Detection of dependence patterns with delay

The Unitary Events (UE) method is a popular and efficient method used this last decade to detect dependence patterns of joint spike activity among simultaneously recorded neurons. The first introduced method is based on binned coincidence count \citep{Grun1996} and can be applied on two or more simultaneously recorded neurons. Among the improvements of the methods, a transposition to the continuous framework has recently been proposed in \citep{muino2014frequent} and fully investigated in \citep{MTGAUE} for two neurons. The goal of the present paper is to extend this study to more than two neurons. The main result is the determination of the limit distribution of the coincidence count. This leads to the construction of an independence test between $L\geq 2$ neurons. Finally we propose a multiple test procedure via a Benjamini and Hochberg approach \citep{Benjamini1995}. All the theoretical results are illustrated by a simulation study, and compared to the UE method proposed in \citep{Grun2002}. Furthermore our method is applied on real data

Unified View on L\'evy White Noises: General Integrability Conditions and Applications to Linear SPDE

There exists several ways of constructing L\'evy white noise, for instance are as a generalized random process in the sense of I.M. Gelfand and N.Y. Vilenkin, or as an independently scattered random measure introduced by B.S. Rajput and J. Rosinski. In this article, we unify those two approaches by extending the L\'evy white noise, defined as a generalized random process, to an independently scattered random measure. We are then able to give general integrability conditions for L\'evy white noises, thereby maximally extending their domain of definition. Based on this connection, we provide new criteria for the practical determination of this domain of definition, including specific results for the subfamilies of Gaussian, symmetric-$\alpha$-stable, Laplace, and compound Poisson noises. We also apply our results to formulate a general criterion for the existence of generalized solutions of linear stochastic partial differential equations driven by a L\'evy white noise.Comment: 43 page

Optimal polarisation equations in FLRW universes

This paper presents the linearised Boltzmann equation for photons for scalar, vector and tensor perturbations in flat, open and closed FLRW cosmologies. We show that E- and B-mode polarisation for all types can be computed using only a single hierarchy. This was previously shown explicitly for tensor modes in flat cosmologies but not for vectors, and not for non-flat cosmologies.Comment: 27 pages, prepared for submission to JCAP. Matches published versio

The effective gravitational decoupling between dark matter and the CMB

We present a detailed and self-contained analytical derivation of the evolution of sub-horizon cosmological perturbations before decoupling, based on previous work by S. Weinberg. These solutions are valid in the minimal LCDM scenario, to first order in perturbation theory, in the tight-coupling limit and neglecting neutrino shear stress. We compare them to exact numerical solutions computed by a Boltzmann code, and we find the two to be in very good agreement. The analytic solutions show explicitly that CDM and the baryon-photon fluid effectively behave as separate self-gravitating fluids until the epoch of baryon drag. This in turn leads to the surprising conclusion that the CMB is much less sensitive to the clustering properties of minimally coupled Dark Matter models than what would be naively expected.Comment: 23 pages, 8 figures, 2 references added, few sentences clarifie

Remnants of galactic subhalos and their impact on indirect dark-matter searches

Dark-matter subhalos, predicted in large numbers in the cold-dark-matter scenario, should have an impact on dark-matter-particle searches. Recent results show that tidal disruption of these objects in computer simulations is overefficient due to numerical artifacts and resolution effects. Accounting for these results, we re-estimated the subhalo abundance in the Milky Way using semianalytical techniques. In particular, we showed that the boost factor for gamma rays and cosmic-ray antiprotons is increased by roughly a factor of twoJ.L. and M.S. are partly supported by the Agence Nationale pour la Recherche (ANR) Project No. ANR-18-CE31-0006, the Origines, Constituants, et EVolution de l’Univers (OCEVU) Labex (No. ANR-11-LABX-0060), the CNRS IN2P3-Theory/INSU-PNHE-PNCG project “Galactic Dark Matter,” and the European Union’s Horizon 2020 Research and Innovation Program under Marie Skłodowska-Curie Grant Agreements No. 690575 and No. 674896, in addition to recurrent funding by the Centre National de la Recherche Scientifique (CNRS) and the University of Montpellier. T.L. is supported by the European Union’s Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie grant agreement No. 713366. The work of TL was also supported by the Spanish Agencia Estatal de Investigación through grants PGC2018-095161-B-I00, IFT Centro de Excelencia Severo Ochoa SEV-2016-0597, and Red Consolider MultiDark FPA2017-90566-RED

Continuous Learning in a Hierarchical Multiscale Neural Network

We reformulate the problem of encoding a multi-scale representation of a sequence in a language model by casting it in a continuous learning framework. We propose a hierarchical multi-scale language model in which short time-scale dependencies are encoded in the hidden state of a lower-level recurrent neural network while longer time-scale dependencies are encoded in the dynamic of the lower-level network by having a meta-learner update the weights of the lower-level neural network in an online meta-learning fashion. We use elastic weights consolidation as a higher-level to prevent catastrophic forgetting in our continuous learning framework.Comment: 5 pages, 2 figures, accepted as short paper at ACL 201

On the delooping of (framed) embedding spaces

It is known that the bimodule derived mapping spaces between two operads have a delooping in terms of the operadic mapping space. We show a relative version of that statement. The result has applications to the spaces of disc embeddings fixed near the boundary and framed disc embeddings.Comment: arXiv admin note: text overlap with arXiv:1704.0706