Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria. The first one is an unconstrained mean-variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor. (C) 2011 Elsevier Ltd. All rights reserved.

Physical objects on navigation channal simulation models

This paper presents the results of a simulation using physical objects. This concept integrates the physical dimensions of an entity such as length, width, and weight, with the usual process flow paradigm, recurrent in the discrete event simulation models. Based on a naval logistics system, we applied this technique in an access channel of the largest port of Latin America. This system is composed by vessel movement constrained by the access channel dimensions. Vessel length and width dictates whether it is safe or not to have one or two ships simultaneously. The success delivered by the methodology proposed was an accurate validation of the model, approximately 0.45% of deviation, when compared to real data. Additionally, the model supported the design of new terminals operations for Santos, delivering KPIs such as: canal utilization, queue time, berth utilization, and throughput capability

Multiresolution spherical wavelet analysis in global seismic tomography

Every seismic event produces seismic waves which travel throughout the Earth. Seismology is the science of interpreting measurements to derive information about the structure of the Earth. Seismic tomography is the most powerful tool for determination of 3D structure of deep Earth's interiors. Tomographic models obtained at the global and regional scales are an underlying tool for determination of geodynamical state of the Earth, showing evident correlation with other geophysical and geological characteristics. The global tomographic images of the Earth can be written as a linear combinations of basis functions from a specifically chosen set, defining the model parameterization. A number of different parameterizations are commonly seen in literature: seismic velocities in the Earth have been expressed, for example, as combinations of spherical harmonics or by means of the simpler characteristic functions of discrete cells. With this work we are interested to focus our attention on this aspect, evaluating a new type of parameterization, performed by means of wavelet functions. It is known from the classical Fourier theory that a signal can be expressed as the sum of a, possibly infinite, series of sines and cosines. This sum is often referred as a Fourier expansion. The big disadvantage of a Fourier expansion is that it has only frequency resolution and no time resolution. The Wavelet Analysis (or Wavelet Transform) is probably the most recent solution to overcome the shortcomings of Fourier analysis. The fundamental idea behind this innovative analysis is to study signal according to scale. Wavelets, in fact, are mathematical functions that cut up data into different frequency components, and then study each component with resolution matched to its scale, so they are especially useful in the analysis of non stationary process that contains multi-scale features, discontinuities and sharp strike. Wavelets are essentially used in two ways when they are applied in geophysical process or signals studies: 1) as a basis for representation or characterization of process; 2) as an integration kernel for analysis to extract information about the process. These two types of applications of wavelets in geophysical field, are object of study of this work. At the beginning we use the wavelets as basis to represent and resolve the Tomographic Inverse Problem. After a briefly introduction to seismic tomography theory, we assess the power of wavelet analysis in the representation of two different type of synthetic models; then we apply it to real data, obtaining surface wave phase velocity maps and evaluating its abilities by means of comparison with an other type of parametrization (i.e., block parametrization). For the second type of wavelet application we analyze the ability of Continuous Wavelet Transform in the spectral analysis, starting again with some synthetic tests to evaluate its sensibility and capability and then apply the same analysis to real data to obtain Local Correlation Maps between different model at same depth or between different profiles of the same model.

Comparison between 2.5-D and 3-D realistic models for wind field adjustment

[EN]In previous works, many authors have widely used mass consistent models for wind field simulation by the finite element method. On one hand, we have developed a 3-D mass consistent model by using tetrahedral meshes which are simultaneously adapted to complex orography and to terrain roughness length. In addition, we have included a local refinement strategy around several measurement or control points, significant contours, as for example shorelines, or numerical solution singularities. On the other hand, we have developed a 2.5-D model for simulating the wind velocity in a 3-D domain in terms of the terrain elevation, the surface temperature and the meteorological wind, which is consider as an averaged wind on vertical boundaries...

Neutrino velocity measurement with the OPERA experiment in the CNGS beam

In the thesis is presented the measurement of the neutrino velocity with the OPERA experiment in the CNGS beam, a muon neutrino beam produced at CERN. The OPERA detector observes muon neutrinos 730 km away from the source. Previous measurements of the neutrino velocity have been performed by other experiments. Since the OPERA experiment aims the direct observation of muon neutrinos oscillations into tau neutrinos, a higher energy beam is employed. This characteristic together with the higher number of interactions in the detector allows for a measurement with a much smaller statistical uncertainty. Moreover, a much more sophisticated timing system (composed by cesium clocks and GPS receivers operating in “common view mode”), and a Fast Waveform Digitizer (installed at CERN and able to measure the internal time structure of the proton pulses used for the CNGS beam), allows for a new measurement with a smaller systematic error. Theoretical models on Lorentz violating effects can be investigated by neutrino velocity measurements with terrestrial beams. The analysis has been carried out with blind method in order to guarantee the internal consistency and the goodness of each calibration measurement. The performed measurement is the most precise one done with a terrestrial neutrino beam, the statistical accuracy achieved by the OPERA measurement is about 10 ns and the systematic error is about 20 ns.

Quantum hydrodynamic models for semiconductors with and without collisions

In dieser Arbeit werden Quantum-Hydrodynamische (QHD) Modelle betrachtet, die ihren Einsatz besonders in der Modellierung von Halbleiterbauteilen finden. Das QHD Modell besteht aus den Erhaltungsgleichungen für die Teilchendichte, das Momentum und die Energiedichte, inklusive der Quanten-Korrekturen durch das Bohmsche Potential. Zu Beginn wird eine Übersicht über die bekannten Ergebnisse der QHD Modelle unter Vernachlässigung von Kollisionseffekten gegeben, die aus ein­em Schrödinger-System für den gemischten-Zustand oder aus der Wigner-Glei­chung hergeleitet werden können. Nach der Reformulierung der eindimensionalen QHD Gleichungen mit linearem Potential als stationäre Schrö­din­ger-Gleichung werden die semianalytischen Fassungen der QHD Gleichungen für die Gleichspannungs-Kurve betrachtet. Weiterhin werden die viskosen Stabilisierungen des QHD Modells be­rück­sich­tigt, sowie die von Gardner vorgeschlagene numerische Viskosität für das {sf upwind} Finite-Differenzen Schema berechnet. Im Weiteren wird das viskose QHD Modell aus der Wigner-Glei­chung mit Fokker-Planck Kollisions-Ope­ra­tor hergeleitet. Dieses Modell enthält die physikalische Viskosität, die durch den Kollision-Operator eingeführt wird. Die Existenz der Lösungen (mit strikt positiver Teilchendichte) für das isotherme, stationäre, eindimensionale, viskose Modell für allgemeine Daten und nichthomogene Randbedingungen wird gezeigt. Die dafür notwendigen Abschätzungen hängen von der Viskosität ab und erlauben daher den Grenzübergang zum nicht-viskosen Fall nicht. Numerische Simulationen der Resonanz-Tunneldiode modelliert mit dem nichtisothermen, stationären, eindimensionalen, viskosen QHD Modell zeigen den Einfluss der Viskosität auf die Lösung. Unter Verwendung des von Degond und Ringhofer entwickelten Quanten-Entropie-Minimierungs-Verfahren werden die allgemeinen QHD-Gleichungen aus der Wigner-Boltzmann-Gleichung mit dem BGK-Kollisions-Operator hergeleitet. Die Herleitung basiert auf der vorsichtige Entwicklung des Quanten-Max­well­ians in Potenzen der skalierten Plankschen Konstante. Das so erhaltene Modell enthält auch vertex-Terme und dispersive Terme für die Ge­schwin­dig­keit. Dadurch bleibt die Gleichspannungs-Kurve für die Re­so­nanz-Tunnel­diode unter Verwendung des allgemeinen QHD Modells in einer Dimension numerisch erhalten. Die Ergebnisse zeigen, dass der dispersive Ge­schwin­dig­keits-Term die Lösung des Systems stabilisiert.

Development of parallelizable flood inundation models for large scale analysis

Flood disasters are a major cause of fatalities and economic losses, and several studies indicate that global flood risk is currently increasing. In order to reduce and mitigate the impact of river flood disasters, the current trend is to integrate existing structural defences with non structural measures. This calls for a wider application of advanced hydraulic models for flood hazard and risk mapping, engineering design, and flood forecasting systems. Within this framework, two different hydraulic models for large scale analysis of flood events have been developed. The two models, named CA2D and IFD-GGA, adopt an integrated approach based on the diffusive shallow water equations and a simplified finite volume scheme. The models are also designed for massive code parallelization, which has a key importance in reducing run times in large scale and high-detail applications. The two models were first applied to several numerical cases, to test the reliability and accuracy of different model versions. Then, the most effective versions were applied to different real flood events and flood scenarios. The IFD-GGA model showed serious problems that prevented further applications. On the contrary, the CA2D model proved to be fast and robust, and able to reproduce 1D and 2D flow processes in terms of water depth and velocity. In most applications the accuracy of model results was good and adequate to large scale analysis. Where complex flow processes occurred local errors were observed, due to the model approximations. However, they did not compromise the correct representation of overall flow processes. In conclusion, the CA model can be a valuable tool for the simulation of a wide range of flood event types, including lowland and flash flood events.

Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.

A new 3D modelling paradigm for discrete model

Until few years ago, 3D modelling was a topic confined into a professional environment. Nowadays technological innovations, the 3D printer among all, have attracted novice users to this application field. This sudden breakthrough was not supported by adequate software solutions. The 3D editing tools currently available do not assist the non-expert user during the various stages of generation, interaction and manipulation of 3D virtual models. This is mainly due to the current paradigm that is largely supported by two-dimensional input/output devices and strongly affected by obvious geometrical constraints. We have identified three main phases that characterize the creation and management of 3D virtual models. We investigated these directions evaluating and simplifying the classic editing techniques in order to propose more natural and intuitive tools in a pure 3D modelling environment. In particular, we focused on freehand sketch-based modelling to create 3D virtual models, interaction and navigation in a 3D modelling environment and advanced editing tools for free-form deformation and objects composition. To pursuing these goals we wondered how new gesture-based interaction technologies can be successfully employed in a 3D modelling environments, how we could improve the depth perception and the interaction in 3D environments and which operations could be developed to simplify the classical virtual models editing paradigm. Our main aims were to propose a set of solutions with which a common user can realize an idea in a 3D virtual model, drawing in the air just as he would on paper. Moreover, we tried to use gestures and mid-air movements to explore and interact in 3D virtual environment, and we studied simple and effective 3D form transformations. The work was carried out adopting the discrete representation of the models, thanks to its intuitiveness, but especially because it is full of open challenges.

A Framework for the Automation of Discrete-Event Simulation Experiments

Simulation is an important resource for researchers in diverse fields. However, many researchers have found flaws in the methodology of published simulation studies and have described the state of the simulation community as being in a crisis of credibility. This work describes the project of the Simulation Automation Framework for Experiments (SAFE), which addresses the issues that undermine credibility by automating the workflow in the execution of simulation studies. Automation reduces the number of opportunities for users to introduce error in the scientific process thereby improvingthe credibility of the final results. Automation also eases the job of simulation users and allows them to focus on the design of models and the analysis of results rather than on the complexities of the workflow.

LakeMIP Kivu: evaluating the representation of a large, deep tropical lake by a set of one-dimensional lake models

The African great lakes are of utmost importance for the local economy (fishing), as well as being essential to the survival of the local people. During the past decades, these lakes experienced fast changes in ecosystem structure and functioning, and their future evolution is a major concern. In this study, for the first time a set of one-dimensional lake models are evaluated for Lake Kivu (2.28°S; 28.98°E), East Africa. The unique limnology of this meromictic lake, with the importance of salinity and subsurface springs in a tropical high-altitude climate, presents a worthy challenge to the seven models involved in the Lake Model Intercomparison Project (LakeMIP). Meteorological observations from two automatic weather stations are used to drive the models, whereas a unique dataset, containing over 150 temperature profiles recorded since 2002, is used to assess the model’s performance. Simulations are performed over the freshwater layer only (60 m) and over the average lake depth (240 m), since salinity increases with depth below 60 m in Lake Kivu and some lake models do not account for the influence of salinity upon lake stratification. All models are able to reproduce the mixing seasonality in Lake Kivu, as well as the magnitude and seasonal cycle of the lake enthalpy change. Differences between the models can be ascribed to variations in the treatment of the radiative forcing and the computation of the turbulent heat fluxes. Fluctuations in wind velocity and solar radiation explain inter-annual variability of observed water column temperatures. The good agreement between the deep simulations and the observed meromictic stratification also shows that a subset of models is able to account for the salinity- and geothermal-induced effects upon deep-water stratification. Finally, based on the strengths and weaknesses discerned in this study, an informed choice of a one-dimensional lake model for a given research purpose becomes possible.

Theoretical models of planetary system formation: mass vs. semi-major axis

Context. Planet formation models have been developed during the past years to try to reproduce what has been observed of both the solar system and the extrasolar planets. Some of these models have partially succeeded, but they focus on massive planets and, for the sake of simplicity, exclude planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of radial velocity, transit, and direct imaging surveys, seems to be even more pronounced for low-mass planets. These new observations require improving planet formation models, including new physics, and considering the formation of systems. Aims: In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc and show the effect, in terms of architecture and composition of this multiplicity. Methods: We used an N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. Results: We show that the masses and semi-major axes of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping. We find that the fraction of ejected planets increases from nearly 0 to 8% as we change the number of embryos we seed the system with from 2 to 20 planetary embryos. Moreover, our calculations show that, when considering planets more massive than ~5 M⊕, simulations with 10 or 20 planetary embryos statistically give the same results in terms of mass function and period distribution.

Estimating parameters in Markov models for longitudinal studies with missing data or surrogate outcomes

The discrete-time Markov chain is commonly used in describing changes of health states for chronic diseases in a longitudinal study. Statistical inferences on comparing treatment effects or on finding determinants of disease progression usually require estimation of transition probabilities. In many situations when the outcome data have some missing observations or the variable of interest (called a latent variable) can not be measured directly, the estimation of transition probabilities becomes more complicated. In the latter case, a surrogate variable that is easier to access and can gauge the characteristics of the latent one is usually used for data analysis. ^ This dissertation research proposes methods to analyze longitudinal data (1) that have categorical outcome with missing observations or (2) that use complete or incomplete surrogate observations to analyze the categorical latent outcome. For (1), different missing mechanisms were considered for empirical studies using methods that include EM algorithm, Monte Carlo EM and a procedure that is not a data augmentation method. For (2), the hidden Markov model with the forward-backward procedure was applied for parameter estimation. This method was also extended to cover the computation of standard errors. The proposed methods were demonstrated by the Schizophrenia example. The relevance of public health, the strength and limitations, and possible future research were also discussed. ^

Patients' preferences for a prostate cancer consultation, a discrete choice experiment

Four basic medical decision making models are commonly discussed in the literature in reference to physician-patient interactions. All fall short in their attempt to capture the nuances of physician-patient interactions, and none satisfactorily address patients' preferences for communication and other attributes of care. Prostate cancer consultations are one setting where preferences matter and are likely to vary among patients. Fortunately, discrete choice experiments are capable of casting light on patients' preferences for communication and other attributes of value that make up a consultation before the consultation occurs, which is crucial if patients are to derive the most utility from the process of reaching a decision as well as the decision itself. The results of my dissertation provide strong support to the notion that patients, at least in the hypothetical setting of a DCE, have identifiable preferences for the attributes of a prostate cancer consultation and that those preferences are capable of being elicited before a consultation takes place. Further, patients' willingness-to-pay for the non-cost attributes of the consultation is surprisingly robust to a variety of individual level variables of interest. ^

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^