t1/3t^{1/3} Superdiffusivity of Finite-Range Asymmetric Exclusion Processes on Z\mathbb Z

We consider finite-range asymmetric exclusion processes on $\mathbb Z$ with non-zero drift. The diffusivity $D(t)$ is expected to be of ${\mathcal O}(t^{1/3})$. We prove that $D(t)\ge Ct^{1/3}$ in the weak (Tauberian) sense that $\int_0^\infty e^{-\lambda t}tD(t)dt \ge C\lambda^{-7/3}$ as $\lambda\to 0$. The proof employs the resolvent method to make a direct comparison with the totally asymmetric simple exclusion process, for which the result is a consequence of the scaling limit for the two-point function recently obtained by Ferrari and Spohn. In the nearest neighbor case, we show further that $tD(t)$ is monotone, and hence we can conclude that $D(t)\ge Ct^{1/3}(\log t)^{-7/3}$ in the usual sense.Comment: Version 3. Statement of Theorem 3 is correcte

New measurements of thousand-seed weights of species in the Pannonian flora

For understanding local and regional seed dispersal and plant establishment processes and for considering the ecotypes and other forms of specific variability, hard data of locally or regionally measured traits are necessary. We provided newly measured seed weight data of 193 taxa, out of which 24 taxa had not been represented in the SID, LEDA or BiolFlor databases. Our new measurements and formerly published data of locally collected seed weight records together covers over 70% of the Pannonian flora. However, there is still a considerable lack in seed weight data of taxonomically problematic genera, even though they are represented in the Pannonian flora with a relatively high number of species and/or subspecies (e.g. Sorbus, Rosa, Rubus, Crataegus and Hieracium). Our regional database contains very sporadic data on aquatic plants (including also numerous invasive species reported from Hungary and neighbouring countries) and some rare weeds distributed in the southwestern part of the country. These facts indicate the necessity of further seed collection and measurements

Germination capacity of 75 herbaceous species of the pannonian flora and implications for restoration

Seeds ensure the survival and dispersal of the majority of vascular plant species. Seeds require species-specific germination conditions and display very different germination capacities using different germination methods. Despite the importance of plant generative reproduction, little is known about the germination capacity of the seeds of the Pannonian flora, particularly under field conditions. Our aim was to reduce this knowledge gap by providing original data on the germination capacity of 75 herbaceous species. We reported the germination capacity of 8 species for the first time. We also highlighted the year-to-year differences in the germination capacity of 11 species which could be highly variable between years. The data regarding the germination capacity of target species, as well as weeds and invasive species, can be informative for nature conservation and restoration projects. Our findings support the composition of proper seed mixtures for ecological restoration and also highlight the importance of testing seed germination capacity before sowing

Asymptotics for products of characteristic polynomials in classical β\beta-Ensembles

We study the local properties of eigenvalues for the Hermite (Gaussian), Laguerre (Chiral) and Jacobi $\beta$-ensembles of $N\times N$ random matrices. More specifically, we calculate scaling limits of the expectation value of products of characteristic polynomials as $N\to\infty$. In the bulk of the spectrum of each $\beta$-ensemble, the same scaling limit is found to be $e^{p_{1}}{}_1F_{1}$ whose exact expansion in terms of Jack polynomials is well known. The scaling limit at the soft edge of the spectrum for the Hermite and Laguerre $\beta$-ensembles is shown to be a multivariate Airy function, which is defined as a generalized Kontsevich integral. As corollaries, when $\beta$ is even, scaling limits of the $k$-point correlation functions for the three ensembles are obtained. The asymptotics of the multivariate Airy function for large and small arguments is also given. All the asymptotic results rely on a generalization of Watson's lemma and the steepest descent method for integrals of Selberg type.Comment: [v3] 35 pages; this is a revised and enlarged version of the article with new references, simplified demonstations, and improved presentation. To be published in Constructive Approximation 37 (2013

GrassPlot v. 2.00 – first update on the database of multi-scale plant diversity in Palaearctic grasslands

Abstract: GrassPlot is a collaborative vegetation-plot database organised by the Eurasian Dry Grassland Group (EDGG) and listed in the Global Index of Vegetation-Plot Databases (GIVD ID EU-00-003). Following a previous Long Database Report (Dengler et al. 2018, Phyto- coenologia 48, 331–347), we provide here the first update on content and functionality of GrassPlot. The current version (GrassPlot v. 2.00) contains a total of 190,673 plots of different grain sizes across 28,171 independent plots, with 4,654 nested-plot series including at least four grain sizes. The database has improved its content as well as its functionality, including addition and harmonization of header data (land use, information on nestedness, structure and ecology) and preparation of species composition data. Currently, GrassPlot data are intensively used for broad-scale analyses of different aspects of alpha and beta diversity in grassland ecosystems

Supreme activity of gramicidin S against resistant, persistent and biofilm cells of staphylococci and enterococci.

Three promising antibacterial peptides were studied with regard to their ability to inhibit the growth and kill the cells of clinical strains of Staphylococcus aureus, Enterococcus faecalis and Enterococcus faecium. The multifunctional gramicidin S (GS) was the most potent, compared to the membranotropic temporin L (TL), being more effective than the innate-defence regulator IDR-1018 (IDR). These activities, compared across 16 strains as minimal bactericidal and minimal inhibitory concentrations (MIC), are independent of bacterial resistance pattern, phenotype variations and/or biofilm-forming potency. For S. aureus strains, complete killing is accomplished by all peptides at 5 × MIC. For E. faecalis strains, only GS exhibits a rapid bactericidal effect at 5 × MIC, while TL and IDR require higher concentrations. The biofilm-preventing activities of all peptides against the six strains with the largest biofilm biomass were compared. GS demonstrates the lowest minimal biofilm inhibiting concentrations, whereas TL and IDR are consistently less effective. In mature biofilms, only GS completely kills the cells of all studied strains. We compare the physicochemical properties, membranolytic activities, model pharmacokinetics and eukaryotic toxicities of the peptides and explain the bactericidal, antipersister and antibiofilm activities of GS by its elevated stability, pronounced cell-penetration ability and effective utilization of multiple modes of antibacterial action

A practical drug discovery project at the undergraduate level

A practical drug discovery project for third-year undergraduates is described. No previous knowledge of medicinal chemistry is assumed. Initial lecture-workshops cover the basic principles; then students are asked to improve the profile of a weakly potent, poorly soluble PI3K inhibitor (1). Compound array design, molecular modelling and screening data analysis are followed by laboratory work in which each student, as part of a team, attempts to synthesise at least two target compounds. The project benefits from significant industrial support, including lectures, student mentoring and consumables. The aim is to make the learning experience as close as possible to real-life industrial situations. Forty-eight target compounds have been prepared, the best of which (5b, 5j, 6b and 6ap) improved the potency and aqueous solubility of the lead compound (1) by 100-1000 fold and 10-fold, respectively

Species-area relationships in continuous vegetation : evidence from Palaearctic grasslands

Aim Species–area relationships (SARs) are fundamental scaling laws in ecology although their shape is still disputed. At larger areas, power laws best represent SARs. Yet, it remains unclear whether SARs follow other shapes at finer spatial grains in continuous vegetation. We asked which function describes SARs best at small grains and explored how sampling methodology or the environment influence SAR shape. Location Palaearctic grasslands and other non‐forested habitats. Taxa Vascular plants, bryophytes and lichens. Methods We used the GrassPlot database, containing standardized vegetation‐plot data from vascular plants, bryophytes and lichens spanning a wide range of grassland types throughout the Palaearctic and including 2,057 nested‐plot series with at least seven grain sizes ranging from 1 cm2 to 1,024 m2. Using nonlinear regression, we assessed the appropriateness of different SAR functions (power, power quadratic, power breakpoint, logarithmic, Michaelis–Menten). Based on AICc, we tested whether the ranking of functions differed among taxonomic groups, methodological settings, biomes or vegetation types. Results The power function was the most suitable function across the studied taxonomic groups. The superiority of this function increased from lichens to bryophytes to vascular plants to all three taxonomic groups together. The sampling method was highly influential as rooted presence sampling decreased the performance of the power function. By contrast, biome and vegetation type had practically no influence on the superiority of the power law. Main conclusions We conclude that SARs of sessile organisms at smaller spatial grains are best approximated by a power function. This coincides with several other comprehensive studies of SARs at different grain sizes and for different taxa, thus supporting the general appropriateness of the power function for modelling species diversity over a wide range of grain sizes. The poor performance of the Michaelis–Menten function demonstrates that richness within plant communities generally does not approach any saturation, thus calling into question the concept of minimal area.publishedVersio