Traces in braided categories

With any even Hecke symmetry R (that is a Hecke type solution of the Yang-Baxter equation) we associate a quasitensor category. We formulate a condition on R implying that the constructed category is rigid and its commutativity isomorphisms R_{U,V} are natural. We show that this condition leads to rescaling of the initial Hecke symmetry. We suggest a new way of introducing traces as properly normalized categorical morphisms End(V) --> K and deduce the corresponding normalization from categorical dimensions.Comment: Source: Revised version, a more attention is given to the problem of trace definition and its proper normalization in braided categories with Hecke type braidings. Minor corrections in Introduction. LaTex file, all macros included, no figure

The use and function of gestures in word-finding difficulties in aphasia

Background: Gestures are spontaneous hand and arm movements that are part of everyday communication. The roles of gestures in communication are disputed. Most agree that they augment the information conveyed in speech. More contentiously, some argue that they facilitate speech, particularly when word-finding difficulties (WFD) occur. Exploring gestures in aphasia may further illuminate their role. Aims: This study explored the spontaneous use of gestures in the conversation of participants with aphasia (PWA) and neurologically healthy participants (NHP). It aimed to examine the facilitative role of gesture by determining whether gestures particularly accompanied WFD and whether those difficulties were resolved. Methods & Procedures: Spontaneous conversation data were collected from 20 PWA and 21 NHP. Video samples were analysed for gesture production, speech production, and WFD. Analysis 1 examined whether the production of semantically rich gestures in these conversations was affected by whether the person had aphasia, and/or whether there were difficulties in the accompanying speech. Analysis 2 identified all WFD in the data and examined whether these were more likely to be resolved if accompanied by a gesture, again for both groups of participants. Outcomes & Results: Semantically rich gestures were frequently employed by both groups of participants, but with no effect of group. There was an effect of the accompanying speech, with gestures occurring most commonly alongside resolved WFD. An interaction showed that this was particularly the case for PWA. NHP, on the other hand, employed semantically rich gestures most frequently alongside fluent speech. Analysis 2 showed that WFD were common in both groups of participants. Unsurprisingly, these were more likely to be resolved for NHP than PWA. For both groups, resolution was more likely if a WFD was accompanied by a gesture. Conclusions: These findings shed light on the different functions of gesture within conversation. They highlight the importance of gesture during WFD, both in aphasic and neurologically healthy language, and suggest that gesture may facilitate word retrieval