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My chosen topic for this thesis is the newly discovered TRAPPIST-1 planetary system with its seven planets revolving around the nearby ultracool dwarf star. The main need to focus on the TRAPPIST-1 system is to refine the masses of the seven planets, to constrain their composition and also their dynamics. In order to do that we use the measured transit timing variations (TTVs) to constrain their masses, orbits and hence refine the transit parameters through analysis. Measured TTVs are used to detect a change in the orbital period of each planet caused by gravitational pull of the planets in a resonant chain, this causes the planets to accelerate and decelerate along its orbit in a packed planetary system and therefore change the orbital period. We also reduce the photometric data obtained from the Liverpool telescope over the time span of 2017/05/31 to 2017/10/28. The photometric data obtained consists of 19 light curves and each of these light curves were analyzed individually and then a global analysis was performed on all the transits pertaining to a single planet. The individual and global analysis was performed with the most recent version of the adaptive Markov Chain Monte-Carlo (MCMC) code developed by M. Gillon. For the reduction of the data, we first performed differential photometry to measure the flux of our target star with respect to a standard star in the field of view and eventually from this we obtain the dip in the value of the measured flux of a star during a planetary transit. Individual analysis is performed for each light curve to obtain the astrophysical and instrumental effects observed at the photometric variation level and finally we perform global analysis for a set of light curves obtained for the same planet. Both individual and global analysis is done in a preliminary chain of 10,000 steps and a secondary chain of 100,000 steps. In the global analysis, we improve the accuracy of the system parameters, de-trended light curves along with photometric representations which are also included in the report.\

The global analysis result for TRAPPIST-1b gave us a transit duration of 0.025 $pm 0.00050$ days with its 1 − $sigma$ limit of the posterior PDF, similarly we have a value of 0.029$pm0.00076$ days for TRAPPIST-1c and a value of 0.0388$pm0.00075$ days for TRAPPIST-1e. These values are in good agreement with the values obtained from the Spitzer analysis. These timings will be useful to constrain further the dynamics of the TRAPPIST-1 system and the masses and compositions of its planets. We also compare the results with the already reduced Spritzer results, to check the accuracy of the results obtained from the Liverpool telescope. Some of our results are presented in the paper "The 0.6-4.55μm broadband transmission spectra of TRAPPIST-1 planets" (Ducrot et al. 2018, under review).

TRAPPIST-1 --- Exoplanetology --- Markov Chain Monte-Carlo (MCMC) --- Photometry --- Analysis --- Physique, chimie, mathématiques & sciences de la terre > Physique --- Physique, chimie, mathématiques & sciences de la terre > Aérospatiale, astronomie & astrophysique

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The goal of the thesis is the characterization of the substellar companion HD18757B. Several techniques are applied to retrieve the photometric and orbital information of the object. At first, HD18757B is observed in the L' band with the imaging instrument LMIRCam mounted on the Large Binocular Telescope. This observation is based on the high contrast angular differential imaging method and is further processed with the Vortex Image Processing package. Secondly, imaging data is coupled with astrometric observation from Gaia/Hipparcos and radial velocity measurements from Sophie and Elodie to run in a Markov-Chain Monte Carlo simulation. Finally, the measured parameters are compared to the properties of brown dwarfs from evolutionary and formation models.

brown dwarf --- high contrast angular differential imaging --- Vortex Imaging Processing --- Markov-Chain Monte Carlo --- Physique, chimie, mathématiques & sciences de la terre > Aérospatiale, astronomie & astrophysique

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Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate deterministic and stochastic models and methods. Mathematical Tools for Understanding Infectious Disease Dynamics fully explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology. This comprehensive and accessible book also features numerous detailed exercises throughout; full elaborations to all exercises are provided. Covers the latest research in mathematical modeling of infectious disease epidemiology Integrates deterministic and stochastic approaches Teaches skills in model construction, analysis, inference, and interpretation Features numerous exercises and their detailed elaborations Motivated by real-world applications throughout

Epidemiology --- Communicable diseases --- Contagion and contagious diseases --- Contagious diseases --- Infectious diseases --- Microbial diseases in human beings --- Zymotic diseases --- Mathematical models --- Mathematical models. --- Diseases --- Infection --- Epidemics --- Public health --- Bayesian statistical inference. --- ICU model. --- Markov chain Monte Carlo method. --- Markov chain Monte Carlo methods. --- ReedІrost epidemic. --- age structure. --- asymptotic speed. --- bacterial infections. --- biological interpretation. --- closed population. --- compartmental epidemic systems. --- consistency conditions. --- contact duration. --- demography. --- dependence. --- disease control. --- disease outbreaks. --- disease prevention. --- disease transmission. --- endemic. --- epidemic models. --- epidemic outbreak. --- epidemic. --- epidemiological models. --- epidemiological parameters. --- epidemiology. --- general epidemic. --- growth rate. --- homogeneous community. --- hospital infections. --- hospital patients. --- host population growth. --- host. --- human social behavior. --- i-states. --- individual states. --- infected host. --- infection transmission. --- infection. --- infectious disease epidemiology. --- infectious disease. --- infectious diseases. --- infectious output. --- infective agent. --- infectivity. --- intensive care units. --- intrinsic growth rate. --- larvae. --- macroparasites. --- mathematical modeling. --- mathematical reasoning. --- maximum likelihood estimation. --- microparasites. --- model construction. --- outbreak situations. --- outbreak. --- pair approximation. --- parasite load. --- parasite. --- population models. --- propagation speed. --- reproduction number. --- separable mixing. --- sexual activity. --- stochastic epidemic model. --- structured population models. --- susceptibility. --- vaccination.

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Extremely popular for statistical inference, Bayesian methods are also becoming popular in machine learning and artificial intelligence problems. Bayesian estimators are often implemented by Monte Carlo methods, such as the Metropolis–Hastings algorithm of the Gibbs sampler. These algorithms target the exact posterior distribution. However, many of the modern models in statistics are simply too complex to use such methodologies. In machine learning, the volume of the data used in practice makes Monte Carlo methods too slow to be useful. On the other hand, these applications often do not require an exact knowledge of the posterior. This has motivated the development of a new generation of algorithms that are fast enough to handle huge datasets but that often target an approximation of the posterior. This book gathers 18 research papers written by Approximate Bayesian Inference specialists and provides an overview of the recent advances in these algorithms. This includes optimization-based methods (such as variational approximations) and simulation-based methods (such as ABC or Monte Carlo algorithms). The theoretical aspects of Approximate Bayesian Inference are covered, specifically the PAC–Bayes bounds and regret analysis. Applications for challenging computational problems in astrophysics, finance, medical data analysis, and computer vision area also presented.

Research & information: general --- Mathematics & science --- bifurcation --- dynamical systems --- Edward–Sokal coupling --- mean-field --- Kullback–Leibler divergence --- variational inference --- Bayesian statistics --- machine learning --- variational approximations --- PAC-Bayes --- expectation-propagation --- Markov chain Monte Carlo --- Langevin Monte Carlo --- sequential Monte Carlo --- Laplace approximations --- approximate Bayesian computation --- Gibbs posterior --- MCMC --- stochastic gradients --- neural networks --- Approximate Bayesian Computation --- differential evolution --- Markov kernels --- discrete state space --- ergodicity --- Markov chain --- probably approximately correct --- variational Bayes --- Bayesian inference --- Markov Chain Monte Carlo --- Sequential Monte Carlo --- Riemann Manifold Hamiltonian Monte Carlo --- integrated nested laplace approximation --- fixed-form variational Bayes --- stochastic volatility --- network modeling --- network variability --- Stiefel manifold --- MCMC-SAEM --- data imputation --- Bethe free energy --- factor graphs --- message passing --- variational free energy --- variational message passing --- approximate Bayesian computation (ABC) --- differential privacy (DP) --- sparse vector technique (SVT) --- Gaussian --- particle flow --- variable flow --- Langevin dynamics --- Hamilton Monte Carlo --- non-reversible dynamics --- control variates --- thinning --- meta-learning --- hyperparameters --- priors --- online learning --- online optimization --- gradient descent --- statistical learning theory --- PAC–Bayes theory --- deep learning --- generalisation bounds --- Bayesian sampling --- Monte Carlo integration --- PAC-Bayes theory --- no free lunch theorems --- sequential learning --- principal curves --- data streams --- regret bounds --- greedy algorithm --- sleeping experts --- entropy --- robustness --- statistical mechanics --- complex systems

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This book includes papers in cross-disciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cutting-edge research, each chapter is focused on a different problem of modelling human behaviour or engineering problems at different levels. The reader would find this book to be a useful reference in identifying problems of interest in social, medicine and engineering sciences, and in developing mathematical models that could be used to successfully predict behaviours and obtain practical information for specialised practitioners. This book is a must-read for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods.

uncertainty quantification --- neutron diffusion equation --- discrete dynamical systems --- organisational risk --- computational efficiency --- AHP --- random power series --- order of convergence --- IPV --- multi-criteria decision-making --- random non-autonomous second order linear differential equation --- game of life --- immune system --- parameter estimation --- cytokines --- model --- stem cells --- Voynich Manuscript --- uncertainty modelling --- ode --- bottling process --- anti-torpedo decoy --- decision-making --- exponential polynomial --- Hidden Markov models --- systems of nonlinear equations --- iterative methods --- modified block Newton method --- mathematical linguistics --- DEMATEL --- convergence --- F-110 frigate --- Chikungunya disease --- nonlinear dynamical systems --- cellular automata --- mean square analytic solution --- basin of attraction --- violence index --- macrophages --- Markov chain Monte Carlo --- human behaviour --- block preconditioner --- generalized eigenvalue problem --- bone repair --- numerical simulations --- ASW --- Newton’s method --- independence index --- mathematical modeling --- brain dynamics