586 research outputs found
Tropical Fourier-Motzkin elimination, with an application to real-time verification
We introduce a generalization of tropical polyhedra able to express both
strict and non-strict inequalities. Such inequalities are handled by means of a
semiring of germs (encoding infinitesimal perturbations). We develop a tropical
analogue of Fourier-Motzkin elimination from which we derive geometrical
properties of these polyhedra. In particular, we show that they coincide with
the tropically convex union of (non-necessarily closed) cells that are convex
both classically and tropically. We also prove that the redundant inequalities
produced when performing successive elimination steps can be dynamically
deleted by reduction to mean payoff game problems. As a complement, we provide
a coarser (polynomial time) deletion procedure which is enough to arrive at a
simply exponential bound for the total execution time. These algorithms are
illustrated by an application to real-time systems (reachability analysis of
timed automata).Comment: 29 pages, 8 figure
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
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
Direct Power Control Scheme Based on Disturbance Rejection Principle for Three-Phase PWM AC/DC Converter under Different Input Voltage Conditions
Conventional direct power control (DPC) technique is a simple and efficient control strategy for three-phase PWM rectifier. However, its performance is deteriorated when the converter is supplied by unbalanced or distorted grid voltages. This paper describes the design and implementation of a new configuration of DPC based on disturbance rejection principle to achieve near-sinusoidal input current waveforms of the converter under different input voltage conditions. In the proposed DPC scheme, instantaneous active and reactive powers provided by harmonic component of input currents are directly controlled using a predefined switching table. In order to achieve full rejection of the effect of any disturbance on the quality of input currents, the reference of both controlled powers are directly given from the outside of the controller and are equal to zero. Moreover, prior knowledge of disturbance's nature, calculation of positive and negative sequences of unbalanced input voltages and content harmonic extraction are not required for the proposed DPC. Compared to the conventional DPC, the proposed one uses a PLL block to extract the fundamental of input currents and defining the position of the grid voltage vector in α-ÎČ plane without any passive filters. Finally, the simulation results have verified the validity of the proposed DPC and have proven an excellent performance under different input voltage conditions. Full disturbance rejection and good robustness towards supply voltage disturbances are the main advantages of the proposed DPC compared to the conventional one
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 â 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 8â9 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>)
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Containment and equivalence of weighted automata: Probabilistic and max-plus cases
This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain
Using mass-flow controllers for obtaining extremely stable ECR ion source beams
Original publication available at http://www.jacow.orgInternational audienceBeam stability and reproducibility is of paramount importance in applications requiring precise control of implanted radiation dose, like in the case of Hadrontherapy. The beam intensity over several weeks or months should be kept constant. Moreover, the timing for changing the nature of the beam and, as a consequence, the tuning of the source should be minimized. Standard valves usually used in conjunction of ECR ion sources have the disadvantage of controlling the conductance, which can vary significantly with external conditions, like ambient temperature and inlet pressure of the gas. The use of flow controllers is the natural way for avoiding these external constraints. In this contribution we present the results obtained using a new model of Mass-flow controller in the source Supernanogan, for production of C4+ and H3+ beams. Extremely stable beams (± 2.5%) without retuning of the source over several weeks could be obtained. The reproducibility of the source tuning parameters could also be demonstrated
Impact of the channel direction on the 1/f noise in SOI-MOSFETs fabricated on (100) and (110) silicon oriented wafers
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