Supplementary Material for "Using Sonification to detect weak cross-correlations in coupled excitable systems"

We study cross-correlations in irregularly spiking systems. A single system displays spiking sequences that resemble a stochastic (Poisson) process. Linear coupling between two systems leaves the inter-spike interval distribution qualitatively unchanged but induces cross-correlations between the units. For strong coupling this leads to synchronization as expected but for weak coupling, both a good statistic and sonification reveal the presence of ``motifs'', preferred short firing sequences which are due to the deterministic spiking mechanism. We argue that the use of sonification for time series analysis is superior in the case where intrinsic non-stationarity of an experiment cannot be ruled out. #### Audifications S1a: compression factor 2 S1b: compression factor 6 S1c: compression factor 50 #### Amplitude Modulation S2a: rate 0.1 S2b: rate 0.2 S2c: rate 1 #### Event-based rhythms S3a: r=1 D=0 S3b: r=1 D=0.00125 S3c: r=5 D=0 S3d: r=5 D=0.00125 #### Timbre mapping S4a: 20sec D=0 S4d: 20sec D=0.00125 S4b: 60sec D=0 S4e: 60sec D=0.00125 S4c: 240sec D=0 S4f: 240sec D=0.00125 #### Sonifications for coupling drift S5a: D=0..0.005,20sec rhythm S5b: D=0..0.005,20sec pitch deviation S5c: D=0..0.005,20sec timbre #### Timbre Sonifications of Coupling drift S6a: 20sec, D=0..0.00125 S6b: 30sec, D=0..0.00125 S6c 20sec, D=0..0.005 S6d 30sec, D=0..0.005

本研究聚焦于非规则脉冲发放系统中的互相关性。单个脉冲发放系统的发放序列近似服从随机（泊松（Poisson））过程。两系统间的线性耦合不会从本质上改变脉冲发放间隔分布，却会引发各单元间的互相关性。当耦合强度较高时，如预期会出现同步现象；而在弱耦合条件下，通过优质统计分析与听觉化（sonification）手段均可观测到"基序（motifs）"的存在——这类受确定性脉冲发放机制驱动的、具有偏好性的短时序发放序列。本研究认为，当无法排除实验存在内在非平稳性时，采用听觉化方法开展时序分析具备更优表现。
#### 听觉化示例（Audifications）：S1a：压缩系数2；S1b：压缩系数6；S1c：压缩系数50
#### 幅度调制（Amplitude Modulation）：S2a：调制速率0.1；S2b：调制速率0.2；S2c：调制速率1
#### 基于事件的节律（Event-based rhythms）：S3a：r=1，D=0；S3b：r=1，D=0.00125；S3c：r=5，D=0；S3d：r=5，D=0.00125
#### 音色映射（Timbre mapping）：S4a：时长20秒，D=0；S4d：时长20秒，D=0.00125；S4b：时长60秒，D=0；S4e：时长60秒，D=0.00125；S4c：时长240秒，D=0；S4f：时长240秒，D=0.00125
#### 耦合漂移听觉化示例（Sonifications for coupling drift）：S5a：D取值范围0~0.005，节律时长20秒；S5b：D取值范围0~0.005，音高偏差时长20秒；S5c：D取值范围0~0.005，音色
#### 耦合漂移音色听觉化（Timbre Sonifications of Coupling drift）：S6a：时长20秒，D取值范围0~0.00125；S6b：时长30秒，D取值范围0~0.00125；S6c：时长20秒，D取值范围0~0.005；S6d：时长30秒，D取值范围0~0.005