Block thresholding for wavelet-based estimation of function derivatives from a heteroscedastic multichannel convolution model

We observe $n$ heteroscedastic stochastic processes $\{Y_v(t)\}_{v}$, where for any $v\in\{1,\ldots,n\}$ and $t \in [0,1]$, $Y_v(t)$ is the convolution product of an unknown function $f$ and a known blurring function $g_v$ corrupted by Gaussian noise. Under an ordinary smoothness assumption on $g_1,\ldots,g_n$, our goal is to estimate the $d$-th derivatives (in weak sense) of $f$ from the observations. We propose an adaptive estimator based on wavelet block thresholding, namely the "BlockJS estimator". Taking the mean integrated squared error (MISE), our main theoretical result investigates the minimax rates over Besov smoothness spaces, and shows that our block estimator can achieve the optimal minimax rate, or is at least nearly-minimax in the least favorable situation. We also report a comprehensive suite of numerical simulations to support our theoretical findings. The practical performance of our block estimator compares very favorably to existing methods of the literature on a large set of test functions

On the estimation of density-weighted average derivative by wavelet methods under various dependence structures

International audienceThe problem of estimating the density-weighted average derivative of a regression function is considered. We present a new consistent estimator based on a plug-in approach and wavelet projections. Its performances are explored under various dependence structures on the observations: the independent case, the $\rho$-mixing case and the $\alpha$-mixing case. More precisely, denoting $n$ the number of observations, in the independent case, we prove that it attains $1/n$ under the mean squared error, in the $\rho$-mixing case, $1/\sqrt{n}$ under the mean absolute error, and, in the $\alpha$-mixing case, $\sqrt{\ln n /n}$ under the mean absolute error. A short simulation study illustrates the theory

On adaptive wavelet estimation of a class of weighted densities

We investigate the estimation of a weighted density taking the form $g=w(F)f$, where $f$ denotes an unknown density, $F$ the associated distribution function and $w$ is a known (non-negative) weight. Such a class encompasses many examples, including those arising in order statistics or when $g$ is related to the maximum or the minimum of $N$ (random or fixed) independent and identically distributed (\iid) random variables. We here construct a new adaptive non-parametric estimator for $g$ based on a plug-in approach and the wavelets methodology. For a wide class of models, we prove that it attains fast rates of convergence under the $\mathbb{L}_p$ risk with $p\ge 1$ (not only for $p = 2$ corresponding to the mean integrated squared error) over Besov balls. The theoretical findings are illustrated through several simulations

Nonparametric estimation in a regression model with additive and multiplicative noise

In this paper, we consider an unknown functional estimation problem in a general nonparametric regression model with the characteristic of having both multiplicative and additive noise. We propose two wavelet estimators, which, to our knowledge, are new in this general context. We prove that they achieve fast convergence rates under the mean integrated square error over Besov spaces. The rates obtained have the particularity of being established under weak conditions on the model. A numerical study in a context comparable to stochastic frontier estimation (with the difference that the boundary is not necessarily a production function) supports the theory

Nonparametric estimation in a regression model with additive and multiplicative noise

In this paper, we consider an unknown functional estimation problem in a general nonparametric regression model with the feature of having both multiplicative and additive noise.We propose two new wavelet estimators in this general context. We prove that they achieve fast convergence rates under the mean integrated square error over Besov spaces. The obtained rates have the particularity of being established under weak conditions on the model. A numerical study in a context comparable to stochastic frontier estimation (with the difference that the boundary is not necessarily a production function) supports the theory

Recombinant protein production facility for fungal biomass-degrading enzymes using the yeast Pichia pastoris

International audienceFilamentous fungi are the predominant source of lignocellulolytic enzymes used in industry for the transformation of plant biomass into high-value molecules and biofuels. The rapidity with which new fungal genomic and post-genomic data are being produced is vastly outpacing functional studies. This underscores the critical need for developing platforms dedicated to the recombinant expression of enzymes lacking confident functional annotation, a prerequisite to their functional and structural study. In the last decade, the yeast Pichia pastoris has become increasingly popular as a host for the production of fungal biomass-degrading enzymes, and particularly carbohydrate-active enzymes (CAZymes). This study aimed at setting-up a platform to easily and quickly screen the extracellular expression of biomass-degrading enzymes in P. pastoris. We first used three fungal glycoside hydrolases (GHs) that we previously expressed using the protocol devised by Invitrogen to try different modifications of the original protocol. Considering the gain in time and convenience provided by the new protocol, we used it as basis to setup the facility and produce a suite of fungal CAZymes (GHs, carbohydrate esterases and auxiliary activity enzyme families) out of which more than 70% were successfully expressed. The platform tasks range from gene cloning to automated protein purifications and activity tests, and is open to the CAZyme users' community

Nanomechanical properties of solvent cast polystyrene and poly(methyl methacrylate) polymer blends and self-assembled block copolymers

© 2015 Society of Photo-Optical Instrumentation Engineers (SPIE). The nanomechanical properties of solvent-cast polymer thin films have been investigated using PeakForce™ Quantitative Nanomechanical Mapping. The samples consisted of films of polystyrene (PS) and poly(methyl methacrylate) (PMMA) obtained after the dewetting of toluene solution on a polymeric brush layer. Additionally, we have probed the mechanical properties of poly(styrene-b-methyl methacrylate) block copolymers (BCP) as randomly oriented thin films. The probed films have a critical thickness <50 nm and present features to be resolved <42 nm. The Young's modulus values obtained through several nanoindentation experiments present a good agreement with previous literature, suggesting that the PeakForce™ technique could be crucial for BCP investigations, e.g., as a predictor of the mechanical stability of the different phases.This work was partially funded by the projects SNM (FP7-ICT-2011-8) and FORCE-for-FUTURE (CSD2010-00024).Peer Reviewe

Automated assay for screening the enzymatic release of reducing sugars from micronized biomass

<p>Abstract</p> <p>Background</p> <p>To reduce the production cost of bioethanol obtained from fermentation of the sugars provided by degradation of lignocellulosic biomass (<it>i.e</it>., second generation bioethanol), it is necessary to screen for new enzymes endowed with more efficient biomass degrading properties. This demands the set-up of high-throughput screening methods. Several methods have been devised all using microplates in the industrial SBS format. Although this size reduction and standardization has greatly improved the screening process, the published methods comprise one or more manual steps that seriously decrease throughput. Therefore, we worked to devise a screening method devoid of any manual steps.</p> <p>Results</p> <p>We describe a fully automated assay for measuring the amount of reducing sugars released by biomass-degrading enzymes from wheat-straw and spruce. The method comprises two independent and automated steps. The first step is the making of "substrate plates". It consists of filling 96-well microplates with slurry suspensions of micronized substrate which are then stored frozen until use. The second step is an enzymatic activity assay. After thawing, the substrate plates are supplemented by the robot with cell-wall degrading enzymes where necessary, and the whole process from addition of enzymes to quantification of released sugars is autonomously performed by the robot. We describe how critical parameters (amount of substrate, amount of enzyme, incubation duration and temperature) were selected to fit with our specific use. The ability of this automated small-scale assay to discriminate among different enzymatic activities was validated using a set of commercial enzymes.</p> <p>Conclusions</p> <p>Using an automatic microplate sealer solved three main problems generally encountered during the set-up of methods for measuring the sugar-releasing activity of plant cell wall-degrading enzymes: throughput, automation, and evaporation losses. In its present set-up, the robot can autonomously process 120 triplicate wheat-straw samples per day. This throughput can be doubled if the incubation time is reduced from 24 h to 4 h (for initial rates measurements, for instance). This method can potentially be used with any insoluble substrate that is micronizable. A video illustrating the method can be seen at the following URL: <url>http://www.youtube.com/watch?v=NFg6TxjuMWU</url></p