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Due to their physical properties, nanomechanical sensors (NEMS) can achieve mass measurements in the mega- to gigadalton range, which is hardly obtained with conventional mass-spectrometers. However, NEMS signals are subject to noise, causing a loss of mass resolution and thus emphasizing the need of noise control. We propose a denoising model that relies on a total variation formulation, which deals with different noise models (particularly colored noise) affecting NEMS. The model also takes into account the physics of NEMS, such as the non-linear coupling between signals of individual NEMS. The performance of the proposed model is tested on simulated data which parameters are chosen similar to true experimental conditions. The obtained results confirm the interest of our model with a mass-resolution increase over 20% compared to methods used in literature.

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Algorithms for automatically selecting a scalar or locally varying
regularization parameter for total variation models with an $L^{\tau}$-data
fidelity term, $\tau\in \{1,2\}$, are presented. The automated selection of the
regularization parameter is based on the discrepancy principle, whereby in each
iteration a total variation model has to be minimized. In the case of a locally
varying parameter this amounts to solve a multi-scale total variation
minimization problem. For solving the constituted multi-scale total variation
model convergent first and second order methods are introduced and analyzed.
Numerical experiments for image denoising and image deblurring show the
efficiency, the competitiveness, and the performance of the proposed fully
automated scalar and locally varying parameter selection algorithms.

The aim of the project is to bring a proof of concept of a simplified mass spectrometer architecture using an ultra dense network of NEMS in association with elements of CMOS circuit as sensors in order to amplify the signal in situ and adress them individually. Since several years, Roukes' team at Caltech has demonstrated a mass spectrometry with a NEMS. In parallel, the CEA/LETI-MINATEC has developped a fabrication approach called VLSI of NEMS and an electromecanical simulation method of these elements The first objective of this thesis is to study the noise phenomenon currently limiting our mass resolution in order to reach 10 Da instead of current 1000 Da on ranges going from 10 Da to 1MDa. In a second step, the concept of NEMS-based mass spectrometry is validated by comparison a nanometric cluster spectra with those from a conventional time-of-flight mass spectrometer. Then, a frequency addressing technique is applied on an NEMS array to allow for quasi simultaneous tracking of 20 different resonators. Finally, the NEMS array is inserted in the nanocluster bench to measure 20 spectra in parallel and validate a first proof of concept.

Frequency stability is key to performance of nanoresonators and their
applications. This stability is thought to reach a limit with the resonator's
ability to resolve thermally-induced vibrations. Although measurements and
predictions of resonator stability usually disregard fluctuations in the
mechanical frequency response, these fluctuations have recently attracted
considerable theoretical interest. However, their existence is extremely
difficult to demonstrate experimentally. Here, through a literature review, we
show that all studies of frequency stability report values several orders of
magnitude larger than the limit imposed by thermomechanical noise. We studied a
monocrystalline silicon nanoresonator at room temperature, and found a similar
discrepancy, not linked to thermal noise. With a pure silicon device, this
level of frequency fluctuations was not expected. The fluctuations were not due
to the instrumentation system, or to any other of the known sources
investigated. These results challenge our current understanding of frequency
fluctuations and call for a change in practices.

Nanoelectromechanical systems (NEMS) resonators can detect mass with exceptional sensitivity. Previously, mass spectra from several hundred adsorption events were assembled in NEMS-based mass spectrometry using statistical analysis. Here, we report the first realization of single-molecule NEMS-based mass spectrometry in real time. As each molecule in the sample adsorbs on the resonator, its mass and position of adsorption are determined by continuously tracking two driven vibrational modes of the device. We demonstrate the potential of multimode NEMS-based mass spectrometry by analysing IgM antibody complexes in real time. NEMS-based mass spectrometry is a unique and promising new form of mass spectrometry: it can resolve neutral species, provide a resolving power that increases markedly for very large masses, and allow the acquisition of spectra, molecule-by-molecule, in real time.

A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lanrange multipliers. The solution is obtained using the gradient-projection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t → ∞ the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear to be state-of-the-art for very noisy images. The method is noninvasive, yielding sharp edges in the image. The technique could be interpreted as a first step of moving each level set of the image normal to itself with velocity equal to the curvature of the level set divided by the magnitude of the gradient of the image, and a second step which projects the image back onto the constraint set.

This paper presents new algorithms to minimize total variation and more generally $l^1$-norms under a general convex constraint. The algorithms are based on a recent advance in convex optimization proposed by Yurii Nesterov. Depending on the regularity of the data fidelity term, we solve either a primal problem, either a dual problem. First we show that standard first order schemes allow to get solutions of precision $\epsilon$ in $O(\frac{1}{\epsilon^2})$ iterations at worst. For a general convex constraint, we propose a scheme that allows to obtain a solution of precision $\epsilon$ in $O(\frac{1}{\epsilon})$ iterations. For a strongly convex constraint, we solve a dual problem with a scheme that requires $O(\frac{1}{\sqrt{\epsilon}})$ iterations to get a solution of precision $\epsilon$. Thus, depending on the regularity of the data term, we gain from one to two orders of magnitude in the convergence rates with respect to standard schemes. Finally we perform some numerical experiments which confirm the theoretical results on various problems.

Bridging the mass gap
Viruses and many large biomolecule complexes are in a mass range that is challenging to measure with conventional mass spectrometry methods. Nanomechanical resonators can determine masses of impacting molecules, but separation methods often lose too much of the sample to be efficient. Dominguez-Medina et al. used an aerodynamic lens that improved separation and focusing of nebulized molecules with increasing mass. The mass of both filled and empty viral capsids was determined with an array of 20 nanoresonators.
Science , this issue p. 918

We present a method to determine accurately the position and mass of an entity attached to the surface of an electrostatically actuated clamped–clamped microbeam implemented as a mass sensor. In the theoretical investigation, the microbeam is modeled as a nonlinear Euler– Bernoulli beam and a perturbation technique is used to develop a closed-form expression for the frequency shift due to an added mass at a specific location on the microbeam surface. The experimental investigation was conducted on a microbeam made of Polyimide with
a special lower electrode to excite both of the first and second modes of vibration. Using
an ink-jet printer, we deposited droplets of polymers with a defined mass and position on
the surface of the microbeam and we measured the shifts in its resonance frequencies. The theoretical predictions of the mass and position of the deposited droplets match well with the experimental measurements.

We give a new description of a fast algorithm for total varia- tion minimization proposed recently by Dorit Hochbaum (1).

We study here a classical image denoising technique introduced by L. Rudin and S. Osher a few years ago, namely the constrained
minimization of the total variation (TV) of the image. First, we give results of existence and uniqueness and prove the link
between the constrained minimization problem and the minimization of an associated Lagrangian functional. Then we describe
a relaxation method for computing the solution, and give a proof of convergence. After this, we explain why the TV-based model
is well suited to the recovery of some images and not of others. We eventually propose an alternative approach whose purpose
is to handle the minimization of the minimum of several convex functionals. We propose for instance a variant of the original
TV minimization problem that handles correctly some situations where TV fails.

L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. It is intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems. L-BFGS-B can also be used for unconstrained problems and in this case performs similarly to its predessor, algorithm L-BFGS (Harwell routine VA15). The algorithm is implemented in Fortran 77.

We consider the class of iterative shrinkage-thresholding algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods, which can be viewed as an ex- tension of the classical gradient algorithm, is attractive due to its simplicity and thus is adequate for solving large-scale problems even with dense matrix data. However, such methods are also known to converge quite slowly. In this paper we present a new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically. Initial promising nu- merical results for wavelet-based image deblurring demonstrate the capabilities of FISTA which is shown to be faster than ISTA by several orders of magnitude.

An algorithm for solving large nonlinear optimization problems with simple bounds is described.

Traitement de l’information en mode comptage appliqué aux détecteurs spectrométriques

- perenon

Traitement de l’information en mode comptage appliqué aux détecteurs spectrométriques

- R Perenon

Lecture on Convex Optimization