Above are papers related to the following paper: [Paper_ID] Paper #158812. 	[Title] Synchronization and Desynchronization in a Network of Locally Coupled Wilson-Cowan Oscillators [Abstract] A network of Wilson-Cowan oscillators is constructed, and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis. The network is a two-dimensional matrix, where each oscillator is coupled only to its neighbors. We show analytically that a chain of locally coupled oscillators (the piece-wise linear approximation to the Wilson-Cowan oscillator) synchronizes, and present a technique to rapidly entrain finite numbers of oscillators. The coupling strengths change on a fast time scale based on a Hebbian rule. A global separator is introduced which receives input from and sends feedback to each oscillator in the matrix. The global separator is used to desynchronize different oscillator groups. Unlike many other models, the properties of this network emerge from local connections, that preserve spatial relationships among components, and are critical for encoding Gestalt principles of feature grouping. The ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure/ground segregation based on oscillatory correlation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1127812. 	[Title] Meter as Mechanism: A Neural Network that Learns Metrical Patterns [Abstract] One kind of prosodic structure that apparently underlies both music and language is meter. Yet detailed measurements of both music and speech show that the nested periodicities that define metrical structure are noisy in some sense. What kind of system could produce or perceive such variable metrical timing? And what would it take to store particular metrical patterns in the long-term memory of the system? We have developed a network of coupled oscillators that both produces and perceives metrical patterns of pulses. In addition, beginning with an initial state with no biases, it learns to prefer 3-beat patterns (like waltzes) over 2-beat patterns. Models of this general class could learn to entrain to musical patterns. And given a way to process speech to extract appropriate pulses, the model should be applicable to metrical structure in speech as well. Is language metrical? Meter refers both to particular sorts of patterns in time and to an abstract description of such patterns, potentially a cognitive representation of them. In both cases there are two or more hierarchical levels at which equally spaced events occur, and the periods characterizing these levels are integral multiples of each other (usually 2 or 3). The hierarchy is implied in standard Western musical notation, where the different levels are indicated by kinds of notes (quarter notes, half notes, etc.) and by bars separating measures. For example, in a basic waltz-time meter, there are individual beats, all with the same spacing, grouped into sets of three with every third one receiving a stronger accent. In such a meter, there is a hierarchy consisting of both a faster periodic cycle (at the beat level) and a slower one (the measure level) that is 1/3 as fast with its onset (or zero phase angle) coinciding with the zero phase angle of every third beat. Metrical systems like this seem to underlie most forms of music around the world and are often said to underlie human speech as well (Jones, 1932; Martin, 1972). However, an awkward difficulty is that the definition employs the notion of an integer since data on both music and speech show clearly that the perfect temporal ratios predicted by such a definition are not observed in performance. In music performance, various kinds of systematic temporal deviations in the timing specified by musical notation are known to Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #567018. 	[Title] Representing Rhythmic Patterns in a Network of Oscillators [Abstract] This paper describes an evolving computational model of the perception and production of simple rhythmic patterns. The model consists of a network of oscillators of different resting frequencies which couple with input patterns and with each other. Oscillators whose frequencies match periodicities in the input tend to become activated. Metrical structure is represented explicitly in the network in the form of clusters of oscillators whose frequencies and phase angles are constrained to maintain the harmonic relationships that characterize meter. Rests in rhythmic patterns are represented by explicit rest oscillators in the network, which become activated when an expected beat in the pattern fails to appear. The model makes predictions about the relative difficulty of The nested periodicity that defines musical, and probably also linguistic, meter appears to be fundamental to the way in which people perceive and produce patterns in time. Meter by itself, however, is not sufficient to describe patterns which are interesting or memorable because of how they deviate from the metrical hierarchy. The simplest deviations are rests or gaps where one or more levels in the hierarchy would normally have a beat. When beats are removed at regular intervals which match the period of some level of the metrical hierarchy, we have what we will call a simple rhythmic pattern. Figure 1 shows an example of a simple rhythmic pattern. Below it is a grid representation of the meter which is behind the pattern. patterns and the effect of deviations from periodicity in the input. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #249421. 	[Title] PERCEPTION OF TIME AS PHASE: TOWARD AN ADAPTIVE-OSCILLATOR MODEL OF RHYTHMIC PATTERN PROCESSING 1 [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #219446. 	[Title] RESONANCE AND THE PERCEPTION OF MUSICAL METER [Abstract] 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 listeners internal processing mechanisms. This article introduces a novel connectionist unit, based upon a mathematical model of entrainment, capable of phase and frequency-locking to periodic components of incoming rhythmic patterns. Networks of these units can self-organize 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. Please summarise all the given information.

Paper #158812 has the title `Synchronization and Desynchronization in a Network of Locally Coupled Wilson-Cowan Oscillators  
` and the abstract `A network of Wilson-Cowan oscillators is constructed, and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis. The network is a two-dimensional matrix, where each oscillator is coupled only to its neighbors. We show analytically that a chain of locally coupled oscillators (the piece-wise linear approximation to the Wilson-Cowan oscillator) synchronizes, and present a technique to rapidly entrain finite numbers of oscillators. The coupling strengths change on a fast time scale based on a Hebbian rule. A global separator is introduced which receives input from and sends feedback to each oscillator in the matrix. The global separator is used to desynchronize different oscillator groups. Unlike many other models, the properties of this network emerge from local connections, that preserve spatial relationships among components, and are critical for encoding Gestalt principles of feature grouping. The ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure/ground segregation based on oscillatory correlation. 
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Question: Which category should Paper #158812 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #158812 has the title `Synchronization and Desynchronization in a Network of Locally Coupled Wilson-Cowan Oscillators  
` and the abstract `A network of Wilson-Cowan oscillators is constructed, and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis. The network is a two-dimensional matrix, where each oscillator is coupled only to its neighbors. We show analytically that a chain of locally coupled oscillators (the piece-wise linear approximation to the Wilson-Cowan oscillator) synchronizes, and present a technique to rapidly entrain finite numbers of oscillators. The coupling strengths change on a fast time scale based on a Hebbian rule. A global separator is introduced which receives input from and sends feedback to each oscillator in the matrix. The global separator is used to desynchronize different oscillator groups. Unlike many other models, the properties of this network emerge from local connections, that preserve spatial relationships among components, and are critical for encoding Gestalt principles of feature grouping. The ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure/ground segregation based on oscillatory correlation. 
`.
Question: Which category should Paper #158812 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks