6,406 research outputs found
Stein's method, Malliavin calculus, Dirichlet forms and the fourth moment theorem
The fourth moment theorem provides error bounds of the order in the central limit theorem for elements of Wiener chaos of
any order such that . It was proved by Nourdin and
Peccati (2009) using Stein's method and the Malliavin calculus. It was also
proved by Azmoodeh, Campese and Poly (2014) using Stein's method and Dirichlet
forms. This paper is an exposition on the connections between Stein's method
and the Malliavin calculus and between Stein's method and Dirichlet forms, and
on how these connections are exploited in proving the fourth moment theorem
Generic design of Chinese remaindering schemes
We propose a generic design for Chinese remainder algorithms. A Chinese
remainder computation consists in reconstructing an integer value from its
residues modulo non coprime integers. We also propose an efficient linear data
structure, a radix ladder, for the intermediate storage and computations. Our
design is structured into three main modules: a black box residue computation
in charge of computing each residue; a Chinese remaindering controller in
charge of launching the computation and of the termination decision; an integer
builder in charge of the reconstruction computation. We then show that this
design enables many different forms of Chinese remaindering (e.g.
deterministic, early terminated, distributed, etc.), easy comparisons between
these forms and e.g. user-transparent parallelism at different parallel grains
On-the-job learning and earnings
A simple model of informal learning on-the-job which combines learning by oneself and learning from others is proposed in this paper. It yields a closed-form solution that revises Mincer-Jovanovic's (1981) treatment of tenure in the human capital earnings function by relating earnings to the individual's learning potential from jobs and firms. We estimate the structural parameters of this non-linear model on a large French survey with matched employer-employee data. We find that workers on average can learn from others ten percent of their own human capital on entering the firm, and catch half of their learning potential in just two years. The measurement of worker's learning potential in their jobs and establishments provides a simple characterization of primary-type and secondary-type jobs and establishments. We find a strong relationship between the job-specific learning potential and tenure. Predictions of dual labor market theory regarding the positive match of primary-type firms (which offer high learning opportunities) with highly endowed workers (educated, high wages) are visible at the establishment level but seem to vanish at the job's level.Human capital, earnings functions, informal training, learning from others, learning by oneself, returns to tenure, dualism.
The representation of the symmetric group on m-Tamari intervals
An m-ballot path of size n is a path on the square grid consisting of north
and east unit steps, starting at (0,0), ending at (mn,n), and never going below
the line {x=my}. The set of these paths can be equipped with a lattice
structure, called the m-Tamari lattice and denoted by T_n^{m}, which
generalizes the usual Tamari lattice T_n obtained when m=1. This lattice was
introduced by F. Bergeron in connection with the study of diagonal coinvariant
spaces in three sets of n variables. The representation of the symmetric group
S_n on these spaces is conjectured to be closely related to the natural
representation of S_n on (labelled) intervals of the m-Tamari lattice, which we
study in this paper. An interval [P,Q] of T_n^{m} is labelled if the north
steps of Q are labelled from 1 to n in such a way the labels increase along any
sequence of consecutive north steps. The symmetric group S_n acts on labelled
intervals of T_n^{m} by permutation of the labels. We prove an explicit
formula, conjectured by F. Bergeron and the third author, for the character of
the associated representation of S_n. In particular, the dimension of the
representation, that is, the number of labelled m-Tamari intervals of size n,
is found to be (m+1)^n(mn+1)^{n-2}. These results are new, even when m=1. The
form of these numbers suggests a connection with parking functions, but our
proof is not bijective. The starting point is a recursive description of
m-Tamari intervals. It yields an equation for an associated generating
function, which is a refined version of the Frobenius series of the
representation. This equation involves two additional variables x and y, a
derivative with respect to y and iterated divided differences with respect to
x. The hardest part of the proof consists in solving it, and we develop
original techniques to do so, partly inspired by previous work on polynomial
equations with "catalytic" variables.Comment: 29 pages --- This paper subsumes the research report arXiv:1109.2398,
which will not be submitted to any journa
Analysis and modeling of green wood milling: Chip production by slabber
During the primary transformation of wood, logs are faced with slabber heads. Chips produced are raw materials for pulp paper and particleboard industries. Efficiency of these industries is partly due to particle size distribution. Command of this distribution is no easy matter because of great dependence on cutting conditions and variability in material. This study aimed a better understanding and predictionof chip fragmentation. It starts with a detailed description of cutting kinematic and interaction between knife and log. This leads to the numerical development of a generic slabber head. Chip fragmentation phenomena were studied through experiments in dynamic conditions. These experiments were carried out thanks to a pendulum (Vc = 400 m/min). It was instrumented with piezoelectric force sensors and high speed camera. Obtained results agreed very well with previous quasi-static experiments
Phase Space Engineering in Optical Microcavities I: Preserving near-field uniformity while inducing far-field directionality
Optical microcavities have received much attention over the last decade from
different research fields ranging from fundamental issues of cavity QED to
specific applications such as microlasers and bio-sensors. A major issue in the
latter applications is the difficulty to obtain directional emission of light
in the far-field while keeping high energy densities inside the cavity (i.e.
high quality factor). To improve our understanding of these systems, we have
studied the annular cavity (a dielectric disk with a circular hole), where the
distance cavity-hole centers, d, is used as a parameter to alter the properties
of cavity resonances. We present results showing how one can affect the
directionality of the far-field while preserving the uniformity (hence the
quality factor) of the near-field simply by increasing the value of d.
Interestingly, the transition between a uniform near- and far-field to a
uniform near- and directional far-field is rather abrupt. We can explain this
behavior quite nicely with a simple model, supported by full numerical
calculations, and we predict that the effect will also be found in a large
class of eigenmodes of the cavity.Comment: 12th International Conference on Transparent Optical Network
Searching for supersymmetry using deep learning with the ATLAS detector
Le Modèle Standard de la physique des particules (MS) est une théorie
fondamentale de la nature dont la validité a été largement établie par
diverses expériences. Par contre, quelques problèmes théoriques et
expérimentaux subsistent, ce qui motive la recherche de théories
alternatives. La Supersymétrie (SUSY), famille de théories dans
laquelle une nouvelle particule est associée à chaque particules du
MS, est une des théories ayant les meilleures motivations pour étendre
la portée du modèle. Par exemple, plusieurs théories supersymétriques
prédisent de nouvelles particules stables et interagissant seulement
par la force faible, ce qui pourrait expliquer les observations
astronomiques de la matière sombre. La découverte de SUSY
représenterait aussi une importante étape dans le chemin vers une
théorie unifiée de l'univers. Les recherches de supersymétrie sont au
coeur du programme expérimental de la collaboration ATLAS, qui
exploite un détecteur de particules installé au Grand Collisioneur de
Hadrons (LHC) au CERN à Genève, mais à ce jours aucune preuve en
faveur de la supersymétrie n'a été enregistrée par les présentes
analyses, largement basées sur des techniques simples et bien
comprises.
Cette thèse documente l'implémentation d'une nouvelle approche à la
recherche de particules basée sur l'apprentissage profond, utilisant
seulement les quadri-impulsions comme variables discriminatoires;
cette analyse utilise l'ensemble complet de données d'ATLAS enregistré
en 2015-2018. Les problèmes de la naturalité du MS et de la matière
sombre orientent la recherche vers les partenaires supersymétriques du
gluon (le gluino), des quarks de troisième génération (stop et
sbottom), ainsi que des bosons de gauge (le neutralino). Plusieurs
techniques récentes sont employées, telles que l'utilisation directe
des quadri-impulsions reconstruites à partir des données enregistrées
par le détecteur ATLAS ainsi que la paramétrisation d'un réseau de
neurone avec les masses des particules recherchées, ce qui permet
d'atteindre une performance optimale quelle que soit l'hypothèse de
masses. Cette méthode améliore la signification statistique par un
facteur 85 par rapport au dernier résultat d'ATLAS pour certaines
hypothèses de masses, et ce avec la même luminosité.
Aucun excès signifif au-delà du Modèle Standard n'est observé. Les
masses du gluino en deçà de 2.45 TeV et du neutralino en deça de
1.7 TeV sont exclues à un niveau de confiance de 95%, ce qui étend
largement les limites précédentes sur deux modèles de productions de
paires de gluinos faisant intervenir des stops et des sbottoms,
respectivement.The Standard Model of particle physics (SM) is a fundamental theory of
nature whose validity has been extensively confirmed by
experiments. However, some theoretical and experimental problems
subsist, which motivates searches for alternative theories to
supersede it. Supersymmetry (SUSY), which associate new fundamental
particles to each SM particle, is one of the best-motivated such
theory and could solve some of the biggest outstanding problems with
the SM. For example, many SUSY scenarios predict stable neutral
particles that could explain observations of dark matter in the
universe. The discovery of SUSY would also represent a huge step towards a
unified theory of the universe. Searches for SUSY are at the heart of
the experimental program of the ATLAS collaboration, which exploits a
state-of-the-art particle detector installed at the Large Hadron
Collider (LHC) at CERN in Geneva. The probability to observe many
supersymmetric particles went up when the LHC ramped up
its collision energy to 13~TeV, the highest ever achieved in
laboratory, but so far no evidence for SUSY has been recorded by
current searches, which are mostly based on well-known simple
techniques such as counting experiments.
This thesis documents the implementation of a novel deep
learning-based approach using only the four-momenta of selected
physics objects, and its application to the search for supersymmetric
particles using the full ATLAS 2015-2018
dataset. Motivated by naturalness considerations as well as by the
problem of dark matter, the search focuses on finding evidence for
supersymmetric partners of the gluon (the gluino), third generation
quarks (the stop and the sbottom), and gauge bosons (the neutralino).
Many recently introduced physics-specific machine learning
developments are employed, such as directly using detector-recorded
energies and momenta of produced particles instead of first deriving a
restricted set of physically motivated variables and parametrizing the
classification model with the masses of the particles searched for,
which allows optimal sensitivity for all mass hypothesis. This method
improves the statistical significance of the search by up to 85 times
that of the previous ATLAS analysis for some mass hypotheses, after
accounting for the luminosity difference.
No significant excesses above the SM background are recorded. Gluino
masses below 2.45 TeV and neutralino masses below 1.7 TeV are excluded
at the 95% confidence level, greatly increasing the previous limit on
two simplified models of gluino pair production with off-shell stops
and sbottoms, respectively
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