and sB are equal, then the skew shapes $A$ and $B$ must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a much weaker condition than Schur equality: that sA and sB have the same support when expanded in the fundamental quasisymmetric basis F. Surprisingly, there is significant evidence supporting a conjecture that the converse is also true. In fact, we work in terms of inequalities, showing that if the F-support of sA contains that of sB, then the row overlap partitions of A are dominated by those of B, and again conjecture that the converse also holds. Our evidence in favor of these conjectures includes their consistency with a complete determination of all F-support containment relations for F-multiplicity-free skew Schur functions. We conclude with a consideration of how some other quasisymmetric bases fit into our framework.

Tests for Comparing Mark-Specific Hazards and Cumulative Incidence Functions

It is of interest in some applications to determine whether there is a relationship between a hazard rate function (or a cumulative incidence function) and a mark variable which is only observed at uncensored failure times. We develop nonparametric tests for this problem when the mark variable is continuous. Tests are developed for the null hypothesis that the mark-specific hazard rate is independent of the mark versus ordered and two-sided alternatives expressed in terms of mark-specific hazard functions and mark-specific cumulative incidence functions. The test statistics are based on functionals of a bivariate test process equal to a weighted average of differences between a Nelson--Aalen-type estimator of the mark-specific cumulative hazard function and a nonparametric estimator of this function under the null hypothesis. The weight function in the test process can be chosen so that the test statistics are asymptotically distribution-free.Asymptotically correct critical values are obtained through a simple simulation procedure. The testing procedures are shown to perform well in numerical studies, and are illustrated with an AIDS clinical trial example. Specifically, the tests are used to assess if the instantaneous or absolute risk of treatment failure depends on the amount of accumulation of drug resistance mutations in a subject's HIV virus. This assessment helps guide development of anti-HIV therapies that surmount the problem of drug resistance.

Snake C-type lectin-like proteins and platelet receptors

Snake venoms are complex mixtures of biologically active proteins and peptides. Many affect haemostasis by activating or inhibiting coagulant factors or platelets, or by disrupting endothelium. Snake venom components are classified into various families, such as serine proteases, metalloproteinases, C-type lectin-like proteins, disintegrins and phospholipases. Snake venom C-type lectin-like proteins have a typical fold resembling that in classic C-type lectins such as the selectins and mannose-binding proteins. Many snake venom C-type lectin-like proteins have now been characterized, as heterodimeric structures with alpha and beta subunits that often form large molecules by multimerization. They activate platelets by binding to VWF or specific receptors such as GPIb, alpha2beta1 and GPVI. Simple heterodimeric GPIb-binding molecules mainly inhibit platelet functions, whereas multimeric ones activate platelets. A series of tetrameric snake venom C-type lectin-like proteins activates platelets by binding to GPVI while another series affects platelet function via integrin alpha2beta1. Some act by inducing VWF to bind to GPIb. Many structures of these proteins, often complexed with their ligands, have been determined. Structure-activity studies show that these proteins are quite complex despite similar backbone folding. Snake C-type lectin-like proteins often interact with more than one platelet receptor and have complex mechanisms of action.

A BAYESIAN HIERARCHICAL MODEL FOR CONSTRAINED DISTRIBUTED LAG FUNCTIONS: ESTIMATING THE TIME COURSE OF HOSPITALIZATION ASSOCIATED WITH AIR POLLUTION EXPOSURE

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological questions: (1) How can we estimate the shape of the distributed lag between increased air pollution exposure and increased mortality or morbidity? and (2) How should we estimate the cumulative population health risk from short-term exposure to air pollution? Distributed lag models are appropriate tools for estimating air pollution health effects that may be spread over several days. However, estimation for distributed lag models in air pollution and health applications is hampered by the substantial noise in the data and the inherently weak signal that is the target of investigation. We introduce an hierarchical Bayesian distributed lag model that incorporates prior information about the time course of pollution effects and combines information across multiple locations. The model has a connection to penalized spline smoothing using a special type of penalty matrix. We apply the model to estimating the distributed lag between exposure to particulate matter air pollution and hospitalization for cardiovascular and respiratory disease using data from a large United States air pollution and hospitalization database of Medicare enrollees in 94 counties covering the years 1999-2002.

Snake venom C-type lectins interacting with platelet receptors. Structure-function relationships and effects on haemostasis

Snake venoms contain components that affect the prey either by neurotoxic or haemorrhagic effects. The latter category affect haemostasis either by inhibiting or activating platelets or coagulation factors. They fall into several types based upon structure and mode of action. A major class is the snake C-type lectins or C-type lectin-like family which shows a typical folding like that in classic C-type lectins such as the selectins and mannose-binding proteins. Those in snake venoms are mostly based on a heterodimeric structure with two subunits alpha and beta, which are often oligomerized to form larger molecules. Simple heterodimeric members of this family have been shown to inhibit platelet functions by binding to GPIb but others activate platelets via the same receptor. Some that act via GPIb do so by inducing von Willebrand factor to bind to it. Another series of snake C-type lectins activate platelets by binding to GPVI while yet another series uses the integrin alpha(2)beta(1) to affect platelet function. The structure of more and more of these C-type lectins have now been, and are being, determined, often together with their ligands, casting light on binding sites and mechanisms. In addition, it is relatively easy to model the structure of the C-type lectins if the primary structure is known. These studies have shown that these proteins are quite a complex group, often with more than one platelet receptor as ligand and although superficially some appear to act as inhibitors, in fact most function by inducing thrombocytopenia by various routes. The relationship between structure and function in this group of venom proteins will be discussed.

Insulin-like growth factor type-1 receptor down-regulation associated with dwarfism in Holstein calves

Perturbations in endocrine functions can impact normal growth. Endocrine traits were studied in three dwarf calves exhibiting retarded but proportionate growth and four phenotypically normal half-siblings, sired by the same bull, and four unrelated control calves. Plasma 3,5,3'-triiodothyronine and thyroxine concentrations in dwarfs and half-siblings were in the physiological range and responded normally to injected thyroid-releasing hormone. Plasma glucagon concentrations were different (dwarfs, controls>half-siblings; P<0.05). Plasma growth hormone (GH), insulin-like growth factor-1 (IGF-1) and insulin concentrations in the three groups during an 8-h period were similar, but integrated GH concentrations (areas under concentration curves) were different (dwarfs>controls, P<0.02; half-siblings>controls, P=0.08). Responses of GH to xylazine and to a GH-releasing-factor analogue were similar in dwarfs and half-siblings. Relative gene expression of IGF-1, IGF-2, GH receptor (GHR), insulin receptor, IGF-1 type-1 and -2 receptors (IGF-1R, IGF-2R), and IGF binding proteins were measured in liver and anconeus muscle. GHR mRNA levels were different in liver (dwarfs