Renormalized energy concentration in random matrices

We define a "renormalized energy" as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line. The definition is inspired by ideas of [SS1,SS3]. Roughly speaking, it is obtained by subtracting two leading terms from the Coulomb potential on a growing number of charges. The functional is expected to be a good measure of disorder of a configuration of points. We give certain formulas for its expectation for general stationary random point processes. For the random matrix $\beta$-sine processes on the real line (beta=1,2,4), and Ginibre point process and zeros of Gaussian analytic functions process in the plane, we compute the expectation explicitly. Moreover, we prove that for these processes the variance of the renormalized energy vanishes, which shows concentration near the expected value. We also prove that the beta=2 sine process minimizes the renormalized energy in the class of determinantal point processes with translation invariant correlation kernels.Comment: last version, to appear in Communications in Mathematical Physic

The scaling limit of the critical one-dimensional random Schrodinger operator

We consider two models of one-dimensional discrete random Schrodinger operators (H_n \psi)_l ={\psi}_{l-1}+{\psi}_{l +1}+v_l {\psi}_l, {\psi}_0={\psi}_{n+1}=0 in the cases v_k=\sigma {\omega}_k/\sqrt{n} and v_k=\sigma {\omega}_k/ \sqrt{k}. Here {\omega}_k are independent random variables with mean 0 and variance 1. We show that the eigenvectors are delocalized and the transfer matrix evolution has a scaling limit given by a stochastic differential equation. In both cases, eigenvalues near a fixed bulk energy E have a point process limit. We give bounds on the eigenvalue repulsion, large gap probability, identify the limiting intensity and provide a central limit theorem. In the second model, the limiting processes are the same as the point processes obtained as the bulk scaling limits of the beta-ensembles of random matrix theory. In the first model, the eigenvalue repulsion is much stronger.Comment: 36 pages, 2 figure

Vergleich von artenreichen Begrünungsmischungen in ungarischen Weingebieten

Intensive mechanical soil cultivation and herbicide treatment was often the preferred technology in vineyards in the second half of the 20th century. In the last decades we increasingly experienced the disadvantages of these technologies: soil degradation, erosion and deflation damages. The use of well-adapted cover-crop mixtures could be an alternative. In 2012 we started to study three different species-rich cover crop mixtures (Biocont-Ecovin, Legume mixture, Grass-herb mixture) in Hungarian vineyards. For 2013 we detected lower weed coverage in the inter-rows sown with the Grass-herb and Legume mixtures, while in control and Biocont-Ecovin inter-rows we detected increasing weed coverage. In the third year (2014) we found in case of every plot that the grass-herb mixture-covered inter-rows were the least weedy. The most successful species in the inter-rows are: Coronilla varia, Lotus corniculatus, Medicago lupulina, Onobrychis viciifolia, Plantago lanceolata, Trifolium repens, Trifolium pratense

Evaluation of Frac-and-Pack Completions in the Eugene Island

Abstract This paper presents a systematic evaluation of frac&pack completions conducted in the Eugene Island region of the Gulf of Mexico. Reservoir, treatment and production data are analyzed from a unified viewpoint. First a completion design strategy is described which is centered around the dual goals of optimal stimulation and sufficient sand control. Then a method is presented to evaluate the technical success of the completion using 3-D reservoir/fracture simulators and the recently developed Slopes Analysis method. Finally, a simple but practical frac&pack treatment design and optimization procedure is presented for improving the performance of frac&pack completions. An example of frac&pack treatment design using the new design philosophy is provided in details showing how to achieve the stimulation goals in a theoretically optimum manner and why often the actual treatment has to depart from the theoretical optimum

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

Acceptance of near-natural greenspace management relates to ecological and socio-cultural assigned values among European urbanites

Grasslands are widespread elements of urban greenspace providing recreational, psychological and aesthetic benefits to city residents. Two urban grassland types of contrasting management dominate urban greenspaces: frequently mown, species-poor short-cut lawns and less intensively managed, near-natural tall-grass meadows. The higher conservation value of tall-grass meadows makes management interventions such as converting short-cut lawns into tall-grass meadows a promising tool for urban biodiversity conservation. The societal success of such interventions, however, depends on identifying the values urban residents assign to different types of urban grasslands, and how these values translate to attitudes towards greenspace management. Using 2027 questionnaires across 19 European cities, we identify the assigned values that correlate with people's personal greenspace use and their preferences for different types of urban grasslands to determine how these values relate to the agreement with a scenario of converting 50 of their cities� short-cut lawns into tall-grass meadows. We found that most people assigned nature-related values, such as wildness, to tall-grass meadows and utility-related values, such as recreation, to short-cut lawns. Positive value associations of wildness and species richness with tall-grass meadows, and social and nature-related greenspace activities, positively correlated with agreeing to convert short-cut lawns into tall-grass meadows. Conversely, disapproval of lawn conversion correlated with positive value associations of cleanliness and recreation potential with short-cut lawns. Here, people using greenspaces for nature-related activities were outstandingly positive about lawn conversion. The results show that the plurality of values assigned to different types of urban grasslands should be considered in urban greenspace planning. For example, tall-grass meadows could be managed to also accommodate the values associated with short-cut lawns, such as tidiness and recreation potential, to support their societal acceptance

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

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

Three years of vegetation development worth 30 years of secondary succession in urban-industrial grassland restoration

Questions: The restoration of unused urban-industrial areas has largely been neglected despite their great potential for nature conservation purposes. We applied three plant introduction treatments at a highly degraded industrial area to test whether plant material introduced onto industrial areas initiates plant assemblages similar in composition to those of reference grasslands. We specifically asked (a) Does restoration differ between primary and secondary reference sites in terms of overall species richness and cover three years after the introduction of plant material? (b) What is the sociability of species of the vegetation resulting from different treatments? Location: Restoration and reference grassland sites with acidic sandy soil in the temperate region of the EU, NE Hungary, Nyírség. Methods: As restoration techniques, we (a) directly seeded a single dominant species, (b) applied a commercial seed mixture, and (c) transferred hay. We compared species composition, cover, species richness and sociability of species in restoration treatments to reference grasslands. Inventories of vascular plant species were made at five randomly placed 2 m × 2 m sampling units per plot. Results: The species composition of seeded restoration plots (with a single dominant species and a commercial seed mixture) became similar to that of reference grasslands. Both types of seeding resulted in a similar cover, whereas seeding a commercial seed mixture and hay transfer resulted in a species richness similar to that of reference grasslands. The cover of the natural constituents (NC) of seeded plots also reached that of reference grasslands, while hay addition resulted in a lower cover and a higher number of NC than other methods. Conclusions: The introduction of propagules in degraded industrial areas can provide communities similar, after three years, to those of secondary reference grasslands that are 30 years of age. We conclude that investing in the restoration of native grasslands at unused urban-industrial sites can be a great opportunity to enhance biodiversity