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 analogues of a Dempe-Franke bilevel optimization problem

We consider the tropical analogues of a particular bilevel optimization problem studied by Dempe and Franke and suggest some methods of solving these new tropical bilevel optimization problems. In particular, it is found that the algorithm developed by Dempe and Franke can be formulated and its validity can be proved in a more general setting, which includes the tropical bilevel optimization problems in question. We also show how the feasible set can be decomposed into a finite number of tropical polyhedra, to which the tropical linear programming solvers can be applied.Comment: 11 pages, 1 figur

Stability and convergence in discrete convex monotone dynamical systems

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is weaker than Lyapunov stability. Among others we show that the set of tangentially stable fixed points is isomorphic to a convex inf-semilattice, and a criterion is given for the existence of a unique tangentially stable fixed point. We also show that periods of tangentially stable periodic points are orders of permutations on $n$ letters, where $n$ is the dimension of the underlying space, and a sufficient condition for global convergence to periodic orbits is presented.Comment: 36 pages, 1 fugur

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

Computation of the Transient in Max-Plus Linear Systems via SMT-Solving

This paper proposes a new approach, grounded in Satisfiability Modulo Theories (SMT), to study the transient of a Max-Plus Linear (MPL) system, that is the number of steps leading to its periodic regime. Differently from state-of-the-art techniques, our approach allows the analysis of periodic behaviors for subsets of initial states, as well as the characterization of sets of initial states exhibiting the same specific periodic behavior and transient. Our experiments show that the proposed technique dramatically outperforms state-of-the-art methods based on max-plus algebra computations for systems of large dimensions.Comment: The paper consists of 22 pages (including references and Appendix). It is accepted in FORMATS 2020 First revisio

Satellite data reveal a common combustion emission pathway for major cities in China

Extensive fossil fuel combustion in rapidly developing cities severely affects air quality and public health. We report observational evidence of decadal changes in the efficiency and cleanness of bulk combustion over large cities in mainland China. In order to estimate the trends in enhancement ratios of CO and SO2 to NO2 (ΔCO∕ΔNO2 and ΔSO2∕ΔNO2) and infer emergent bulk combustion properties over these cities, we combine air quality retrievals from widely used satellite instruments across 2005–2014. We present results for four Chinese cities (Shenyang, Beijing, Shanghai, and Shenzhen) representing four levels of urban development. Our results show a robust coherent progression of declining to growing ΔCO∕ΔNO2 relative to 2005 (−5.4±0.7 to +8.3±3.1 %&thinsp;yr−1) and slowly declining ΔSO2∕ΔNO2 (−6.0±1.0 to −3.4±1.0&thinsp;%&thinsp;yr−1) across the four cities. The coherent progression we find is not evident in the trends of emission ratios reported in Representative Concentration Pathway (RCP8.5) inventory. This progression is likely due to a shift towards cleaner combustion from industrial and residential sectors in Shanghai and Shenzhen that is not yet seen in Shenyang and Beijing. This overall trend is presently obfuscated by China's still relatively higher dependence on coal. Such progression is well-correlated with economic development and traces a common emission pathway that resembles evolution of air pollution in more developed cities. Our results highlight the utility of augmenting observing and modeling capabilities by exploiting enhancement ratios in constraining the time variation in emission ratios in current inventories. As cities and/or countries continue to socioeconomically develop, the ability to monitor combustion efficiency and effectiveness of pollution control becomes increasingly important in assessing sustainable control strategies.</p