Rates in the Central Limit Theorem and diffusion approximation via Stein's Method

We present a way to use Stein's method in order to bound the Wasserstein distance of order $2$ between two measures $\nu$ and $\mu$ supported on $\mathbb{R}^d$ such that $\mu$ is the reversible measure of a diffusion process. In order to apply our result, we only require to have access to a stochastic process $(X_t)_{t \geq 0}$ such that $X_t$ is drawn from $\nu$ for any $t > 0$. We then show that, whenever $\mu$ is the Gaussian measure $\gamma$, one can use a slightly different approach to bound the Wasserstein distances of order $p \geq 1$ between $\nu$ and $\gamma$ under an additional exchangeability assumption on the stochastic process $(X_t)_{t \geq 0}$. Using our results, we are able to obtain convergence rates for the multi-dimensional Central Limit Theorem in terms of Wasserstein distances of order $p \geq 2$. Our results can also provide bounds for steady-state diffusion approximation, allowing us to tackle two problems appearing in the field of data analysis by giving a quantitative convergence result for invariant measures of random walks on random geometric graphs and by providing quantitative guarantees for a Monte Carlo sampling algorithm

Persistence-based Pooling for Shape Pose Recognition

International audienceIn this paper, we propose a novel pooling approach for shape classification and recognition using the bag-of-words pipeline, based on topological persistence, a recent tool from Topological Data Analysis. Our technique extends the standard max-pooling, which summarizes the distribution of a visual feature with a single number, thereby losing any notion of spatiality. Instead, we propose to use topological persistence, and the derived persistence diagrams, to provide significantly more informative and spatially sensitive characterizations of the feature functions, which can lead to better recognition performance. Unfortunately, despite their conceptual appeal, persistence diagrams are difficult to handle , since they are not naturally represented as vectors in Euclidean space and even the standard metric, the bottleneck distance is not easy to compute. Furthermore, classical distances between diagrams, such as the bottleneck and Wasserstein distances, do not allow to build positive definite kernels that can be used for learning. To handle this issue, we provide a novel way to transform persistence diagrams into vectors, in which comparisons are trivial. Finally, we demonstrate the performance of our construction on the Non-Rigid 3D Human Models SHREC 2014 dataset, where we show that topological pooling can provide significant improvements over the standard pooling methods for the shape pose recognition within the bag-of-words pipeline

Clustering soft par diffusion basée sur la densité

Submitted to Pattern Recognition LettersInternational audienceIn this paper, we propose a new fuzzy clustering algorithm based on the modeseekingframework. Given a dataset in Rd, we define regions of high density thatwe call cluster cores. We then consider a random walk on a neighborhood graphbuilt on top of our data points which is designed to be attracted by high densityregions. The strength of this attraction is controlled by a temperature parameterbeta > 0. The membership of a point to a given cluster is then the probability for therandom walk to hit the corresponding cluster core before any other. While manyproperties of random walks (such as hitting times, commute distances, etc. . . ) havebeen shown to enventually encode purely local information when the number ofdata points grows, we show that the regularization introduced by the use of clustercores solves this issue. Empirically, we show how the choice of beta influences thebehavior of our algorithm: for small values of beta the result is close to hard modeseekingwhereas when beta is close to 1 the result is similar to the output of a (fuzzy)spectral clustering. Finally, we demonstrate the scalability of our approach by providingthe fuzzy clustering of a protein configuration dataset containing a milliondata points in 30 dimensions.Cet article promeut l'usage de processus de diffusion basés sur la densité pour effectuer du clustering soft. Notre approche interpole entre la recherche de modes classique et le clustering spectral, et elle est paramétrée par un paramètre de temếrature β > 0 contrôlant la quantité de mouvement Brownien ajoutée à la montée de gradient. En pratique nous simulons le processus de diffusion dans le domaine continu par des marches aléatoires dans des graphes de voisinage construits sur les points de données. Nous prouvons la convergence de ce schéma sous des hypothèses d'échantillonnage faibles, et nous dérivons des garanties sur le clustering obtenu en termes de fonctions d'appartenance. Nos résultats théoriques sont corroborés par des expériences préliminaires sur des données synthétiques et des données réelles

Imaging striatal dopamine release using a nongenetically encoded near infrared fluorescent catecholamine nanosensor.

Neuromodulation plays a critical role in brain function in both health and disease, and new tools that capture neuromodulation with high spatial and temporal resolution are needed. Here, we introduce a synthetic catecholamine nanosensor with fluorescent emission in the near infrared range (1000-1300 nm), near infrared catecholamine nanosensor (nIRCat). We demonstrate that nIRCats can be used to measure electrically and optogenetically evoked dopamine release in brain tissue, revealing hotspots with a median size of 2 µm. We also demonstrated that nIRCats are compatible with dopamine pharmacology and show D2 autoreceptor modulation of evoked dopamine release, which varied as a function of initial release magnitude at different hotspots. Together, our data demonstrate that nIRCats and other nanosensors of this class can serve as versatile synthetic optical tools to monitor neuromodulatory neurotransmitter release with high spatial resolution

Differential branching fraction and angular analysis of the decay B0→K∗0μ+μ−

The angular distribution and differential branching fraction of the decay B 0→ K ∗0 μ + μ − are studied using a data sample, collected by the LHCb experiment in pp collisions at s√=7 TeV, corresponding to an integrated luminosity of 1.0 fb−1. Several angular observables are measured in bins of the dimuon invariant mass squared, q 2. A first measurement of the zero-crossing point of the forward-backward asymmetry of the dimuon system is also presented. The zero-crossing point is measured to be q20=4.9±0.9GeV2/c4 , where the uncertainty is the sum of statistical and systematic uncertainties. The results are consistent with the Standard Model predictions

Opposite-side flavour tagging of B mesons at the LHCb experiment

The calibration and performance of the oppositeside flavour tagging algorithms used for the measurements of time-dependent asymmetries at the LHCb experiment are described. The algorithms have been developed using simulated events and optimized and calibrated with B + →J/ψK +, B0 →J/ψK ∗0 and B0 →D ∗− μ + νμ decay modes with 0.37 fb−1 of data collected in pp collisions at √ s = 7 TeV during the 2011 physics run. The oppositeside tagging power is determined in the B + → J/ψK + channel to be (2.10 ± 0.08 ± 0.24) %, where the first uncertainty is statistical and the second is systematic