I construct a finite-dimensional quantum theory from general relativity by a homotopy method. Its quantum history is made up of at least two levels of fermionic elements. Its unitary group has the diffeomorphism group as singular limit. Its gravitational metrical form is the algebraic square. Its spinors are multivectors.

In this paper we obtain multifractal generalizations of classical results by Lévy and Khintchin in metrical Diophantine approximations and measure theory of continued fractions. We give a complete multifractal analysis for Stern–Brocot intervals, for continued fractions and for certain Diophantine growth rates. In particular, we give detailed discussions of two multifractal spectra closely rela...

Previous phonetic studies of metrical prominence have primarily focused on its acoustic manifestations, including pitch, intensity, duration, spectral tilt, etc. In this paper we outline our new research program in which we explore jaw displacement patterns as another articulatory reflex of metrical prominence. We present our studies of English and Japanese in some detail, which show that jaw m...

We present a general theory of topological maps whereby sensory input, topological and local metrical information are combined to define the topological maps explaining such information. Topological maps correspond to the minimal models of an axiomatic theory describing the relationships between the different sources of information explained by a map. We use a circumscriptive theory to specify ...

How do perceivers apply knowledge to instances they have never experienced before? On one hand, listeners might use idealized representations that do not contain specific details. On the other, they might recognize and process information based on more detailed memory representations. The current study examined the latter possibility with respect to musical meter perception, previously thought ...

The goal of this study is the automatic detection of onsets of the singing voice in polyphonic audio recordings. Starting with a hypothesis that the knowledge of the current position in a metrical cycle (i.e. metrical accent) can improve the accuracy of vocal note onset detection, we propose a novel probabilistic model to jointly track beats and vocal note onsets. The proposed model extends a s...

In this paper, we analyze Levitan and Bebutov metrical approximations of functions $F :\Lambda \times X \rightarrow Y$ by trigonometric polynomials $\rho$-periodic type functions, where $\emptyset \neq \Lambda \subseteq {\mathbb R}^{n}$, $X$ $Y$ are complex Banach spaces, $\rho$ is a general binary relation on $Y$. We also various classes multidimensional almost periodic in metric uniformly rec...

Brett Hyde Phonology / Volume 29 / Issue 03 / December 2012, pp 383 ­ 431 DOI: 10.1017/S0952675712000218, Published online: 13 December 2012 Link to this article: http://journals.cambridge.org/abstract_S0952675712000218 How to cite this article: Brett Hyde (2012). The odd­parity input problem in metrical stress theory. Phonology, 29, pp 383­431 doi:10.1017/S0952675712000218 Request Permissions ...

Musical rhythms encompass temporal patterns that often yield regular metrical accents (e.g., a beat). There have been mixed results regarding perception as a function of metrical saliency, namely, whether sensitivity to a deviant was greater in metrically stronger or weaker positions. Besides, effects of metrical position have not been examined in non-isochronous rhythms, or with respect to mul...