Cluster structures on quantum coordinate rings

We show that the quantum coordinate ring of the unipotent subgroup N(w) of a symmetric Kac-Moody group G associated with a Weyl group element w has the structure of a quantum cluster algebra. This quantum cluster structure arises naturally from a subcategory C_w of the module category of the corresponding preprojective algebra. An important ingredient of the proof is a system of quantum determinantal identities which can be viewed as a q-analogue of a T-system. In case G is a simple algebraic group of type A, D, E, we deduce from these results that the quantum coordinate ring of an open cell of a partial flag variety attached to G also has a cluster structure.Comment: v2: minor corrections. v3: references updated, final version to appear in Selecta Mathematic

Reconstruction of time-consistent species trees

Background The history of gene families—which are equivalent to event-labeled gene trees—can to some extent be reconstructed from empirically estimated evolutionary event-relations containing pairs of orthologous, paralogous or xenologous genes. The question then arises as whether inferred event-labeled gene trees are “biologically feasible” which is the case if one can find a species tree with which the gene tree can be reconciled in a time-consistent way. Results In this contribution, we consider event-labeled gene trees that contain speciations, duplications as well as horizontal gene transfer (HGT) and we assume that the species tree is unknown. Although many problems become NP-hard as soon as HGT and time-consistency are involved, we show, in contrast, that the problem of finding a time-consistent species tree for a given event-labeled gene can be solved in polynomial-time. We provide a cubic-time algorithm to decide whether a “time-consistent” species tree for a given event-labeled gene tree exists and, in the affirmative case, to construct the species tree within the same time-complexity

Stochastic population growth in spatially heterogeneous environments

Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study the following model for population abundances in $n$ patches: the conditional law of $X_{t+dt}$ given $X_t=x$ is such that when $dt$ is small the conditional mean of $X_{t+dt}^i-X_t^i$ is approximately $[x^i\mu_i+\sum_j(x^j D_{ji}-x^i D_{ij})]dt$, where $X_t^i$ and $\mu_i$ are the abundance and per capita growth rate in the $i$-th patch respectivly, and $D_{ij}$ is the dispersal rate from the $i$-th to the $j$-th patch, and the conditional covariance of $X_{t+dt}^i-X_t^i$ and $X_{t+dt}^j-X_t^j$ is approximately $x^i x^j \sigma_{ij}dt$. We show for such a spatially extended population that if $S_t=(X_t^1+...+X_t^n)$ is the total population abundance, then $Y_t=X_t/S_t$, the vector of patch proportions, converges in law to a random vector $Y_\infty$ as $t\to\infty$, and the stochastic growth rate $\lim_{t\to\infty}t^{-1}\log S_t$ equals the space-time average per-capita growth rate \sum_i\mu_i\E[Y_\infty^i] experienced by the population minus half of the space-time average temporal variation \E[\sum_{i,j}\sigma_{ij}Y_\infty^i Y_\infty^j] experienced by the population. We derive analytic results for the law of $Y_\infty$, find which choice of the dispersal mechanism $D$ produces an optimal stochastic growth rate for a freely dispersing population, and investigate the effect on the stochastic growth rate of constraints on dispersal rates. Our results provide fundamental insights into "ideal free" movement in the face of uncertainty, the persistence of coupled sink populations, the evolution of dispersal rates, and the single large or several small (SLOSS) debate in conservation biology.Comment: 47 pages, 4 figure

Evaluation of ECMWF-IFS (version 41R1) operational model forecasts of aerosol transport by using ceilometer network measurements

In this paper, we present a comparison of model simulations of aerosol profiles with measurements of the ceilometer network operated by the German Weather Service (DWD) over 1 year from September 2015 to August 2016. The aerosol forecasts are produced by the Copernicus Atmosphere Monitoring Service (CAMS) using the aerosol module developed within the Global and regional Earth-system Monitoring using Satellite and in-situ data (GEMS) and Monitoring Atmospheric Composition and Climate (MACC) projects and coupled into the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (ECMWF-IFS). As the model output provides mass mixing ratios of different types of aerosol, whereas the ceilometers do not, it is necessary to determine a common physical quantity for the comparison. We have chosen the attenuated backscatter beta* for this purpose. The beta* profiles are calculated from the mass mixing ratios of the model output assuming the inherent aerosol microphysical properties. Comparison of the attenuated backscatter averaged between an altitude of 0.2 km (typical overlap range of ceilometers) and 1 km in general shows similar annual average values. However, the standard deviation of the difference between model and observation is larger than the average in 8 out of 12 sites. To investigate possible reasons for the differences, we have examined the role of the hygroscopic growth of particles and the particle shape. Our results show that using a more recent particle growth model would result in a similar to 22% reduction of particle backscatter for sea salt aerosols, corresponding to a 10% reduction of the total backscatter signal on average. Accounting for nonspherical dust particles in the model would reduce attenuated backscatter of dust particles by similar to 30 %. As the concentration of dust aerosol is in general very low in Germany, a significant effect on the total backscatter signal is restricted to dust episodes. In summary, consideration of both effects tends to improve the agreement between model and observations but without leading to a perfect consistency. In addition, a strong Saharan dust event was investigated to study the agreement of the spatiotemporal distribution of particles. It was found that the arrival time of the dust layer and its vertical extent very well agree between model and ceilometer measurements for several stations. This underlines the potential of a network of ceilometers to validate the dispersion of aerosol layers

Rigid and Schurian modules over cluster-tilted algebras of tame type

We give an example of a cluster-tilted algebra Λ with quiver Q, such that the associated cluster algebra A(Q) has a denominator vector which is not the dimension vector of any indecomposable Λ-module. This answers a question posed by T. Nakanishi. The relevant example is a cluster-tilted algebra associated with a tame hereditary algebra. We show that for such a cluster-tilted algebra Λ, we can write any denominator vector as a sum of the dimension vectors of at most three indecomposable rigid Λ-modules. In order to do this it is necessary, and of independent interest, to first classify the indecomposable rigid Λ-modules in this case

PORGY: Strategy-Driven Interactive Transformation of Graphs

This paper investigates the use of graph rewriting systems as a modelling tool, and advocates the embedding of such systems in an interactive environment. One important application domain is the modelling of biochemical systems, where states are represented by port graphs and the dynamics is driven by rules and strategies. A graph rewriting tool's capability to interactively explore the features of the rewriting system provides useful insights into possible behaviours of the model and its properties. We describe PORGY, a visual and interactive tool we have developed to model complex systems using port graphs and port graph rewrite rules guided by strategies, and to navigate in the derivation history. We demonstrate via examples some functionalities provided by PORGY.Comment: In Proceedings TERMGRAPH 2011, arXiv:1102.226

Perzentile für den Body-mass-Index für das Kindes- und Jugendalter unter Heranziehung verschiedener deutscher Stichproben

Fragestellung: Sowohl die Childhood Group der International Obesity Task Force (IOTF) als auch die European Childhood Obesity Group (ECOG) empfehlen den Body-mass-Index als Beurteilungskriterium für Übergewicht und Adipositas bei Kindern und Jugendlichen. Im Erwachsenenalter erfolgt die Definition von Übergewicht und Adipositas anhand fester Grenzwerte, bei der Beurteilung von Kindern und Jugendlichen müssen die alters- und geschlechtsspezifischen Veränderungen des BMI berücksichtigt werden. Methode: Unter Heranziehung von 17 bereits durchgeführten Untersuchungen aus verschiedenen Regionen Deutschlands wurden BMI-Perzentile für Kinder und Jugendliche erstellt. Die Berechnung der Perzentile basiert auf den Körperhöhen- und Körpergewichtsdaten von 17.147 Jungen und 17.275 Mädchen im Alter von 0–18 Jahren. Ergebnisse und Schlussfolgerung: Die vorgestellten Perzentile sollten als Referenz für deutsche Kinder und Jugendliche angewendet werden. Die Arbeitsgemeinschaft „Adipositas im Kindes- und Jugendalter“ (AGA) hat in ihren Leitlinien die Anwendung der hier vorgestellten 90. und 97. Perzentile zur Definition von Übergewicht und Adipositas empfohlen.Objectives: Both the Childhood Group of the International Obesity Task Force (IOTF) and the European Childhood Obesity Group (ECOG) recommend to use the body mass index (BMI = weight in kilograms/height in meter2) to evaluate overweight and obesity in children and adolescents. Whereas it is customary with adults to use fixed cut off points to define overweight and obesity, in children and adolescents age and sex specific developmental changes in BMI need to be addressed, which are due to physiological alterations of fat mass. Method: Because a national reference population for children and adolescents does not exist in Germany, a BMI reference data set was compiled. Therefore measurements of height and weight from 17 different regional studies including 17147 boys and 17275 girls aged 0 to 18 years were used. Results and conclusions: We recommend the use of the presented percentiles as reference to asses under- and overweight (obesity) in German children and adolescents. In the guidelines of the “Arbeitsgruppe Adipositas im Kindes- und Jugendalter”(AGA) the 90th and 97th BMI percentiles as calculated in this reference population are proposed as cut-off points for the definition of overweight and obesity in German children and adolescents