The geometry of variations in Batalin-Vilkovisky formalism

This is a paper about geometry of (iterated) variations. We explain why no sources of divergence are built into the Batalin-Vilkovisky (BV) Laplacian, whence there is no need to postulate any ad hoc conventions such as "$\delta(0)=0$" and "$\log\delta(0)=0$" within BV-approach to quantisation of gauge systems. Remarkably, the geometry of iterated variations does not refer at all to the construction of Dirac's $\delta$-function as a limit of smooth kernels. We illustrate the reasoning by re-deriving - but not just "formally postulating" - the standard properties of BV-Laplacian and Schouten bracket and by verifying their basic inter-relations (e.g., cohomology preservation by gauge symmetries of the quantum master-equation).Comment: XXI International Conference on Integrable Systems and Quantum Symmetries (ISQS21) 11-16 June 2013 at CVUT Prague, Czech Republic; 51 pages (9 figures). - Main Example 2.4 on pp.34-36 retained from arXiv:1302.4388v1, standard proofs in Appendix A amended and quoted from arXiv:1302.4388v1 (joint with S.Ringers). - Solution to Exercise 11.6 from IHES/M/12/13 by the same autho

The impact of shared knowledge on speakers’ prosody

International audienceHow does the knowledge shared by interlocutors during interaction modify the way speakers speak? Specifically, how does prosody change when speakers know that their addressees do not share the same knowledge as them? We studied these effects in an interactive paradigm in which French speakers gave instructions to addressees about where to place a cross between different objects (e.g., You put the cross between the red mouse and the red house). We manipulated (i) whether the two interlocutors shared or did not necessarily share the same objects and (ii) the informational status of referents. We were interested in two types of prosodic variations: global prosodic variations that affect entire utterances (i.e., pitch range and speech rate variations) and more local prosodic variations that encode infor-mational status of referents (i.e., prosodic phrasing for French). We found that participants spoke more slowly and with larger pitch excursions in the not-shared knowledge condition than in the shared knowledge condition while they did not prosodically encode the informa-tional status of referents regardless of the knowledge condition. Results demonstrated that speakers kept track of what the addressee knew, and that they adapted their global prosody to their interlocutors. This made the task too cognitively demanding to allow the prosodic encoding of the informational status of referents. Our findings are in line with the idea that complex reasoning usually implicated in constructing a model of the addressee co-exists with speaker-internal constraints such as cognitive load to affect speaker's prosody during interaction

Distinguishing schemes and tasks in children's development of multiplicative reasoning

We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children’s thinking, and learning situations must be organized to (a) build on children’s available schemes, (b) promote the next scheme in the sequence, and (c) link to intended mathematical concepts