Approximate smoothness in normed linear spaces

We introduce the notion of approximate smoothness in a normed linear space. We characterize this property and show the connections between smoothness and approximate smoothness for some spaces. As an application, we consider in particular the Birkhoff-James orthogonality and its right-additivity under the assumption of approximate smoothness

Comparative genomic analysis of the ‘pseudofungus’ Hyphochytrium catenoides

Eukaryotic microbes have three primary mechanisms for obtaining nutrients and energy: phagotrophy, photosynthesis and osmotrophy. Traits associated with the latter two functions arose independently multiple times in the eukaryotes. The Fungi successfully coupled osmotrophy with filamentous growth, and similar traits are also manifested in the Pseudofungi (oomycetes and hyphochytriomycetes). Both the Fungi and the Pseudofungi encompass a diversity of plant and animal parasites. Genome-sequencing efforts have focused on host-associated microbes (mutualistic symbionts or parasites), providing limited comparisons with free-living relatives. Here we report the first draft genome sequence of a hyphochytriomycete ‘pseudofungus’; Hyphochytrium catenoides. Using phylogenomic approaches, we identify genes of recent viral ancestry, with related viral derived genes also present on the genomes of oomycetes, suggesting a complex history of viral coevolution and integration across the Pseudofungi. H. catenoides has a complex life cycle involving diverse filamentous structures and a flagellated zoospore with a single anterior tinselate flagellum. We use genome comparisons, drug sensitivity analysis and high-throughput culture arrays to investigate the ancestry of oomycete/pseudofungal characteristics, demonstrating that many of the genetic features associated with parasitic traits evolved specifically within the oomycete radiation. Comparative genomics also identified differences in the repertoire of genes associated with filamentous growth between the Fungi and the Pseudofungi, including differences in vesicle trafficking systems, cell-wall synthesis pathways and motor protein repertoire, demonstrating that unique cellular systems underpinned the convergent evolution of filamentous osmotrophic growth in these two eukaryotic groups

Discovery of Fungal Cell Wall Components Using Evolutionary and Functional Genomics

Understanding the various processes/pathways necessary for the biogenesis and maintenance of the cell wall is of immense value as that knowledge can be used for developing antifungals. This dissertation attempts to make a significant contribution in furthering our understanding of the fungal cell wall and its various components. I have identified and characterized genes involved in cell wall growth and maintenance in the model fungus Neurospora crassa by employing a functional screen. I utilized comparative genomics approaches to reconstruct the evolutionary history of cell wall polysaccharides chitin and glucan in the early diverging fungal clades- Microsporidia, Cryptomycota, Chytridiomycota, Blastocladiomycota and Mucormycota. Using a combination of biochemical and comparative genomics I attempted to compare and contrast the cell wall composition of the early diverging fungal clades Chytridiomycota, Blastocladiomycota and Mucormycota to the recently diverged Dikarya fungi. The research presented in this dissertation should lead to the characterization of novel cell wall genes in the filamentous fungi that eventually will lead to development of better drug targets for designing anti-fungal drugs. Also it will lead to better understanding of the cell walls of evolutionarily distinct fungi, which will enable us to combat the pathogenic fungi in a more powerful way. In terms of broader impact this research will be an important contribution to the knowledge of cell wall in the fungal community

Symmetric points in spaces of linear operators between Banach spaces

We explore the relation between left-symmetry (right-symmetry) of elements in a real Banach space and right-symmetry (left-symmetry) of their supporting functionals. We obtain a complete characterization of symmetric functionals on a reflexive, strictly convex and smooth Banach space. We also prove that a bounded linear operator from a reflexive, Kadets–Klee and strictly convex Banach space to any Banach space is symmetric if and only if it is the zero operator. We further characterize left-symmetric operators from ℓ n 1 , n ≥ 2, to any Banach space X. This improves a previously obtained characterization of left-symmetric operators from ℓ n 1 , n ≥ 2, to a reflexive smooth Banach space X

Hybrid Precoder Using Stiefel Manifold Optimization for Mm-Wave Massive MIMO System

Due to the increasing demand for fast data rates and large spectra, millimeter-wave technology plays a vital role in the advancement of 5G communication. The idea behind Mm-Wave communications is to take advantage of the huge and unexploited bandwidth to cope with future multigigabit-per-second mobile data rates, imaging, and multimedia applications. In Mm-Wave systems, digital precoding provides optimal performance at the cost of complexity and power consumption. Therefore, hybrid precoding, i.e., analog–digital precoding, has received significant consideration as a favorable alternative to digital precoding. The conventional methods related to hybrid precoding suffer from low spectral efficiency and large processing time due to nested loops and the number of iterations. A manifold optimization-based algorithm using the gradient method is proposed to increase the spectral efficiency to be near optimal and to speed up the processing speed. A comparison of performances is shown using the simulation outcomes of the proposed work and those of the existing techniques

Shared signatures of parasitism and phylogenomics unite Cryptomycota and microsporidia.

Fungi grow within their food, externally digesting it and absorbing nutrients across a semirigid chitinous cell wall. Members of the new phylum Cryptomycota were proposed to represent intermediate fungal forms, lacking a chitinous cell wall during feeding and known almost exclusively from ubiquitous environmental ribosomal RNA sequences that cluster at the base of the fungal tree [1, 2]. Here, we sequence the first Cryptomycotan genome (the water mold endoparasite Rozella allomycis) and unite the Cryptomycota with another group of endoparasites, the microsporidia, based on phylogenomics and shared genomic traits. We propose that Cryptomycota and microsporidia share a common endoparasitic ancestor, with the clade unified by a chitinous cell wall used to develop turgor pressure in the infection process [3, 4]. Shared genomic elements include a nucleotide transporter that is used by microsporidia for stealing energy in the form of ATP from their hosts [5]. Rozella harbors a mitochondrion that contains a very rapidly evolving genome and lacks complex I of the respiratory chain. These degenerate features are offset by the presence of nuclear genes for alternative respiratory pathways. The Rozella proteome has not undergone major contraction like microsporidia; instead, several classes have undergone expansion, such as host-effector, signal-transduction, and folding proteins

Shared signatures of parasitism and phylogenomics unite Cryptomycota and microsporidia.

Fungi grow within their food, externally digesting it and absorbing nutrients across a semirigid chitinous cell wall. Members of the new phylum Cryptomycota were proposed to represent intermediate fungal forms, lacking a chitinous cell wall during feeding and known almost exclusively from ubiquitous environmental ribosomal RNA sequences that cluster at the base of the fungal tree [1, 2]. Here, we sequence the first Cryptomycotan genome (the water mold endoparasite Rozella allomycis) and unite the Cryptomycota with another group of endoparasites, the microsporidia, based on phylogenomics and shared genomic traits. We propose that Cryptomycota and microsporidia share a common endoparasitic ancestor, with the clade unified by a chitinous cell wall used to develop turgor pressure in the infection process [3, 4]. Shared genomic elements include a nucleotide transporter that is used by microsporidia for stealing energy in the form of ATP from their hosts [5]. Rozella harbors a mitochondrion that contains a very rapidly evolving genome and lacks complex I of the respiratory chain. These degenerate features are offset by the presence of nuclear genes for alternative respiratory pathways. The Rozella proteome has not undergone major contraction like microsporidia; instead, several classes have undergone expansion, such as host-effector, signal-transduction, and folding proteins