On the geometry of C^3/D_27 and del Pezzo surfaces

We clarify some aspects of the geometry of a resolution of the orbifold X = C3/D_27, the noncompact complex manifold underlying the brane quiver standard model recently proposed by Verlinde and Wijnholt. We explicitly realize a map between X and the total space of the canonical bundle over a degree 1 quasi del Pezzo surface, thus defining a desingularization of X. Our analysis relys essentially on the relationship existing between the normalizer group of D_27 and the Hessian group and on the study of the behaviour of the Hesse pencil of plane cubic curves under the quotient.Comment: 23 pages, 5 figures, 2 tables. JHEP style. Added references. Corrected typos. Revised introduction, results unchanged

Superconformal Block Quivers, Duality Trees and Diophantine Equations

We generalize previous results on N = 1, (3 + 1)-dimensional superconformal block quiver gauge theories. It is known that the necessary conditions for a theory to be superconformal, i.e. that the beta and gamma functions vanish in addition to anomaly cancellation, translate to a Diophantine equation in terms of the quiver data. We re-derive results for low block numbers revealing an new intriguing algebraic structure underlying a class of possible superconformal fixed points of such theories. After explicitly computing the five block case Diophantine equation, we use this structure to reorganize the result in a form that can be applied to arbitrary block numbers. We argue that these theories can be thought of as vectors in the root system of the corresponding quiver and superconformality conditions are shown to associate them to certain subsets of imaginary roots. These methods also allow for an interpretation of Seiberg duality as the action of the affine Weyl group on the root lattice

High-level classification of the Fungi and a tool for evolutionary ecological analyses

High-throughput sequencing studies generate vast amounts of taxonomic data. Evolutionary ecological hypotheses of the recovered taxa and Species Hypotheses are difficult to test due to problems with alignments and the lack of a phylogenetic backbone. We propose an updated phylum-and class-level fungal classification accounting for monophyly and divergence time so that the main taxonomic ranks are more informative. Based on phylogenies and divergence time estimates, we adopt phylum rank to Aphelidiomycota, Basidiobolomycota, Calcarisporiellomycota, Glomeromycota, Entomophthoromycota, Entorrhizomycota, Kickxellomycota, Monoblepharomycota, Mortierellomycota and Olpidiomycota. We accept nine subkingdoms to accommodate these 18 phyla. We consider the kingdom Nucleariae (phyla Nuclearida and Fonticulida) as a sister group to the Fungi. We also introduce a perl script and a newick-formatted classification backbone for assigning Species Hypotheses into a hierarchical taxonomic framework, using this or any other classification system. We provide an example of testing evolutionary ecological hypotheses based on a global soil fungal data set.Peer reviewe

Multigene Phylogeny of Choanozoa and the Origin of Animals

Animals are evolutionarily related to fungi and to the predominantly unicellular protozoan phylum Choanozoa, together known as opisthokonts. To establish the sequence of events when animals evolved from unicellular ancestors, and understand those key evolutionary transitions, we need to establish which choanozoans are most closely related to animals and also the evolutionary position of each choanozoan group within the opisthokont phylogenetic tree. Here we focus on Ministeria vibrans, a minute bacteria-eating cell with slender radiating tentacles. Single-gene trees suggested that it is either the closest unicellular relative of animals or else sister to choanoflagellates, traditionally considered likely animal ancestors. Sequencing thousands of Ministeria protein genes now reveals about 14 with domains of key significance for animal cell biology, including several previously unknown from deeply diverging Choanozoa, e.g. domains involved in hedgehog, Notch and tyrosine kinase signaling or cell adhesion (cadherin). Phylogenetic trees using 78 proteins show that Ministeria is not sister to animals or choanoflagellates (themselves sisters to animals), but to Capsaspora, another protozoan with thread-like (filose) tentacles. The Ministeria/Capsaspora clade (new class Filasterea) is sister to animals and choanoflagellates, these three groups forming a novel clade (filozoa) whose ancestor presumably evolved filose tentacles well before they aggregated as a periciliary collar in the choanoflagellate/sponge common ancestor. Our trees show ichthyosporean choanozoans as sisters to filozoa; a fusion between ubiquitin and ribosomal small subunit S30 protein genes unifies all holozoa (filozoa plus Ichthyosporea), being absent in earlier branching eukaryotes. Thus, several successive evolutionary innovations occurred among their unicellular closest relatives prior to the origin of the multicellular body-plan of animals

Notes for genera: basal clades of Fungi (including Aphelidiomycota, Basidiobolomycota, Blastocladiomycota, Calcarisporiellomycota, Caulochytriomycota, Chytridiomycota, Entomophthoromycota, Glomeromycota, Kickxellomycota, Monoblepharomycota, Mortierellomycota, Mucoromycota, Neocallimastigomycota, Olpidiomycota, Rozellomycota and Zoopagomycota)

Compared to the higher fungi (Dikarya), taxonomic and evolutionary studies on the basal clades of fungi are fewer in number. Thus, the generic boundaries and higher ranks in the basal clades of fungi are poorly known. Recent DNA based taxonomic studies have provided reliable and accurate information. It is therefore necessary to compile all available information since basal clades genera lack updated checklists or outlines. Recently, Tedersoo et al. (MycoKeys 13:1--20, 2016) accepted Aphelidiomycota and Rozellomycota in Fungal clade. Thus, we regard both these phyla as members in Kingdom Fungi. We accept 16 phyla in basal clades viz. Aphelidiomycota, Basidiobolomycota, Blastocladiomycota, Calcarisporiellomycota, Caulochytriomycota, Chytridiomycota, Entomophthoromycota, Glomeromycota, Kickxellomycota, Monoblepharomycota, Mortierellomycota, Mucoromycota, Neocallimastigomycota, Olpidiomycota, Rozellomycota and Zoopagomycota. Thus, 611 genera in 153 families, 43 orders and 18 classes are provided with details of classification, synonyms, life modes, distribution, recent literature and genomic data. Moreover, Catenariaceae Couch is proposed to be conserved, Cladochytriales Mozl.-Standr. is emended and the family Nephridiophagaceae is introduced