Models of non-relativistic quantum gravity: the good, the bad and the healthy

Horava's proposal for non-relativistic quantum gravity introduces a preferred time foliation of space-time which violates the local Lorentz invariance. The foliation is encoded in a dynamical scalar field which we call `khronon'. The dynamics of the khronon field is sensitive to the symmetries and other details of the particular implementations of the proposal. In this paper we examine several consistency issues present in three non-relativistic gravity theories: Horava's projectable theory, the healthy non-projectable extension, and a new extension related to ghost condensation. We find that the only model which is free from instabilities and strong coupling is the non-projectable one. We elaborate on the phenomenology of the latter model including a discussion of the couplings of the khronon to matter. In particular, we obtain the parameters of the post-Newtonian expansion in this model and show that they are compatible with current observations.Comment: 50 pages, JHEP styl

Automated medical scheduling : fairness and quality

Dans cette thèse, nous étudions les façons de tenir compte de la qualité et de l’équité dans les algorithmes de confection automatique d’horaires de travail. Nous découpons ce problème en deux parties. La modélisation d’un problème d’horaires permet de créer des horaires plus rapidement qu’un humain peut le faire manuellement, puisqu’un ordinateur peut évaluer plusieurs horaires simultanément et donc prendre des décisions en moins de temps. La première partie du problème étudié consiste à améliorer la qualité des horaires en encodant des contraintes et des préférences à l’aide de modèles mathématiques. De plus, puisque la création est plus rapide à l’aide d’un ordinateur, il est plus facile pour un ordinateur de trouver l’horaire ayant la meilleure qualité lorsque les règles et préférences sont clairement définies. Toutefois, déterminer les règles et préférences d’un groupe de personne n’est pas une tâche facile. Ces individus ont souvent de la difficulté à exprimer formellement leurs besoins et leurs préférences. Par conséquent, la création d’un bon modèle mathématique peut prendre beaucoup de temps, et cela même pour un expert en création d’horaires de travail. C’est pourquoi la deuxième partie de cette thèse concerne la réduction du temps de modélisation à l’aide d’algorithmes capable d’apprendre un modèle mathématique à partir de solutions données comme par exemple, dans notre cas, des horaires de travail.In this thesis, we study the ways to take quality and fairness into account in the algorithms of automatic creation of work schedules. We separate this problem into two subproblems. The modeling of a scheduling problem allows a faster creation of schedules than what a human can produce manually. A computer can generate and evaluate multiple schedules at a time and therefore make decisions in less time. This first part of the studied problem consists in improving the quality of medical schedules by encoding constraints and preferences using mathematical models. Moreover, since the creation is faster, it is easier for a computer to find the schedule with the highest quality when the rules and the preferences are clearly defined. However, determining the rules and preferences of a group of people is not an easy task. Those individuals often have difficulties formally expressing their requirements and preferences. Therefore, the creation a good mathematical model might take a long time, even for a scheduling expert. This is why the second part of this thesis concerns the reduction of modeling time using algorithms able to learn mathematical models from given solutions, in our case schedules

Bumpy black holes from spontaneous Lorentz violation

We consider black holes in Lorentz violating theories of massive gravity. We argue that in these theories black hole solutions are no longer universal and exhibit a large number of hairs. If they exist, these hairs probe the singularity inside the black hole providing a window into quantum gravity. The existence of these hairs can be tested by future gravitational wave observatories. We generically expect that the effects we discuss will be larger for the more massive black holes. In the simplest models the strength of the hairs is controlled by the same parameter that sets the mass of the graviton (tensor modes). Then the upper limit on this mass coming from the inferred gravitational radiation emitted by binary pulsars implies that hairs are likely to be suppressed for almost the entire mass range of the super-massive black holes in the centers of galaxies.Comment: 40 pages, 4 figure

Effective Field Theory of Broken Spatial Diffeomorphisms

We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constant for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. We discuss several examples relevant to theories of massive gravity.Comment: 26 pages, V2 more references, several remarks and a new subsection are added, V3 a major revision, with two new subsections added, as well as several new discussions on the construction of our EF

Solving Systems of Linear Equalities in Modular Arithmetic with Applications to Model Counting in Constraint Programming

Résumé Le comptage et l’échantillonnage de modèles sont deux problèmes fondamentaux en intelligence artificielle. La théorie de ces problèmes remonte aux années 1980. Il existe différents problèmes dans divers domaines, tels que l’apprentissage automatique, la planification, les statistiques, etc., dont on sait qu’ils sont difficiles à calculer. Même trouver une solution unique peut être une lutte pour de tels problèmes; compter le nombre de solutions est beaucoup plus difficile. Ainsi, le comptage approximatif des modèles pourrait être utile pour les résoudre. L’ideé de ce travail vient des travaux précédents qui sont davantage axés sur les variables binaires. Ils utilisent des techniques basées sur le hachage en générant des contraintes XOR de manière aléatoire pour partitionner l’espace des solutions en petites cellules, puis en utilisant un solveur SAT pour compter à l’intérieur d’une cellule aléatoire. Les solveurs SAT sont utilisés pour les domaines binaires, mais nous proposons ici d’utiliser des solveurs CP pour les domaines non binaires. Le but de cette recherche est de présenter un algorithme permettant de compter approximativement le nombre de solutions d’un modèle de CP. Dans la première étape, nous commençons à diviser l’espace des solutions en p petites cellules à chaque contrainte de mod p ajoutée conformément à l’arithmétique modulaire p. Ensuite, en utilisant l’algorithme d’élimination de Gauss-Jordan, nous essayons de simplifier le système de contraintes linéaires générées aléatoirement. De plus, nous introduisons un algorithme qui, en créant un graphe, filtre les domaines des variables dans une petite cellule aléatoire. Après avoir compté le nombre de solutions dans une petite cellule, nous estimons le nombre de solutions en multipliant le nombre de solutions dans une cellule par le nombre de cellules.----------ABSTRACT: Model counting and sampling are two fundamental problems in artificial intelligence. The theory of these problems goes back to the 1980s. There are different problems in various areas like machine learning, planning, statistics and so on which are known to be computationally hard. Even finding a single solution can be a struggle for such problems; counting the number of solutions is much harder. Thus, approximate model counting could be useful to solve them. The idea of this work comes from previous works which are focused more on binary variables. They use hashing-based techniques by generating random XOR constraints to partition the solution space into small cells and then use a SAT solver to count inside a random cell. SAT solvers are used for binary domains but we propose here to use CP solvers for non-binary domains. The goal of this research is to present an algorithm for approximately counting the number of solutions of a CP model. In the first step, we start to divide the solution space into p small cells at each added mod p constraint according to modular arithmetic p. Then by using the Gauss-Jordan elimination algorithm we try to simplify the system of randomly generated linear constraints. Moreover we introduce an algorithm that by creating a graph incrementally filters variable domains in one random small cell. After counting the number of solutions in one small cell we estimate the number of solutions by multiplying the number of solutions in one cell by the number of cells

Why are some firms more internationally committed thand others? The role of knowledge, firm development stage, and optimism

In this study we use a unique data set to examine factors related to international commitment of owner-managed firms. We draw on different streams of research�such as the knowledge-based view, the stage theory of internationalization and the new venture theory of internationalization to study firms involvement in foreign markets. Our results suggest that knowledge-based resources embedded in the management team and the firms attitude towards innovation increase international commitment. Further, consistent with the stage theory of internationalization, we find that firms demonstrate a pattern of steadily increasing foreign commitment. However, this latter finding was obtained only after taking into account the firms optimism in terms of future growth. Optimism among start-ups therefore may obscure the relationship between firm development stage on the one hand and international commitment on the other.

On the core-halo distribution of dark matter in galaxies

We investigate the distribution of dark matter in galaxies by solving the equations of equilibrium of a self-gravitating system of massive fermions (`inos') at selected temperatures and degeneracy parameters within general relativity. Our most general solutions show, as a function of the radius, a segregation of three physical regimes: 1) an inner core of almost constant density governed by degenerate quantum statistics; 2) an intermediate region with a sharply decreasing density distribution followed by an extended plateau, implying quantum corrections; 3) an asymptotic, $\rho\propto r^{-2}$ classical Boltzmann regime fulfilling, as an eigenvalue problem, a fixed value of the flat rotation curves. This eigenvalue problem determines, for each value of the central degeneracy parameter, the mass of the ino as well as the radius and mass of the inner quantum core. Consequences of this alternative approach to the central and halo regions of galaxies, ranging from dwarf to big spirals, for SgrA*, as well as for the existing estimates of the ino mass, are outlined.Comment: 8 pages, 5 figures. Accepted for publication by MNRA

Toward ab initio density functional theory for nuclei

We survey approaches to nonrelativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using orbital-based functionals, which generalize the conventional local-density-plus-gradients form. The orbitals satisfy single-particle equations with multiplicative (local) potentials. The DFT functionals can be developed starting from internucleon forces using wave-function based methods or by Legendre transform via effective actions. We describe known and unresolved issues for applying these formulations to the nuclear many-body problem and discuss how ab initio approaches can help improve empirical energy density functionals.Comment: 69 pages, 16 figures, many revisions based on feedback. To appear in Progress in Particle and Nuclear Physic