On the construction and topology of multi-type ancestral trees

Branching processes or Galton-Watson processes can be used to model the genealogy of a population of different species, where birth and death events represent speciation and extinction. In the more general context of multi-type branching processes, species are classified under phenotypical traits, and the probability of speciation and extinction is dependent on individual types. Since most accessible biological data concerns surviving species, it becomes necessary to extract information about the shape of genealogical trees from the available knowledge on the standing population, and to devise random models allowing backward reconstruction of ancestry under the rules of a particular branching process. We present two investigations on the topology of ancestral multi-type branching trees, generalizing several known results from the single-type case, and obtaining some new results that can only be formulated in the multi-type setting. In the first part of the thesis, we present a backward construction algorithm for the ancestral tree of a planar embedding of a multi-type Galton-Watson tree assumed to be quasi-stationary, and we derive formulae for the conditional distribution of the time to the most recent common ancestor of two consecutive individuals at the present time, and of two individuals of the same type. We specialize these formulae to multi-type linear-fractional branching processes, and observe some effects of the symmetry of the parameters in the two-type case. In the second part of the thesis, we extend the concepts of cherries and pendant edges from rooted binary trees to the multi-type setting, and compute expressions and asymptotic properties for mean numbers and variances of these structures under the neutral two-type Yule model. We explain how type mutations appear naturally in ancestral trees of multi-type birth-death processes, and show that these ancestral trees are Markovian and behave as pure-birth processes, by giving explicit time-dependent rates. We derive formulae and asymptotic properties for the mean number of cherries and pendant edges of each type in a multi-type pure-birth process with mutations. We show that sometimes it is possible to recover the defining rates of this process from the asymptotic proportion of leaves, cherries and pendant edges of each type

Inférence et réseaux complexes

Tableau d'honneur de la Faculté des études supérieures et postdoctorales, 2018-2019Les objets d’études de la science moderne sont souvent complexes : sociétés, pandémies, grilles électriques, niches écologiques, etc. La science des réseaux cherche à mieux com- prendre ces systèmes en examinant leur structure. Elle fait abstraction du détail, en rédui- sant tout système à une simple collection de noeuds (les éléments constitutifs du système) connectés par des liens (interactions). Fort d’une vingtaine d’années de recherche, on peut constater que cette approche a mené à de grands succès scientifiques. Cette thèse est consacrée à l’intersection entre la science des réseaux et l’inférence statistique. On y traite de deux problèmes d’inférence classiques : estimation et test d’hypothèses. La partie principale de la thèse est dédiée à l’estimation. Dans un premier temps, on étu- die un modèle génératif bien connu (le modèle stochastique par blocs), développé dans le but d’identifier les régularités de la structure des réseaux complexes. Les contributions origi- nales de cette partie sont (a) l’unification de la grande majorité des méthodes de détection de régularités sous l’égide du modèle par blocs, et (b) une analyse en taille finie de la cohérence de ce modèle. La combinaison de ces analyses place l’ensemble des méthodes de détection de régularités sur des bases statistiques solides. Dans un deuxième temps, on se penche sur le problème de la reconstruction du passé d’un réseau, à partir d’une seule observation. À nouveau, on l’aborde à l’aide de modèles génératifs, le transformant ainsi en un problème d’estimation. Les résultats principaux de cette partie sont des méthodes algorithmiques per- mettant de solutionner la reconstruction efficacement, et l’identification d’une transition de phase dans la qualité de la reconstruction, lorsque le niveau d’inégalité des réseaux étudiés est varié. On se penche finalement sur un traitement par test d’hypothèses des systèmes complexes. Cette partie, plus succincte, est présentée dans un langage mathématique plus général que celui des réseaux, soit celui des complexes simpliciaux. On obtient un modèle aléatoire pour complexe simplicial, ainsi qu’un algorithme d’échantillonnage efficace pour ce modèle. On termine en montrant qu’on peut utiliser ces outils pour tester des hypothèses sur la structure des systèmes complexes réels, via une propriété inaccessible dans la représentation réseau (les groupes d’homologie des complexes).Modern science is often concerned with complex objects of inquiry: intricate webs of social interactions, pandemics, power grids, ecological niches under climatological pressure, etc. When the goal is to gain insights into the function and mechanism of these complex systems, a possible approach is to map their structure using a collection of nodes (the parts of the systems) connected by edges (their interactions). The resulting complex networks capture the structural essence of these systems. Years of successes show that the network abstraction often suffices to understand a plethora of complex phenomena. It can be argued that a principled and rigorous approach to data analysis is chief among the challenges faced by network science today. With this in mind, the goal of this thesis is to tackle a number of important problems at the intersection of network science and statistical inference, of two types: The problems of estimations and the testing of hypotheses. Most of the thesis is devoted to estimation problems. We begin with a thorough analysis of a well-known generative model (the stochastic block model), introduced 40 years ago to identify patterns and regularities in the structure of real networks. The main original con- tributions of this part are (a) the unification of the majority of known regularity detection methods under the stochastic block model, and (b) a thorough characterization of its con- sistency in the finite-size regime. Together, these two contributions put regularity detection methods on firmer statistical foundations. We then turn to a completely different estimation problem: The reconstruction of the past of complex networks, from a single snapshot. The unifying theme is our statistical treatment of this problem, again based on generative model- ing. Our major results are: the inference framework itself; an efficient history reconstruction method; and the discovery of a phase transition in the recoverability of history, driven by inequalities (the more unequal, the harder the reconstruction problem). We conclude with a short section, where we investigate hypothesis testing in complex sys- tems. This epilogue is framed in the broader mathematical context of simplicial complexes, a natural generalization of complex networks. We obtain a random model for these objects, and the associated efficient sampling algorithm. We finish by showing how these tools can be used to test hypotheses about the structure of real systems, using their homology groups

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio