Reachability Analysis of Innermost Rewriting

We consider the problem of inferring a grammar describing the output of a functional program given a grammar describing its input. Solutions to this problem are helpful for detecting bugs or proving safety properties of functional programs and, several rewriting tools exist for solving this problem. However, known grammar inference techniques are not able to take evaluation strategies of the program into account. This yields very imprecise results when the evaluation strategy matters. In this work, we adapt the Tree Automata Completion algorithm to approximate accurately the set of terms reachable by rewriting under the innermost strategy. We prove that the proposed technique is sound and precise w.r.t. innermost rewriting. The proposed algorithm has been implemented in the Timbuk reachability tool. Experiments show that it noticeably improves the accuracy of static analysis for functional programs using the call-by-value evaluation strategy

Exploring optimal stomatal control under alternative hypotheses for the regulation of plant sources and sinks

Summary Experimental evidence that nonstomatal limitations to photosynthesis (NSLs) correlate with leaf sugar and/or leaf water status suggests the possibility that stomata adjust to maximise photosynthesis through a trade-off between leaf CO2 supply and NSLs, potentially involving source-sink interactions. However, the mechanisms regulating NSLs and sink strength, as well as their implications for stomatal control, remain uncertain. We used an analytically solvable model to explore optimal stomatal control under alternative hypotheses for source and sink regulation. We assumed that either leaf sugar concentration or leaf water potential regulates NSLs, and that either phloem turgor pressure or phloem sugar concentration regulates sink phloem unloading. All hypotheses lead to realistic stomatal responses to light, CO2 and air humidity, including conservative behaviour for the intercellular-to-atmospheric CO2 concentration ratio. Sugar- and water-regulated NSLs are distinguished by the presence/absence of a stomatal closure response to changing sink strength. Turgor- and sugar-regulated phloem unloading are distinguished by the presence/absence of stomatal closure under drought and avoidance/occurrence of negative phloem turgor. Results from girdling and drought experiments on Pinus sylvestris, Betula pendula, Populus tremula and Picea abies saplings are consistent with optimal stomatal control under sugar-regulated NSLs and turgor-regulated unloading. Our analytical results provide a simple representation of stomatal responses to above- and below-ground environmental factors and sink activity.Experimental evidence that nonstomatal limitations to photosynthesis (NSLs) correlate with leaf sugar and/or leaf water status suggests the possibility that stomata adjust to maximise photosynthesis through a trade-off between leaf CO2 supply and NSLs, potentially involving source-sink interactions. However, the mechanisms regulating NSLs and sink strength, as well as their implications for stomatal control, remain uncertain. We used an analytically solvable model to explore optimal stomatal control under alternative hypotheses for source and sink regulation. We assumed that either leaf sugar concentration or leaf water potential regulates NSLs, and that either phloem turgor pressure or phloem sugar concentration regulates sink phloem unloading. All hypotheses led to realistic stomatal responses to light, CO2 and air humidity, including conservative behaviour for the intercellular-to-atmospheric CO2 concentration ratio. Sugar-regulated and water-regulated NSLs are distinguished by the presence/absence of a stomatal closure response to changing sink strength. Turgor-regulated and sugar-regulated phloem unloading are distinguished by the presence/absence of stomatal closure under drought and avoidance/occurrence of negative phloem turgor. Results from girdling and drought experiments on Pinus sylvestris, Betula pendula, Populus tremula and Picea abies saplings are consistent with optimal stomatal control under sugar-regulated NSLs and turgor-regulated unloading. Our analytical results provide a simple representation of stomatal responses to above-ground and below-ground environmental factors and sink activity.Peer reviewe

Analyse d'atteignabilité pour les programmes fonctionnels avec stratégie d'évaluation en profondeur

Proving that programs behave correctly is difficult; one uses proof tools, which must rely on overapproximation (because of Rice's theorem). Automaton completion is such a tool, which overapproximates the set of reachable terms during the execution of a program represented as a TRS. An evaluation strategy dictates which subterm of a term should be rewritten first; taking this into account allows for a better approximation. Our thesis sets forward an adaptation of automaton completion to the innermost strategy, which is used among others by OCaml. We prove the soundness and the precision of our adaptation and show how it is part of a greater framework for analysis of functional programms (OCaml).Établir des preuves de bon fonctionnement des programmes est délicat ; on a recours à des outils de preuve, qui doivent procéder par surapproximation (à cause du théorème de Rice). La complétion d'automate est un tel outil, qui surapproxime l'ensemble des termes accessibles lors de l'exécution d'un programme représenté par un système de réécriture. La stratégie d'évaluation donne l'ordre dans lequel les sous-termes d'un terme doivent être réécrits ; en tenir compte permet une meilleur précision de l'analyse. Notre thèse propose une adaptation de la complétion d'automate à la stratégie en profondeur, utilisée notamment par OCaml. Nous établissons la correction et la précision de notre méthode et montrons comment elle s'inscrit dans le cadre plus large de l'analyse de programmes fonctionnels (OCaml)

Effects of Ontogeny on delta C-13 of Plant- and Soil-Respired CO2 and on Respiratory Carbon Fractionation in C-3 Herbaceous Species

Knowledge gaps regarding potential ontogeny and plant species identity effects on carbon isotope fractionation might lead to misinterpretations of carbon isotope composition (delta C-13) of respired CO2, a widely-used integrator of environmental conditions. In monospecific mesocosms grown under controlled conditions, the delta C-13 of C pools and fluxes and leaf ecophysiological parameters of seven herbaceous species belonging to three functional groups (crops, forage grasses and legumes) were investigated at three ontogenetic stages of their vegetative cycle (young foliage, maximum growth rate, early senescence). Ontogeny-related changes in delta C-13 of leaf-and soil-respired CO2 and C-13/C-12 fractionation in respiration (Delta(R)) were species-dependent and up to 7 parts per thousand, a magnitude similar to that commonly measured in response to environmental factors. At plant and soil levels, changes in delta C-13 of respired CO2 and Delta(R) with ontogeny were related to changes in plant physiological status, likely through ontogeny-driven changes in the C sink to source strength ratio in the above-ground plant compartment. Our data further showed that lower Delta(R) values (i.e. respired CO2 relatively less depleted in C-13) were observed with decreasing net assimilation. Our findings highlight the importance of accounting for ontogenetic stage and plant community composition in ecological studies using stable carbon isotopes.Peer reviewe

Inspection of gas bubbles in frozen Betula pendula xylem with micro-CT: Conduit size, water status and bark permeability affect bubble characteristics

Abstract Bubbles of gas trapped in the xylem during freezing are a major cause of damage for trees growing at high altitudes or latitudes, as the bubbles may cause embolism during thawing. Yet the factors controlling bubble formation upon freeze-thaw cycles remain poorly understood. Especially the size of the bubbles formed in the ice is crucial for winter embolism formation. We used high-resolution X-ray microtomography combined with freezing experiments to investigate the size and shape of 68 343 gas bubbles in frozen conduits in branches of Betula pendula. We also studied how conduit size, tree water status (-0.2 MPa vs -0.6 MPa) and bark permeability to gases (decreased by Vaseline-coating) affect the gas bubbles characteristics. High-resolution X-ray images allowed us to detect gas bubbles down to 1.0 ?m in diameter and revealed that not only small spherical gas bubbles but gaseous volumes of various shapes and sizes were found from the frozen xylem indicating that gas bubbles may have started to grow already during the freezing propagation. Most of the gas bubbles were found in fibers, but the rare gas bubbles found in the vessels were larger than those in the fibers. Bubble volume increased with conduit volume in both fibers and vessels, but conduit size alone could not explain gas bubble volume. Low water potential and restriction of gas escape from the branch seem to cause more, larger, and less spherical bubbles and thus increase the risk of embolism formation. These findings open new research avenues for further studies of winter embolism formation. This article is protected by copyright. All rights reserved.Peer reviewe

Measurement of Inner Bark and Leaf Osmolality

Non peer reviewe

Reachability Analysis of Innermost Rewriting

Approximating the set of terms reachable by rewriting finds more and more applications ranging from termination proofs of term rewriting systems, cryp- tographic protocol verification to static analysis of programs. However, since approximation techniques do not take rewriting strategies into account, they build very coarse approximations when rewriting is constrained by a specific strategy. In this work, we propose to adapt the Tree Automata Completion algorithm to accurately approximate the set of terms reachable by rewriting under the inner- most strategy. We prove that the proposed technique is sound and precise w.r.t. innermost rewriting. The proposed algorithm has been implemented in the Timbuk reachability tool. Experiments shows that it noticeably improves the accuracy of static analysis for functional programs using the call-by-value evaluation strategy. In particular, for some functional programs needing lazy evaluation to terminate, the computed approximations are precise enough to prove the absence of innermost normal forms, i.e. prove non termination of the program with call-by-value

A Novel Method to Simultaneously Measure Leaf Gas Exchange and Water Content

Understanding the relationship between plant water status and productivity and between plant water status and plant mortality is required to effectively quantify and predict the effects of drought on plants. Plant water status is closely linked to leaf water content that may be estimated using remote sensing technologies. Here, we used an inexpensive miniature hyperspectral spectrometer in the 1550–1950 nm wavelength domain to measure changes in silver birch (Betula pendula Roth) leaf water content combined with leaf gas exchange measurements at a sub-minute time resolution, under increasing vapor pressure deficit, CO2 concentrations, and light intensity within the measurement cuvette; we also developed a novel methodology for calibrating reflectance measurements to predict leaf water content for individual leaves. Based on reflectance at 1550 nm, linear regression modeling explained 98–99% of the variation in leaf water content, with a root mean square error of 0.31–0.43 g cm−2. The prediction accuracy of the model represents a c. ten-fold improvement compared to previous studies that have used destructive sampling measurements of several leaves. This novel methodology allows the study of interlinkages between leaf water content, transpiration, and assimilation at a high time resolution that will increase understanding of the movement of water within plants and between plants and the atmosphere

Comparison of Stomatal Conductance Approaches in JSBACH

Non peer reviewe