MATHEMATICAL CURIOSITIES ABOUT DIVISION OF INTEGERS

As mathematics educators, our focus of attention is mainly placed on the learning and teaching of mathematics. But, as we study phenomena of mathematical learning and teaching, we often come across intriguing mathematical phenomena that capture our interest. We find ourselves often bouncing mathematical ideas back and forth, not just looking for (new/better) ways of teaching or presenting a mathematical concept, but also of uncovering and discovering potential understandings of the concept. These mathematical issues we encounter represent for us a significant aspect of our work, and are also very stimulating. One of these issues arose for us as we were tackling issues of division of numbers and of conventions relating to the remainder; issues that are, mathematically speaking, as we hope to communicate, very interesting and thought provoking. Thus, we explore four different avenues/curiosities about division, where operations with positive and negative numbers are considered, as well as the meaning one can draw out of these operations

Development of genetic models to breed for mixed cropping systems

Introduction Mixed cropping, i.e. mixing different crops in the same field, provides agronomic advantages as increased productivity under low inputs conditions (e.g. for organic farming: Bedoussac et al. 2015) and higher yield stability (Raseduzzaman and Jensen 2017). In mixed cropping, choosing the right cultivars is critical for the performance of the mixture, as shown for pea-barley mixtures (Hauggaard-Nielsen and Jensen 2001) and maize-bean mixtures (Hoppe 2016). As performance in pure stand can strongly diverge from performance in mixture, estimating the ability of a cultivar to be mixed with another crop is therefore of utmost importance. For this purpose, concepts of General and Specific Combining Ability in hybrid breeding (Griffing 1956) have been adapted to cultivar and crop mixtures. Thus, these effects are called General Mixing Ability (GMA) and Specific Mixing Ability (SMA) (Federer 1993). In contrast to intraspecific mixtures, interspecific mixed cropping experiments often provide additional information, since harvested lots can be separated into their different grain fractions. Until now, statistical developments mobilizing the additional information provided by separated harvest lots to estimate mixing abilities in intercropping experiments have been neglected. The concept of Producer- and Associate-effects (abbreviated Pr and As, respectively) describes interactions between varieties sown in alternate row trials (Forst 2018). The producer effect Pr is the average performance of a cultivar grown in mixture with other crop-species, whereas the associate effect As is the average effect of a cultivar on the performance of the mixing partner. We used the fraction yields of a spring-pea (Pisum sativum L.) and spring-barley (Hordeum vulgare L.) mixed cropping experiment to determine Pr and As effects of different pea genotypes. The additional information provided by this approach is biologically more informative than GMA/SMA estimates, since it better reflects competition and facilitation occurring between different cultivars of the two crop-species

Is transcriptomic regulation of berry development more important at night than during the day?

Diurnal changes in gene expression occur in all living organisms and have been studied on model plants such as Arabidopsis thaliana. To our knowledge the impact of the nycthemeral cycle on the genetic program of fleshly fruit development has been hitherto overlooked. In order to circumvent environmental changes throughout fruit development, young and ripening berries were sampled simultaneously on continuously flowering microvines acclimated to controlled circadian light and temperature changes. Gene expression profiles along fruit development were monitored during both day and night with whole genome microarrays (Nimblegen® vitis 12x), yielding a total number of 9273 developmentally modulated probesets. All day-detected transcripts were modulated at night, whereas 1843 genes were night-specific. Very similar developmental patterns of gene expression were observed using independent hierarchical clustering of day and night data, whereas functional categories of allocated transcripts varied according to time of day. Many transcripts within pathways, known to be up-regulated during ripening, in particular those linked to secondary metabolism exhibited a clearer developmental regulation at night than during the day. Functional enrichment analysis also indicated that diurnally modulated genes considerably varied during fruit development, with a shift from cellular organization and photosynthesis in green berries to secondary metabolism and stress-related genes in ripening berries. These results reveal critical changes in gene expression during night development that differ from daytime development, which have not been observed in other transcriptomic studies on fruit development thus far. © 2014 Rienth et al.This work is part of the DURAVITIS program which is financially supported by the ANR (Agence national de la recherche) -Genopole (project ANR-2010-GENM-004-01) and the Jean Poupelain foundation (30 Rue Gâte Chien, 16100 Javrezac, France).Peer Reviewe

New breeding strategies for mixed cropping in a barley (H. vulgare L.) pea (P. sativum L.) model system

Crop mixtures consisting of cereals and legumes have proven as a well-adapted arrangement due to their complementarity towards important resources, especially nitrogen. Crop mixtures combine high yield performance and yield stability. They can contribute to a diversified cropping landscape and adaptation to climate change. The search for alternatives to protein imports from overseas and investments in post-harvest separation technologies are currently fostering their adoption by farmers in Western-Europe, especially under organic and lowinput farming conditions. However, screening and breeding for mixed cropping has hardly been explored for arable crops. Thus, the objective was to develop novel breeding strategies and tools specifically for mixed cropping systems. We tested mixtures and pure stands of a morphologically diverse panel of 32 spring pea (Pisum sativum L.) and eight spring barley (Hordeum vulgare L.) cultivars in replicated field trials at two locations in Switzerland over two years with pea as the focal species. In an incomplete factorial design (Fig. 1) we determined general and specific mixing ability (GMA and SMA, respectively) of pea and barley in analogy to GCA and SCA (general and specific combining ability) in hybrid breeding. Key traits, such as early vigour, canopy height and leaf morphology parameters were measured, due to their potential use as covariates or indirect selection criteria for mixing ability. Our results show that total yield of mixtures can only partly be explained by pea pure stand yields (R² = 0.35), making the latter a weak predictor for mixture yield. Pea GMA variance was predominant over SMA variance which underlines the potential for breeding for mixing ability using a tester. Key traits, such as pea stipule area were correlated (R² = 0.56) with total mixture yield and merit further investigation as indirect selection criteria. The separated yield fractions of pea and barley in mixtures allow to decompose GMA of pea into the producer effect of pea cultivar on pea fraction yield and the associate effect of pea on barley fraction yield. This novel concept allows to elucidate key trait effects on fraction yields of pea and barley which might otherwise be masked when solely using a GMA approach

Fatigue life and initiation mechanisms in wrought Inconel 718 DA for different microstructures

International audienceWrought Inconel 718 DA superalloy disk zones present a wide range of behavior in fatigue life due to the variability of the microstructure. In order to link the effect of the forging conditions and achieved microstructure to the fatigue life, two microstructures have been tested in fatigue. Fatigue tests under strain control were performed at 450°C. Grain size distributions and phase distributions were characterized in the specimens and related to fatigue failure initiation modes. Fatigue crack initiation was seen to occur on large grains in stage I for the larger grain material whereas for the material with slightly smaller grains initiation from internal nitrides caused failure via so-called fish-eye cracks. The different steps of these failure modes are discussed using data from the literature to gather the ingredients for a quantitative assessment of the fatigue lifetime using fracture mechanics

Maximizing energy deposition by shaping few-cycle laser pulses

We experimentally investigate the impact of pulse shape on the dynamics of laser-generated plasma in rare gases. Fast-rising triangular pulses with a slower decay lead to early ionization of the gas and depose energy more efficiently than their temporally reversed counterparts. As a result, in both argon and krypton, the induced shockwave as well as the plasma luminescence are stronger. This is due to an earlier availability of free electrons to undergo inverse Bremsstrahlung on the pulse trailing edge. Our results illustrate the ability of adequately tailored pulse shapes to optimize the energy deposition in gas plasmas

Die Erbsensorte entscheidet über den Erfolg der Mischung

Sommer-Eiweisserbsen und zweizeilige Gerste sind gute Mischungspartner. Doch gewisse Sortenkombinationen sind besser als andere. Das hat das FiBL in einem zweijährigen Versuch gezeigt

Laser vaporization of cirrus-like ice particles with secondary ice multiplication

We investigate the interaction of ultrashort laser filaments with individual 90-μm ice particles, representative of cirrus particles. The ice particles fragment under laser illumination. By monitoring the evolution of the corresponding ice/vapor system at up to 140,000 frames per second over 30 ms, we conclude that a shockwave vaporization supersaturates the neighboring region relative to ice, allowing the nucleation and growth of new ice particles, supported by laser-induced plasma photochemistry. This process constitutes the first direct observation of filament-induced secondary ice multiplication, a process that strongly modifies the particle size distribution and, thus, the albedo of typical cirrus clouds

Centronuclear myopathy in labrador retrievers: a recent founder mutation in the PTPLA gene has rapidly disseminated worldwide

Centronuclear myopathies (CNM) are inherited congenital disorders characterized by an excessive number of internalized nuclei. In humans, CNM results from ~70 mutations in three major genes from the myotubularin, dynamin and amphiphysin families. Analysis of animal models with altered expression of these genes revealed common defects in all forms of CNM, paving the way for unified pathogenic and therapeutic mechanisms. Despite these efforts, some CNM cases remain genetically unresolved. We previously identified an autosomal recessive form of CNM in French Labrador retrievers from an experimental pedigree, and showed that a loss-of-function mutation in the protein tyrosine phosphatase-like A (PTPLA) gene segregated with CNM. Around the world, client-owned Labrador retrievers with a similar clinical presentation and histopathological changes in muscle biopsies have been described. We hypothesized that these Labradors share the same PTPLA<sup>cnm</sup> mutation. Genotyping of an international panel of 7,426 Labradors led to the identification of PTPLA<sup>cnm</sup> carriers in 13 countries. Haplotype analysis demonstrated that the PTPLA<sup>cnm</sup> allele resulted from a single and recent mutational event that may have rapidly disseminated through the extensive use of popular sires. PTPLA-deficient Labradors will help define the integrated role of PTPLA in the existing CNM gene network. They will be valuable complementary large animal models to test innovative therapies in CNM