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This work provides an overview on deterministic and stochastic models that have previously been proposed by us to study the transmission dynamics of the Coronavirus Disease 2019 (COVID-19) in Europe and USA. Briefly, we describe realistic deterministic and stochastic models for the evolution of the COVID-19 pandemic, subject to the lockdown and quarantine measures, which take into account the time-delay for recovery or death processes. Realistic dynamic equations for the entire process have been derived by adopting the so-called "kinetic-type reactions approach". The lockdown and the quarantine measures are modelled by some kind of inhibitor reactions where susceptible and infected individuals can be "trapped" into inactive states. The dynamics for the recovered people is obtained by accounting people who are only traced back to hospitalised infected people. To model the role of the Hospitals we take inspiration from the Michaelis-Menten's enzyme-substrate reaction model (the so-called "MM reaction") where the "enzyme" is associated to the "available hospital beds", the "substrate" to the "infected people", and the "product" to the "recovered people", respectively. The statistical properties of the models, in particular the relevant correlation functions and the probability density functions, have duly been evaluated. We validate our theoretical predictions with a large series of experimental data for Italy, Germany, France, Belgium and United States, and we also compare data for Italy and Belgium with the theoretical predictions of the logistic model. We found that our predictions are in good agreement with the real world since the onset of COVID 19, contrary to the the logistics model that only applies in the first days of the pandemic. In the final part of the work, we can find the (theoretical) relationships that should be satisfied to obtain the disappearance of the virus., 51 pages, 39 Figures. Review/Research Manuscript on modelling the dynamics of SARS-CoV 2 Infection. arXiv admin note: text overlap with arXiv:2101.05596, arXiv:2012.01869

Based on the Bezout approach we propose a simple algorithm to determine the {\tt gcd} of two polynomials which doesn't need division, like the Euclidean algorithm, or determinant calculations, like the Sylvester matrix algorithm. The algorithm needs only $n$ steps for polynomials of degree $n$. Formal manipulations give the discriminant or the resultant for any degree without needing division nor determinant calculation., 9 pages, 0 Figures

A new coronavirus disease, called COVID-19, appeared in the Chinese region of Wuhan at the end of last year; since then the virus spread to other countries, including most of Europe. We propose a differential equation governing the evolution of the COVID-19. This dynamic equation also describes the evolution of the number of infected people for 13 common respiratory viruses (including the SARS-CoV-2). We validate our theoretical predictions with experimental data for Italy, Belgium and Luxembourg, and compare them with the predictions of the logistic model. We find that our predictions are in good agreement with the real world since the beginning of the appearance of the COVID-19; this is not the case for the logistic model that only applies to the first days. The second part of the work is devoted to modelling the descending phase, i.e. the decrease of the number of people tested positive for COVID-19. Also in this case, we propose a new set of dynamic differential equations that we solved numerically. We use our differential equations parametrised with experimental data to make several predictions, such as the date when Italy, Belgium, and Luxembourg will reach a peak number of SARS-CoV-2 infected people. The descending curves provide valuable information such as the duration of the COVID-19 epidemic in a given Country and therefore when it will be possible to return to normal life. The study of the the dynamics of COVID-19 when the population have been subject to less restrictive measures is beyond the scope of this work and it will be matter of future works., 34 pages, 19 figures, 6 tables

Here, we propose a new tool to estimate the complexity of a time series: the entropy of difference (ED). The method is based solely on the sign of the difference between neighboring values in a time series. This makes it possible to describe the signal as efficiently as prior proposed parameters such as permutation entropy (PE) or modified permutation entropy (mPE), but (1) reduces the size of the sample that is necessary to estimate the parameter value, and (2) enables the use of the Kullback-Leibler divergence to estimate the distance between the time series data and random signals., 10 pages, 6 figures

Electroencephalogram (EEG) is an important diagnostic tool in clinical neurophysiology. However, EEGs are not often used in clinical studies because of intrinsic problem like the huge quantity of data or artifacts. In this paper, we shall describe statistical tools to detect and quantify the effect of drugs on the brain by the analysis of EEGs. We first use Independent Component Analysis (ICA) to detect and remove automatically artifacts from EEGs. In the second step, ICA reduces the dimension of the problem. Using data from a clinical trial, we show that eight ICA components can reconstruct more than 80 percents of the data from the twenty-eight electrodes. Some of these eight ICA components can reconstruct an interesting characteristic of the signals (an event-related potential named P300). Finally, we shall show how the analysis of these two components allow to detect and quantify a treatment effect. Lorazepam decreases the P300 peak amplitude and increases the time of occurrence of the P300 peak.

In recent years, the use of conformal transformation techniques has become widespread in the literature on gravitational theories alternative to general relativity, on cosmology, and on nonminimally coupled scalar fields. Typically, the transformation to the Einstein frame is generated by a fundamental scalar field already present in the theory. In this context, the problem of which conformal frame is the physical one has to be dealt with and, in the general case, it has been clarified only recently; the formulation of a theory in the ``new'' conformal frame leads to departures from canonical Einstein gravity. In this article, we review the literature on conformal transformations in classical gravitational theories and in cosmology, seen both as purely mathematical tools and as maps with physically relevant aspects. It appears particularly urgent to refer the analysis of experimental tests of Brans-Dicke and scalar-tensor theories of gravity, as well as the predictions of cosmological inflationary scenarios, to the physical conformal frame, in order to have a meaningful comparison with the observations., LaTeX, 54 pages, no figures. To appear in Fundamentals of Cosmic Physics

En radiothérapie, le niveau de précision de la dose délivrée au patient au cours de son traitement est d’une importance essentielle dans l’évolution vers une amélioration de la qualité et de la cohérence des données de suivi. L’une des premières étapes vers un système de support à la décision clinique (Clinical-Decision Support System CDSS) est la reconstruction précise de cette dose délivrée, en prenant en compte les nombreux facteurs pouvant générer des déviations significatives entre la dose planifiée visualisée à l’écran par l’utilisateur et la dose réellement accumulée lors des séances de traitement. Ces facteurs incluent les variations de débit de l’accélérateur, les incertitudes d’étalonnage, de calcul de dose, les mouvements du patient et des organes, etc.L’objectif de cette étude est d’implémenter et tester une plate-forme de calcul Monte Carlo pour la validation des systèmes Cyberknife et Tomothérapie installés au Centre Oscar Lambret. L’étude d’un détecteur dédié aux petits faisceaux (la chambre d’ionisation microLion) est également incluse, ce détecteur étant particulièrement adapté aux mesures sur le système Cyberknife.Le contexte et les concepts théoriques sont introduits dans les deux premiers chapitres. Dans le troisième chapitre, la modélisation Monte Carlo du Cyberknife et du détecteur microLion est détaillée. La quatrième partie inclut la description de la plate-forme Moderato et de son module d’évaluation. Dans le dernier chapitre, la modélisation du dernier modèle de Cyberknife (M6) équipé d’un collimateur multi-lames est décrite. Une nouvelle technique est également introduite dans le but d’accélérer la recherche des paramètres du faisceau d’électrons pour un modèle Monte Carlo, permettant une intégration plus simple et automatisée de nouveaux appareils dans Moderato., In radiation therapy, the accuracy of the dose delivered to the patient during the course of treatment is of great importance to progress towards improved quality and coherence of the outcome data. One of the first steps to evolve towards a Clinical-Decision Support System (CDSS) is to be able to accurately reconstruct that delivered dose, taking into account the range of factors that can potentially generate significant differences between the planned dose visualized on the screen of the dosimetrist, and the actually delivered dose accumulated during the treatment sessions. These factors include accelerator output variations, commissioning uncertainties, dose computation errors, patient and organ movement, etc.The objective of this work is to implement and test a Monte Carlo platform for the validation of the Cyberknife and Tomotherapy systems installed at Centre Oscar Lambret. A study of a small field-dedicated detector (the microLion ionization chamber) is also included, this detector being particularly suited for measurements on the Cyberknife system.The context and theoretical concepts are introduced in the first two chapters. In the third chapter, the Monte Carlo modelling of the Cyberknife and microLion detector is detailed. The fourth part includes the description of the Monte Carlo platform Moderato and its evaluation module. In the final chapter, the modelling of the latest MLC-equipped Cyberknife model (the M6) is described. A new technique is also introduced to accelerate the optimization of the beam electron parameters of a Monte Carlo model, thus allowing for an easier and more automated use of the Moderato system., Doctorat en Sciences biomédicales et pharmaceutiques (Médecine), info:eu-repo/semantics/nonPublished

In this thesis, we present a theoretical investigation of reactive processes involving the HeH$^+$ molecular ion, with applications in laboratory and astrophysical plasma physics. We consider in particular two processes, which are the charge transfer in H + He$^+$ collisions at low energy from a molecular approach and the photodissociation of HeH$^+$.At the molecular level, the cross section is the basic quantity that has to be determined in order to achieve an understanding of reactive processes. Its calculation will be based on the description of the reactions using an emph{ab initio}, quantum mechanical approach. In this work, we will rely on the Born-Oppenheimer approximation, which allows the molecular motion to be separated into an electronic and a nuclear motion. The evaluation of cross sections then follows two steps.The first is the determination of the electronic structure of the molecule. We will calculate the adiabatic potential energy curves of the excited electronic states as well as the dipole matrix elements between these states. The non-adiabatic radial and rotational couplings, which result from the breakdown of the Born-Oppenheimer approximation, are also estimated. The second step is to solve the nuclear motion, which we achieve using a time-dependent method based on the propagation of wave packets on the coupled electronic states. A particular emphasis will be put on the importance of the excited states and of the non-adiabatic couplings in the description of reactive processes. In the treatment of the charge transfer reaction between H and He$^+$ in excited states, it is well known that the non-adiabatic radial couplings cannot be neglected. However, we will show that the inclusion of the non-adiabatic rotational couplings is also necessary in order to obtain accurate state-to-state cross sections.In the description of the photodissociation of HeH$^+$ from its ground state, we will show the influence of the excited states on the rate constant and the role of the non-adiabatic radial couplings in the determination of partial cross sections.We will also consider the possible astrophysical applications of the first triplet state of HeH$^+$. We will show that this state is metastable by evaluating its lifetime, and calculate the cross sections and rate constants for the photodissociation and radiative association of HeH$^+$ in this state., Doctorat en Sciences, info:eu-repo/semantics/nonPublished