Monotone independence, comb graphs and Bose-Einstein condensation

The adjacency matrix of a comb graph is decomposed into a sum of monotone independent random variables with respect to the vacuum state. The vacuum spectral distribution is shown to be asymptotically the arcsine law as a consequence of the monotone central limit theorem. As an example the comb lattice is studied with explicit calculation

A Logical Product Approach to Zonotope Intersection

We define and study a new abstract domain which is a fine-grained combination of zonotopes with polyhedric domains such as the interval, octagon, linear templates or polyhedron domain. While abstract transfer functions are still rather inexpensive and accurate even for interpreting non-linear computations, we are able to also interpret tests (i.e. intersections) efficiently. This fixes a known drawback of zonotopic methods, as used for reachability analysis for hybrid sys- tems as well as for invariant generation in abstract interpretation: intersection of zonotopes are not always zonotopes, and there is not even a best zonotopic over-approximation of the intersection. We describe some examples and an im- plementation of our method in the APRON library, and discuss some further in- teresting combinations of zonotopes with non-linear or non-convex domains such as quadratic templates and maxplus polyhedra

Along-strike variations of P-T conditions in accretionary wedges and syn-orogenic extension, the HP-LT Phyllite-Quartzite Nappe in Crete and the Peloponnese

International audienceSyn-orogenic detachments in accretionary wedges make the exhumation of high-pressure and low-temperature metamorphic rocks possible with little erosion. The velocity of exhumation within the subduction channel or the accretionary complex, and thus the shape of P-T paths, depend upon the kinematic boundary conditions. A component of slab retreat tends to open the channel and facilitates the exhumation. We document the effect of slab retreat on the shape of P-T paths using the example of the Phyllite-Quartzite Nappe that has been exhumed below the Cretan syn-orogenic detachment during the Miocene in Crete and the Peloponnese. Data show a clear tendency toward colder conditions at peak pressure and during exhumation where the intensity of slab retreat is larger. This spatial evolution of P-T gradient is accompanied with an evolution from a partly coaxial regime below the Peloponnese section of the detachment toward a clearly non-coaxial regime in Crete

Yeast biota of naturally fermented black olives in different brines made from cv. Gemlik grown in various districts of the Cukurova region of Turkey

In this study, the yeast microbiota of naturally fermented black olives made from cv. Gemlik, grown in three different districts of the Çukurova region of Turkey, were investigated. Fermentations were conducted for 180 days in three different brines, including NaCl 10% w/v, NaCl 8% w/v and NaCl 8% w/v added with glucose 0.5%. In total, 223 yeasts were isolated and then identified by PCR–RFLP analysis of the 5.8S ITS rRNA region and sequence information for the D1/D2 domains of the 26S rRNA gene. A broad range of yeast biodiversity was identified, including eight genera and nine species. Candida boidinii (41%), Wickerhamomyces anomalus (32%) and Saccharomyces sp. (18%) were predominant yeasts throughout the fermentations. To a lesser extent, the other species, Candida aaseri, Meyerozyma sp., Zygoascus hellenicus, Pichia kudriavzevii, Schwanniomyces etchellsii and Candida atlantica were also members of the olive-fermenting microbiota. In Tarsus and Bahçe districts C. boidinii and in Serinyol district Saccharomyces sp. were the most frequently identified species. W. anomalus was the most frequently isolated species (by 48% of total yeasts) in NaCl 10% brines. C. boidinii was the most dominant species in the brines, including NaCl 8% and NaCl 8% + glucose 0.5%, with frequencies of 42% and 61%, respectively. At the end of the 180 days of fermentation, total acidity values of the brines were in the range 1.04–8.1 g/l lactic acid. Copyright © 2016 John Wiley & Sons, Ltd

An Axiomatic Approach to Liveness for Differential Equations

This paper presents an approach for deductive liveness verification for ordinary differential equations (ODEs) with differential dynamic logic. Numerous subtleties complicate the generalization of well-known discrete liveness verification techniques, such as loop variants, to the continuous setting. For example, ODE solutions may blow up in finite time or their progress towards the goal may converge to zero. Our approach handles these subtleties by successively refining ODE liveness properties using ODE invariance properties which have a well-understood deductive proof theory. This approach is widely applicable: we survey several liveness arguments in the literature and derive them all as special instances of our axiomatic refinement approach. We also correct several soundness errors in the surveyed arguments, which further highlights the subtlety of ODE liveness reasoning and the utility of our deductive approach. The library of common refinement steps identified through our approach enables both the sound development and justification of new ODE liveness proof rules from our axioms.Comment: FM 2019: 23rd International Symposium on Formal Methods, Porto, Portugal, October 9-11, 201

Interval Slopes as Numerical Abstract Domain for Floating-Point Variables

The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known to only provide approximated results, is omnipresent in this activity. In order to validate the behaviors of numerical simulations using abstract interpretation-based static analysis, we present, theoretically and with experiments, a new partially relational abstract domain dedicated to floating-point variables. It comes from interval expansion of non-linear functions using slopes and it is able to mimic all the behaviors of the floating-point arithmetic. Hence it is adapted to prove the absence of run-time errors or to analyze the numerical precision of embedded control systems