Computing the vertices of tropical polyhedra using directed hypergraphs

We establish a characterization of the vertices of a tropical polyhedron defined as the intersection of finitely many half-spaces. We show that a point is a vertex if, and only if, a directed hypergraph, constructed from the subdifferentials of the active constraints at this point, admits a unique strongly connected component that is maximal with respect to the reachability relation (all the other strongly connected components have access to it). This property can be checked in almost linear-time. This allows us to develop a tropical analogue of the classical double description method, which computes a minimal internal representation (in terms of vertices) of a polyhedron defined externally (by half-spaces or hyperplanes). We provide theoretical worst case complexity bounds and report extensive experimental tests performed using the library TPLib, showing that this method outperforms the other existing approaches.Comment: 29 pages (A4), 10 figures, 1 table; v2: Improved algorithm in section 5 (using directed hypergraphs), detailed appendix; v3: major revision of the article (adding tropical hyperplanes, alternative method by arrangements, etc); v4: minor revisio

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

The Hausdorff and dynamical dimensions of self-affine sponges : a dimension gap result

We construct a self-affine sponge in R 3 whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. This resolves a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff dimension. More generally we compute the Hausdorff and dynamical dimensions of a large class of self-affine sponges, a problem that previous techniques could only solve in two dimensions. The Hausdorff and dynamical dimensions depend continuously on the iterated function system defining the sponge, implying that sponges with a dimension gap represent a nonempty open subset of the parameter space

Population Analysis of the Fusarium graminearum Species Complex from Wheat in China Show a Shift to More Aggressive Isolates

A large number of Fusarium isolates was collected from blighted wheat spikes originating from 175 sampling sites, covering 15 provinces in China. Species and trichothecene chemotype determination by multilocus genotyping (MLGT) indicated that F. graminearum s. str. with the 15-acetyl deoxynivalenol (15ADON) chemotype and F. asiaticum with either the nivalenol (NIV) or the 3-acetyl deoxynivalenol (3ADON) chemotype were the dominant causal agents. Bayesian model-based clustering with allele data obtained with 12 variable number of tandem repeats (VNTR) markers, detected three genetic clusters that also show distinct chemotypes. High levels of population genetic differentiation and low levels of effective number of migrants were observed between these three clusters. Additional genotypic analyses revealed that F. graminearum s. str. and F. asiaticum are sympatric. In addition, composition analysis of these clusters indicated a biased gene flow from 3ADON to NIV producers in F. asiaticum. In phenotypic analyses, F. asiaticum that produce 3ADON revealed significant advantages over F. asiaticum that produce NIV in pathogenicity, growth rate, fecundity, conidial length, trichothecene accumulation and resistance to benzimidazole. These results suggest that natural selection drives the spread of a more vigorous, more toxigenic pathogen population which also shows higher levels of fungicide resistance

Effects of the fungicide metiram in outdoor freshwater microcosms: responses of invertebrates, primary producers and microbes

The ecological impact of the dithiocarbamate fungicide metiram was studied in outdoor freshwater microcosms, consisting of 14 enclosures placed in an experimental ditch. The microcosms were treated three times (interval 7 days) with the formulated product BAS 222 28F (Polyram®). Intended metiram concentrations in the overlying water were 0, 4, 12, 36, 108 and 324 μg a.i./L. Responses of zooplankton, macroinvertebrates, phytoplankton, macrophytes, microbes and community metabolism endpoints were investigated. Dissipation half-life (DT50) of metiram was approximately 1–6 h in the water column of the microcosm test system and the metabolites formed were not persistent. Multivariate analysis indicated treatment-related effects on the zooplankton (NOECcommunity = 36 μg a.i./L). Consistent treatment-related effects on the phytoplankton and macroinvertebrate communities and on the sediment microbial community could not be demonstrated or were minor. There was no evidence that metiram affected the biomass, abundance or functioning of aquatic hyphomycetes on decomposing alder leaves. The most sensitive populations in the microcosms comprised representatives of Rotifera with a NOEC of 12 μg a.i./L on isolated sampling days and a NOEC of 36 μg a.i./L on consecutive samplings. At the highest treatment-level populations of Copepoda (zooplankton) and the blue-green alga Anabaena (phytoplankton) also showed a short-term decline on consecutive sampling days (NOEC = 108 μg a.i./L). Indirect effects in the form of short-term increases in the abundance of a few macroinvertebrate and several phytoplankton taxa were also observed. The overall community and population level no-observed-effect concentration (NOECmicrocosm) was 12–36 μg a.i./L. At higher treatment levels, including the test systems that received the highest dose, ecological recovery of affected measurement endpoints was fast (effect period < 8 weeks)

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)

The influence of macrophytes on sediment resuspension and the effect of associated nutrients in a shallow and large lake (Lake Taihu, China)

A yearlong campaign to examine sediment resuspension was conducted in large, shallow and eutrophic Lake Taihu, China, to investigate the influence of vegetation on sediment resuspension and its nutrient effects. The study was conducted at 6 sites located in both phytoplankton-dominated zone and macrophyte-dominated zone of the lake, lasting for a total of 13 months, with collections made at two-week intervals. Sediment resuspension in Taihu, with a two-week high average rate of 1771 g.m(-2).d(-1) and a yearly average rate of 377 g.m(-2).d(-1), is much stronger than in many other lakes worldwide, as Taihu is quite shallow and contains a long fetch. The occurrence of macrophytes, however, provided quite strong abatement of sediment resuspension, which may reduce the sediment resuspension rate up to 29-fold. The contribution of nitrogen and phosphorus to the water column from sediment resuspension was estimated as 0.34 mg.L-1 and 0.051 mg.L-1 in the phytoplankton-dominated zone. Sediment resuspension also largely reduced transparency and then stimulated phytoplankton growth. Therefore, sediment resuspension may be one of the most important factors delaying the recovery of eutrophic Lake Taihu, and the influence of sediment resuspension on water quality must also be taken into account by the lake managers when they determine the restoration target.Peer reviewe