Apport de l'ACP probabiliste pour la gestion des données manquantes en ACP

International audienceDans cette présentation, nous nous intéressons à la gestion des données manquantes en Analyse en Composantes Principales (ACP). Une solution classique pour réaliser une ACP sur données incomplètes consiste à chercher les axes et les composantes qui minimisent l'erreur de reconstitution sur les données présentes. Pour ce faire, différents algorithmes ont été proposés dans la littérature dont une approche par moindres carrés alternés pondérés et une approche par ACP itérative. Cette dernière consiste en une imputation itérative des données au cours du processus d'estimation et s'apparente à un algorithme EM d'un modèle particulier. Nous détaillons dans un premier temps ces deux algorithmes et donnons leurs propriétés. Nous évoquons ensuite les difficultés rencontrées par ces algorithmes pour nous focaliser sur le problème de surajustement. Puis nous montrons comment la formulation probabiliste de l'ACP (Bishop et Tipping, 1997) offre un terme de régularisation adapté pour pallier au surajustement. Enfin, les performances de ces algorithmes sont évaluées à partir de simulations et d'exemples réels

Analyse de données avec R - Complémentarité des méthodes d'analyse factorielle et de classification

International audienceL'objectif de cet exposé est de présenter les fonctionnalités disponibles sur R en analyse de données. R est un langage gratuit en pleine expansion et de plus en plus utilisé tant par le monde de l'entreprise, de l'enseignement et de la recherche. La spécificité de l'analyse des données à la française est présente dans ce logiciel grâce à plusieurs bibliothèques de fonctions. Dans une première partie de l'exposé, on montrera comment mettre en oeuvre, sous R, des méthodes d'analyses factorielles classiques (ACP, AFC ou ACM) et plus avancées (Analyse factorielle Multiple ou AFM Hiérarchique) à partir du package FactoMineR. Dans une seconde partie, on se focalisera sur la complémentarité des méthodes d'analyses factorielles et de classification pour visualiser des données. On s'appuiera sur plusieurs exemples et on mettra l'accent sur l'intérêt d'un tel outil dans le cadre de l'enseignement : gratuité et facilité de téléchargement du logiciel pour les étudiants en stage, mais également facilité d'accès du logiciel par des menus interactifs et performance du logiciel pour des méthodes évoluées

Radiative effects in the scalar sector of vector leptoquark models

Abstract: Gauge models with massive vector leptoquarks at the TeV scale provide a successful framework for addressing the $B$-physics anomalies. Among them, the 4321 model has been considered as the low-energy limit of some complete theories of flavor. In this work, we study the renormalization group evolution of this model, laying particular emphasis on the scalar sector. We find that, despite the asymptotic freedom of the gauge couplings, Landau poles can arise at relatively low scales due to the fast running of quartic couplings. Moreover, we discuss the possibility of radiative electroweak symmetry breaking and characterize the fine-tuning associated with the hierarchy between the electroweak scale and the additional TeV-scale scalars. Finally, the idea of scalar fields unification is explored, motivated by ultraviolet embeddings of the 4321 model

Radiative effects in the scalar sector of vector leptoquark models

Gauge models with massive vector leptoquarks at the TeV scale provide a successful framework for addressing the B-physics anomalies. Among them, the 4321 model has been considered as the low-energy limit of some complete theories of flavor. In this work, we study the renormalization group evolution of this model, laying particular emphasis on the scalar sector. We find that, despite the asymptotic freedom of the gauge couplings, Landau poles can arise at relatively low scales due to the fast running of quartic couplings. Moreover, we discuss the possibility of radiative electroweak symmetry breaking and characterize the fine-tuning associated with the hierarchy between the electroweak scale and the additional TeV-scale scalars. Finally, the idea of scalar fields unification is explored, motivated by ultraviolet embeddings of the 4321 model

An Algebraic Formula for Two Loop Renormalization of Scalar Quantum Field Theory

We give a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, which extends 't Hooft's one-loop result. We show that factorizable topologies do not contribute to the renormalization group equations. The results will be combined with the geometric method in a subsequent paper to obtain the renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order.Comment: 25 pages, 8 figure

Flavor non-universal Pati-Salam unification and neutrino masses

We analyze the neutrino mass spectrum and discuss the extra-dimensional interpretation of a three-site Pati-Salam model which i) unifies all families of quark and leptons, ii) provides a natural description of the Standard Model Yukawa couplings, iii) could account for the recent B-physics anomalies. The key feature of the model is a breaking of the Pati-Salam and electroweak gauge symmetries localized on opposite sites, communicated to the other sites in an attenuated manner via nearest-neighbor interactions. We show that in this context gauge-singlet fermions localized on each site, receiving hierarchical Majorana masses, can allow the implementation of an inverse seesaw mechanism leading to light anarchic neutrino masses consistent with data. The continuum limit of this three-site setup has a natural interpretation in terms of a warped extra dimension with three defects, where the required exponential hierarchies can be achieved from differences in the bulk field masses

Two Loop Renormalization of Scalar Theories using a Geometric Approach

We derive a general formula for two-loop counterterms in Effective Field Theories (EFTs) using a geometric approach. This formula allows the two-loop results of our previous paper to be applied to a wide range of theories. The two-loop results hold for loop graphs in EFTs where the interaction vertices contain operators of arbitrarily high dimension, but at most two derivatives. We also extend our previous one-loop result to include operators with an arbitrary number of derivatives, as long as there is at most one derivative acting on each field. The final result for the two-loop counterterms is written in terms of geometric quantities such as the Riemann curvature tensor of the scalar manifold and its covariant derivatives. As applications of our results, we give the two-loop counterterms and renormalization group equations for the O(n) EFT to dimension six, the scalar sector of the Standard Model Effective Field Theory (SMEFT) to dimension six, and chiral perturbation theory to order $p^6$.Comment: ChPT results to O($p^6$) now agree with Bijnens, Colangelo, and Ecker, hep-ph/990733

Flavor Non-universal Pati-Salam Unification and Neutrino Masses

We analyze the neutrino mass spectrum and discuss the extra-dimensional interpretation of a three-site Pati-Salam model which i) unifies all families of quark and leptons, ii) provides a natural description of the Standard Model Yukawa couplings, iii) could account for the recent $B$-physics anomalies. The key feature of the model is a breaking of the Pati-Salam and electroweak gauge symmetries localized on opposite sites, communicated to the other sites in an attenuated manner via nearest-neighbor interactions. We show that in this context gauge-singlet fermions localized on each site, receiving hierarchical Majorana masses, can allow the implementation of an inverse seesaw mechanism leading to light anarchic neutrino masses consistent with data. The continuum limit of this three-site setup has a natural interpretation in terms of a warped extra dimension with three defects, where the required exponential hierarchies can be achieved from $\mathcal{O}(1)$ differences in the bulk field masses.Comment: 14 pages, 2 figure

SuperTracer: a calculator of functional supertraces for one-loop EFT matching

We present SuperTracer, a Mathematica package aimed at facilitating the functional matching procedure for generic UV models. This package automates the most tedious parts of one-loop functional matching computations. Namely, the determination and evaluation of all relevant supertraces, including loop integration and Dirac algebra manipulations. The current version of SuperTracer also contains a limited set of output simplifications. However, a further reduction of the output to a minimal basis using Fierz identities, integration by parts, simplification of Dirac structures, and/or light field redefinitions might still be necessary. The code and example notebooks are publicly available at https://gitlab.com/supertracer/supertracer

A Proof of Concept for Matchete: An Automated Tool for Matching Effective Theories

Studying the impact of new-physics models on low-energy observables necessitates matching to effective field theories at the relevant mass thresholds. We introduce the first public version of Matchete, a computer tool for matching weakly-coupled models at one-loop order. It uses functional methods to directly compute all matching contributions in a manifestly gauge-covariant manner, while simplification methods eliminate redundant operators from the output. We sketch the workings of the program and provide examples of how to match simple Standard Model extensions. The package, documentation, and example notebooks are publicly available at https://gitlab.com/matchete/matchete.Comment: 27 pages, 2 figures, The code and example notebooks are publicly available at https://gitlab.com/matchete/matchet