On effective linearly ordered sets of comparison functions

Both the existence and the non-existence of a linearly ordered (by certain natural order relations) effective set of comparison functions (=dense comparison classes) are compatible with the ZFC axioms of set theory.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

A comparative analysis of multidimensional features of objects resembling sets of graphs

In the present paper, we introduce a notion of a style representing abstract, complex objects having characteristics that can be represented as structured objects. Furthermore, we provide some mathematical properties of such styles. As a main result, we present a novel approach to perform a meaningful comparative analysis of such styles by defining and using graph-theoretic measures. We compare two styles by comparing the underlying feature sets representing sets of graph structurally. To determine the structural similarity between the underlying graphs, we use graph similarity measures that are computationally efficient. More precisely, in order to compare styles, we map each feature set to a so-called median graph and compare the resulting median graphs. As an application, we perform an experimental study to compare special styles representing sets of undirected graphs and present numerical results thereof. (C) 2007 Elsevier Inc. All rights reserved.

Creating a Circus of Words, Music, and Sound: From Roaratorio to Owenvarragh

This article documents the creation of a work by the authors based on a score written by the composer John Cage entitled 'Owenvarragh: A Belfast Circus on The Star Factory.' The article is part of a documentary portfolio in the journal which also includes a volume of the poetry created by Dowling in accordance with the instructions of the Cage score, and a series of documentary videos on the creation of the work and its first performance. Cage's score is based on his work 'Roaratorio: An Irish Circus on Finnegan's Wake' (1979) and it provides a set of detailed instructions for the musical realisation of a literary work. The article documents this first fully realised version of the score since Cage first produced 'Roaratorio' in 1979. The work, which was motivated by the Cage centenary year in 2012, musically realises Carson's book 'The Star Factory' (1998), a novelestic autobiography of Carson's Belfast childhood. The score required the creation of a fixed media piece based on over 300 field recordings of the sounds and places mentioned in the book, a volume of poetry created from the book which is recited to form the rhythmic spine of the work, and the arrangement of a performance including these two components along with live musical performance by the authors in collaboration with three other musicians under their direction, and a video installation created for the work. The piece has been performed three times: in association with the Sonorities 2012 Festival at Queen's University of Belfast (March 2012), at The Belfast Festival at Queen's (October 2012), and in the Rymer Auditoium of the University of York (June 2013).

Additional information:

The work which the article documents was conceived by Monaghan and Dowling, and the project was initiated by Monaghan after a she received a student prize to support its development and first performance. Elements of the project will be included in her PhD dissertation for which Dowling is a supervisor. Monaghan created the fixed media piece based on over 300 field recordings, the largest single aspect of realising Cage's score. Dowling was responsible for initiating the collaboration with Ciaran Carson, and for two other components: the creation of a volume of poetry derived from the literary work which is recited in the performance, and the creation of and supervision of the technical work on a video which accompanies the piece. The co-authors consulted closely during the work on these large components from May 2011 until March 2012 when the first performance took place. The co-authors also shared in numerous other artistic and organisational aspects of the production, including the arrangement and performnance of the music, musical direction to other performers, and marketing.

Reading Elizabeth Bishop's "Artifact of [Words]"

As Emerson noted in his essay 'The Poet' "we are not pans and barrows, not even porters of the fire and torch-bearers, but children of the fire, made of it, and only the same divinity transmuted, and at two or three removes, when we least know about it." For Emerson, the fire is poetry, an elemental force capable of transmutation, transformation and enduring relevance. Moving from Emerson, Elizabeth Bishop rises as the twentieth-century poet most aligned with the possibility of poetry and the powers of its practice, as 'At The Fishhouses' indicates in her clear referencing of Emerson:

"If you should dip your hand in,
your wrist would ache immediately,
your bones would begin to ache and your hand would burn
as if the water were a transmutation of fire
that feeds on stones and burns with a dark gray flame."

This essay will look in detail at Bishop's understanding of the possibility of poetry and how art functions as a multi-dimensional structure that is unsettled as much as it unsettles. In particular, Bishop's poem 'The Monument' will be unpicked as testament both to the practice of Bishop's art and also the role of the poet critic responding to what they uncover

Genome-wide scans of three independent sets of 90 Irish multiplex schizophrenia families and follow-up of selected regions in all families provides evidence for multiple susceptibility genes

From our linkage study of Irish families with a high density of schizophrenia, we have previously reported evidence for susceptibility genes in regions 5q21-31, 6p24-21, 8p22-21, and 10p15-p11. In this report, we describe the cumulative results from independent genome scans of three a priori random subsets of 90 families each, and from multipoint analysis of all 270 families in ten regions. Of these ten regions, three (13q32, 18p11-q11, and 18q22-23) did not generate scores above the empirical baseline pairwise scan results, and one (6q13-26) generated a weak signal. Six other regions produced more positive pairwise and multipoint results. They showed the following maximum multipoint H-LOD (heterogeneity LOD) and NPL scores: 2p14-13: 0.89 (P = 0.06) and 2.08 (P = 0.02), 4q24-32: 1.84 (P = 0.007) and 1.67 (P = 0.03), 5q21-31: 2.88 (P= 0.0007), and 2.65 (P = 0.002), 6p25-24: 2.13 (P = 0.005) and 3.59 (P = 0.0005), 6p23: 2.42 (P = 0.001) and 3.07 (P = 0.001), 8p22-21: 1.57 (P = 0.01) and 2.56 (P = 0.005), 10p15-11: 2.04 (P = 0.005) and 1.78 (P = 0.03). The degree of 'internal replication' across subsets differed, with 5q, 6p, and 8p being most consistent and 2p and 10p being least consistent. On 6p, the data suggested the presence of two susceptibility genes, in 6p25-24 and 6p23-22. Very few families were positive on more than one region, and little correlation between regions was evident, suggesting substantial locus heterogeneity. The levels of statistical significance were modest, as expected from loci contributing to complex traits. However, our internal replications, when considered along with the positive results obtained in multiple other samples, suggests that most of these six regions are likely to contain genes that influence liability to schizophrenia.

Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

Sets of p-multiplicity in locally compact groups

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E∗={(s,t):ts−1∈E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone–von Neumann Theorem.

Will your article be found? Authors choose a confusing variety of words to describe dental survival analyses

OBJECTIVES: Identify the words and phrases that authors used to describe time-to-event outcomes of dental treatments in patients.

MATERIALS AND METHODS: A systematic handsearch of 50 dental journals with the highest Citation Index for 2008 identified articles reporting dental treatment with time-to-event statistics (included "case" articles, n = 95), without time-to-event statistics (active "control" articles, n = 91), and all other articles (passive "control" articles n = 6796). The included and active controls were read, identifying 43 English words across the title, aim and abstract, indicating that outcomes were studied over time. Once identified, these words were sought within the 6796 passive controls. Words were divided into six groups. Differences in use of words were analyzed with Pearson's chi-square across these six groups, and the three locations (title, aim, and abstract).

RESULTS: In the abstracts, included articles used group 1 (statistical technique) and group 2 (statistical terms) more frequently than the active and passive controls (group 1: 35%, 2%, 0.37%, P < 0.001 and group 2: 31%, 1%, 0.06%, P < 0.001). The included and active controls used group 3 (quasi-statistical) equally, but significantly more often than the passive controls (82%, 78%, 3.21%, P < 0.001). In the aims, use of target words was similar for included and active controls, but less frequent for groups 1-4 in the passive controls (P < 0.001). In the title, group 2 (statistical techniques) and groups 3-5 (outcomes) were similar for included and active controls, but groups 2 and 3 were less frequent in the passive controls (P < 0.001). Significantly more included articles used group 6 words (stating the study duration) (54%, 30%, P = 0.001).

CONCLUSION: All included articles used time-to-event analyses, but two-thirds did not include words to highlight this in the abstract. There is great variation in the words authors used to describe dental time-to-event outcomes. Electronic identification of such articles would be inconsistent, with low sensitivity and specificity. Authors should improve the reporting quality. Journals should allow sufficient space in abstracts to summarize research, and not impose unrealistic word limits. Readers should be mindful of these problems when searching for relevant articles. Additional research is required in this field.