Algorithmic aspects of a chip-firing game

Algorithmic aspects of a chip-firing game on a graph introduced by Biggs are studied. This variant of the chip-firing game, called the dollar game, has the properties that every starting configuration leads to a so-called critical configuration. The set of critical configurations has many interesting properties. In this paper it is proved that the number of steps needed to reach a critical configuration is polynomial in the number of edges of the graph and the number of chips in the starting configuration, but not necessarily in the size of the input. An alternative algorithm is also described and analysed

Long cycles in graphs with large degree sums and neighborhood unions

We present and prove several results concerning the length of longest cycles in 2-connected or 1-tough graphs with large degree sums. These results improve many known results on long cycles in these graphs. We also consider the sharpness of the results and discuss some possible strengthenings

Formation of the Galactic Millisecond Pulsar Triple System PSR J0337+1715 - a Neutron Star with Two Orbiting White Dwarfs

The millisecond pulsar in a triple system (PSR J0337+1715, recently discovered by Ransom et al.) is an unusual neutron star with two orbiting white dwarfs. The existence of such a system in the Galactic field poses new challenges to stellar astrophysics for understanding evolution, interactions and mass-transfer in close multiple stellar systems. In addition, this system provides the first precise confirmation for a very wide-orbit system of the white dwarf mass-orbital period relation. Here we present a self-consistent, semi-analytical solution to the formation of PSR J0337+1715. Our model constrains the peculiar velocity of the system to be less than 160 km/s and brings novel insight to, for example, common envelope evolution in a triple system, for which we find evidence for in-spiral of both outer stars. Finally, we briefly discuss our scenario in relation to alternative models.Comment: ApJ Letters, in press (6 pages, 3 figures, 1 table

Does bank capital matter for monetary transmission?

Paper for a conference sponsored by the Federal Reserve Bank of New York entitled Financial Innovation and Monetary TransmissionBank capital ; Monetary policy

The origin of single radio pulsars

By comparing relative rates of supernovae versus formation rates of single radio pulsars, recycled pulsars, binary pulsars and X-ray binaries we put strong limits on the progenitors of radio pulsars and on the requirement of an asymmetry in the supernova. The assumption that radio pulsars are only formed in type Ib and type Ic supernovae from interacting binaries (Iben & Tutukov 1996) breaks down on the implication that in that case either the formation rate of binary pulsars (double neutron stars) should be of the order of 20%, of the single pulsar birthrate or, alternatively, almost all single pulsars (85% to 98%) should originate from Thorne-Zytkow stars. In the latter case the pulsar velocity distribution is inconsistent with observations. Also, in that case the difference between the supernova rate and the pulsar formation rate would be about one order of magnitude, i.e.: much larger than observed. Allowing type II supernovae from single stars and non-interacting binaries to form radio pulsars solves this conundrum, but then a kick is required in order to explain the high velocities of single radio pulsars. A kick is also required to understand the small birthrate, relative to the supernova rate, of binary pulsars consisting of two neutron stars.Comment: 15 pages, New Astronomy in pres

Awareness, requirements and barriers to use of Assistive Technology designed to enable independence of people suffering from Dementia (ATD)

This article is available through the Brunel Open Access Publishing Fund. Copyright @ 2012 IOS PressThis study investigated the awareness and use of assistive technology for people with dementia. The aim of the study was to explore barriers to the uptake of, and the unmet needs for, assistive technology for dementia (ATD) The work was carried out with family carers of people with dementia because carers are often the purchasers, end users and main beneficiaries of this type of technology. Focus groups were used to explore carers’ views on ATD use, and the problems that might be addressed by ATD, in order to develop a questionnaire for dementia carers. The questionnaire was administered at Alzheimer’s Society carer support groups in South Bucks and in Hillingdon Borough (UK). None of the 16 focus group participants or the 42 respondents to the questionnaire had any personal experience of ATD. The dementia carers reported a number of concerns, problems and unmet needs that could be addressed by existing, commercially available ATD products. Some needs for new technology development were identified in the study, but the lack of awareness of ATD appears to be the most important barrier to technology adoption

A holding cost bound for the economic lot-sizing problem with time-invariant cost parameters

In this paper we derive a new structural property for an optimal solution of the economic lot-sizing problem with time-invariant cost parameters. We show that the total holding cost in an order interval of an optimal solution is bounded from above by a quantity proportional to the setup cost and the logarithm of the number of periods in the interval. Since we can also show that this bound is tight, this is in contrast to the optimality property of the economic order quantity (EOQ) model, where setup cost and holding cost are perfectly balanced. Furthermore, we show that this property can be used for the design of a new heuristic and that the result may be useful in worst case analysis.