Fic. 2. Temporal correlation and oscillation burst life-time analyses characterize the non-random temporal structure of amplitude fluctuations in oscillations. (A) The study of spatial and temporal dimensions of neuronal processing requires different correlation analyses. Coordination of anatomically distributed activity (parallel processing) may be studied by computing correlations between neuronal signals from different hippocampal regions (Cross-correlations). In contrast, coordination of brain activity over time (serial processing) may be studied by computing temporal auto-correlations in neuronal signals within a single hippocampal region (Auto-correlations). Serial processing requires a sequence of causally related neuronal activities, which is likely to give rise to correlations over time (temporal correlations), e.g. persistent oscillatory activity as reflected in a slow amplitude modulation as studied here. Thus, by studying auto-correlation properties we may learn about novel mechanisms of attention and memory. Figure from Montez et al. (2009). ©2009 National Academy of Sciences, USA. (B) The raw signal was band-pass filtered around its peak frequency (thick blue line), and the amplitude envelope (thin red line) was extracted using the Hilbert transform. To quantify differences in oscillation burst dynamics on short to intermediate time scales (< | s), we introduced a threshold at multiples of the median amplitude envelope (exemplified by the median threshold, top horizontal dashed line, black areas) and 0.5*median amplitude (lower horizontal dashed line, black and blue areas), and defined the start and end of an oscillation burst as the time points of crossing this threshold. The oscillation burst structure is largely independent of which threshold is used. (C) Cumulative probability distribution plot of life-times calculated using 0.5*median as the threshold at different concentrations. (D) Three-dimensional plot showing the 95th percentile life-time vs. carbachol (carbamylcholine chloride) (CCH) concentration, normalized with the life-time at the first period with 1 wm CCH, for different thresholds. We tested thresholds in the range of 0.1—1.1 times the median amplitude envelope. We normalized the life-time to avoid displaying the trivial effects of increased life-time with lower threshold. We observed that the life-time is largely independent of which threshold is used. (E) Amplitude envelopes of a signal with a low DFA exponent (0.52; 1 mM CCH, blue trace), a high DFA exponent (0.65; 10 um CCH, red trace), and an intermediate exponent (0.55; 20 uM CCH, green trace). Visual inspection of the amplitude modulation at different CCH concentrations reveals a more stable modulation (high DFA exponent, long life- time) at physiologically relevant concentrations (15 M) compared with higher CCH concentrations. Example segments of the amplitude envelope from the same slice at different CCH concentration. (F) Visualization of DFA for a signal with a low DFA exponent (0.52; blue circles), an intermediate exponent (0.55; green squares) and a high DFA exponent (0.63; red pluses). When the signal with high DFA is shuffled in oscillation cycle wide windows, the correlations disappear (0.50, black dots). The DFA exponents are the slopes of the lines obtained with linear regression in log-log coordinates. The DFA plots correspond to the amplitude envelopes partially shown in E. (G) Auto-correlations of the amplitude envelopes in E [1 wm CCH (blue circles), 20 mM CCH (green squares) and 10 uM CCH (red pluses)]. When the amplitude envelope of the 10 wm CCH is shuffled in oscillation cycle wide windows, the correlations disappear (black dots, Supporting Information Fig. S5). For interpretation of color references in figure legend, please refer to the Web version of this article.