Degree Sequences and the Existence of kk-Factors

We consider sufficient conditions for a degree sequence $\pi$ to be forcibly $k$-factor graphical. We note that previous work on degrees and factors has focused primarily on finding conditions for a degree sequence to be potentially $k$-factor graphical. We first give a theorem for $\pi$ to be forcibly 1-factor graphical and, more generally, forcibly graphical with deficiency at most $\beta\ge0$. These theorems are equal in strength to Chv\'atal's well-known hamiltonian theorem, i.e., the best monotone degree condition for hamiltonicity. We then give an equally strong theorem for $\pi$ to be forcibly 2-factor graphical. Unfortunately, the number of nonredundant conditions that must be checked increases significantly in moving from $k=1$ to $k=2$, and we conjecture that the number of nonredundant conditions in a best monotone theorem for a $k$-factor will increase superpolynomially in $k$. This suggests the desirability of finding a theorem for $\pi$ to be forcibly $k$-factor graphical whose algorithmic complexity grows more slowly. In the final section, we present such a theorem for any $k\ge2$, based on Tutte's well-known factor theorem. While this theorem is not best monotone, we show that it is nevertheless tight in a precise way, and give examples illustrating this tightness.Comment: 19 page

Discovery of Two Relativistic Neutron Star-White Dwarf Binaries

We have discovered two recycled pulsars in relativistic orbits as part of the first high-frequency survey of intermediate Galactic latitudes. PSR J1157-5112 is a 44 ms pulsar and the first recycled pulsar with an ultra-massive (M > 1.14 Mo) white dwarf companion. Millisecond pulsar J1757-5322 is a relativistic circular-orbit system which will coalesce due to the emission of gravitational radiation in less than 9.5 Gyr. Of the ~40 known circular orbit pulsars, J1757-5322 and J1157-5112 have the highest projected orbital velocities. There are now three local neutron-star/white-dwarf binaries that will coalesce in less than a Hubble time, implying a large coalescence rate for these objects in the local Universe. Systems such as J1141-6545 (Kaspi et al. 2000) are potential gamma-ray burst progenitors and dominate the coalescence rate, whilst lighter systems make excellent progenitors of millisecond pulsars with planetary or ultra-low mass companions.Comment: 4 pages, to appear in ApJ Letters. Uses aastex v 5.0, emulateapj5.sty, apjfonts.st

Towards the development of the psychosocial impact of assistive devices scale for continence (C-PIADS)

BACKGROUND: Current outcome measures for continence management devices do not adequately address psychosocial impact. The PIADS is an assessment tool that has been shown to reliably predict the adoption and use of assistive technology devices, but it is not widely used for continence devices. OBJECTIVE: To explore whether the PIADS requires modification to address the particular needs of continence device users and to inform any subsequent item development. METHODS: The study used interpretive methods in which qualitative information from semi-structured interviews was combined with the findings from cognitive interviews for questionnaire pre-testing. A total of 40 participants in UK and Canada were interviewed. RESULTS: Few participants had difficulty in understanding or relating to the majority of PIADS items. Several items were not considered relevant to continence and some areas for potential new items were uncovered. Embarrassment and concealment of urinary incontinence from others were common topics. CONCLUSIONS: The PIADS appears to fundamentally address many, but not all, of the important psychosocial concerns of adults who have continence difficulties. A version for continence, the C-PIADS, will require modification of the PIADS and is likely to contain some new items

The CLARIN Knowledge Centre for Atypical Communication Expertise

In this chapter we introduce the CLARIN Knowledge Centre for Atypical Communication Expertise. The mission of ACE is to support researchers engaged in languages which pose particular challenges for analysis; for this, we use the umbrella term “atypical communication”. This includes language use by second-language learners, people with language disorders or those suffering from lan-guage disabilities, and languages that pose unique challenges for analysis, such as sign languages and languages spoken in a multilingual context. The chapter presents details about the collaborations and outreach of the centre, the services offered, and a number of showcases for its activities

A Survey of Best Monotone Degree Conditions for Graph Properties

We survey sufficient degree conditions, for a variety of graph properties, that are best possible in the same sense that Chvatal's well-known degree condition for hamiltonicity is best possible.Comment: 25 page