We study a hybrid tree/finite-difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new simulation scheme to be used for Monte Carlo evaluations. Numerical results show the reliability and the efficiency of the proposed methods.

PDE models for network flows are used in a number of different applications, including modeling of water channel networks. While the theory and first-order numerics are well developed, there is a lack of high-order schemes. We propose a Runge-Kutta discontinu- ous Galerkin method as an efficient, effective and compact numerical approach for numerical simulations of water flow in open canals. Our numerical tests show the advantages of RKDG over first-order schemes.

An integro-differential model for evolutionary dynamics with mutations is investigated by improving the understanding of its behaviour using numerical simulations. The proposed numerical approach can handle also density dependent fitness, and gives new insights about the role of mutation in the preservation of cooperation.

We introduce a new class of finite differences schemes to approximate one dimensional dissipative semilinear hyperbolic systems with a BGK structure. Using precise analytical time-decay estimates of the local truncation error, it is possible to design schemes, based on the standard upwind approximation, which are increasingly accurate for large times when approximating small perturbations of constant asymptotic states. Numerical tests show their better performances with respect to those of other schemes.

We consider finite difference schemes which approximate one-dimensional dissipative hyperbolic systems. Using precise analytical time-decay estimates of the local truncation error, we show that it is possible to introduce some suitable modification in standard upwinding schemes to design schemes which are increasingly accurate for large times when approximating small perturbations of stable asymptotic states, respectively, around stationary solutions and in the diffusion (Chapman-Enskog) limit.

Partial integro-differential equation (PIDE) formulations are often preferable for pricing options under models with stochastic volatility and jumps. In this talk, we consider the numerical approximation of such models. On one hand, due to the non-local nature of the integral term, we propose to use Implicit-Explicit (IMEX) Runge-Kutta methods for the time integration to solve the integral term explicitly, giving higher order accuracy schemes under weak stability time-step restrictions. On the other hand, we propose a hybrid tree-finite difference method to approximate the Heston model, possibly in the presence of jumps. Numerical tests are presented to show the computational efficiency of the approximation.

Il 14 dicembre del 1955, presso la sede Centrale del CNR, il Presidente della Repubblica, Giovanni Gronchi, inaugurava il calcolatore elettronico Ferranti Mark1* dell'Istituto Nazionale per le Applicazioni del Calcolo, alla presenza del fondatore e direttore dell'Istituto, il matematico Mauro Picone. Dal nome del costruttore e dalla sigla dell'istituto, la macchina venne denominata FINAC. Si trattava del secondo calcolatore elettronico installato in Italia, preceduto di pochi mesi dal CRC-102A del Politecnico di Milano. L'acquisto era avvenuto grazie agli sforzi di Picone per dotare il suo istituto di una delle 'potenti macchine calcolatrici elettroniche', all'epoca solo anglo-americane. Negli anni precedenti Picone era giunto più volte ad un passo dal realizzare il suo intento di costruire quello che, sarebbe stato il primo calcolatore italiano. Aveva maturato questo proposito viaggiando negli USA, dove l'analisi numerica progrediva enormemente con lo sviluppo di progetti su 'macchine calcolatrici a cifre ad alta velocità'. Poiché una serie di impedimenti, internazionali e interni, rischiavano di prolungare eccessivamente i tempi, Picone scelse di acquistare un'apparecchiatura già in commercio, che sarebbe poi stata la FINAC, che per alcuni anni rimase il più potente computer italiano. Con esso vennero sviluppate molte ricerche sui temi più svariati, dal modello econometrico della Banca d'Italia ai calcoli per la progettazione di ponti e dighe. Un lavoro, particolarmente significativo per lo sviluppo dell'informatica italiana, fu la realizzazione di un simulatore della CEP, futura Calcolatrice Elettronica Pisana. Con questo anniversario si vuole celebrare, tra le altre cose, l'intuizione di Mauro Picone, la sua capacità innovativa e la scelta di investire generosamente nel futuro, conferendo grande impulso alla soluzione di problemi reali attraverso la modellizzazione matematica, creando anche in Italia i presupposti per lo sviluppo della moderna matematica applicata e dell'informatica

In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this formulation the junctions disappear since each path is considered as a single uninterrupted road. We consider a Godunov-based approximation scheme for the system which is very easy to implement. Besides basic properties like the conservation of cars and positive bounded solutions, the scheme exhibits other nice properties, being able to select automatically a solution at network's nodes without requiring external procedures (e.g., maximization of the flux via a linear programming method). Moreover, the scheme can be interpreted as a discretization of the traffic models with buffer, although no buffer is introduced here. Finally, we show how the scheme can be recast in the framework of the classical theory of traffic flow on networks, where a conservation law has to be solved on each arc of the network. This is achieved by solving the Riemann problem for a modified equation, and showing that its solution corresponds to the one computed by the numerical scheme.

A conference on the occasion of the 60th birthday of Maurizio Falcone

In this paper, the lab-on-chip section for a protein assay is designed and optimized. To avoid severe reliability problems related to activated surface stability, a dynamic assay approach is adopted: protein-to-protein neutralization is performed while proteins diffuse freely in the reaction chamber. The related refraction index change is detected via an integrated interferometer. The structure is also design to provide a functional test of the reference protein solution, which is generally required for qualification for medical uses.

Premixed combustion modes in compression ignition engines are studied as a promising solution to meet fuel economy and increasingly stringent emissions regulations. Nevertheless, PCCI combustion systems are not yet consolidated enough for practical applications. The high complexity of such combustion systems in terms of both air-fuel charge preparation and combustion process control requires the employment of robust and reliable numerical tools to provide adequate comprehension of the phenomena. Object of this work is the development and validation of suitable models to evaluate the effects of charge premixing levels in Diesel combustion. This activity was performed using the Lib-ICE code, which is a set of applications and libraries for IC engine simulations developed using the OpenFOAM® technology. In particular, a turbulence-chemistry interaction model, based on the simple Eddy Dissipation Approach, was introduced to account for the effects of turbulent mixing on chemical reaction rates. It is a tentative solution to represent the effects of sub-grid mixing on the chemical reaction rates when detailed reaction mechanisms are adopted. Chemical reaction rates were computed by a robust semi-implicit extrapolation method for integrating stiff Ordinary Differential Equations with monitoring of both local and global error to adjust stepsize. To reduce the CPU time when detailed chemistry was used, both the ISAT (in-situ adaptive tabulation) and DAC (dynamic adaptive chemistry) techniques were adopted in combination. Simulations were performed by varying the charge premixing level from the typical diesel combustion mode towards an almost completely premixed/HCCI mode using n-heptane, whose injected mass was split between portinjection and direct-injection. This allowed a detailed investigation of the “mixed injection conditions”, that are typical of dual fuel configurations without employing fuels of different chemical nature, composition and ignition tendency. The choice of using a single fuel was motivated by the need to isolate the effects of different premixing levels and the resulting interaction between the charge and the fuel spray. Measurements for validation were collected by means of specific experiments on a fully instrumented single cylinder research engine, having the injection and the combustion systems architecture typical of the current light duty diesel engine technology. To realize homogeneous air-fuel charge, the intake manifold is modified to provide the desired extent of fuel port-injection.

We have developed a rat brain organotypic culture model, in which tissue slices contain cortex-subventricular zone-striatum regions, to model neuroblast activity in response to in vitro ischemia. Neuroblast activation has been described in terms of two main parameters, proliferation and migration from the subventricular zone into the injured cortex. We observed distinct phases of neuroblast activation as is known to occur after in vivo ischemia. Thus, immediately after oxygen/glucose deprivation (6–24 hours), neuroblasts reduce their proliferative and migratory activity, whereas, at longer time points after the insult (2 to 5 days), they start to proliferate and migrate into the damaged cortex. Antagonism of ionotropic receptors for extracellular ATP during and after the insult unmasks an early activation of neuroblasts in the subventricular zone, which responded with a rapid and intense migration of neuroblasts into the damaged cortex (within 24 hours). The process is further enhanced by elevating the production of the chemoattractant SDf-1α and may also be boosted by blocking the activation of microglia. This organotypic model which we have developed is an excellent in vitro system to study neurogenesis after ischemia and other neurodegenerative diseases. Its application has revealed a SOS response to oxygen/glucose deprivation, which is inhibited by unfavorable conditions due to the ischemic environment. Finally, experimental quantifications have allowed us to elaborate a mathematical model to describe neuroblast activation and to develop a computer simulation which should have promising applications for the screening of drug candidates for novel therapies of ischemia-related pathologies.

We have developed a rat brain organotypic culture model, in which tissue slices contain cortex-subventricular zone-striatum regions, to model neuroblast activity in response to in vitro ischemia. Neuroblast activation has been described in terms of two main parameters, proliferation and migration from the subventricular zone into the injured cortex. We observed distinct phases of neuroblast activation as is known to occur after in vivo ischemia. Thus, immediately after oxygen/glucose deprivation (6-24 hours), neuroblasts reduce their proliferative and migratory activity, whereas, at longer time points after the insult (2 to 5 days), they start to proliferate and migrate into the damaged cortex. Antagonism of ionotropic receptors for extracellular ATP during and after the insult unmasks an early activation of neuroblasts in the subventricular zone, which responded with a rapid and intense migration of neuroblasts into the damaged cortex (within 24 hours). The process is further enhanced by elevating the production of the chemoattractant SDf-1alpha and may also be boosted by blocking the activation of microglia. This organotypic model which we have developed is an excellent in vitro system to study neurogenesis after ischemia and other neurodegenerative diseases. Its application has revealed a SOS response to oxygen/glucose deprivation, which is inhibited by unfavorable conditions due to the ischemic environment. Finally, experimental quantifications have allowed us to elaborate a mathematical model to describe neuroblast activation and to develop a computer simulation which should have promising applications for the screening of drug candidates for novel therapies of ischemia-related pathologies.