N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds

We study the elliptic genera of hyperKahler manifolds using the representation theory of N=4 superconformal algebra. We consider the decomposition of the elliptic genera in terms of N=4 irreducible characters, and derive the rate of increase of the multiplicities of half-BPS representations making use of Rademacher expansion. Exponential increase of the multiplicity suggests that we can associate the notion of an entropy to the geometry of hyperKahler manifolds. In the case of symmetric products of K3 surfaces our entropy agrees with the black hole entropy of D5-D1 system.Comment: 25 pages, 1 figur

Modular Invariance and Uniqueness of Conformal Characters

We show that the conformal characters of various rational models of W-algebras can be already uniquely determined if one merely knows the central charge and the conformal dimensions. As a side result we develop several tools for studying representations of SL(2,Z) on spaces of modular functions. These methods, applied here only to certain rational conformal field theories, may be useful for the analysis of many others.Comment: 21 pages (AMS TeX), BONN-TH-94-16, MPI-94-6

What infant-directed speech tells us about the development of compensation for assimilation

In speech addressed to adults, words are seldom realized in their canonical, or citation, form. For example, the word ‘green’ in the phrase ‘green beans’ can often be realized as ‘greem’ due to English place assimilation, where word-final coronals take on the place of articulation of neighboring velars. In such a situation, adult listeners readily ‘undo’ the assimilatory process and perceive the underlying intended lexical form of ‘greem’ (i.e. they access the lexical representation ‘green’). An interesting developmental question is how children, with their limited lexical knowledge, come to cope with phonologically conditioned connected speech processes such as place assimilation. Here, we begin to address this issue by examining the occurrence of place assimilation in the input to English-learning 18-month-olds. Perceptual and acoustic analyses of elicited speech, as well as analysis of a corpus of spontaneous speech, all converge on the finding that caregivers do not spoon-feed their children canonical tokens of words. Rather, infant-directed speech contains just as many non-canonical realizations of words in place assimilation contexts as adult-directed speech. Implications for models of developmental speech perception are discussed

The time course of auditory and language-specific mechanisms in compensation for sibilant assimilation

Models of spoken-word recognition differ on whether compensation for assimilation is language-specific or depends on general auditory processing. English and French participants were taught words that began or ended with the sibilants /s/ and /∫/. Both languages exhibit some assimilation in sibilant sequences (e.g., /s/ becomes like [∫] in dress shop and classe chargée), but they differ in the strength and predominance of anticipatory versus carryover assimilation. After training, participants were presented with novel words embedded in sentences, some of which contained an assimilatory context either preceding or following. A continuum of target sounds ranging from [s] to [∫] was spliced into the novel words, representing a range of possible assimilation strengths. Listeners' perceptions were examined using a visual-world eyetracking paradigm in which the listener clicked on pictures matching the novel words. We found two distinct language-general context effects: a contrastive effect when the assimilating context preceded the target, and flattening of the sibilant categorization function (increased ambiguity) when the assimilating context followed. Furthermore, we found that English but not French listeners were able to resolve the ambiguity created by the following assimilatory context, consistent with their greater experience with assimilation in this context. The combination of these mechanisms allows listeners to deal flexibly with variability in speech forms

Twist-bend coupling and the statistical mechanics of the twistable wormlike-chain model of DNA: Perturbation theory and beyond

The simplest model of DNA mechanics describes the double helix as a continuous rod with twist and bend elasticity. Recent work has discussed the relevance of a little-studied coupling G between twisting and bending, known to arise from the groove asymmetry of the DNA double helix. Here the effect of G on the statistical mechanics of long DNA molecules subject to applied forces and torques is investigated. We present a perturbative calculation of the effective torsional stiffness C_{eff} for small twist-bend coupling. We find that the "bare" G is "screened" by thermal fluctuations, in the sense that the low-force, long-molecule effective free energy is that of a model with G=0 but with long-wavelength bending and twisting rigidities that are shifted by G-dependent amounts. Using results for torsional and bending rigidities for freely fluctuating DNA, we show how our perturbative results can be extended to a nonperturbative regime. These results are in excellent agreement with numerical calculations for Monte Carlo "triad" and molecular dynamics "oxDNA" models, characterized by different degrees of coarse graining, validating the perturbative and nonperturbative analyses. While our theory is in generally good quantitative agreement with experiment, the predicted torsional stiffness does systematically deviate from experimental data, suggesting that there are as-yet-uncharacterized aspects of DNA twisting-stretching mechanics relevant to low-force, long-molecule mechanical response, which are not captured by widely used coarse-grained models.status: publishe