Constructing good deals in discrete time arbitrage-free dynamic pricing models

Recent literature has proved that many classical pricing models (Black and Scholes, Heston, etc.) and risk measures (V aR, CV aR, etc.) may lead to “pathological meaningless situations”, since traders can build sequences of portfolios whose risk leveltends to −infinity and whose expected return tends to +infinity, i.e., (risk = −infinity, return = +infinity). Such a sequence of strategies may be called “good deal”. This paper focuses on the risk measures V aR and CV aR and analyzes this caveat in a discrete time complete pricing model. Under quite general conditions the explicit expression of a good deal is given, and its sensitivity with respect to some possible measurement errors is provided too. We point out that a critical property is the absence of short sales. In such a case we first construct a “shadow riskless asset” (SRA) without short sales and then the good deal is given by borrowing more and more money so as to invest in the SRA. It is also shown that the SRA is interested by itself, even if there are short selling restrictions.

Monte Carlo simulation of the basic features of the GE Millennium MG single photon emission computed tomography gamma camera

Objective - To describe and validate the simulation of the basic features of GE Millennium MG gamma camera using the GATE Monte Carlo platform. Material and methods - Crystal size and thickness, parallel-hole collimation and a realistic energy acquisition window were simulated in the GATE platform. GATE results were compared to experimental data in the following imaging conditions: a point source of 99mTc at different positions during static imaging and tomographic acquisitions using two different energy windows. The accuracy between the events expected and detected by simulation was obtained with the Mann–Whitney–Wilcoxon test. Comparisons were made regarding the measurement of sensitivity and spatial resolution, static and tomographic. Simulated and experimental spatial resolutions for tomographic data were compared with the Kruskal–Wallis test to assess simulation accuracy for this parameter. Results - There was good agreement between simulated and experimental data. The number of decays expected when compared with the number of decays registered, showed small deviation (≤0.007%). The sensitivity comparisons between static acquisitions for different distances from source to collimator (1, 5, 10, 20, 30cm) with energy windows of 126–154 keV and 130–158 keV showed differences of 4.4%, 5.5%, 4.2%, 5.5%, 4.5% and 5.4%, 6.3%, 6.3%, 5.8%, 5.3%, respectively. For the tomographic acquisitions, the mean differences were 7.5% and 9.8% for the energy window 126–154 keV and 130–158 keV. Comparison of simulated and experimental spatial resolutions for tomographic data showed no statistically significant differences with 95% confidence interval. Conclusions - Adequate simulation of the system basic features using GATE Monte Carlo simulation platform was achieved and validated.

Validação do uso de cone-beam computed tomography de kilovoltagem de um LINAC para a realização de estudos dosimétricos

Mestrado em Radioterapia

Radioterapia adaptativa: utilização do cone-beam computed tomography para o cálculo de dose em radioterapia

Mestrado em Radiações Aplicadas às Tecnologias da Saúde - Ramo de especialização: Terapia com Radiações

Optimising protocol of acquisition and post-processing procedures in the assessment of coronary artery disease by computed tomography

Coronary artery disease (CAD) is currently one of the most prevalent diseases in the world population and calcium deposits in coronary arteries are one direct risk factor. These can be assessed by the calcium score (CS) application, available via a computed tomography (CT) scan, which gives an accurate indication of the development of the disease. However, the ionising radiation applied to patients is high. This study aimed to optimise the protocol acquisition in order to reduce the radiation dose and explain the flow of procedures to quantify CAD. The main differences in the clinical results, when automated or semiautomated post-processing is used, will be shown, and the epidemiology, imaging, risk factors and prognosis of the disease described. The software steps and the values that allow the risk of developingCADto be predicted will be presented. A64-row multidetector CT scan with dual source and two phantoms (pig hearts) were used to demonstrate the advantages and disadvantages of the Agatston method. The tube energy was balanced. Two measurements were obtained in each of the three experimental protocols (64, 128, 256 mAs). Considerable changes appeared between the values of CS relating to the protocol variation. The predefined standard protocol provided the lowest dose of radiation (0.43 mGy). This study found that the variation in the radiation dose between protocols, taking into consideration the dose control systems attached to the CT equipment and image quality, was not sufficient to justify changing the default protocol provided by the manufacturer.

Equilibrium distributions of discrete non-autonomous graphs

We introduce the notions of equilibrium distribution and time of convergence in discrete non-autonomous graphs. Under some conditions we give an estimate to the convergence time to the equilibrium distribution using the second largest eigenvalue of some matrices associated with the system.

Implementation of a new reference values database for semiquantification in123I-FP-CIT brain single emission tomography

Brain dopamine transporters imaging by Single Emission Tomography (SPECT) with 123I-FP-CIT (DaTScanTM) has become an important tool in the diagnosis and evaluation of Parkinson syndromes.This diagnostic method allows the visualization of a portion of the striatum – where healthy pattern resemble two symmetric commas - allowing the evaluation of dopamine presynaptic system, in which dopamine transporters are responsible for dopamine release into the synaptic cleft, and their reabsorption into the nigrostriatal nerve terminals, in order to be stored or degraded. In daily practice for assessment of DaTScan TM, it is common to rely only on visual assessment for diagnosis. However, this process is complex and subjective as it depends on the observer’s experience and it is associated with high variability intra and inter observer. Studies have shown that semiquantification can improve the diagnosis of Parkinson syndromes. For semiquantification, analysis methods of image segmentation using regions of interest (ROI) are necessary. ROIs are drawn, in specific - striatum - and in nonspecific – background – uptake areas. Subsequently, specific binding ratios are calculated. Low adherence of semiquantification for diagnosis of Parkinson syndromes is related, not only with the associated time spent, but also with the need of an adapted database of reference values for the population concerned, as well as, the examination of each service protocol. Studies have concluded, that this process increases the reproducibility of semiquantification. The aim of this investigation was to create and validate a database of healthy controls for Dopamine transporters with DaTScanTM named DBRV. The created database has been adapted to the Nuclear Medicine Department’s protocol, and the population of Infanta Cristina’s Hospital located in Badajoz, Spain.

Influence of computed tomography attenuation correction in myocardial perfusion imaging in obese population

Marked regional variations in myocardial activity that are not related to myocardial perfusion defects.Verify the influence of CT-AC inMPI results in patients with BMI between 30 and 35 and higher than 30 for male and female population.

Caracterização por optical coherence tomography (OCT) de placas coronárias sujeitas a cutting balloon: contributo das técnicas bidiomensional e tridimensional

Mestrado em Tecnologia de Diagnóstico e Intervenção Cardiovascular - Área de especialização: Intervenção cardiovascular

Upper crustal structure of Madeira Island revealed from ambient noise tomography

We present the first image of the Madeira upper crustal structure, using ambient seismic noise tomography. 16 months of ambient noise, recorded in a dense network of 26 seismometers deployed across Madeira, allowed reconstructing Rayleigh wave Green's functions between receivers. Dispersion analysis was performed in the short period band from 1.0 to 4.0 s. Group velocity measurements were regionalized to obtain 20 tomographic images, with a lateral resolution of 2.0 km in central Madeira. Afterwards, the dispersion curves, extracted from each cell of the 2D group velocity maps, were inverted as a function of depth to obtain a 3D shear wave velocity model of the upper crust, from the surface to a depth of 2.0 km. The obtained 3D velocity model reveals features throughout the island that correlates well with surface geology and island evolution. (C) 2015 Elsevier B.V. All rights reserved.

Upper crustal structure of Madeira Island revealed from ambient noise tomography

We present the first image of the Madeira upper crustal structure, using ambient seismic noise tomography. 16 months of ambient noise, recorded in a dense network of 26 seismometers deployed across Madeira, allowed reconstructing Rayleigh wave Green's functions between receivers. Dispersion analysis was performed in the short period band from 1.0 to 4.0 s. Group velocity measurements were regionalized to obtain 20 tomographic images, with a lateral resolution of 2.0 km in central Madeira. Afterwards, the dispersion curves, extracted from each cell of the 2D group velocity maps, were inverted as a function of depth to obtain a 3D shear wave velocity model of the upper crust, from the surface to a depth of 2.0 km. The obtained 3D velocity model reveals features throughout the island that correlates well with surface geology and island evolution. (C) 2015 Elsevier B.V. All rights reserved.

Ambient noise tomography of the East African Rift in Mozambique

Seismic ambient noise tomography is applied to central and southern Mozambique, located in the tip of the East African Rift (EAR). The deployment of MOZART seismic network, with a total of 30 broad-band stations continuously recording for 26 months, allowed us to carry out the first tomographic study of the crust under this region, which until now remained largely unexplored at this scale. From cross-correlations extracted from coherent noise we obtained Rayleigh wave group velocity dispersion curves for the period range 5–40 s. These dispersion relations were inverted to produce group velocity maps, and 1-D shear wave velocity profiles at selected points. High group velocities are observed at all periods on the eastern edge of the Kaapvaal and Zimbabwe cratons, in agreement with the findings of previous studies. Further east, a pronounced slow anomaly is observed in central and southern Mozambique, where the rifting between southern Africa and Antarctica created a passive margin in the Mesozoic, and further rifting is currently happening as a result of the southward propagation of the EAR. In this study, we also addressed the question concerning the nature of the crust (continental versus oceanic) in the Mozambique Coastal Plains (MCP), still in debate. Our data do not support previous suggestions that the MCP are floored by oceanic crust since a shallow Moho could not be detected, and we discuss an alternative explanation for its ocean-like magnetic signature. Our velocity maps suggest that the crystalline basement of the Zimbabwe craton may extend further east well into Mozambique underneath the sediment cover, contrary to what is usually assumed, while further south the Kaapval craton passes into slow rifted crust at the Lebombo monocline as expected. The sharp passage from fast crust to slow crust on the northern part of the study area coincides with the seismically active NNE-SSW Urema rift, while further south the Mazenga graben adopts an N-S direction parallel to the eastern limit of the Kaapvaal craton. We conclude that these two extensional structures herald the southward continuation of the EAR, and infer a structural control of the transition between the two types of crust on the ongoing deformation.

Spectral invariants of periodic nonautonomous discrete dynamical systems

For an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems.

Exploiting the bin-class histograms for feature selection on discrete data

In machine learning and pattern recognition tasks, the use of feature discretization techniques may have several advantages. The discretized features may hold enough information for the learning task at hand, while ignoring minor fluctuations that are irrelevant or harmful for that task. The discretized features have more compact representations that may yield both better accuracy and lower training time, as compared to the use of the original features. However, in many cases, mainly with medium and high-dimensional data, the large number of features usually implies that there is some redundancy among them. Thus, we may further apply feature selection (FS) techniques on the discrete data, keeping the most relevant features, while discarding the irrelevant and redundant ones. In this paper, we propose relevance and redundancy criteria for supervised feature selection techniques on discrete data. These criteria are applied to the bin-class histograms of the discrete features. The experimental results, on public benchmark data, show that the proposed criteria can achieve better accuracy than widely used relevance and redundancy criteria, such as mutual information and the Fisher ratio.