Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in $(0,\pi)$. Two sequences of circle patterns are employed to approximate a given conformal map $g$ and its first derivative. For the domain of $g$ we use embedded circle patterns where all circles have the same radius decreasing to 0 and which have uniformly bounded intersection angles. The image circle patterns have the same combinatorics and intersection angles and are determined from boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$ or $\arg g'$). For quasicrystallic circle patterns the convergence result is strengthened to $C^\infty$-convergence on compact subsets.Comment: 36 pages, 7 figure

Snus and Snuff Use in Switzerland Among Young Men: Are There Beneficial Effects on Smoking?

There are few recent longitudinal studies on smokeless tobacco (SLT) products and smoking outside the United States or European Nordic countries. The present longitudinal study tests whether Swedish-type snus and nasal snuff use decreases smoking incidence and prevalence in a central European country. The sample consisted of 5198 Swiss men (around 20 years of age). Retention rate was 91.5% over 15 months. Regression models, adjusting for a variety of psychosocial, smoking-related, and other risk factors, assessed whether no, low (less than weekly), and high (weekly or more) use baseline groups showed changes or maintenance in snus and snuff use related to smoking initiation, cessation, and reduction. Among baseline nonsmokers, snus initiators (OR = 1.90, p = .003) and low baseline maintainers (OR = 4.51, p < .001) were more likely to start smoking (reference: persistent nonusers of snus). Among baseline smokers, initiators (OR = 2.79, p < .001) and low baseline maintainers (OR = 2.71, p = .005) more often continued smoking, whereas snus quitters less frequently continued smoking (OR = 0.57, p = .009). High baseline maintainers were non-significantly less likely to continue smoking (OR = 0.71, p = .315). Among continuing smokers, only snus quitters significantly reduced the number of cigarettes smoked per day (b = -1.61, p = .002) compared with persistent nonusers of snus. Results were similar for snuff. SLT use did not have any significant beneficial effects on young men in Switzerland but significantly increased the likelihood of smoking initiation and continuation, independent of whether the substance is legally sold (snuff) or not (snus). This does not exclude that there may be beneficial effects at older ages. Our research provides evidence that SLT use has no benefits for cigarette smoking initiation, cessation, or reduction among young men in a central European country, where SLT is not highly promoted or receives tax incentives. This is true for both legally sold nasal snuff and Swedish-type snus that cannot be legally sold. Results indicate that without incentives for using it, among young people shifts from smoking to SLT use are questionable and confirms the need for country-specific studies before the global public health community engages in promoting SLT

Mycorrhization of fagaceae forests within mediterranean ecosystems

Mediterranean Fagaceae forests are valuable due to their ecological and socioeconomic aspects. Some profitable plant species, such as Castanea (timber and chestnut), Quercus (timber and cork), and Fagus (timber), encounter in this habitat the excellent edaphoclimatic conditions to develop. All Fagaceae plants are commonly associated to ECM fungal species, which are found in these forests in quite stable communities, mainly enriched in Russulaceae and Telephoraceae species. Currently, the Mediterranean Basin is considered as one of the global biodiversity hotspots, since many of their endemic plant species are not found elsewhere and are now under threat. Due to climate changing and introduction of disease agents, Fagaceae forests are facing an adaptation challenge to both biotic and abiotic threats. Although ECM communities are highly disturbed by climate factors and tree disease incidence, they could play an important role in increasing water availability to the plant and also improving plant tree defense against pathogens. Recent advances, namely, on genomics and transcriptomics, are providing tools for increasing the understanding of Fagaceae mycorrhization process and stress responses to biotic and abiotic stresses. Such studies can provide new information for the implementation of the most adequate management policies for protecting threaten Mediterranean forests.info:eu-repo/semantics/publishedVersio

Triacylglyceride Metabolism by Fusarium graminearum During Colonization and Sexual Development on Wheat

Fusarium graminearum, a devastating pathogen of small grains, overwinters on crop residues and produces ephemeral perithecia. Accumulation of lipids in overwintering hyphae would provide reserves for overwinter survival and perithecium development. Fatty acid composition of cultures during perithecium development indicated a drop in neutral lipid levels during development but little change in fatty acid composition across stages. Microscopic examination of cultures early in sexual development revealed hyphal cells engorged with lipid bodies. In comparison, vegetative hyphae contained few lipid bodies. Microarray analysis was performed on wheat stems at stages of colonization through perithecium development. Gene expression analysis during stages of perithecium development both in planta and in vitro (previously published) supports the view that lipid biosynthesis occurs during early stages of wheat colonization leading to sexual development and that lipid oxidation occurs as perithecia are developing. Analysis of gene expression during the stages of wheat stem colonization also revealed sets of genes unique to these stages. These results support the view that lipids accumulate in hyphae colonizing wheat stalks and are subsequently used in perithecium formation on stalk tissue. These results indicate that extensive colonization of plant tissue prior to harvest is essential for subsequent sporulation on crop residues and, thus, has important implications for inoculum reduction