1. Frequency-Domain Order Parameter for Synchronization Transition of Bursting Neurons Woochang Lim1 and Sang-Yoon Kim2 1Department of Science Education, Daegu National University of Education 2Research Division, LABASIS Co. Introduction  Burstings with the Slow and Fast Time Scales Bursting: Neuronal activity alternates, on a slow timescale, between a silent phase and an active (bursting) phase of fast repetitive spikings Representative examples of bursting neurons: chattering neurons in the cortex, thalamocortical relay neurons, thalamic reticular neurons, hippocampal pyramidal neurons, Purkinje cells in the cerebellum, pancreatic -cells, and respiratory neurons in pre-Botzinger complex  Synchronization of Bursting Neurons Two Different Synchronization Patterns Due to the Slow and Fast Time Scales of Bursting Activity  Burst Synchronization: Synchrony on the Slow Bursting Timescale Temporal coherence between the active phase (bursting) onset or offset times of bursting neurons  Spike Synchronization: Synchrony on the Fast Spiking Timescale Temporal coherence between intraburst spikes fired by bursting neurons in their respective active phases Characterization of Intraburst Spiking Transition Based on Rs  Investigation of Intraburst Spiking States via Separation of Fast Time Scale and in the Frequency Domain IPSR Rs via band-pass filtering [lower and higher cut-off frequencies of 30Hz (high-ass filter) and 90 Hz (low-pass filter)] As D is increased, stripes in the burst band becomes smeared and overlap.  Amplitude of Rs decreases.  Peak in the power spectra of Rs decreases.  Frequency-Domain Spiking Order Parameter Unsynchronized Spiking State: N, then <s>r0 Synchronized Spiking State: N, then <s>r Non-zero value Bursting Transition occurs for Inhibitory Population of Bursting Neurons Characterization of Bursting Transition Based on Bursting Onset and Offset Times  Investigation of Population Bursting States Based on Bursting Onset and Offset Times and in the Frequency Domain Another Raster plots of bursting onset and offset times and IPBR and As D is increased, bursting stripes in the raster plots becomes smeared and overlap.  Amplitude of both and decreases.  Peak in the power spectra of and of decreases.  Frequency-Domain Bursting Order Parameter Unsynchronized Bursting State: N, then Synchronized Bursting State: N, then  Non-zero value Bursting Transition occurs for Parameters in the single Hindmarsh-Rose (HR) neuron Parameters for the synaptic current Bursting Activity in the HR Neuron  Bursting Transition in the Single Neuron Transition to bursting occurs IDC=I*DC (~1.268) Characterization of Bursting Transition in Terms of Bursting Order Parameter  Investigation of Population Bursting States via Separation of Slow Timescale Separation of the slow timescale from IPFR R via low-pass filtering (fc=10Hz)  IPBR Rb As D is increased, bursting bands in the raster plots becomes smeared and overlap.  Amplitude of Rb decreases.  Investigation of Population Bursting States in the Frequency Domain Power spectra of Rb Bursting Coherence Factor Hp and fp: Height and frequency of bursting peak fp: width of the bursting peak at the height of e-1/2 Hp.  Frequency-Domain Bursting Order Parameter Unsynchronized Bursting State: N, then <b>r0 Synchronized Bursting State: N, then <b>r Non-zero value Bursting Transition occurs for Summary  Synchronization of Bursting Neurons: Burst and Spike Synchronizations Due to the Slow and Fast Timescales of Bursting Activity  Characterization of Burst and Spike Synchronizations via Separation of the Slow (Bursting) and Fast (Spiking) Time Scales by Frequency Filtering IPFR R  IPBR Rb (Describing the Slow Bursting Behavior) and IPSR Rs (Describing the Fast Spiking Behavior)  Characterization of Burst Synchronization Based on Bursting Onset and Offset Times Direct Investigation of Bursting Behavior without Separation of Timescales  Characterization of Burst and Spike Synchronization in the Frequency Domain Power Spectrum: Practical Analysis Tools in the Experiments  Frequency-Domain Order Parameter: Realistic Order Parameter Applicable in the Real Experiment (Raster Plots, IPFR, and Power Spectrum: Directly Obtained in the Experiments)