Almost reducibility for finitely differentiable SL(2,R)-valued quasi-periodic cocycles

Quasi-periodic cocycles with a diophantine frequency and with values in SL(2,R) are shown to be almost reducible as long as they are close enough to a constant, in the topology of k times differentiable functions, with k great enough. Almost reducibility is obtained by analytic approximation after a loss of differentiability which only depends on the frequency and on the constant part. As in the analytic case, if their fibered rotation number is diophantine or rational with respect to the frequency, such cocycles are in fact reducible. This extends Eliasson's theorem on Schr\"odinger cocycles to the differentiable case

H\"older Continuity of the Integrated Density of States for the Fibonacci Hamiltonian

We prove H\"older continuity of the integrated density of states for the Fibonacci Hamiltonian for any positive coupling, and obtain the asymptotics of the H\"older exponents for large and small couplings.Comment: 18 page

Improved control of Septoria tritici blotch in durum wheat using cultivar mixtures

Mixtures of cultivars with contrasting levels of disease resistance are capable of suppressing infectious diseases in wheat, as demonstrated in numerous field experiments. Most studies focused on airborne pathogens in bread wheat, while splash-dispersed pathogens have received less attention, and no studies have been conducted in durum wheat. We conducted a two-year field experiment in Tunisia, a major durum wheat producer in the Mediterranean region, to evaluate the performance of cultivar mixtures in controlling the polycyclic, splash-dispersed disease Septoria tritici blotch (STB) in durum wheat. To measure STB severity, we used a novel, high-throughput method based on digital analysis of images captured from 3074 infected leaves collected from 42 and 40 experimental plots on the first and the second year, respectively. This method allowed us to quantify pathogen reproduction on wheat leaves and to acquire a large dataset that exceeds previous studies with respect to accuracy and statistical power. Our analyses show that introducing only 25% of a disease-resistant cultivar into a pure stand of a susceptible cultivar provides a substantial reduction of almost 50% in disease severity. However, adding a second resistant cultivar to the mixture did not further improve disease control, contrary to predictions of epidemiological theory. Susceptible cultivars can be agronomically superior to resistant cultivars or be better accepted by growers for other reasons. Hence, if mixtures with only a moderate proportion of the resistant cultivar provide similar degree of disease control as resistant pure stands, as our analysis indicates, such mixtures are more likely to be accepted by growers

Resonance tongues in the quasi-periodic Hill-Schrödinger equation with three frequencies

n this article we investigate numerically the spectrum of some representative examples of discrete one-dimensional Schrödinger operators with quasi-periodic potential in terms of a perturbative constant b and the spectral parameter a. Our examples include the well-known Almost Mathieu model, other trigonometric potentials with a single quasi-periodic frequency and generalisations with two and three frequencies. We computed numerically the rotation number and the Lyapunov exponent to detect open and collapsed gaps, resonance tongues and the measure of the spectrum. We found that the case with one frequency was significantly different from the case of several frequencies because the latter has all gaps collapsed for a sufficiently large value of the perturbative constant and thus the spectrum is a single spectral band with positive Lyapunov exponent. In contrast, in the cases with one frequency considered, gaps are always dense in the spectrum, although some gaps may collapse either for a single value of the perturbative constant or for a range of values. In all cases we found that there is a curve in the (a, b)-plane which separates the regions where the Lyapunov exponent is zero in the spectrum and where it is positive. Along this curve, which is b = 2 in the Almost Mathieu case, the measure of the spectrum is zero.Peer ReviewedPostprint (published version

Fusarium: more than a node or a foot-shaped basal cell

Recent publications have argued that there are potentially serious consequences for researchers in recognising distinct genera in the terminal fusarioid clade of the family Nectriaceae. Thus, an alternate hypothesis, namely a very broad concept of the genus Fusarium was proposed. In doing so, however, a significant body of data that supports distinct genera in Nectriaceae based on morphology, biology, and phylogeny is disregarded. A DNA phylogeny based on 19 orthologous protein-coding genes was presented to support a very broad concept of Fusarium at the F1 node in Nectriaceae. Here, we demonstrate that re-analyses of this dataset show that all 19 genes support the F3 node that represents Fusarium sensu stricto as defined by F. sambucinum (sexual morph synonym Gibberella pulicaris). The backbone of the phylogeny is resolved by the concatenated alignment, but only six of the 19 genes fully support the F1 node, representing the broad circumscription of Fusarium. Furthermore, a re-analysis of the concatenated dataset revealed alternate topologies in different phylogenetic algorithms, highlighting the deep divergence and unresolved placement of various Nectriaceae lineages proposed as members of Fusarium. Species of Fusarium s. str. are characterised by Gibberella sexual morphs, asexual morphs with thin- or thick-walled macroconidia that have variously shaped apical and basal cells, and trichothecene mycotoxin production, which separates them from other fusarioid genera. Here we show that the Wollenweber concept of Fusarium presently accounts for 20 segregate genera with clear-cut synapomorphic traits, and that fusarioid macroconidia represent a character that has been gained or lost multiple times throughout Nectriaceae. Thus, the very broad circumscription of Fusarium is blurry and without apparent synapomorphies, and does not include all genera with fusarium-like macroconidia, which are spread throughout Nectriaceae (e.g., Cosmosporella, Macroconia, Microcera). In this study four new genera are introduced, along with 18 new species and 16 new combinations. These names convey information about relationships, morphology, and ecological preference that would otherwise be lost in a broader definition of Fusarium. To assist users to correctly identify fusarioid genera and species, we introduce a new online identification database, Fusarioid-ID, accessible at www.fusarium.org. The database comprises partial sequences from multiple genes commonly used to identify fusarioid taxa (act1, CaM, his3, rpb1, rpb2, tef1, tub2, ITS, and LSU). In this paper, we also present a nomenclator of names that have been introduced in Fusarium up to January 2021 as well as their current status, types, and diagnostic DNA barcode data. In this study, researchers from 46 countries, representing taxonomists, plant pathologists, medical mycologists, quarantine officials, regulatory agencies, and students, strongly support the application and use of a more precisely delimited Fusarium (= Gibberella) concept to accommodate taxa from the robust monophyletic node F3 on the basis of a well-defined and unique combination of morphological and biochemical features. This F3 node includes, among others, species of the F. fujikuroi, F. incarnatum-equiseti, F. oxysporum, and F. sambucinum species complexes, but not species of Bisifusarium [F. dimerum species complex (SC)], Cyanonectria (F. buxicola SC), Geejayessia (F. staphyleae SC), Neocosmospora (F. solani SC) or Rectifusarium (F. ventricosum SC). The present study represents the first step to generating a new online monograph of Fusarium and allied fusarioid genera (www.fusarium.org)

Fusarium : more than a node or a foot-shaped basal cell

Recent publications have argued that there are potentially serious consequences for researchers in recognising distinct genera in the terminal fusarioid clade of the family Nectriaceae. Thus, an alternate hypothesis, namely a very broad concept of the genus Fusarium was proposed. In doing so, however, a significant body of data that supports distinct genera in Nectriaceae based on morphology, biology, and phylogeny is disregarded. A DNA phylogeny based on 19 orthologous protein-coding genes was presented to support a very broad concept of Fusarium at the F1 node in Nectriaceae. Here, we demonstrate that re-analyses of this dataset show that all 19 genes support the F3 node that represents Fusarium sensu stricto as defined by F. sambucinum (sexual morph synonym Gibberella pulicaris). The backbone of the phylogeny is resolved by the concatenated alignment, but only six of the 19 genes fully support the F1 node, representing the broad circumscription of Fusarium. Furthermore, a re-analysis of the concatenated dataset revealed alternate topologies in different phylogenetic algorithms, highlighting the deep divergence and unresolved placement of various Nectriaceae lineages proposed as members of Fusarium. Species of Fusarium s. str. are characterised by Gibberella sexual morphs, asexual morphs with thin- or thick-walled macroconidia that have variously shaped apical and basal cells, and trichothecene mycotoxin production, which separates them from other fusarioid genera. Here we show that the Wollenweber concept of Fusarium presently accounts for 20 segregate genera with clear-cut synapomorphic traits, and that fusarioid macroconidia represent a character that has been gained or lost multiple times throughout Nectriaceae. Thus, the very broad circumscription of Fusarium is blurry and without apparent synapomorphies, and does not include all genera with fusarium-like macroconidia, which are spread throughout Nectriaceae (e.g., Cosmosporella, Macroconia, Microcera). In this study four new genera are introduced, along with 18 new species and 16 new combinations. These names convey information about relationships, morphology, and ecological preference that would otherwise be lost in a broader definition of Fusarium. To assist users to correctly identify fusarioid genera and species, we introduce a new online identification database, Fusarioid-ID, accessible at www.fusarium.org. The database comprises partial sequences from multiple genes commonly used to identify fusarioid taxa (act1, CaM, his3, rpb1, rpb2, tef1, tub2, ITS, and LSU). In this paper, we also present a nomenclator of names that have been introduced in Fusarium up to January 2021 as well as their current status, types, and diagnostic DNA barcode data. In this study, researchers from 46 countries, representing taxonomists, plant pathologists, medical mycologists, quarantine officials, regulatory agencies, and students, strongly support the application and use of a more precisely delimited Fusarium (= Gibberella) concept to accommodate taxa from the robust monophyletic node F3 on the basis of a well-defined and unique combination of morphological and biochemical features. This F3 node includes, among others, species of the F. fujikuroi, F. incarnatum-equiseti, F. oxysporum, and F. sambucinum species complexes, but not species of Bisifusarium [F. dimerum species complex (SC)], Cyanonectria (F. buxicola SC), Geejayessia (F. staphyleae SC), Neocosmospora (F. solani SC) or Rectifusarium (F. ventricosum SC). The present study represents the first step to generating a new online monograph of Fusarium and allied fusarioid genera (www.fusarium.org).http://www.studiesinmycology.org/BiochemistryForestry and Agricultural Biotechnology Institute (FABI)GeneticsMicrobiology and Plant PathologyPlant Production and Soil Scienc

Fusarium: more than a node or a foot-shaped basal cell

Recent publications have argued that there are potentially serious consequences for researchers in recognising distinct genera in the terminal fusarioid clade of the family Nectriaceae. Thus, an alternate hypothesis, namely a very broad concept of the genus Fusarium was proposed. In doing so, however, a significant body of data that supports distinct genera in Nectriaceae based on morphology, biology, and phylogeny is disregarded. A DNA phylogeny based on 19 orthologous protein-coding genes was presented to support a very broad concept of Fusarium at the F1 node in Nectriaceae. Here, we demonstrate that re-analyses of this dataset show that all 19 genes support the F3 node that represents Fusarium sensu stricto as defined by F. sambucinum (sexual morph synonym Gibberella pulicaris). The backbone of the phylogeny is resolved by the concatenated alignment, but only six of the 19 genes fully support the F1 node, representing the broad circumscription of Fusarium. Furthermore, a re-analysis of the concatenated dataset revealed alternate topologies in different phylogenetic algorithms, highlighting the deep divergence and unresolved placement of various Nectriaceae lineages proposed as members of Fusarium. Species of Fusarium s. str. are characterised by Gibberella sexual morphs, asexual morphs with thin- or thick-walled macroconidia that have variously shaped apical and basal cells, and trichothecene mycotoxin production, which separates them from other fusarioid genera. Here we show that the Wollenweber concept of Fusarium presently accounts for 20 segregate genera with clear-cut synapomorphic traits, and that fusarioid macroconidia represent a character that has been gained or lost multiple times throughout Nectriaceae. Thus, the very broad circumscription of Fusarium is blurry and without apparent synapomorphies, and does not include all genera with fusarium-like macroconidia, which are spread throughout Nectriaceae (e.g., Cosmosporella, Macroconia, Microcera). In this study four new genera are introduced, along with 18 new species and 16 new combinations. These names convey information about relationships, morphology, and ecological preference that would otherwise be lost in a broader definition of Fusarium. To assist users to correctly identify fusarioid genera and species, we introduce a new online identification database, Fusarioid-ID, accessible at www.fusarium.org. The database comprises partial sequences from multiple genes commonly used to identify fusarioid taxa (act1, CaM, his3, rpb1, rpb2, tef1, tub2, ITS, and LSU). In this paper, we also present a nomenclator of names that have been introduced in Fusarium up to January 2021 as well as their current status, types, and diagnostic DNA barcode data. In this study, researchers from 46 countries, representing taxonomists, plant pathologists, medical mycologists, quarantine officials, regulatory agencies, and students, strongly support the application and use of a more precisely delimited Fusarium (= Gibberella) concept to accommodate taxa from the robust monophyletic node F3 on the basis of a well-defined and unique combination of morphological and biochemical features. This F3 node includes, among others, species of the F. fujikuroi, F. incarnatum-equiseti, F. oxysporum, and F. sambucinum species complexes, but not species of Bisifusarium [F. dimerum species complex (SC)], Cyanonectria (F. buxicola SC), Geejayessia (F. staphyleae SC), Neocosmospora (F. solani SC) or Rectifusarium (F. ventricosum SC). The present study represents the first step to generating a new online monograph of Fusarium and allied fusarioid genera (www.fusarium.org)