Zero-one survival behavior of cyclically competing species

Coexistence of competing species is, due to unavoidable fluctuations, always transient. In this Letter, we investigate the ultimate survival probabilities characterizing different species in cyclic competition. We show that they often obey a surprisingly simple, though non-trivial behavior. Within a model where coexistence is neutrally stable, we demonstrate a robust zero-one law: When the interactions between the three species are (generically) asymmetric, the `weakest' species survives at a probability that tends to one for large population sizes, while the other two are guaranteed to extinct. We rationalize our findings from stochastic simulations by an analytic approach.Comment: 4 pages, 3 figure

Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices

We study the fluctuations of eigenvalues from a class of Wigner random matrices that generalize the Gaussian orthogonal ensemble. We begin by considering an $n \times n$ matrix from the Gaussian orthogonal ensemble (GOE) or Gaussian symplectic ensemble (GSE) and let $x_k$ denote eigenvalue number $k$. Under the condition that both $k$ and $n-k$ tend to infinity with $n$, we show that $x_k$ is normally distributed in the limit. We also consider the joint limit distribution of $m$ eigenvalues from the GOE or GSE with similar conditions on the indices. The result is an $m$-dimensional normal distribution. Using a recent universality result by Tao and Vu, we extend our results to a class of Wigner real symmetric matrices with non-Gaussian entries that have an exponentially decaying distribution and whose first four moments match the Gaussian moments.Comment: 21 pages, to appear, J. Stat. Phys. References and other corrections suggested by the referees have been incorporate

Cut Points and Diffusions in Random Environment

In this article we investigate the asymptotic behavior of a new class of multi-dimensional diffusions in random environment. We introduce cut times in the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], in the discrete setting providing a decoupling effect in the process. This allows us to take advantage of an ergodic structure to derive a strong law of large numbers with possibly vanishing limiting velocity and a central limit theorem under the quenched measure.Comment: 44 pages; accepted for publication in "Journal of Theoretical Probability

A preferential attachment model with random initial degrees

In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$ edges attached to it, is added to the graph. The new edges added at time t are then preferentially connected to older vertices, i.e., conditionally on $G(t-1)$, the probability that a given edge is connected to vertex i is proportional to $d_i(t-1)+\delta$, where $d_i(t-1)$ is the degree of vertex $i$ at time $t-1$, independently of the other edges. The main result is that the asymptotical degree sequence for this process is a power law with exponent $\tau=\min\{\tau_{W}, \tau_{P}\}$, where $\tau_{W}$ is the power-law exponent of the initial degrees $(W_t)_{t\geq 1}$ and $\tau_{P}$ the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze, which is surveyed.Comment: In the published form of the paper, the proof of Proposition 2.1 is incomplete. This version contains the complete proo

Versuchsbeschrieb und Qualität des frischen Wiesenfutters : Serie Systemvergleich Hohenrain II

Im Systemvergleich Hohenrain II wurden drei Fütterungssysteme auf Basis von frischem Wiesenfutter miteinander verglichen. Dazu wurden von 2014-2016 die zwei Systeme Teilweide mit Eingrasen und reduzierter (EGKF) beziehungsweise erhöhter Kraftfuttergabe (EGKFplus) mit der Vollweide (VW) als Referenzsystem verglichen. Auf dem Gutsbetrieb des BBZN Hohenrain in Luzern wurden drei Herden in je einem Fütterungssystem gehalten. Allen Herden stand dieselbe Futterfläche zur Verfügung. Auch 36 Pilotbetriebe aus dem Schweizer Mittelland beteiligten sich am Projekt und unterstützten über die Teilnahme an Arbeitskreisen die Praxisverknüpfung und den Wissenstransfer. Die höchsten Energiegehalte im Eingrasfutter wurden im Frühjahr erreicht. Diese sind mit den bekannten Tabellenwerten vergleichbar. Gegenüber den Kurzrasenweiden lagen die Gehalte bedeutend tiefer und waren insbesondere über die Sommermonate starken Schwankungen unterworfen. Dies wird auf das Nutzungsstadium und die sommerlichen Witterungseinflüsse zurückgeführt, welche die Verdaulichkeit des Wiesenfutters wesentlich beeinflussen. Analog zur Weide sollten deshalb Entscheidungshilfen entwickelt werden, welche die Praxis bei der Nutzung der Eingrasbestände im optimalen Stadium unterstützen.In Svizzera molte aziende produttrici di latte fanno uso di sostanziali percentuali di foraggio verde nella razione alimentare. Obiettivo di questo progetto è stata la comparazione tra tre sistemi che si basano sull’alimentazione del bestiame con man-gime verde fresco. A tale scopo, tra il 2014 e il 2016, i due sistemi a pascolo parziale con afforaggiamento di erba fresca e apporto di concentrati ridotto (EGKF) o maggiorato (EGKFplus) sono stati messi a confronto, assumendo il pascolo integrale (VW) come sistema di riferimento. Il presente articolo informa sul dispositivo dell’esperimento e sui primi risultati riguardanti il contenuto di energia del foraggio verde fresco. Nell’a-zienda agricola del centro di formazione professionale BBZN di Hohenrain (LU) il bestiame da latte (70 capi) è stato suddiviso in tre mandrie e inserito nei rispettivi sistemi di foraggiamento. Ad ogni mandria è stata messa a disposizione la stessa superficie di terreno per il pascolo o le colture foraggere (12 ha), mentre la media del numero di mucche e la quantità di mangime concen-trato impiegato erano differenziate in base ai diversi sistemi. Anche 36 aziende agricole dell’altopiano svizzero hanno preso parte al progetto, sostenendo la messa in pratica e il trasferimento del sapere tramite la parteci-pazione a gruppi di lavoro. I tenori più alti di energia netta di lattazione (NEL) nel forag-gio verde (MJ/kg SS) sono stati raggiunti in primavera, ed erano paragonabili ai valori delle tabelle di riferimento. I tenori sono risultati essere significativamente inferiori rispetto a quelli del pascolo ad erba corta e sono stati soggetti a forti oscillazioni soprat-tutto nei mesi estivi. Ciò è da ricondurre all’irregolare stadio di maturazione dell’erba al momento della raccolta e alle condizioni metereologiche, che influenzano di molto la digeribilità del foraggio verde. Supporti decisionali alla pratica dell’afforaggiamento di erba fresca potrebbero contribuire a migliorare la situazione.Partial grazing with indoor feeding of fresh grass is an important feeding system for Swiss dairy farms. From 2014 to 2016, three production systems – ‘partial grazing with indoor feeding of fresh grass with reduced (EGKF, 418 kg) and increased concentrate supplementation (EGKFplus; 1161 kg) was compared with full-time grazing (FG) with reduced concentrate supplementation on 36 pilot farms in Switzerland. This article describes the set-up and initial results regarding the energy content of the fresh grass. The seventy-head dairy herd on the BBZN Hohenrain school farm in Lucerne was divided into three sub-herds, each of which was kept in one of the three feeding systems. While all three herds had the same amount of land at their disposal as pasture or foddergrowing land (12 ha), the average number of cows and the quantity of concentrate used differed according to the system. Thirty-six pilot farms in the Swiss Plateau were also involved in the project and gave support by participating in study groups focussing on linking practice and transferring knowledge. The highest NEL contents in grass fodder (MJ/kg DM) were measured in spring. These were comparable with reference values. However, compared to continuous grazing, the contents were significantly lower and, particularly during summer, were subject to strong fluctuations. This is a result of the irregular utilisation stage and the influence of summer weather conditions, both of which significantly impact the digestibility of grass fodder. Decision-making aids to support practitioners with forage harvesting could lead to improvements here

Structural diversity of biologically interesting datasets: a scaffold analysis approach

ABSTRACT:The recent public availability of the human metabolome and natural product datasets has revitalized "metabolite-likeness" and "natural product-likeness" as a drug design concept to design lead libraries targeting specific pathways. Many reports have analyzed the physicochemical property space of biologically important datasets, with only a few comprehensively characterizing the scaffold diversity in public datasets of biological interest. With large collections of high quality public data currently available, we carried out a comparative analysis of current day leads with other biologically relevant datasets.In this study, we note a two-fold enrichment of metabolite scaffolds in drug dataset (42%) as compared to currently used lead libraries (23%). We also note that only a small percentage (5%) of natural product scaffolds space is shared by the lead dataset. We have identified specific scaffolds that are present in metabolites and natural products, with close counterparts in the drugs, but are missing in the lead dataset. To determine the distribution of compounds in physicochemical property space we analyzed the molecular polar surface area, the molecular solubility, the number of rings and the number of rotatable bonds in addition to four well-known Lipinski properties. Here, we note that, with only few exceptions, most of the drugs follow Lipinski's rule. The average values of the molecular polar surface area and the molecular solubility in metabolites is the highest while the number of rings is the lowest. In addition, we note that natural products contain the maximum number of rings and the rotatable bonds than any other dataset under consideration.Currently used lead libraries make little use of the metabolites and natural products scaffold space. We believe that metabolites and natural products are recognized by at least one protein in the biosphere therefore, sampling the fragment and scaffold space of these compounds, along with the knowledge of distribution in physicochemical property space, can result in better lead libraries. Hence, we recommend the greater use of metabolites and natural products while designing lead libraries. Nevertheless, metabolites have a limited distribution in chemical space that limits the usage of metabolites in library design.14 page(s