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

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

Seagrass structural and elemental indicators reveal high nutrient availability within a tropical lagoon in Panama

Seagrass meadows are valued coastal habitats that provide ecological and economic benefits around the world. Despite their importance, many meadows are in decline, driven by a variety of anthropogenic impacts. While these declines have been well documented in some regions, other locations (particularly within the tropics) lack long-term monitoring programs needed to resolve seagrass trends over time. Effective and spatially-expansive monitoring within under-represented regions is critical to provide an accurate perspective on seagrass status and trends. We present a comprehensive dataset on seagrass coverage and composition across 24 sites in Bahía Almirante, a lagoon along the Caribbean coast of Panama. Using a single survey, we focus on capturing spatial variation in seagrass physical and elemental characteristics and provide data on key seagrass bio-indicators, such as leaf morphology (length and width), elemental content (% nitrogen and phosphorus) and stable isotopic signatures (δ13C and δ15N). We further explore relationships between these variables and water depth (proxy for light availability) and proximity to shore (proxy for terrestrial inputs). The seagrass assemblage was mostly monospecific (dominated by Thalassia testudinum) and restricted to shallow water (\u3c3 m). Above-ground biomass varied widely, averaging 71.7 g dry mass m-2, yet ranging from 24.8 to 139.6 g dry mass m-2. Leaf nitrogen content averaged 2.2%, ranging from 1.76 to 2.57%, while phosphorus content averaged 0.19% and ranged from 0.15 to 0.23%. These values were high compared to other published reports for T. testudinum, indicating elevated nutrient availability within the lagoon. Seagrass stable isotopic characteristics varied slightly and were comparable with other published values. Leaf carbon signatures (δ13C) ranged from -11.74 to -6.70h and were positively correlated to shoreline proximity, suggesting a contribution of terrestrial carbon to seagrass biomass. Leaf nitrogen signatures (δ15N) ranged from -1.75 to 3.15h and showed no correlation with shoreline proximity, suggesting that N sources within the bay were not dominated by localized point-source discharge of treated sewage. Correlations between other seagrass bio-indicators and environmental metrics were mixed: seagrass cover declined with depth, while biomass was negatively correlated with N, indicating that light and nutrient availability may jointly regulate seagrass cover and biomass. Our work documents the response of seagrass in Bahía Almirante to light and nutrient availability and highlights the eutrophic status of this bay. Using the broad spatial coverage of our survey as a baseline, we suggest the future implementation of a continuous and spatially expansive seagrass monitoring program within this region to assess the health of these important systems subject to global and local stressors

Developmental Restriction of Retrotransposition Activated in Arabidopsis by Environmental Stress

Retrotransposons (RTs) may rapidly increase in copy number due to periodic bursts of transposition. Such bursts are mutagenic and thus potentially deleterious. However, certain transposition-induced gain-of-function or regulatory mutations may be of selective advantage. How an optimal balance between these opposing effects arises is not well characterized. Here, we studied transposition bursts of a heat-activated retrotransposon family in Arabidopsis. We recorded a high inter- and intra-plant variation in the number and chromosomal position of new insertions, which usually did not affect plant fertility and were equally well transmitted through male and female gametes, even though 90% of them were within active genes. We found that a highly heterogeneous distribution of these new retroelement copies result from a combination of two mechanisms, of which the first prevents multiple transposition bursts in a given somatic cell lineage that later contributes to differentiation of gametes, and the second restricts the regulatory influence of new insertions towards neighbouring chromosomal DNA. As a whole, such regulatory characteristics of this family of RTs ensure its rapid but stepwise accumulation in plant populations experiencing transposition bursts accompanied by high diversity of chromosomal sites harbouring new RT insertions.This work was supported by European Research Council (EVOBREED) [322621] and Gatsby Fellowship [AT3273/GLE]

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

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

High metabolic variation for seaweeds in response to environmental changes: a case study of the brown algae <i>Lobophora</i> in coral reefs

In the marine environment, macroalgae face changing environmental conditions and some species are known for their high capacity to adapt to the new factors of their ecological niche. Some macroalgal metabolites play diverse ecological functions and belong to the adaptive traits of such species. Because algal metabolites are involved in many processes that shape marine biodiversity, understanding their sources of variation and regulation is therefore of utmost relevance. This work aims at exploring the possible sources of metabolic variations with time and space of four common algal species from the genus Lobophora (Dictyotales, Phaeophyceae) in the New Caledonian lagoon using a UHPLC-HRMS metabolomic fingerprinting approach. While inter-specific differences dominated, a high variability of the metabolome was noticed for each species when changing their natural habitats and types of substrates. Fatty acids derivatives and polyolefins were identified as chemomarkers of these changing conditions. The four seaweeds metabolome also displayed monthly variations over the 13-months survey and a significant correlation was made with sea surface temperature and salinity. This study highlights a relative plasticity for the metabolome of Lobophora species

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

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

Toward a chemical reanalysis in a coupled chemistry-climate model: an evaluation of MOPITT CO assimilation and its impact on tropospheric composition

We examine in detail a 1 year global reanalysis of carbon monoxide (CO) that is based on joint assimilation of conventional meteorological observations and Measurement of Pollution in The Troposphere (MOPITT) multispectral CO retrievals in the Community Earth System Model (CESM). Our focus is to assess the impact to the chemical system when CO distribution is constrained in a coupled full chemistry-climate model like CESM. To do this, we first evaluate the joint reanalysis (MOPITT Reanalysis) against four sets of independent observations and compare its performance against a reanalysis with no MOPITT assimilation (Control Run). We then investigate the CO burden and chemical response with the aid of tagged sectoral CO tracers. We estimate the total tropospheric CO burden in 2002 (from ensemble mean and spread) to be 371 ± 12% Tg for MOPITT Reanalysis and 291 ± 9% Tg for Control Run. Our multispecies analysis of this difference suggests that (a) direct emissions of CO and hydrocarbons are too low in the inventory used in this study and (b) chemical oxidation, transport, and deposition processes are not accurately and consistently represented in the model. Increases in CO led to net reduction of OH and subsequent longer lifetime of CH4 (Control Run: 8.7 years versus MOPITT Reanalysis: 9.3 years). Yet at the same time, this increase led to 5-10% enhancement of Northern Hemisphere O3 and overall photochemical activity via HOx recycling. Such nonlinear effects further complicate the attribution to uncertainties in direct emissions alone. This has implications to chemistry-climate modeling and inversion studies of longer-lived species