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

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% 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% 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

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

White Matter Integrity, Facial Emotion Perception, and Socialization in Autism Spectrum Disorders

Difficulty interpreting facial expressions is an important component of social deficits seen in Autism Spectrum Disorders (ASDs). The amygdalo-fusiform white matter tract is theorized to contribute to facial expression interpretation. The current study examined relationships between white matter integrity (WMI) along the aymgdalo-fusiform pathway, facial emotion perception (FEP), and socialization skill (SS) in a sample of typically developing (TD) participants and participants with ASDs. Groups were differentiated by WMI along the amygdalo-fusiform tract. Results suggested unexpected negative relationships between WMI and SS, and between WMI and FEP in the ASD group. A group interaction was suggested for WMI and FEP such that participants with ASDs demonstrated a negative relationship, whereas TD participants displayed the hypothesized positive relationship. Overall, findings suggest that measures of WMI along the amygdalo-fusiform tract should not be conceptualized identically in participants with ASDs and controls

Initiatives—Enemy of the Republic

The Seattle University Law Review\u27s Symposium on the initiative process in Washington State addresses an issue of both transcendent importance to the health of the Republic and immediate challenge to the welfare of the children of this state. This discussion could not be more timely, and not just locally. Here\u27s why. Devolution, tax cuts for the rich and the super rich, welfare reform, and a more conservative, market-oriented philosophy of government lay on the states and low income parents and children the burden of meeting the most critical needs of children-from prenatal care through college. With twenty percent of our children living in poverty and that many or more living in dysfunctional families, or in no families at all, the situation has reached crisis proportions. Enter the initiative. All along the West Coast, ill advised and ill intentioned initiatives have produced a severe crisis, albeit one obscure to many citizens. Initiatives have effectively, and in my view unconstitutionally, taken the appropriation and revenue raising responsibilities away from the legislature and passed them not to the people, as initiative supporters argue, but to special interest groups