PAC-Bayes and Domain Adaptation

We provide two main contributions in PAC-Bayesian theory for domain adaptation where the objective is to learn, from a source distribution, a well-performing majority vote on a different, but related, target distribution. Firstly, we propose an improvement of the previous approach we proposed in Germain et al. (2013), which relies on a novel distribution pseudodistance based on a disagreement averaging, allowing us to derive a new tighter domain adaptation bound for the target risk. While this bound stands in the spirit of common domain adaptation works, we derive a second bound (introduced in Germain et al., 2016) that brings a new perspective on domain adaptation by deriving an upper bound on the target risk where the distributions' divergence-expressed as a ratio-controls the trade-off between a source error measure and the target voters' disagreement. We discuss and compare both results, from which we obtain PAC-Bayesian generalization bounds. Furthermore, from the PAC-Bayesian specialization to linear classifiers, we infer two learning algorithms, and we evaluate them on real data.Comment: Neurocomputing, Elsevier, 2019. arXiv admin note: substantial text overlap with arXiv:1503.0694

Weak Lensing from Space I: Instrumentation and Survey Strategy

A wide field space-based imaging telescope is necessary to fully exploit the technique of observing dark matter via weak gravitational lensing. This first paper in a three part series outlines the survey strategies and relevant instrumental parameters for such a mission. As a concrete example of hardware design, we consider the proposed Supernova/Acceleration Probe (SNAP). Using SNAP engineering models, we quantify the major contributions to this telescope's Point Spread Function (PSF). These PSF contributions are relevant to any similar wide field space telescope. We further show that the PSF of SNAP or a similar telescope will be smaller than current ground-based PSFs, and more isotropic and stable over time than the PSF of the Hubble Space Telescope. We outline survey strategies for two different regimes - a ``wide'' 300 square degree survey and a ``deep'' 15 square degree survey that will accomplish various weak lensing goals including statistical studies and dark matter mapping.Comment: 25 pages, 8 figures, 1 table, replaced with Published Versio

Dimension dependent hypercontractivity for Gaussian kernels

We derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture refined properties of Markov kernels, such as trace estimates. They imply classical bounds on the Ornstein-Uhlenbeck semigroup and a dimensional and refined (transportation) Talagrand inequality when applied to the Hamilton-Jacobi equation. Hypercontractive bounds on the Ornstein-Uhlenbeck semigroup driven by a non-diffusive L\'evy semigroup are also investigated. Curvature-dimension criteria are the main tool in the analysis.Comment: 24 page

Automata, reduced words, and Garside shadows in Coxeter groups

In this article, we introduce and investigate a class of finite deterministic automata that all recognize the language of reduced words of a finitely generated Coxeter system (W,S). The definition of these automata is straightforward as it only requires the notion of weak order on (W,S) and the related notion of Garside shadows in (W,S), an analog of the notion of a Garside family. Then we discuss the relations between this class of automata and the canonical automaton built from Brink and Howlett's small roots. We end this article by providing partial positive answers to two conjectures: (1) the automata associated to the smallest Garside shadow is minimal; (2) the canonical automaton is minimal if and only if the support of all small roots is spherical, i.e., the corresponding root system is finite.Comment: 21 pages, 7 figures; v2: 23 pages, 8 figures, Remark 3.15 added, accepted in Journal of Algebra, computational sectio

Pairs of orthogonal countable ordinals

We characterize pairs of orthogonal countable ordinals. Two ordinals $\alpha$ and $\beta$ are orthogonal if there are two linear orders $A$ and $B$ on the same set $V$ with order types $\alpha$ and $\beta$ respectively such that the only maps preserving both orders are the constant maps and the identity map. We prove that if $\alpha$ and $\beta$ are two countable ordinals, with $\alpha \leq \beta$, then $\alpha$ and $\beta$ are orthogonal if and only if either $\omega + 1\leq \alpha$ or $\alpha =\omega$ and $\beta < \omega \beta$

A calcareous nannofossil and organic geochemical study of marine palaeoenvironmental changes across the Sinemurian/Pliensbachian (early Jurassic, ~191Ma) in Portugal

The Sinemurian/Pliensbachian boundary (~ 191 Ma) is acknowledged as one of the most important steps in the radiation of planktonic organisms, especially primary producers such as dinoflagellates and coccolithophores. To date, there is no detailed study documenting changes in planktonic assemblages related to palaeoceanographic changes across this boundary. The aim of this study is to characterize the palaeoenvironmental changes occurring across the Sinemurian/Pliensbachian boundary at the São Pedro de Moel section (Lusitanian Basin, Portugal) using micropalaeontology and organic geochemistry approaches. Combined calcareous nannofossil assemblage and lipid biomarker data document for a decrease in primary productivity in relation to a major sea-level rise occurring above the boundary. The Lusitanian Basin was particularly restricted during the late Sinemurian with a relatively low sea level, a configuration that led to the recurrent development of black shales. After a sharp sea-level fall, the basin became progressively deeper and more open during the earliest Pliensbachian, subsequently to a major transgression. This sea-level increase seems to have been a global feature and could have been related to the opening of the Hispanic Corridor that connected the Tethys and palaeo-Pacific oceans. The palaeoceanographic and palaeoclimatic changes induced by this opening may have played a role in the diversification of coccolithophores with the first occurrence or colonization of Tethyan waters by placolith-type coccoliths

Degradation of alumina and zirconia toughened alumina (ZTA) hip prostheses tested under microseparation conditions in a shock device

This paper considers the degradation of alumina and zirconia toughened alumina vs. alumina for hip implants. The materials are as assumed to be load bearing surfaces subjected to shocks in wet conditions. The load is a peak of force; 9 kN was applied over 15 ms at 2 Hz for 800,000 cycles. The volumetric wear and roughness are lower for ZTA than for alumina. The long ZTA ageing did not seem to have a direct influence on the roughness. The ageing increased the wear volumes of ZTA and it was found to have a higher wear resistance compared to alumina.Comment: International Conference on BioTribology (ICoBT 2011), Londres, 18 au 21 septembre 2011, Londres : United Kingdom (2011

Epstein-Barr virus nuclear antigen 1 interacts with regulator of chromosome condensation 1 dynamically throughout the cell cycle

The Epstein-Barr virus (EBV) nuclear antigen 1 (EBNA1) is a sequence-specific DNA binding protein which plays an essential role in viral episome replication and segregation, by recruiting the cellular complex of DNA replication onto the origin (oriP) and by tethering the viral DNA onto the mitotic chromosomes. Whereas the mechanisms of viral DNA replication are well documented, those involved in tethering EBNA1 to the cellular chromatin are far from being understood. Here, we have identified Regulator of Chromosome Condensation 1 (RCC1) as a novel cellular partner for EBNA1. RCC1 is the major nuclear guanine nucleotide exchange factor (RanGEF) for the small GTPase Ran enzyme. RCC1, associated with chromatin, is involved in the formation of RanGTP gradients critical for nucleo-cytoplasmic transport, mitotic spindle formation, and nuclear envelope reassembly following mitosis. Using several approaches, we have demonstrated a direct interaction between these two proteins and found that the EBNA1 domains responsible for EBNA1 tethering to the mitotic chromosomes are also involved in the interaction with RCC1. The use of an EBNA1 peptide array confirmed the interaction of RCC1 with these regions and also the importance of the N-terminal region of RCC1 in this interaction. Finally, using confocal microscopy and FRET analysis to follow the dynamics of interaction between the two proteins throughout the cell cycle, we have demonstrated that EBNA1 and RCC1 closely associate on the chromosomes during metaphase, suggesting an essential role for the interaction during this phase, perhaps in tethering EBNA1 to mitotic chromosomes

On the coniveau of certain sub-Hodge structures

We study the generalized Hodge conjecture for certain sub-Hodge structure defined as the kernel of the cup product map with a big cohomology class, which is of Hodge coniveau at least 1. As predicted by the generalized Hodge conjecture, we prove that the kernel is supported on a divisor, assuming the Lefschetz standard conjecture.Comment: 23 pages. V2: Typos corrected. Comments still welcome. To appear in Math.Res.Let

Type decomposition in NIP theories

We prove that any type in an NIP theory can be decomposed into a stable part (a generically stable partial type) and a distal-like quotient.Comment: Several improvements made following the referee repor