497 research outputs found
The level set method for the two-sided eigenproblem
We consider the max-plus analogue of the eigenproblem for matrix pencils
Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible
values of lambda), which is a finite union of intervals, can be computed in
pseudo-polynomial number of operations, by a (pseudo-polynomial) number of
calls to an oracle that computes the value of a mean payoff game. The proof
relies on the introduction of a spectral function, which we interpret in terms
of the least Chebyshev distance between Ax and lambda Bx. The spectrum is
obtained as the zero level set of this function.Comment: 34 pages, 4 figures. Changes with respect to the previous version: we
explain relation to mean-payoff games and discrete event systems, and show
that the reconstruction of spectrum is pseudopolynomia
Tropical polyhedra are equivalent to mean payoff games
We show that several decision problems originating from max-plus or tropical
convexity are equivalent to zero-sum two player game problems. In particular,
we set up an equivalence between the external representation of tropical convex
sets and zero-sum stochastic games, in which tropical polyhedra correspond to
deterministic games with finite action spaces. Then, we show that the winning
initial positions can be determined from the associated tropical polyhedron. We
obtain as a corollary a game theoretical proof of the fact that the tropical
rank of a matrix, defined as the maximal size of a submatrix for which the
optimal assignment problem has a unique solution, coincides with the maximal
number of rows (or columns) of the matrix which are linearly independent in the
tropical sense. Our proofs rely on techniques from non-linear Perron-Frobenius
theory.Comment: 28 pages, 5 figures; v2: updated references, added background
materials and illustrations; v3: minor improvements, references update
First detection of insertion sequence element ISPa1328 in the oprD porin gene of an imipenem-resistant Pseudomonas aeruginosa isolate from an idiopathic pulmonary fibrosis patient in Marseille, France
AbstractWe report here the first case of a carbapenem-resistant Pseudomonas aeruginosa clinical isolate harboring the insertion sequence (IS) element ISPa1328 in the oprD gene in an idiopathic pulmonary fibrosis patient in France previously treated with imipenem
Reachability problems for products of matrices in semirings
We consider the following matrix reachability problem: given square
matrices with entries in a semiring, is there a product of these matrices which
attains a prescribed matrix? We define similarly the vector (resp. scalar)
reachability problem, by requiring that the matrix product, acting by right
multiplication on a prescribed row vector, gives another prescribed row vector
(resp. when multiplied at left and right by prescribed row and column vectors,
gives a prescribed scalar). We show that over any semiring, scalar reachability
reduces to vector reachability which is equivalent to matrix reachability, and
that for any of these problems, the specialization to any is
equivalent to the specialization to . As an application of this result and
of a theorem of Krob, we show that when , the vector and matrix
reachability problems are undecidable over the max-plus semiring
. We also show that the matrix, vector, and scalar
reachability problems are decidable over semirings whose elements are
``positive'', like the tropical semiring .Comment: 21 page
Cyclic projectors and separation theorems in idempotent convex geometry
Semimodules over idempotent semirings like the max-plus or tropical semiring
have much in common with convex cones. This analogy is particularly apparent in
the case of subsemimodules of the n-fold cartesian product of the max-plus
semiring it is known that one can separate a vector from a closed subsemimodule
that does not contain it. We establish here a more general separation theorem,
which applies to any finite collection of closed semimodules with a trivial
intersection. In order to prove this theorem, we investigate the spectral
properties of certain nonlinear operators called here idempotent cyclic
projectors. These are idempotent analogues of the cyclic nearest-point
projections known in convex analysis. The spectrum of idempotent cyclic
projectors is characterized in terms of a suitable extension of Hilbert's
projective metric. We deduce as a corollary of our main results the idempotent
analogue of Helly's theorem.Comment: 20 pages, 1 figur
Assimilation of IASI partial tropospheric columns with an Ensemble Kalman Filter over Europe
Partial lower tropospheric ozone columns provided by the IASI (Infrared Atmospheric Sounding Interferometer) instrument have been assimilated into a chemistry-transport model at continental scale (CHIMERE) using an Ensemble Square Root Kalman Filter (EnSRF). Analyses are made for the month of July 2007 over the European domain. Launched in 2006, aboard the MetOp-A satellite, IASI shows high sensitivity for ozone in the free troposphere and low sensitivity at the ground; therefore it is important to evaluate if assimilation of these observations can improve free tropospheric ozone, and possibly surface ozone. The analyses are validated against independent ozone observations from sondes, MOZAIC<sup>1</sup> aircraft and ground based stations (AIRBASE – the European Air quality dataBase) and compared with respect to the free run of CHIMERE. These comparisons show a decrease in error of 6 parts-per-billion (ppb) in the free troposphere over the Frankfurt area, and also a reduction of the root mean square error (respectively bias) at the surface of 19% (33%) for more than 90% of existing ground stations. This provides evidence of the potential of data assimilation of tropospheric IASI columns to better describe the tropospheric ozone distribution, including surface ozone, despite the lower sensitivity. <br><br> The changes in concentration resulting from the observational constraints were quantified and several geophysical explanations for the findings of this study were drawn. The corrections were most pronounced over Italy and the Mediterranean region, we noted an average reduction of 8–9 ppb in the free troposphere with respect to the free run, and still a reduction of 5.5 ppb at ground, likely due to a longer residence time of air masses in this part associated to the general circulation pattern (i.e. dominant western circulation) and to persistent anticyclonic conditions over the Mediterranean basin. This is an important geophysical result, since the ozone burden is large over this area, with impact on the radiative balance and air quality. <br><br><br> <sup>1</sup> Measurements of OZone, water vapour, carbon monoxide and nitrogen oxides by in-service AIrbus airCraft (<a href="http://mozaic.aero.obs-mip.fr/web/"target="_blank">http://mozaic.aero.obs-mip.fr/web/</a>)
Tropospheric and total ozone columns over Paris (France) measured using medium-resolution ground-based solar-absorption Fourier-transform infrared spectroscopy
Ground-based Fourier-transform infrared (FTIR) solar absorption spectroscopy is a powerful remote sensing technique providing information on the vertical distribution of various atmospheric constituents. This work presents the first evaluation of a mid-resolution ground-based FTIR to measure tropospheric ozone, independently of stratospheric ozone. This is demonstrated using a new atmospheric observatory (named OASIS for "Observations of the Atmosphere by Solar absorption Infrared Spectroscopy"), installed in Créteil (France). The capacity of the technique to separate stratospheric and tropospheric ozone is demonstrated. Daily mean tropospheric ozone columns derived from the Infrared Atmospheric Sounding Interferometer (IASI) and from OASIS measurements are compared for summer 2009 and a good agreement of −5.6 (±16.1) % is observed. Also, a qualitative comparison between in-situ surface ozone measurements and OASIS data reveals OASIS's capacity to monitor seasonal tropospheric ozone variations, as well as ozone pollution episodes in summer 2009 around Paris. Two extreme pollution events are identified (on the 1 July and 6 August 2009) for which ozone partial columns from OASIS and predictions from a regional air-quality model (CHIMERE) are compared following strict criteria of temporal and spatial coincidence. An average bias of 0.2%, a mean square error deviation of 7.6%, and a correlation coefficient of 0.91 is found between CHIMERE and OASIS, demonstrating the potential of a mid-resolution FTIR instrument in ground-based solar absorption geometry for tropospheric ozone monitoring
Droplet actuation induced by coalescence: experimental evidences and phenomenological modeling
This paper considers the interaction between two droplets placed on a
substrate in immediate vicinity. We show here that when the two droplets are of
different fluids and especially when one of the droplet is highly volatile, a
wealth of fascinating phenomena can be observed. In particular, the interaction
may result in the actuation of the droplet system, i.e. its displacement over a
finite length. In order to control this displacement, we consider droplets
confined on a hydrophilic stripe created by plasma-treating a PDMS substrate.
This controlled actuation opens up unexplored opportunities in the field of
microfluidics. In order to explain the observed actuation phenomenon, we
propose a simple phenomenological model based on Newton's second law and a
simple balance between the driving force arising from surface energy gradients
and the viscous resistive force. This simple model is able to reproduce
qualitatively and quantitatively the observed droplet dynamics
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