Computing Monodromy via Continuation Methods on Random Riemann Surfaces

International audienceWe consider a Riemann surface $X$ defined by a polynomial $f(x,y)$ of degree $d$, whose coefficients are chosen randomly. Hence, we can suppose that $X$ is smooth, that the discriminant $\delta(x)$ of $f$ has $d(d-1)$ simple roots, $\Delta$, and that $\delta(0) \neq 0$ i.e. the corresponding fiber has $d$ distinct points $\{y_1, \ldots, y_d\}$. When we lift a loop 0 \in \gamma \subset \Ci - \Delta by a continuation method, we get $d$ paths in $X$ connecting $\{y_1, \ldots, y_d\}$, hence defining a permutation of that set. This is called monodromy. Here we present experimentations in Maple to get statistics on the distribution of transpositions corresponding to loops around each point of $\Delta$. Multiplying families of ''neighbor'' transpositions, we construct permutations and the subgroups of the symmetric group they generate. This allows us to establish and study experimentally two conjectures on the distribution of these transpositions and on transitivity of the generated subgroups. Assuming that these two conjectures are true, we develop tools allowing fast probabilistic algorithms for absolute multivariate polynomial factorization, under the hypothesis that the factors behave like random polynomials whose coefficients follow uniform distributions.On considere une surface de Riemann dont l'equation f(x,y)=0 est un polynome dont les coefficients sont des variables aleatoires Gaussiennes standards, ainsi que sa projection p sur l'axe des x. Puis on etudie et calcule des generateurs du groupe de monodromie correspondant a p

Mechanisms Underlying the Environmentally Induced Plasticity of Leaf Morphology

The primary function of leaves is to provide an interface between plants and their environment for gas exchange, light exposure and thermoregulation. Leaves have, therefore a central contribution to plant fitness by allowing an efficient absorption of sunlight energy through photosynthesis to ensure an optimal growth. Their final geometry will result from a balance between the need to maximize energy uptake while minimizing the damage caused by environmental stresses. This intimate relationship between leaf and its surroundings has led to an enormous diversification in leaf forms. Leaf shape varies between species, populations, individuals or even within identical genotypes when those are subjected to different environmental conditions. For instance, the extent of leaf margin dissection has, for long, been found to inversely correlate with the mean annual temperature, such that Paleobotanists have used models based on leaf shape to predict the paleoclimate from fossil flora. Leaf growth is not only dependent on temperature but is also regulated by many other environmental factors such as light quality and intensity or ambient humidity. This raises the question of how the different signals can be integrated at the molecular level and converted into clear developmental decisions. Several recent studies have started to shed the light on the molecular mechanisms that connect the environmental sensing with organ-growth and patterning. In this review, we discuss the current knowledge on the influence of different environmental signals on leaf size and shape, their integration as well as their importance for plant adaptation

Effects of parasite and historic driven selection on the diversity and structure of a MHC-II gene in a small mammal species (Peromyscus leucopus) undergoing range expansion.

Abstract Genetic diversity may decrease from the centre to the margin of a species distribution range due to neutral stochastic processes. Selection may also alter genetic diversity in non-neutral markers, such as genes associated with the immune system. Both neutral processes and selection on the immune system are thus expected to affect the spatial distribution of such markers, but the relative strength of each has been scarcely studied. Here, we compared the diversity of a neutral marker (mitochondrial cytochrome b)and a selected marker (DRB gene from the MHC-II), in eastern-North American populations of white-footed mice (Peromyscus leucopus), a species known for its role of main reservoir of the Lyme disease. We observed distinct phylogeographic patterns with these two markers, which may be the result of selection pressure acting upon the DRB gene. As predicted by the central marginal hypothesis, we observed a loss of neutral genetic diversity toward the margin of the species distribution. A decrease in diversity was also observed for the DRB gene, likely due to genetic drift and positive selection operated by helminth parasites. Such a loss in genetic diversity at the range margin may slow down the ongoing expansion of P. leucopus, by counterbalancing the effect of global warming on the mouse survival at higher latitude

Photon correlation spectroscopy on a single quantum dot embedded in a nanowire

We have observed strong photoluminescence from a single CdSe quantum dot embedded in a ZnSe nanowire. Exciton, biexciton and charged exciton lines have been identified unambiguously using photon correlation spectroscopy. This technique has provided a detailed picture of the dynamics of this new system. This type of semi conducting quantum dot turns out to be a very efficient single photon source in the visible. Its particular growth technique opens new possibilities as compared to the usual self-asssembled quantum dots

Assessing the connectivity of riparian forests across a gradient of human disturbance: the potential of Copernicus "Riparian Zones" in two hydroregions

The connectivity of riparian forests can be used as a proxy for the capacity of riparian zones to provide ecological functions, goods and services. In this study, we aim to test the potential of the freely available Copernicus “Riparian Zones” dataset to characterize the connectivity of riparian forests located in two European bioclimatic regions—the Mediterranean and the Central Baltic hydroregions—when subject to a gradient of human disturbance characterized by land-use/landcover and hydromorphological pressures. We extracted riparian patches using the Copernicus “Actual Riparian Zone” (ARZ) layer and calculated connectivity using the Integral Index of Connectivity (IIC). We then compared the results with a “Manual Riparian Zone” (MRZ) layer, produced by manually digitizing riparian vegetation patches over a very high-resolution World Imagery layer. Our research evidenced reduced forest connectivity in both hydroregions, with the exception of Least Disturbed sites in the Central Baltic hydroregion. The ARZ layer exhibited overall suitability to assess the connectivity of riparian forests in the Central Baltic hydroregion, while the Mediterranean hydroregion displayed a consistent pattern of connectivity overestimation in all levels of human disturbance. To address this, we recommend some improvements in the spatial resolution and thematic accuracy of the Copernicus ARZ layerinfo:eu-repo/semantics/publishedVersio

First report of Filaria martis Gmelin, 1790 in the European mink, Mustela lutreola (Linnaeus, 1761)

The riparian European mink (Mustela lutreola), currently surviving in only three unconnected sites in Europe, is now listed as a critically endangered species according to the IUCN. Habitat loss and degradation, anthropic mortality, interaction with the feral American mink (Neovison vison), and infectious diseases are among the principal causes of its decline. Surveys of helminth parasites of this host that also include focus on subcutaneous potentially pathogenic helminths such as those belonging to the genus Filaria are very scarce. We report here the presence of specimens of Filaria martis in the subcutaneous connective tissues of three M. lutreola individuals from Spain. This is the first finding of a subcutaneous nematode in a representative of the genus Mustela. The report also enlarges the known range of the definitive hosts of this nematode. These worms were mainly located in the dorsal region of mink and more rarely in the knees, elbows, and hips. Skin sloughing was only observed in one M. lutreola with both septicaemia and an associated high burden of F. martis. Therefore, more attention should be paid to potentially pathogenic helminths when designing conservation programs dedicated to M. lutreola

Dark exciton optical spectroscopy of a semiconducting quantum dot embedded in a nanowire

Photoluminescence of a single CdSe quantum dot embedded in a ZnSe nanowire has been investigated. It has been found that the dark exciton has a strong influence on the optical properties. The most visible influence is the strongly reduced excitonic emission compared to the biexcitonic one. Temperature dependent lifetime measurements have allowed us to measure a large splitting of $\Delta E = 6$ meV between the dark and the bright exciton as well as the spin flip rates between these two states

Comparison of two paradigms based on stimulation with images in a spelling brain-computer interface.

A BCI Speller is a typical Brain-Computer Interface (BCI) system for communication purposes. This technology can provide users with severe motor disability with an assistive device controlled by brain activity. The present preliminary study, with only four subjects, is focused on the control of a 5x5 P300-based speller matrix for communication purposes. In this work, we study the effect of flashing stimuli used to highlight the letters in two conditions: pictures and red famous faces (that is, famous faces coloured in red). These preliminary results, based on performance and the Information Transfer Rate (ITR), showed that both conditions are similar, obtaining very good performance compared to conventional P300-speller. In this sense, the use of pictures does not make the performance worse, allowing to develop more attractive and usable interfaces. More tests would confirm if there is a difference in performance between the two conditions proposed.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech