On the multipacking number of grid graphs

In 2001, Erwin introduced broadcast domination in graphs. It is a variant of classical domination where selected vertices may have different domination powers. The minimum cost of a dominating broadcast in a graph $G$ is denoted $\gamma_b(G)$. The dual of this problem is called multipacking: a multipacking is a set $M$ of vertices such that for any vertex $v$ and any positive integer $r$, the ball of radius $r$ around $v$ contains at most $r$ vertices of $M$ . The maximum size of a multipacking in a graph $G$ is denoted mp(G). Naturally mp(G) $\leq \gamma_b(G)$. Earlier results by Farber and by Lubiw show that broadcast and multipacking numbers are equal for strongly chordal graphs. In this paper, we show that all large grids (height at least 4 and width at least 7), which are far from being chordal, have their broadcast and multipacking numbers equal

Sonically-enhanced widgets: comments on Brewster and Clarke, ICAD 1997

This paper presents a review of the research surrounding the paper “The Design and Evaluation of a Sonically Enhanced Tool Palette” by Brewster and Clarke from ICAD 1997. A historical perspective is given followed by a discussion of how this work has fed into current developments in the area

A Dichotomy Theorem for Circular Colouring Reconfiguration

The "reconfiguration problem" for circular colourings asks, given two $(p,q)$-colourings $f$ and $g$ of a graph $G$, is it possible to transform $f$ into $g$ by changing the colour of one vertex at a time such that every intermediate mapping is a $(p,q)$-colouring? We show that this problem can be solved in polynomial time for $2\leq p/q <4$ and is PSPACE-complete for $p/q\geq 4$. This generalizes a known dichotomy theorem for reconfiguring classical graph colourings.Comment: 22 pages, 5 figure

Using non-speech sounds to provide navigation cues

This article describes 3 experiments that investigate the possibiity of using structured nonspeech audio messages called earcons to provide navigational cues in a menu hierarchy. A hierarchy of 27 nodes and 4 levels was created with an earcon for each node. Rules were defined for the creation of hierarchical earcons at each node. Participants had to identify their location in the hierarchy by listening to an earcon. Results of the first experiment showed that participants could identify their location with 81.5% accuracy, indicating that earcons were a powerful method of communicating hierarchy information. One proposed use for such navigation cues is in telephone-based interfaces (TBIs) where navigation is a problem. The first experiment did not address the particular problems of earcons in TBIs such as “does the lower quality of sound over the telephone lower recall rates,” “can users remember earcons over a period of time.” and “what effect does training type have on recall?” An experiment was conducted and results showed that sound quality did lower the recall of earcons. However; redesign of the earcons overcame this problem with 73&#37; recalled correctly. Participants could still recall earcons at this level after a week had passed. Training type also affected recall. With personal training participants recalled 73&#37; of the earcons, but with purely textual training results were significantly lower. These results show that earcons can provide good navigation cues for TBIs. The final experiment used compound, rather than hierarchical earcons to represent the hierarchy from the first experiment. Results showed that with sounds constructed in this way participants could recall 97% of the earcons. These experiments have developed our general understanding of earcons. A hierarchy three times larger than any previously created was tested, and this was also the first test of the recall of earcons over time

Mating Success of Gypsy Moth (Lepidoptera: Lymantriidae) Females in Southern Wisconsin

Mating success of laboratory-reared gypsy moth Lymantria dispar (L.) females exposed for 24 hr on tree boles and its relationship to male moth counts in pheromone-baited traps was studied in southern Wisconsin. The relationship between mating probability of gypsy moth females and male moth counts in traps corresponded to an exponential model that can be used for predicting mating probabilities in sparse isolated populations. Relative attractiveness of females compared with traps was 0.23, which is similar to earlier estimated relative attractiveness of females in Virginia. The mortality of females from predation, however, was found to be significantly lower in Wisconsin than in Virginia, which may contribute to a larger degree of mating success. Increased long-distance dispersal of males could also contribute to the increased mating success of females. The higher rate of spread of gypsy moth populations in Wisconsin compared with other areas may be due to the increased mating success caused by the lower female mortality and higher long-distance dispersal of males

Cardiovascular disease and air pollution in Scotland: no association or insufficient data and study design?

&lt;p&gt;&lt;b&gt;Background:&lt;/b&gt; Coronary heart disease and stroke are leading causes of mortality and ill health in Scotland, and clear associations have been found in previous studies between air pollution and cardiovascular disease. This study aimed to use routinely available data to examine whether there is any evidence of an association between short-term exposure to particulate matter (measured as PM10, particles less than 10 micrograms per cubic metre) and hospital admissions due to cardiovascular disease, in the two largest cities in Scotland during the years 2000 to 2006.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Methods:&lt;/b&gt; The study utilised an ecological time series design, and the analysis was based on overdispersed Poisson log-linear models.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Results:&lt;/b&gt; No consistent associations were found between PM10 concentrations and cardiovascular hospital admissions in either of the cities studied, as all of the estimated relative risks were close to one, and all but one of the associated 95% confidence intervals contained the null risk of one.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Conclusions:&lt;/b&gt; This study suggests that in small cities, where air quality is relatively good, then either PM10 concentrations have no effect on cardiovascular ill health, or that the routinely available data and the corresponding study design are not sufficient to detect an association.&lt;/p&gt

The complexity of signed graph and edge-coloured graph homomorphisms

We study homomorphism problems of signed graphs from a computational point of view. A signed graph $(G,\Sigma)$ is a graph $G$ where each edge is given a sign, positive or negative; $\Sigma\subseteq E(G)$ denotes the set of negative edges. Thus, $(G, \Sigma)$ is a $2$-edge-coloured graph with the property that the edge-colours, $\{+, -\}$, form a group under multiplication. Central to the study of signed graphs is the operation of switching at a vertex, that results in changing the sign of each incident edge. We study two types of homomorphisms of a signed graph $(G,\Sigma)$ to a signed graph $(H,\Pi)$: ec-homomorphisms and s-homomorphisms. Each is a standard graph homomorphism of $G$ to $H$ with some additional constraint. In the former, edge-signs are preserved. In the latter, edge-signs are preserved after the switching operation has been applied to a subset of vertices of $G$. We prove a dichotomy theorem for s-homomorphism problems for a large class of (fixed) target signed graphs $(H,\Pi)$. Specifically, as long as $(H,\Pi)$ does not contain a negative (respectively a positive) loop, the problem is polynomial-time solvable if the core of $(H,\Pi)$ has at most two edges, and is NP-complete otherwise. (Note that this covers all simple signed graphs.) The same dichotomy holds if $(H,\Pi)$ has no negative digons, and we conjecture that it holds always. In our proofs, we reduce s-homomorphism problems to certain ec-homomorphism problems, for which we are able to show a dichotomy. In contrast, we prove that a dichotomy theorem for ec-homomorphism problems (even when restricted to bipartite target signed graphs) would settle the dichotomy conjecture of Feder and Vardi.Comment: 21 pages; 6 figures. In this version, we have adopted some changes in terminology and notatio

Variations in the propagation of UH-nuclei

Calculations of the propagation of UH-nuclei were improved by extending the number of individual nuclides considered, and by using more recent evaluations of the rigidity dependence of the escape length, the possible source composition, and altered cross sections. The effects of using different expressions for the dependence of abundances on first ionization potentials (FIP) are outlined. The sensitivity of the calculated elemental abundances to the various changes made in the propagation assumptions are discussed