论文标题
基于订单 - 索引的基于事件的地图，用于学习节拍
Order-indeterminant event-based maps for learning a beat
论文作者
论文摘要
人们认为，人类与音乐节拍同步的过程是通过错误纠正发生的，即个人对节拍时间的时期和阶段的估计值进行了迭代调整以与外部刺激保持一致。从数学上讲，可以使用二维映射来描述误差校正，其中收敛到固定点对应于同步与BEAT。在本文中，我们展示了一种称为Beat Generator的神经系统如何通过错误校正来调整其振荡行为，以使其同步到外部周期信号。我们构建了一个基于二维事件的映射，该图迭代地调整了节拍发生器的内部参数，以加快或减慢其振荡行为，以使其与周期性刺激同步。该地图是新颖的，因为定义地图的事件的顺序不是先验的。取而代之的是，在地图的每个迭代中进行的错误校正调整的类型由一系列预期事件确定。该地图拥有丰富的动力学曲目，包括定期解决方案和混沌轨道。
The process by which humans synchronize to a musical beat is believed to occur through error-correction where an individual's estimates of the period and phase of the beat time are iteratively adjusted to align with an external stimuli. Mathematically, error-correction can be described using a two-dimensional map where convergence to a fixed point corresponds to synchronizing to the beat. In this paper, we show how a neural system, called a beat generator, learns to adapt its oscillatory behaviour through error-correction to synchronize to an external periodic signal. We construct a two-dimensional event-based map which iteratively adjusts an internal parameter of the beat generator to speed up or slow down its oscillatory behaviour to bring it into synchrony with the periodic stimulus. The map is novel in that the order of events defining the map are not a priori known. Instead, the type of error-correction adjustment made at each iterate of the map is determined by a sequence of expected events. The map possesses a rich repertoire of dynamics, including periodic solutions and chaotic orbits.
