The Density of Expected Persistence Diagrams and its Kernel Based Estimation

Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane R^2 that can equivalently be seen as discrete measures in R^2. When the data come as a random point cloud, these discrete measures become random measures whose expectation is studied in this paper. First, we show that for a wide class of filtrations, including the Cech and Rips-Vietoris filtrations, the expected persistence diagram, that is a deterministic measure on R^2, has a density with respect to the Lebesgue measure. Second, building on the previous result we show that the persistence surface recently introduced in [Adams et al., 2017] can be seen as a kernel estimator of this density. We propose a cross-validation scheme for selecting an optimal bandwidth, which is proven to be a consistent procedure to estimate the density

The density of expected persistence diagrams and its kernel based estimation

Extended version of the SoCG proceedings, submitted to a journalInternational audiencePersistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane R 2 that can equivalently be seen as discrete measures in R 2. When the data come as a random point cloud, these discrete measures become random measures whose expectation is studied in this paper. First, we show that for a wide class of filtrations, including the Čech and Rips-Vietoris filtrations, the expected persistence diagram, that is a deterministic measure on R 2 , has a density with respect to the Lebesgue measure. Second, building on the previous result we show that the persistence surface recently introduced in [Adams & al., Persistenceimages: a stable vector representation of persistent homology] can be seen as a kernel estimator of this density. We propose a cross-validation scheme for selecting an optimal bandwidth, which is proven to be a consistent procedure to estimate the density

On the choice of weight functions for linear representations of persistence diagrams

Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert space, standard statistical methods cannot be directly applied to them. Instead, feature maps (or representations) are commonly used for the analysis. A large class of feature maps, which we call linear, depends on some weight functions, the choice of which is a critical issue. An important criterion to choose a weight function is to ensure stability of the feature maps with respect to Wasserstein distances on diagrams. We improve known results on the stability of such maps, and extend it to general weight functions. We also address the choice of the weight function by considering an asymptotic setting; assume that $\mathbb{X}_n$ is an i.i.d. sample from a density on $[0,1]^d$. For the \v{C}ech and Rips filtrations, we characterize the weight functions for which the corresponding feature maps converge as $n$ approaches infinity, and by doing so, we prove laws of large numbers for the total persistences of such diagrams. Those two approaches (stability and convergence) lead to the same simple heuristic for tuning weight functions: if the data lies near a $d$-dimensional manifold, then a sensible choice of weight function is the persistence to the power $\alpha$ with $\alpha \geq d$

Non-Saccharomyces Killer Toxins: Possible Biocontrol Agents Against Brettanomyces in Wine?

Red wine spoiled by the yeast Brettanomyces bruxellensis is characterised by off-odours commonlydescribed as horse sweat, phenolic, varnish and band-aid. The growth of this yeast in wine is traditionallycontrolled by the use of sulphur dioxide (SO2). However, the concentration of SO2, the pH of the wine,the presence of SO2-binding chemical compounds in the wine, as well as the strain of B. bruxellensis,determine the effectiveness of SO2. Other chemical preservatives have been tested, but are not much moreefficient than SO2, and methods used to clean barrels are only partially effective. Filtration of wine andthe use of electric currents/fields are also reported to alter the physical and sensory properties of wine. Inthis context, alternative methods are currently sought to achieve full control of this yeast in wine. Killertoxins have recently been proposed to fulfil this purpose. They are antimicrobial compounds secretedby Saccharomyces and non-Saccharomyces yeasts, displaying killer activity against other yeasts andfilamentous fungi. They are believed to play a role in yeast population dynamics, and this killer phenotypepotentially could be exploited to inhibit the growth of undesired microorganisms within a microbialecosystem such as that occurring in wine. In this review, non-Saccharomyces killer toxins are describedand their potential application in inhibiting B. bruxellensis in wine is discussed in comparison to othertried methods and techniques

A Shotgun Metagenomic Sequencing Exploration of Cabernet Sauvignon Grape Must Reveals Yeast Hydrolytic Enzymes

Shotgun sequencing was employed to explore the community structure (phylotyping of rRNA genes) andfunctional potential of Cabernet Sauvignon grape must microbiome. A metagenomic library, representing92.6 Mb of genetic information, was generated from DNA obtained from Cabernet Sauvignon grapemust.. Fungi were identified as the dominant domain (59.5%) followed by Streptophyta (39%). Amongthe 84 fungal species, 22 were yeasts of various genera. Additionally, grapevine endophytes such asDavidiella sp., Botryotinia fuckeliana, Alternaria sp., and Cladosporium sp. were identified. An unusuallyhigh prevalence of Mucor spp. was evidenced. Functional annotation revealed sequences of genesinvolved in metabolism (35.6%), followed by poorly characterized categories (28.3%), cellular processesand signalling (18.4%), and finally information storage (17.8%). Among the former, glycosidases wereabundant followed by glycogen debranching enzyme, 6-phosphofructokinase and trehalose-6-phosphatesynthase. Furthermore, the taxonomic analysis of the functional sequence data exhibited the eukaryoticgene pool that predominantly contains sequences derived from Streptophyta (mainly Vitis vinifera) 60% >Ascomycota (32%) > Basidiomycota (5%) > Bacteria (2.5%). Finally, sequences of a variety of hydrolyticenzymes of potential oenological relevance were retrieved, thereby confirming that grape juice is a richreservoir for valuable biocatalysts that should be explored further

Kinetic-Ion Simulations Addressing Whether Ion Trapping Inflates Stimulated Brillouin Backscattering Reflectivities

An investigation of the possible inflation of stimulated Brillouin backscattering (SBS) due to ion kinetic effects is presented using electromagnetic particle simulations and integrations of three-wave coupled-mode equations with linear and nonlinear models of the nonlinear ion physics. Electrostatic simulations of linear ion Landau damping in an ion acoustic wave, nonlinear reduction of damping due to ion trapping, and nonlinear frequency shifts due to ion trapping establish a baseline for modeling the electromagnetic SBS simulations. Systematic scans of the laser intensity have been undertaken with both one-dimensional particle simulations and coupled-mode-equations integrations, and two values of the electron-to-ion temperature ratio (to vary the linear ion Landau damping) are considered. Three of the four intensity scans have evidence of SBS inflation as determined by observing more reflectivity in the particle simulations than in the corresponding three-wave mode-coupling integrations with a linear ion-wave model, and the particle simulations show evidence of ion trapping.Comment: 56 pages, 20 figure

Estimation minimax adaptative en inférence géométrique

International audienceWe focus on the problem of manifold estimation: given a set of observations sampled close to some unknown submanifold M , one wants to recover information about the geometry of M . Minimax estimators which have been proposed so far all depend crucially on the a priori knowledge of parameters quantifying the underlying distribution generating the sample (such as bounds on its density), whereas those quantities will be unknown in practice. Our contribution to the matter is twofold. First, we introduce a one-parameter family of manifold estimators (M t) t≥0 based on a localized version of convex hulls, and show that for some choice of t, the corresponding estimator is minimax on the class of models of C 2 manifolds introduced in [Genovese et al., Manifold estimation and singular deconvolution under Hausdorff loss]. Second, we propose a completely data-driven selection procedure for the parameter t, leading to a minimax adaptive manifold estimator on this class of models. This selection procedure actually allows us to recover the Hausdorff distance between the set of observations and M , and can therefore be used as a scale parameter in other settings, such as tangent space estimation

Focusing of Intense Subpicosecond Laser Pulses in Wedge Targets

Two dimensional particle-in-cell simulations characterizing the interaction of ultraintense short pulse lasers in the range 10^{18} \leq I \leq 10^{20} W/cm^{2} with converging target geometries are presented. Seeking to examine intensity amplification in high-power laser systems, where focal spots are typically non-diffraction limited, we describe key dynamical features as the injected laser intensity and convergence angle of the target are systematically varied. We find that laser pulses are focused down to a wavelength with the peak intensity amplified by an order of magnitude beyond its vacuum value, and develop a simple model for how the peak location moves back towards the injection plane over time. This performance is sustained over hundreds of femtoseconds and scales to laser intensities beyond 10^{20} W/cm^{2} at 1 \mu m wavelength.Comment: 5 pages, 6 figures, accepted for publication in Physics of Plasma

La microbiologie des vins issus des raisins botrytisés au cours de l'élevage. Caractérisation des souches de "Saccharomyces cerevisiae" responsables de refermentations.

La fermentation alcoolique des vins liquoreux français issus de raisin botrytisés est arrêtée brutalement par ajout massif de dioxyde de soufre après qu'un certain équilibre est atteint entre la teneur en alcool formé et la concentration en sucres résiduels. Certaines souches de levures fermentaires survivent et parfois se multiplient provoquant une nouvelle fermentation alcoolique indésirable ; c'est la refermentation. Le suivi microbiologique de nombreux lots de vin a permis de montrer que des levures sont dans un état physiologique similaire à celui décrit chez les bactéries sous l'appellation de viable non cultivable. Cet état explique l'apparente stérilité du vin après le mutage. Au sein de l'espèce Saccharomyces cerevisiae, une sélection naturelle se produit, ne laissant souvent la place qu'à une seule souche de refermentation, tolérante au dioxyde de soufre. Une étude écologique a montré que seules certaines espèces fermentaires et oxydatives survivent. Les plus tolérantes au dioxyde de soufre forment de l'éthanal au cours de l'élevage, malgré un métabolisme ralenti, et augmente la combinaison du dioxyde de soufre libre. Cet éthanal vient progressivement combiner le dioxyde de soufre libre. La sortie de l'état viable non cultivable est probablement la clef des mécanismes engendrant les refermentations. L'utilisation du diméthyldicarbonate au moment du mutage a été étudiée en couplage avec le dioxyde de soufre. Des souches de Saccharomyces cerevisiae de refermentation ont été isolées. Elles exhibent des singularités de séquence de leur ADNr, les apparentant aux souches de voile de certains vins spéciaux. Ces souches surexpriment constitutivement le gène SSU1 et synthétisent rapidement une forte concentration d'éthanal en réponse à la présence de dioxyde de soufre. La présence de fortes concentrations de dioxyde de soufre sélectionne les souches les plus résistantes. La refermentation est donc le résultat d'une adaptation génétique et d'une sélection, fruit d'une multitude de paramètres microbiologiques, physico-chimiques et humains. Botrytis-affected wines microbiology during maturation. Characterization of Saccharomyces cerevisiae strains responsible for refermentation. ABSTRACT : The alcoholic fermentation of Botrytis-affected wines is stopped by addition of sulphur dioxide. Some fermenting yeast species can survive during maturation and grow in spite of high ethanol, sugars and sulphur dioxide concentrations. An undesirable new fermentation, named "refermentation", can sometimes occur. In this study, it was proved that some yeast species were able to survive in a viable but non-culturable-like state. This state explains the apparent sterility of wines during maturation. Within Saccharomyces cerevisiae species, an intraspecific selection was spontaneously operated. After some weeks, only one strain could often survive. An ecological study was realized. Some highly fermentative and oxidative species could survive. In spite of slower metabolism, they synthesized acetaldehyde during maturation. The exit from the VBNC state and the high sulphur dioxide binding power were the keys of refermentations. The use of dimethyldicarbonate to stop alcoholic fermentation was studied. The most efficient action was observed for the mixed sulphur dioxide and DMDC addition. Some Saccharomyces cerevisiae strains responsible for refermentations were isolated. These strains exhibited rDNA sequence singularities, showing that they were close to flor strains, responsible for velum formation in some special wines. Moreover, those strains constitutively over-expressed SSU1 gene and could rapidly synthesize high concentrations of acetaldehyde in response to sulphur dioxide addition. High sulphur dioxide concentrations had probably selected the most resistant strains. Refermentation is the result of genetic adaptation and selection, under the influence of microbiological, physical, chemical and human parameters