Third case of the Cyclic Coloring Conjecture

The Cyclic Coloring Conjecture asserts that the vertices of every plane graph with maximum face size D can be colored using at most 3D/2 colors in such a way that no face is incident with two vertices of the same color. The Cyclic Coloring Conjecture has been proven only for two values of D: the case D=3 is equivalent to the Four Color Theorem and the case D=4 is equivalent to Borodin's Six Color Theorem, which says that every graph that can be drawn in the plane with each edge crossed by at most one other edge is 6-colorable. We prove the case D=6 of the conjecture

Representation, space and Hollywood Squares: Looking at things that aren't there anymore

It has been argued that the human cognitive system is capable of using spatial indexes or oculomotor coordinates to relieve working memory load (Ballard, Hayhoe, Pook & Rao, 1997) track multiple moving items through occlusion (Scholl & Pylyshyn, 1999) or link incompatible cognitive and sensorimotor codes (Bridgeman and Huemer, 1998). Here we examine the use of such spatial information in memory for semantic information. Previous research has often focused on the role of task demands and the level of automaticity in the encoding of spatial location in memory tasks. We present five experiments where location is irrelevant to the task, and participants' encoding of spatial information is measured implicitly by their looking behavior during recall. In a paradigm developed from Spivey and Geng (submitted), participants were presented with pieces of auditory, semantic information as part of an event occurring in one of four regions of a computer screen. In front of a blank grid, they were asked a question relating to one of those facts. Under certain conditions it was found that during the question period participants made significantly more saccades to the empty region of space where the semantic information had been previously presented. Our findings are discussed in relation to previous research on memory and spatial location, the dorsal and ventral streams of the visual system, and the notion of a cognitive-perceptual system using spatial indexes to exploit the stability of the external world

How can I help you? User instructions in telephone calls

We a small corpus of instructions given in phone calls to customers who need support for programming their universal remote control, to make it suitable for their particular TV set VCR, Audio, etc. Typically, in these calls the operator or 'agent' coaches the client while the client is performing actions with the equipment (turning it on, pressing buttons and codes, directing it towards the TV, etc.). We compared these oral instructions with the concept of a 'streamlined step procedure' (Farkas, 1999) and other principles that are well-known from the literature about written instructions. Our conclusion is that many problems arise because the operator does not provide 'meta-communication' about the goals that have to be achieved, and because the feedback given by the client is neglected or misinterpreted

Relative cellular algebras

In this paper we generalize cellular algebras by allowing different partial orderings relative to fixed idempotents. For these relative cellular algebras we classify and construct simple modules, and we obtain other characterizations in analogy to cellular algebras. We also give several examples of algebras that are relative cellular, but not cellular. Most prominently, the restricted enveloping algebra and the small quantum group for $\mathfrak{sl}_{2}$, and an annular version of arc algebras.Comment: 39 pages, many figures, revised version, to appear in Transform. Groups, comments welcom