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Resonance and the Perception of Musical Meter
 CONNECTION SCIENCE
, 1994
"... Many connectionist approaches to musical expectancy and music composition let the question of "What next?" overshadow the equally important question of "When next?". One cannot escape the latter question, one of temporal structure, when considering the perception of musical meter ..."
Abstract

Cited by 94 (3 self)
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Many connectionist approaches to musical expectancy and music composition let the question of "What next?" overshadow the equally important question of "When next?". One cannot escape the latter question, one of temporal structure, when considering the perception of musical meter. We view the perception of metrical structure as a dynamic process where the temporal organization of external musical events synchronizes, or entrains, a listener's internal processing mechanisms. This article introduces a novel connectionist unit, based upon a mathematical model of entrainment, capable of phase and frequencylocking to periodic components of incoming rhythmic patterns. Networks of these units can selforganize temporally structured responses to rhythmic patterns. The resulting network behavior embodies the perception of metrical structure. The article concludes with a discussion of the implications of our approach for theories of metrical structure and musical expectancy.
Mixed memory Markov models: decomposing complex stochastic processes as mixtures of simpler ones
, 1998
"... . We study Markov models whose state spaces arise from the Cartesian product of two or more discrete random variables. We show how to parameterize the transition matrices of these models as a convex combinationor mixtureof simpler dynamical models. The parameters in these models admit a simple ..."
Abstract

Cited by 64 (1 self)
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. We study Markov models whose state spaces arise from the Cartesian product of two or more discrete random variables. We show how to parameterize the transition matrices of these models as a convex combinationor mixtureof simpler dynamical models. The parameters in these models admit a simple probabilistic interpretation and can be fitted iteratively by an ExpectationMaximization (EM) procedure. We derive a set of generalized BaumWelch updates for factorial hidden Markov models that make use of this parameterization. We also describe a simple iterative procedure for approximately computing the statistics of the hidden states. Throughout, we give examples where mixed memory models provide a useful representation of complex stochastic processes. Keywords: Markov models, mixture models, discrete time series 1. Introduction The modeling of time series is a fundamental problem in machine learning, with widespread applications. These include speech recognition (Rabiner, 1989), natu...
Preface
"... This book is the result of an unsuccessful joke. During the summer of 1990, we were both participating in the Complex Systems Summer School of the Santa Fe Institute. Like many such programs dealing with “complexity, ” this one was full of exciting examples of how it can be possible to recognize whe ..."
Abstract
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This book is the result of an unsuccessful joke. During the summer of 1990, we were both participating in the Complex Systems Summer School of the Santa Fe Institute. Like many such programs dealing with “complexity, ” this one was full of exciting examples of how it can be possible to recognize when apparently complex behavior has a simple understandable origin. However, as is often the case in young disciplines, little effort was spent trying to understand how such techniques are interrelated, how they relate to traditional practices, and what the bounds on their reliability are. These issues must be addressed if suggestive results are to grow into a mature discipline. Problems were particularly apparent in time series analysis, an area that we both arrived at in our respective physics theses. Out of frustration with the fragmented and anecdotal literature, we made what we thought was a humorous suggestion: run a competition. Much to our surprise, no one laughed and, to our further surprise, the Santa Fe Institute promptly agreed to support it. The rest is history (630 pages worth). Reasons why a competition might be a bad idea abound: science is a thoughtful activity, not a simple race; the relevant disciplines are too dissimilar and the questions too difficult to permit meaningful comparisons; and the required effort might be prohibitively large in return for potentially misleading results. On the other hand, regardless of the very different techniques and language games of the different disciplines that study time series (physics, biology, economics,...), very