1,165 research outputs found
On deconvolution problems: numerical aspects
An optimal algorithm is described for solving the deconvolution problem of
the form given the noisy data ,
The idea of the method consists of the
representation , where is a compact operator, is
injective, is the identity operator, is not boundedly invertible, and
an optimal regularizer is constructed for . The optimal regularizer is
constructed using the results of the paper MR 40#5130.Comment: 7 figure
Ions in Fluctuating Channels: Transistors Alive
Ion channels are proteins with a hole down the middle embedded in cell
membranes. Membranes form insulating structures and the channels through them
allow and control the movement of charged particles, spherical ions, mostly
Na+, K+, Ca++, and Cl-. Membranes contain hundreds or thousands of types of
channels, fluctuating between open conducting, and closed insulating states.
Channels control an enormous range of biological function by opening and
closing in response to specific stimuli using mechanisms that are not yet
understood in physical language. Open channels conduct current of charged
particles following laws of Brownian movement of charged spheres rather like
the laws of electrodiffusion of quasi-particles in semiconductors. Open
channels select between similar ions using a combination of electrostatic and
'crowded charge' (Lennard-Jones) forces. The specific location of atoms and the
exact atomic structure of the channel protein seems much less important than
certain properties of the structure, namely the volume accessible to ions and
the effective density of fixed and polarization charge. There is no sign of
other chemical effects like delocalization of electron orbitals between ions
and the channel protein. Channels play a role in biology as important as
transistors in computers, and they use rather similar physics to perform part
of that role. Understanding their fluctuations awaits physical insight into the
source of the variance and mathematical analysis of the coupling of the
fluctuations to the other components and forces of the system.Comment: Revised version of earlier submission, as invited, refereed, and
published by journa
Development of Muon Drift-Tube Detectors for High-Luminosity Upgrades of the Large Hadron Collider
The muon detectors of the experiments at the Large Hadron Collider (LHC) have
to cope with unprecedentedly high neutron and gamma ray background rates. In
the forward regions of the muon spectrometer of the ATLAS detector, for
instance, counting rates of 1.7 kHz/square cm are reached at the LHC design
luminosity. For high-luminosity upgrades of the LHC, up to 10 times higher
background rates are expected which require replacement of the muon chambers in
the critical detector regions. Tests at the CERN Gamma Irradiation Facility
showed that drift-tube detectors with 15 mm diameter aluminum tubes operated
with Ar:CO2 (93:7) gas at 3 bar and a maximum drift time of about 200 ns
provide efficient and high-resolution muon tracking up to the highest expected
rates. For 15 mm tube diameter, space charge effects deteriorating the spatial
resolution at high rates are strongly suppressed. The sense wires have to be
positioned in the chamber with an accuracy of better than 50 ?micons in order
to achieve the desired spatial resolution of a chamber of 50 ?microns up to the
highest rates. We report about the design, construction and test of prototype
detectors which fulfill these requirements
Solution to the problem of tomographic scanning of objects by small area X-Ray detectors
Standard X-Ray tomographic setups basically consist of 3 parts: radiation source, mechanics for mounting a sample and detector system. Each part of tomographic setup in one way or another contributes into the quality of reconstructed images. Detector system is responsible for data acquisition process. Development of detectors improves them in terms of resolution, acquisition speed, dark current etc. Such improvements increases costs for producing of detectors as well as their final price. Tomographic scanning of long objects requires using detectors of corresponding size. It makes tomographic setups expensive, because the price of detectors also increases with increasing of their size. Presented work proposes to solve this problem by shifting detector along the longest dimension of the sample and applying optimized filtered backprojection algorithm
On the Calibration of a Size-Structured Population Model from Experimental Data
The aim of this work is twofold. First, we survey the techniques developed in
(Perthame, Zubelli, 2007) and (Doumic, Perthame, Zubelli, 2008) to reconstruct
the division (birth) rate from the cell volume distribution data in certain
structured population models. Secondly, we implement such techniques on
experimental cell volume distributions available in the literature so as to
validate the theoretical and numerical results. As a proof of concept, we use
the data reported in the classical work of Kubitschek [3] concerning
Escherichia coli in vitro experiments measured by means of a Coulter
transducer-multichannel analyzer system (Coulter Electronics, Inc., Hialeah,
Fla, USA.) Despite the rather old measurement technology, the reconstructed
division rates still display potentially useful biological features
The density of states of chaotic Andreev billiards
Quantum cavities or dots have markedly different properties depending on
whether their classical counterparts are chaotic or not. Connecting a
superconductor to such a cavity leads to notable proximity effects,
particularly the appearance, predicted by random matrix theory, of a hard gap
in the excitation spectrum of quantum chaotic systems. Andreev billiards are
interesting examples of such structures built with superconductors connected to
a ballistic normal metal billiard since each time an electron hits the
superconducting part it is retroreflected as a hole (and vice-versa). Using a
semiclassical framework for systems with chaotic dynamics, we show how this
reflection, along with the interference due to subtle correlations between the
classical paths of electrons and holes inside the system, are ultimately
responsible for the gap formation. The treatment can be extended to include the
effects of a symmetry breaking magnetic field in the normal part of the
billiard or an Andreev billiard connected to two phase shifted superconductors.
Therefore we are able to see how these effects can remold and eventually
suppress the gap. Furthermore the semiclassical framework is able to cover the
effect of a finite Ehrenfest time which also causes the gap to shrink. However
for intermediate values this leads to the appearance of a second hard gap - a
clear signature of the Ehrenfest time.Comment: Refereed version. 23 pages, 19 figure
Elastic-Net Regularization: Error estimates and Active Set Methods
This paper investigates theoretical properties and efficient numerical
algorithms for the so-called elastic-net regularization originating from
statistics, which enforces simultaneously l^1 and l^2 regularization. The
stability of the minimizer and its consistency are studied, and convergence
rates for both a priori and a posteriori parameter choice rules are
established. Two iterative numerical algorithms of active set type are
proposed, and their convergence properties are discussed. Numerical results are
presented to illustrate the features of the functional and algorithms
Parameter identification in a semilinear hyperbolic system
We consider the identification of a nonlinear friction law in a
one-dimensional damped wave equation from additional boundary measurements.
Well-posedness of the governing semilinear hyperbolic system is established via
semigroup theory and contraction arguments. We then investigte the inverse
problem of recovering the unknown nonlinear damping law from additional
boundary measurements of the pressure drop along the pipe. This coefficient
inverse problem is shown to be ill-posed and a variational regularization
method is considered for its stable solution. We prove existence of minimizers
for the Tikhonov functional and discuss the convergence of the regularized
solutions under an approximate source condition. The meaning of this condition
and some arguments for its validity are discussed in detail and numerical
results are presented for illustration of the theoretical findings
Adaptive Covariance Estimation with model selection
We provide in this paper a fully adaptive penalized procedure to select a
covariance among a collection of models observing i.i.d replications of the
process at fixed observation points. For this we generalize previous results of
Bigot and al. and propose to use a data driven penalty to obtain an oracle
inequality for the estimator. We prove that this method is an extension to the
matricial regression model of the work by Baraud
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