Comparative analysis of non-linear models with parametric link function based on the family of Czado functions and asymmetric functions of Aranda Ordaz

Tese de mestrado, Bioestatística, Universidade de Lisboa, Faculdade de Ciências, 2021For a good clinical practice and management to be attained, statistical analysis can perform a major role. Statistical models can greatly aid in medical decision making, as for example in the admission of critically ill patients to the Intensive Care Units (ICUs). These services have the mission of providing health care to patients in critical situations, which constitutes a challenge to hospital management, considering the heavy budgets that are necessary to maintain the quality of response. Therefore, decisions are made daily bearing in mind the effectiveness of the treatment versus its cost. In order to help the decision-making process metrics can be obtained, usually via Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs). These are generally oriented towards the quantification of the risk of mortality and are characterized by a small number of variables, from which a score is extracted that reflects the patient's state of severity in addition to an in-hospital mortality estimate. Among the components of GLMs and GAMs which can be focused on in order to improve the quality of the models, the link function is highlighted. Recent work using models with flexible parametric link functions, namely with link functions belonging to the family of asymmetric functions of Aranda-Ordaz, showed an improvement in their performance. On the other hand, studies involving link functions belonging to the family of Czado functions are scarce. Using a Czado link function provides a greater flexibility, by it depending on three parameters, rather than the Aranda-Ordaz link function, which merely depends on one. Thus, a comparative analysis of the performance of both models referred (GLM, GAM), using the Aranda-Ordaz and Czado link functions, and considering the Logistic link function as a baseline was the primary line of work. The results presented themselves as inconclusive regarding the greater performance of either of the link functions, which can be related to the data used and not necessarily the actual performance of the models and link functions. Further studies should be carried using different data sets in order to truly access the performance of the models using both Czado and Aranda-Ordaz link functions

Spinful Algorithmization of High Energy Diffraction

High energy diffraction probes fundamental interactions, the vacuum, and quantum mechanically coherent matter waves at asymptotic energies. In this work, we algorithmize our abstract ideas and develop a set of rigid rules for diffraction. To get spin under control, we construct a new Monte Carlo simulation engine, GRANIITTI. It is the first event generator with custom spin-dependent scattering amplitudes for the glueball domain semi-exclusive diffraction, driven by fully multithreaded importance sampling and written in C++. Our simulations provide new computational evidence that the enigmatic glueball filter observable is a spin polarization filter for tensor resonances. For algorithmic spin studies, we automate the classic Laplace spherical harmonics inverse expansion, carefully define the geometric acceptance related phase space issues and study the harmonic mixing properties systematically in different Lorentz frames. To improve the big picture, we generalize the standard soft diffraction observables and definitions by developing a high dimensional probabilistic framework based on incidence algebras, Combinatorial Superstatistics, and solve also a new superposition inverse problem using the Möbius inversion theorem. For inverting stochastic autoconvolution integral equations or `inverting the proton', we develop a novel recursive inverse algorithm based on the Fast Fourier Transform and relative entropy minimization. The first algorithmic inverse results of the proton double multiplicity structure and multiparton interaction rates are obtained using the published LHC data, in agreement with standard phenomenology. For optimal inversion of the detector efficiency response, we build the first Deep Learning based solution working in higher phase space dimensions, DeepEfficiency, which inverts the detector response on an event-by-event basis and minimizes the event generator dependence. Using the ALICE experiment proton-proton data at the LHC at 13 TeV, we obtain the first unfolded fiducial measurement of the multidimensional combinatorial partial cross sections, the first multidimensional maximum likelihood fit of the effective soft pomeron intercept and the first multidimensional maximum likelihood fit of the single, double and non-diffractive component cross sections. Great care is taken with the fiducial and non-fiducial definitions. The second topic of measurements centers on semi-exclusive central diffractive production of hadron pairs, which we study with the ALICE data. We measure and fit the resonance spectra of identified pion and kaon pairs, which is crucial on the road towards solving the mysteries of glueballs, the proton structure fluctuations, and the pomeron.Suurenergiadiffraktio heijastelee luonnon perusvuorovaikutuksia, tyhjiötä ja kvanttimekaanisesti koherentteja aaltoja asymptoottisen suurilla energioilla. Tässä työssä teen abstrakteista ideoista algoritmeja ja kehitän joukon täsmällisiä sääntöjä suurenergiadiffraktiolle. Jotta spin ja kulmaliikemäärä saadaan haltuun, rakennan uuden avoimen lähdekoodin Monte Carlo -simulaatiokoneiston nimeltään GRANIITTI. Se on ensimmäinen törmäysgeneraattori, joka kykenee mallintamaan kattavasti spin-riippuvia relativistisia sironta-amplitudeja keskeisdiffraktion prosesseissa. Näitä hiukkassimulaatioita tarvitaan esimerkiksi CERN:in LHC-kiihdyttimellä tehtävissä kokeissa, joissa keskitytään niin kutsuttujen ”liimapallojen” (eng. glueballs) löytämiseen. Liimapallot ovat vahvan vuorovaikutuksen gluonihiukkasten muodostamia resonoivia kvanttitiloja, joilla on teoreettinen yhteys suurenergiadiffraktioon, mutta joita ei ole saatu kokeellisesti vielä yksikäsitteisesti havaittua. Tämä johtuu niiden monikomponenttiliiman kaltaisesta kvanttitilasta, jossa mukana voi olla myös kvarkkeja. Simulaatioiden avulla löydän uutta laskennallista todistetta sille, että liimapallosuotimena tunnettua arvoituksellista observaabelia ajaa resonanssien spin-polarisaatiotiheys. Suurena tavoitteena on kehittää suurenergiadiffraktion kokonaiskuvaa. Tätä varten esittelen uuden matemaattisen koneiston perustuen todennäköisyyslaskentaan ja kombinatorisiin insidenssialgebroihin. Kutsun tätä kombinatoriseksi superstatistiikaksi. Näin saadaan määriteltyä ja ratkaistua heti uusi inversio-ongelma jo tunnetun Möbius-inversiolauseen avulla. Jatkan inversio-ongelmien saralla ja näytän ensimmäisenä kuinka protoni-protoni -törmäyksissä syntyneiden varattujen hiukkasten todennäköisyysjakauma voidaan algoritmillisesti uudelleenorganisoida. Näin saadaan uusia näkökulmia suurenergiaprotonien monimutkaiseen rakenteeseen ja dynamiikkaan, jossa useat partonit protonin sisältä törmäävät samanaikaisesti. LHC-datan avulla saadut algoritmilliset tulokset ovat samansuuntaisia aiempien mallipohjaisten tulkintojen kanssa. Kehitän myös ensimmäisenä algoritmin, joka syväkorjaa lähes optimaalisesti mittauslaitteiston tehokkuusvasteen moniulotteisessa liikemääräavaruudessa törmäys törmäykseltä. Tämä algoritmi perustuu syviin neuroverkkoihin. Työn kokeellisessa osuudessa hyödynnetään työssä kehitettyjä menetelmiä ja algoritmeja LHC:n ALICE-kokeessa, käyttäen LHC-kiihdyttimen tuottamaa protoni-protoni -törmäysdataa 13 TeV:n massakeskipiste-energialla. Näin tehdään ensimmäinen kokonaisvaltainen pehmeiden törmäysten moniulotteinen fidusiaalimittaus ja ensimmäinen moniulotteinen diffraktiivisten vaikutusalojen suurimman uskottavuuden fidusiaalianalyysi. Lisäksi analysoidaan diffraktiofenomenologian oleellisia parametreja. Toinen mittausten aihe on keskeisdiffraktio. Työssä mitataan hadroniset resonanssispektrit, joiden tutkiminen vie meidät kohti liimapallojen, protonin fluktuoivan sisärakenteen ja pomeronin salaisuuksien ratkaisuja

Modelling energy markets and pricing energy derivatives

The main objective of this thesis is to provide an empirical assessment of the popular methodologies for modelling the underlying spot price dynamics in energy markets. After a brief introduction in the alternative forms of derivation that may be used for speculative and risk management purposes in energy markets, we assess the performance of the standard Black's framework in modelling energy prices. For the first time in the literature we use a powerful and realistic data set which covers oil, gas and electricity markets and tests the appropriateness of the Geometric Brownian Motion process to explain the observed dynamics of the spot prices in these markets. We also provide spreadsheet based computer algorithms to price popular energy derivatives based on the Geometric Brownian Motion specifications. In Chapter-3 we try to accommodate observed stylised facts in the spot price behaviour, namely mean reversion and jumps. For the first time in the literature we test a jump diffusion model, and a mean reversion jump diffusion model against our broad data set and compare the findings to the Black's Geometric Brownian Motion specifications. In Chapter-4 we use a forward curve approach as an alternative-modelling framework to the spot price models. Based upon an almost proprietary data set of historical forward curves, we determine the number of independent factors that are needed to model the forward curve's dynamic evolution. After carrying out principal component analysis on historical forward data a threefactor-model emerges as the most appropriate for energy markets in general. The first factor being the volatility (level effect), the second the smile and the third sesonality. Finally in Chapter-5 of the thesis we compare the ability of spot models (Jump Diffusion and Mean Reversion Jump Diffusion Model) and forward curve based models to price WTI options. The results show that the Jump Diffusion Model is the best model as the option prices given are very accurate in comparison with the other models and closest to the market observed options prices

Two dimensional models of tumor angiogenesis

Angiogenesis, the formation of new capillaries from pre-existing vessels, is essential for tumor progression. It is critical for the growth of primary cancers. In this thesis we present a new approach to angiogenesis, based on the theory of reinforced random walks, coupled with a Michaelis-Menten type mechanism. This views the endothelial cell receptors as the catalyst for transforming angiogenic factor into proteolytic enzyme in order to model the first stage. In our model we use a curvature-induced proliferation term for the endothelial cell equation. Our numerical results indicate that the proliferation of endothelial cells is high at the tip. Also, we observe that the tip movement speeds up as it gets close to the tumor;A coupled system of ordinary and partial differential equations is derived which, in the presence of an angiogenic agent, predicts the aggregation of the endothelial cells and the collapse of the vascular lamina, opening a passage into the extracellular matrix. (ECM). We have dynamical equations not only in a two-dimensional region, the ECM, but also in a one-dimensional region, the capillary. We also consider the effect of the angiostatin on the endothelial cell proliferation and fibronectin;Our computations are compared with the results of Judah Folkman\u27s classical rabbit eye experiments in which he demonstrated that tumors can produce angiogenic growth factors. Using only classical enzyme kinetics and reinforced random walk cell transport equations, we are able to predict how long it should take for a new capillary to grow from the limbus of the rabbit eye to an implanted malignancy. The predictions agree very well with the experiments

Application of effective field theory to the study of hypernuclei

Furnstahl, Serot, and Tang have developed a methodology for constructing an effective lagrangian for the nuclear many-body system which contains the underlying symmetries of QCD. Density Functional Theory is used as a theoretical justification for the relativistic Hartree (Kohn-Sham) equations derived from this effective lagrangian. In the present work; this approach is extended to the region of nonzero strangeness in two applications. First, this procedure is applied to strange, neutral, superheavy systems and the surface properties of these nuclei are extracted. Second, single-particle states in Lambda-hypernuclei are investigated, the effective lagrangian is determined to various levels of truncation, and where appropriate, ground-state particle-hole splittings are calculated

Immunogenetics

This open access book explores techniques for working in the field of immunogenetics, i.e. fundamental and translational research into the adaptive immune receptor repertoire. Many chapters are dedicated to lab protocols, bioinformatics, and immunoinformatics analysis of high-resolution immunome analysis, exemplified by numerous applications. Additionally, the newest technological variations on these protocols are discussed, including non-amplicon, single-cell, and cell-free strategies. Written for the highly successful Methods in Molecular Biology series, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Authoritative and practical, Immunogenetics: Methods and Protocols covers a broad spectrum of methodologies for applications in research and clinical diagnostics to illustrate the impact that immunogenetics has achieved and will further expand in all fields of medicine, from infection and (auto)immunity, to vaccination, to lymphoid malignancy and tumor immunity

Sex Differences in Morphine Analgesia and the Descending Modulation of Pain

Morphine is the most widely prescribed opiate for alleviation of persistent pain; however, it is becoming increasingly clear that morphine is less potent in women compared to men. Morphine primarily binds mu opioid receptors, which are densely localized in the midbrain periaqueductal gray (PAG). Anatomical and physiological studies conducted in the 1960s identified the PAG, and its projections to the rostral ventromedial medulla (RVM) and spinal cord dorsal horn, as an essential neural circuit mediating opioid-based analgesia. Remarkably, the majority of studies since then were conducted in males with the implicit assumption that this circuit was the same in females; this is not the case. It is now well established that morphine produces greater analgesia in males compared to females in a wide range of vertebrates, however, the mechanism(s) driving this sex difference is not clear. Our recent studies indicate that two factors appear to be contributing to the sexually dimorphic effects of morphine. First, there are sex differences in the anatomy and physiology of the descending inhibitory pathway on which morphine acts to produce analgesia. Specifically, the projections from the PAG to the RVM are sexually dimorphic and activated to a greater degree by both inflammatory pain and systemic morphine in males. In the absence of pain, the PAG-RVM circuit is activated to a greater degree in males compared to females, while this activation steadily declines during the development of tolerance in males only. We also have evidence of a sexually dimorphic expression of mu opioid receptor within the PAG that appears to contribute to sex differences in morphine potency. Microinjection of morphine directly into the PAG produces significantly greater analgesia in males, indicating that the PAG is sufficient for eliciting this sexually dimorphic behavior. Furthermore, mu opioid receptor-expressing PAG neurons are necessary for eliciting a sexually dimorphic response to morphine as lesioning mu opioid receptor-expressing neurons attenuates analgesia in males only. Together, these data indicate that the PAG-RVM pathway and mu opioid receptor expression in the PAG is sexually dimorphic and provides a primary mechanism for sex differences in morphine potency

Stochastic volatility models: calibration, pricing and hedging

Stochastic volatility models have long provided a popular alternative to the Black- Scholes-Merton framework. They provide, in a self-consistent way, an explanation for the presence of implied volatility smiles/skews seen in practice. Incorporating jumps into the stochastic volatility framework gives further freedom to nancial mathematicians to t both the short and long end of the implied volatility surface. We present three stochastic volatility models here - the Heston model, the Bates model and the SVJJ model. The latter two models incorporate jumps in the stock price process and, in the case of the SVJJ model, jumps in the volatility process. We analyse the e ects that the di erent model parameters have on the implied volatility surface as well as the returns distribution. We also present pricing techniques for determining vanilla European option prices under the dynamics of the three models. These include the fast Fourier transform (FFT) framework of Carr and Madan as well as two Monte Carlo pricing methods. Making use of the FFT pricing framework, we present calibration techniques for tting the models to option data. Speci cally, we examine the use of the genetic algorithm, adaptive simulated annealing and a MATLAB optimisation routine for tting the models to option data via a leastsquares calibration routine. We favour the genetic algorithm and make use of it in tting the three models to ALSI and S&P 500 option data. The last section of the dissertation provides hedging techniques for the models via the calculation of option price sensitivities. We nd that a delta, vega and gamma hedging scheme provides the best results for the Heston model. The inclusion of jumps in the stock price and volatility processes, however, worsens the performance of this scheme. MATLAB code for some of the routines implemented is provided in the appendix

STK /WST 795 Research Reports

These documents contain the honours research reports for each year for the Department of Statistics.Honours Research Reports - University of Pretoria 20XXStatisticsBSs (Hons) Mathematical Statistics, BCom (Hons) Statistics, BCom (Hons) Mathematical StatisticsUnrestricte