Atomistic subsemirings of the lattice of subspaces of an algebra

Let A be an associative algebra with identity over a field k. An atomistic subsemiring R of the lattice of subspaces of A, endowed with the natural product, is a subsemiring which is a closed atomistic sublattice. When R has no zero divisors, the set of atoms of R is endowed with a multivalued product. We introduce an equivalence relation on the set of atoms such that the quotient set with the induced product is a monoid, called the condensation monoid. Under suitable hypotheses on R, we show that this monoid is a group and the class of k1_A is the set of atoms of a subalgebra of A called the focal subalgebra. This construction can be iterated to obtain higher condensation groups and focal subalgebras. We apply these results to G-algebras for G a group; in particular, we use them to define new invariants for finite-dimensional irreducible projective representations.Comment: 14 page

From Bare Metal to Virtual: Lessons Learned when a Supercomputing Institute Deploys its First Cloud

As primary provider for research computing services at the University of Minnesota, the Minnesota Supercomputing Institute (MSI) has long been responsible for serving the needs of a user-base numbering in the thousands. In recent years, MSI---like many other HPC centers---has observed a growing need for self-service, on-demand, data-intensive research, as well as the emergence of many new controlled-access datasets for research purposes. In light of this, MSI constructed a new on-premise cloud service, named Stratus, which is architected from the ground up to easily satisfy data-use agreements and fill four gaps left by traditional HPC. The resulting OpenStack cloud, constructed from HPC-specific compute nodes and backed by Ceph storage, is designed to fully comply with controls set forth by the NIH Genomic Data Sharing Policy. Herein, we present twelve lessons learned during the ambitious sprint to take Stratus from inception and into production in less than 18 months. Important, and often overlooked, components of this timeline included the development of new leadership roles, staff and user training, and user support documentation. Along the way, the lessons learned extended well beyond the technical challenges often associated with acquiring, configuring, and maintaining large-scale systems.Comment: 8 pages, 5 figures, PEARC '18: Practice and Experience in Advanced Research Computing, July 22--26, 2018, Pittsburgh, PA, US

The Cool ISM in S0 Galaxies. I. A Survey of Molecular Gas

Lenticular galaxies remain remarkably mysterious as a class. Observations to date have not led to any broad consensus about their origins, properties and evolution, though they are often thought to have formed in one big burst of star formation early in the history of the Universe, and to have evolved relatively passively since then. In that picture, current theory predicts that stellar evolution returns substantial quantities of gas to the interstellar medium; most is ejected from the galaxy, but significant amounts of cool gas might be retained. Past searches for that material, though, have provided unclear results. We present results from a survey of molecular gas in a volume-limited sample of field S0 galaxies, selected from the Nearby Galaxies Catalog. CO emission is detected from 78 percent of the sample galaxies. We find that the molecular gas is almost always located inside the central few kiloparses of a lenticular galaxy, meaning that in general it is more centrally concentrated than in spirals. We combine our data with HI observations from the literature to determine the total masses of cool and cold gas. Curiously, we find that, across a wide range of luminosity, the most gas rich galaxies have about 10 percent of the total amount of gas ever returned by their stars. That result is difficult to understand within the context of either monolithic or hierarchical models of evolution of the interstellar medium.Comment: 26 pages of text, 15 pages of tables, 10 figures. Accepted for publication in the Astrophysical Journa

Masses, luminosities and dynamics of galactic molecular clouds

Star formation in galaxies takes place in molecular clouds and the Milky Way is the only galaxy in which it is possible to resolve and study the physical properties and star formation activity of individual clouds. The masses, luminosities, dynamics, and distribution of molecular clouds, primarily giant molecular clouds in the Milky Way are described and analyzed. The observational data sets are the Massachusetts-Stony Brook CO Galactic Plane Survey and the IRAS far IR images. The molecular mass and infrared luminosities of glactic clouds are then compared with the molecular mass and infrared luminosities of external galaxies

Sources of phoneme errors in repetition: perseverative, neologistic and lesion patterns in jargon aphasia

This study examined patterns of neologistic and perseverative errors during word repetition in fluent Jargon aphasia. The principal hypotheses accounting for Jargon production indicate that poor activation of a target stimulus leads to weakly activated target phoneme segments, which are outcompeted at the phonological encoding level. Voxel-lesion symptom mapping studies of word repetition errors suggest a breakdown in the translation from auditory-phonological analysis to motor activation. Behavioural analyses of repetition data were used to analyse the target relatedness (Phonological Overlap Index: POI) of neologistic errors and patterns of perseveration in 25 individuals with Jargon aphasia. Lesion-symptom analyses explored the relationship between neurological damage and jargon repetition in a group of 38 aphasia participants. Behavioural results showed that neologisms produced by 23 jargon individuals contained greater degrees of target lexico-phonological information than predicted by chance and that neologistic and perseverative production were closely associated. A significant relationship between jargon production and lesions to temporoparietal regions was identified. Region of interest regression analyses suggested that damage the posterior superior temporal gyrus and superior temporal sulcus in combination was best predictive of a Jargon aphasia profile. Taken together these results suggest that poor phonological encoding secondary to impairment in sensory-motor integration alongside impairments in self-monitoring result in jargon repetition. Insights for clinical management and future directions are discussed

Chemical tracers of high-metallicity environments

We present for the first time a detailed study of the properties of molecular gas in metal-rich environments such as early-type galaxies (ETGs). We have explored Photon-Dominated Region (PDR) chemistry for a wide range of physical conditions likely to be appropriate for these sources. We derive fractional abundances of the 20 most chemically reactive species as a function of the metallicity, as a function of the optical depth and for various volume number gas densities, Far-Ultra Violet (FUV) radiation fields and cosmic ray ionisation rates. We also investigate the response of the chemistry to the changes in $\alpha-$element enhancement as seen in ETGs. We find that the fractional abundances of CS, H$_{2}$S, H$_{2}$CS, H$_{2}$O, H$_{3}$O$^{+}$, HCO$^{+}$ and H$_{2}$CN seem invariant to an increase of metallicity whereas C$^{+}$, CO, C$_{2}$H, CN, HCN, HNC and OCS appear to be the species most sensitive to this change. The most sensitive species to the change in the fractional abundance of $\alpha-$elements are C$^{+}$, C, CN, HCN, HNC, SO, SO$_{2}$, H$_{2}$O and CS. Finally, we provide line brightness ratios for the most abundant species, especially in the range observable with ALMA. Discussion of favorable line ratios to use for the estimation of super-solar metallicities and $\alpha$-elements are also provided.Comment: 15 pages, 6 figures, 4 tables, Accepted for publication into MNRA

The future for Advanced level

There is an increasingly diverse group of students opting for at Advanced level work in design and technology and GNVQ Manufacturing. Broadening the range of students means, in particular, that more academically successful ones are joining manufacturing and design and technology courses, increasing the demand on teachers for versatility. This article begins by considering how to offer appropriate courses for academically successful students, and the teaching and learning styles to which such students respond