Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations

We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable to verify multivariate nonlinear polynomial and non-polynomial inequalities on rectangular domains. One of the main features of our work is an efficient implementation of the verification procedure which can prove non-trivial high-dimensional inequalities in several seconds. We developed the verification tool as a part of the Flyspeck project (a formal proof of the Kepler conjecture). The Flyspeck project includes about 1000 nonlinear inequalities. We successfully tested our method on more than 100 Flyspeck inequalities and estimated that the formal verification procedure is about 3000 times slower than an informal verification method implemented in C++. We also describe future work and prospective optimizations for our method.Comment: 15 page

High-Throughput Cultivation for the Selective Isolation of Acidobacteria From Termite Nests

Microbial communities in the immediate environment of socialized invertebrates can help to suppress pathogens, in part by synthesizing bioactive natural products. Here we characterized the core microbiomes of three termite species (genus Coptotermes) and their nest material to gain more insight into the diversity of termite-associated bacteria. Sampling a healthy termite colony over time implicated a consolidated and highly stable microbiome, pointing toward the fact that beneficial bacterial phyla play a major role in termite fitness. In contrast, there was a significant shift in the composition of the core microbiome in one nest during a fungal infection, affecting the abundance of well-characterized Streptomyces species (phylum Actinobacteria) as well as less-studied bacterial phyla such as Acidobacteria. High-throughput cultivation in microplates was implemented to isolate and identify these less-studied bacterial phylogenetic group. Amplicon sequencing confirmed that our method maintained the bacterial diversity of the environmental samples, enabling the isolation of novel Acidobacteriaceae and expanding the list of cultivated species to include two strains that may define new species within the genera Terracidiphilus and Acidobacterium

Mechanisms controlling anaemia in Trypanosoma congolense infected mice.

Trypanosoma congolense are extracellular protozoan parasites of the blood stream of artiodactyls and are one of the main constraints on cattle production in Africa. In cattle, anaemia is the key feature of disease and persists after parasitaemia has declined to low or undetectable levels, but treatment to clear the parasites usually resolves the anaemia. The progress of anaemia after Trypanosoma congolense infection was followed in three mouse strains. Anaemia developed rapidly in all three strains until the peak of the first wave of parasitaemia. This was followed by a second phase, characterized by slower progress to severe anaemia in C57BL/6, by slow recovery in surviving A/J and a rapid recovery in BALB/c. There was no association between parasitaemia and severity of anaemia. Furthermore, functional T lymphocytes are not required for the induction of anaemia, since suppression of T cell activity with Cyclosporin A had neither an effect on the course of infection nor on anaemia. Expression of genes involved in erythropoiesis and iron metabolism was followed in spleen, liver and kidney tissues in the three strains of mice using microarrays. There was no evidence for a response to erythropoietin, consistent with anaemia of chronic disease, which is erythropoietin insensitive. However, the expression of transcription factors and genes involved in erythropoiesis and haemolysis did correlate with the expression of the inflammatory cytokines Il6 and Ifng. The innate immune response appears to be the major contributor to the inflammation associated with anaemia since suppression of T cells with CsA had no observable effect. Several transcription factors regulating haematopoiesis, Tal1, Gata1, Zfpm1 and Klf1 were expressed at consistently lower levels in C57BL/6 mice suggesting that these mice have a lower haematopoietic capacity and therefore less ability to recover from haemolysis induced anaemia after infection

Rigorous Polynomial Approximation using Taylor Models in Coq

International audienceOne of the most common and practical ways of representing a real function on machines is by using a polynomial approximation. It is then important to properly handle the error introduced by such an approximation. The purpose of this work is to offer guaranteed error bounds for a specific kind of rigorous polynomial approximation called Taylor model. We carry out this work in the Coq proof assistant, with a special focus on genericity and efficiency for our implementation. We give an abstract interface for rigorous polynomial approximations, parameter- ized by the type of coefficients and the implementation of polynomials, and we instantiate this interface to the case of Taylor models with inter- val coefficients, while providing all the machinery for computing them. We compare the performances of our implementation in Coq with those of the Sollya tool, which contains an implementation of Taylor models written in C. This is a milestone in our long-term goal of providing fully formally proved and efficient Taylor models

A formal proof of the Kepler conjecture

This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project

Adapting wine grape production to climate change through canopy architecture manipulation and irrigation in warm climates

Grape growing regions are facing constant warming of the growing season temperature as well as limitations on ground water pumping used for irrigating to overcome water deficits. Trellis systems are utilized to optimize grapevine production, physiology, and berry chemistry. This study aimed to compare 6 trellis systems with 3 levels of applied water amounts based on different replacements of crop evapotranspiration (ETc) in two consecutive seasons. The treatments included a vertical shoot position (VSP), two modified VSPs (VSP60 and VSP80), a single high wire (SH), a high quadrilateral (HQ), and a Guyot pruned VSP (GY) combined with 25%, 50%, and 100% ETc water replacement. The SH had greater yields, whereas HQ was slower to reach full production potential. At harvest in both years, the accumulation of anthocyanin derivatives was enhanced in SH, whereas VSPs decreased them. As crown porosity increased (mostly VSPs), berry flavonol concentration and likewise molar % of quercetin in berries increased. Conversely, as leaf area increased, total flavonol concentration and molar % of quercetin decreased, indicating a preferential arrangement of leaf area along the canopy for overexposure of grape berry with VSP types. The irrigation treatments revealed linear trends for components of yield, where greater applied water resulted in larger berry size and likewise greater yield. 25% ETc was able to increase berry anthocyanin and flavonol concentrations. Overall, this study evidenced the efficiency of trellis systems for optimizing production and berry composition in Californian climate, also, the feasibility of using flavonols as the indicator of canopy architecture

A High Throughput Screen Identifies Chemical Modulators of the Laminin-Induced Clustering of Dystroglycan and Aquaporin-4 in Primary Astrocytes

Background: Aquaporin-4 (AQP4) constitutes the principal water channel in the brain and is clusteredat the perivascular astrocyte endfeet. This specific distribution of AQP4 plays a major role in maintaining water homeostasis in the brain. A growing body of evidence points to a role ofthe dystroglycan complex and its interaction with perivascular laminin in the clusteringof AQP4 atperivascular astrocyte endfeet. Indeed, mice lacking components of this complex or in which laminindystroglycan interaction is disrupted show a delayed onset of brain edema due to a redistribution of AQP4 away from astrocyte endfeet. It is therefore important to identify inhibitory drugs of laminin-dependent AQP4 clustering which may prevent or reduce brain edema. Methodolgy/Principal Findings: In the present study we used primary rat astrocyte cultures toscreen a library of.3,500 chemicals and identified 6 drugs that inhibit the laminin-induced clustering of dystroglycan and AQP4. Detailed analysis of the inhibitory drug, chloranil, revealed that its inhibition of the clustering is due to the metalloproteinase-2-mediated ß-dystroglycan shedding and subsequent loss of laminin interaction with dystroglycan. Furthermore, chemical variants of chloranil induced a similar effect on ß-dystroglycan and this was prevented by the antioxidant N-acetylcysteine. Conclusion/Significance: These findings reveal the mechanism of action of chloranil in preventing the laminin-induced clustering of dystroglycan and AQP4 and validate the use of high-throughput screening as a tool to identify drugs tha