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

Comparison of Perron and Floquet eigenvalues in age structured cell division cycle models

We study the growth rate of a cell population that follows an age-structured PDE with time-periodic coefficients. Our motivation comes from the comparison between experimental tumor growth curves in mice endowed with intact or disrupted circadian clocks, known to exert their influence on the cell division cycle. We compare the growth rate of the model controlled by a time-periodic control on its coefficients with the growth rate of stationary models of the same nature, but with averaged coefficients. We firstly derive a delay differential equation which allows us to prove several inequalities and equalities on the growth rates. We also discuss about the necessity to take into account the structure of the cell division cycle for chronotherapy modeling. Numerical simulations illustrate the results.Comment: 26 page

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

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

Reachability problems for products of matrices in semirings

We consider the following matrix reachability problem: given $r$ 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 $r\geq 2$ is equivalent to the specialization to $r=2$. As an application of this result and of a theorem of Krob, we show that when $r=2$, the vector and matrix reachability problems are undecidable over the max-plus semiring $(Z\cup\{-\infty\},\max,+)$. We also show that the matrix, vector, and scalar reachability problems are decidable over semirings whose elements are ``positive'', like the tropical semiring $(N\cup\{+\infty\},\min,+)$.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

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

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-β 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

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