Abstract
Rhythmic neural firing is thought to underlie the operation of neural function. This triggers the construction of dynamical network models to investigate how the rhythms interact with each other. Recently, an approach concerning neural path pruning has been proposed in a dynamical network system, in which critical neuronal connections are identified and adjusted according to the pruning maps, enabling neurons to produce rhythmic, oscillatory activity in simulation. Here, we construct a sort of homomorphic functions based on different rhythms of neural firing in network dynamics. Armed with the homomorphic functions, the pruning maps can be simply expressed in terms of interactive rhythms of neural firing and allow a concrete analysis of coupling operators to control network dynamics. Such formulation of pruning maps is applied to probe the consolidation of rhythmic patterns between layers of neurons in feedforward neural networks.
Highlights
Lines of research on the roles of rhythms are studied, including synchronous flashing of fireflies [3], pacemaker cells of the heart [4], synchronization of pulse-coupled oscillators [5,6], synchronous neural activity propagating in scale-free networks, random networks, and cortical neural networks [7,8]
Neural path pruning paves an alternative way to derive operators convolving with signals and controlling neural network dynamics
For neurons firing in rhythm, the pruning map can be formulated in terms of quantities related to rhythmic neural firing
Summary
Rhythms are ubiquitous and have been shown to play an important role in living organisms [1,2]. In neural network dynamics, an important issue is to probe activity-dependent plasticity of neural connections entwined with rhythms [9,10,11] Such a kind of plasticity is claimed to be the heart of the organization of behavior [12,13,14,15]. They meet the neurobiological concept called Hebbian synaptic plasticity [12,13,14] Such plasticity operation reflects an internal control in neural network dynamics, enabling neurons to produce rhythmic, oscillatory activity [27]. Neural path pruning paves an alternative way to derive operators convolving with signals and controlling neural network dynamics This motivates us to formulate pruning maps with rhythmic neural firing, which may induce a framework of feedforward neural networks for rhythm formation
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