Some classifications of biharmonic hypersurfaces with constant scalar curvature

We give some classifications of biharmonic hypersurfaces with constant scalar curvature. These include biharmonic Einstein hypersurfaces in space forms, compact biharmonic hypersurfaces with constant scalar curvature in a sphere, and some complete biharmonic hypersurfaces of constant scalar curvature in space forms and in a non-positively curved Einstein space. Our results provide additional cases (Theorem 2.3 and Proposition 2.8) that supports the conjecture that a biharmonic submanifold in a sphere has constant mean curvature, and two more cases that support Chen's conjecture on biharmonic hypersurfaces (Corollaries 2.2,2.7).Comment: 11 page

Popular progression differences in vector spaces II

Green used an arithmetic analogue of Szemer\'edi's celebrated regularity lemma to prove the following strengthening of Roth's theorem in vector spaces. For every $\alpha>0$, $\beta<\alpha^3$, and prime number $p$, there is a least positive integer $n_p(\alpha,\beta)$ such that if $n \geq n_p(\alpha,\beta)$, then for every subset of $\mathbb{F}_p^n$ of density at least $\alpha$ there is a nonzero $d$ for which the density of three-term arithmetic progressions with common difference $d$ is at least $\beta$. We determine for $p \geq 19$ the tower height of $n_p(\alpha,\beta)$ up to an absolute constant factor and an additive term depending only on $p$. In particular, if we want half the random bound (so $\beta=\alpha^3/2$), then the dimension $n$ required is a tower of twos of height $\Theta \left((\log p) \log \log (1/\alpha)\right)$. It turns out that the tower height in general takes on a different form in several different regions of $\alpha$ and $\beta$, and different arguments are used both in the upper and lower bounds to handle these cases.Comment: 34 pages including appendi

A Polyphasic Approach Reveals Novel Genotypes and Updates the Genetic Structure of the Banana Fusarium Wilt Pathogen

Fusarium oxysporum f. sp. cubense (Foc) is a soil-borne fungus that causes Fusarium wilt, a destructive plant disease that has resulted in devastating economic losses to banana production worldwide. The fungus has a complex evolutionary history and taxonomic repute and consists of three pathogenic races and at least 24 vegetative compatibility groups (VCGs). Surveys conducted in Asia, Africa, the Sultanate of Oman and Mauritius encountered isolates of F. oxysporum pathogenic to banana that were not compatible to any of the known Foc VCGs. Genetic relatedness between the undescribed and known Foc VCGs were determined using a multi-gene phylogeny and diversity array technology (DArT) sequencing. The presence of putative effector genes, the secreted in xylem (SIX) genes, were also determined. Fourteen novel Foc VCGs and 17 single-member VCGs were identified. The multi-gene tree was congruent with the DArT-seq phylogeny and divided the novel VCGs into three clades. Clustering analysis of the DArT-seq data supported the separation of Foc isolates into eight distinct clusters, with the suite of SIX genes mostly conserved within these clusters. Results from this study indicates that Foc is more diverse than hitherto assumed

The development of a multiplex PCR assay for the detection of Fusarium oxysporum f. sp. cubense lineage VI strains in East and Central Africa

Banana is a staple food and cash crop grown in East and Central Africa (ECA). The main banana varieties grown in ECA are the East African highland bananas (EAHB), although dessert/beer bananas such as Sukari Ndizi, Kayinja (Pisang Awak) and Gros Michel are also produced due to their high value at local markets. The Fusarium wilt fungus Fusarium oxysporum f. sp. cubense (Foc) causes disease of susceptible dessert/beer bananas, which significantly reduces yields. Banana Fusarium wilt is managed by excluding the pathogen from disease-free areas and by planting disease-resistant varieties in infested fields. Six phylogenetically closely-related vegetative compatibility groups (VCGs) of Foc, VCGs 0124, 0125, 0128, 01212, 01220 and 01222 are present in ECA, which all group together in Foc Lineage VI. Rapid and accurate detection of Foc Lineage VI strains is thus important to prevent its spread to disease-free areas. In this study, molecular markers specific to Foc Lineage VI were therefore developed. Primer sets were then combined in a multiplex PCR assay, and validated on a worldwide population of 623 known Foc isolates, other formae speciales and non-pathogenic Fusarium oxysporum isolates. The Foc Lineage VI multiplex PCR was used to identify Foc isolates collected in banana fields at five locations in Uganda and Tanzania. Foc Lineage VI DNA was detected at a concentration as low as 0.1 ng/μl, both in the absence and presence of banana DNA, and can therefore be used as an accurate diagnostic tool for Foc Lineage VI strains

The distribution and host range of the banana Fusarium wilt fungus, Fusarium oxysporum f. sp. cubense, in Asia

Fusarium oxysporum formae specialis cubense (Foc) is a soil-borne fungus that causes Fusarium wilt, which is considered to be the most destructive disease of bananas. The fungus is believed to have evolved with its host in the Indo-Malayan region, and from there it was spread to other banana-growing areas with infected planting material. The diversity and distribution of Foc in Asia was investigated. A total of 594 F. oxysporum isolates collected in ten Asian countries were identified by vegetative compatibility groups (VCGs) analysis. To simplify the identification process, the isolates were first divided into DNA lineages using PCR-RFLP analysis. Six lineages and 14 VCGs, representing three Foc races, were identified in this study. The VCG complex 0124/5 was most common in the Indian subcontinent, Vietnam and Cambodia; whereas the VCG complex 01213/16 dominated in the rest of Asia. Sixty-nine F. oxysporum isolates in this study did not match any of the known VCG tester strains. In this study, Foc VCG diversity in Bangladesh, Cambodia and Sri Lanka was determined for the first time and VCGs 01221 and 01222 were first reported from Cambodia and Vietnam. New associations of Foc VCGs and banana cultivars were recorded in all the countries where the fungus was collected. Information obtained in this study could help Asian countries to develop and implement regulatory measures to prevent the incursion of Foc into areas where it does not yet occur. It could also facilitate the deployment of disease resistant banana varieties in infested areas.S1 Table. Morphological identity, PCR-RFLP clade and lineage identity, vegetative compatibility group, host and host subgroup, location and origin of Fusariumisolates collected in Asia.S2 Table. Vegetative compatibility tester strains used to characterize compatibility to Asian Fusariumoxysporumf. sp. cubense isolates.http://www.plosone.orgam2018Forestry and Agricultural Biotechnology Institute (FABI)Microbiology and Plant Patholog

Fusaric acid instigates the invasion of banana by Fusarium oxysporum f. sp. cubense TR4

CITATION: Liu, S. et al. 2020. Fusaric acid instigates the invasion of banana by Fusarium oxysporum f. sp. cubense TR4. New Phytologist, 225:913–929, doi:10.1111/nph.16193.The original publication is available at https://nph.onlinelibrary.wiley.comFusaric acid (FSA) is a phytotoxin produced by several Fusarium species and has been associated with plant disease development, although its role is still not well understood. Mutation of key genes in the FSA biosynthetic gene (FUB) cluster in Fusarium oxysporum f. sp. cubense tropical race 4 (Foc TR4) reduced the FSA production, and resulted in decreased disease symptoms and reduced fungal biomass in the host banana plants. When pretreated with FSA, both banana leaves and pseudostems exhibited increased sensitivity to Foc TR4 invasion. Banana embryogenic cell suspensions (ECSs) treated with FSA exhibited a lower rate of O2 uptake, loss of mitochondrial membrane potential, increased reactive oxygen species (ROS) accumulation, and greater nuclear condensation and cell death. Consistently, transcriptomic analysis of FSA-treated ECSs showed that FSA may induce plant cell death through regulating the expression of genes involved in mitochondrial functions. The results herein demonstrated that the FSA from Foc TR4 functions as a positive virulence factor and acts at the early stage of the disease development before the appearance of the fungal hyphae in the infected tissues.https://nph.onlinelibrary.wiley.com/doi/full/10.1111/nph.16193Publisher's versio

Geographical distribution and genetic dversity of the Banana Fusarium Wilt Fungus in Laos and Vietnam

Fusarium wilt, caused by the fungus Fusarium oxysporum f. sp. cubense (Foc), poses a major threat to global banana production. The tropical race 4 (TR4) variant of Foc is a highly virulent form with a large host range, and severely affects Cavendish bananas. Foc TR4 was recently observed within the Greater Mekong Subregion, after Chinese private companies expanded Cavendish pro duction to the region. In this study, extensive surveys conducted across Laos and Vietnam show that Foc TR4 is still mainly constricted to the northern regions of these countries and is limited to Cavendish cultivation settings. In Laos, Foc TR4 is associated with large-scale Cavendish plantations owned by or involved with Chinese companies through which infected planting material could have been imported. In Vietnam, mostly small-holder Cavendish farmers and backyard gardens were affected by Foc TR4. In Vietnam, no direct link is found with Chinese growers, and it is expected the pathogen mainly spreads through local and regional movement of infected planting materials. Foc TR4 was not recorded on banana cultivars other than Cavendish. The extensively cultivated ‘Pisang Awak’ cultivar was solely infected by VCGs belonging to Foc race 1 and 2, with a high occurrence of VCG 0123 across Laos, and of VCG 0124/5 in Vietnam. Substantial diversity of Foc VCGs was recorded (VCGs 0123, 0124/5, 01218 and 01221) from northern to southern regions in both countries, suggesting that Fusarium wilt is well established in the region. Interviews with farmers indicated that the local knowledge of Fusarium wilt epidemiology and options for disease management was limited. Clear communication efforts on disease epidemiology and management with emphasis on biosecurity practices need to be improved in order to prevent further spread of Foc TR4 to mixed variety smallholder settings

Occurrence and spread of the banana fungus Fusarium oxysporum f. sp. cubense TR4 in Mozambique

CITATION: Viljoen, A. et al. 2020. Occurrence and spread of the banana fungus Fusarium oxysporum f. sp. cubense TR4 in Mozambique. South African Journal of Science, 116(11/12):8608, doi:10.17159/sajs.2020/8608.The original publication is available at https://sajs.co.zaFusarium wilt, caused by the soil-borne fungus Fusarium oxysporum f. sp. cubense (Foc), poses a major threat to banana production globally. A variant of Foc that originated in Southeast Asia, called tropical race 4 (TR4), was detected on a Cavendish banana export plantation (Metocheria) in northern Mozambique in 2013. Foc TR4 was rapidly disseminated on the farm, and affected approximately half a million plants within 3 years. The fungus was also detected on a second commercial property approximately 200 km away (Lurio farm) a year later, and on a small-grower’s property near Metocheria farm in 2015. Surveys in Mozambique showed that non-Cavendish banana varieties were only affected by Foc race 1 and race 2 strains. The testing of Cavendish banana somaclones in northern Mozambique revealed that GCTCV-119 was most resistant to Foc TR4, but that GCTCV-218 produced better bunches. The occurrence of Foc TR4 in northern Mozambique poses a potential threat to food security on the African continent, where banana is considered a staple food and source of income to millions of people. Cavendish somaclones can be used, in combination with integrated disease management practices, to replace susceptible Cavendish cultivars in southern Africa. The comprehensive testing of African cooking bananas for resistance to Foc TR4 is required, along with the improvement of biosecurity and preparedness of growers on the African continent.https://sajs.co.za/article/view/8608Publisher's versio

The Survival and Treatment of Fusarium oxysporum f. sp. cubense in Water

Fusarium oxysporum f. sp cubense (Foc), the causal agent of Fusarium wilt, is one of the most devastating constraints to banana production worldwide. The spread of Foc in water is particularly concerning, as infested water can rapidly contaminate disease-free areas. The objectives of this study were to investigate the survival of Foc in water and to test the effectiveness of water treatment with chlorine, ozone, UV, and peracetic acid. The study indicated that Foc spores can survive in water for more than 120 days, but that viability was reduced in stagnant water, probably due to anaerobic conditions when spores settled at the bottom. It is therefore recommended that surface water be extracted and treated before it is used for irrigation. The efficacy of all water treatments was reduced in the presence of soil, implying that water needs to be soil-free before treatment. The use of peracetic acid is recommended to treat Foc-contaminated water, as it is safe for use and does not require installation costs although it is effective at treating Foc-contaminated water, ozone would require significant input costs and chlorine can produce harmful disinfection by-products. UV would be impractical for field application because of the high doses required to eliminate Foc

Quantitative detection of economically important Fusarium oxysporum f. sp. cubense strains in Africa in plants, soil and water.

Banana is an important food crop and source of income in Africa. Sustainable production of banana, however, is at risk because of pests and diseases such as Fusarium wilt, caused by the soil-borne fungus Fusarium oxysporum f. sp. cubense (Foc). Foc can be disseminated from infested to disease-free fields in plant material, water and soil. Early detection of Foc using DNA technologies is thus required to accurately identify the fungus and prevent its further dissemination with plants, soil and water. In this study, quantitative (q)PCR assays were developed for the detection of Foc Lineage VI strains found in central and eastern Africa (Foc races 1 and 2), Foc TR4 (vegetative compatibility groups (VCG) 01213/16) that is present in Mozambique, and Foc STR4 (VCG 0120/15) that occurs in South Africa. A collection of 127 fungal isolates were selected for specificity testing, including endophytic Fusarium isolates from banana pseudostems, non-pathogenic F. oxysporum strains and Foc isolates representing the 24 VCGs in Foc. Primer sets that proved to be specific to Foc Lineage VI, Foc TR4 and Foc STR4 were used to produce standard curves for absolute quantification, and the qPCR assays were evaluated based on the quality of standard curves, repeatability and reproducibility, and limits of quantification (LOQ) and detection (LOD). The qPCR assays for Foc Lineage VI, TR4 and STR4 were repeatable and reproducible, with LOQ values of 10-3-10-4 ng/μL and a LOD of 10-4-10-5 ng/μL. The quantitative detection of Foc strains in Africa could reduce the time and improve the accuracy for identifying the Fusarium wilt pathogen from plants, water and soil on the continent