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PDF statistics: 83 PDF objects out of 1000 (max. 8388607) 50 compressed objects within 1 object stream diff --git a/main.pdf b/main.pdf index e916f20..b77cdbe 100644 Binary files a/main.pdf and b/main.pdf differ diff --git a/main.synctex.gz b/main.synctex.gz index 7ded71d..d5ebd55 100644 Binary files a/main.synctex.gz and b/main.synctex.gz differ diff --git a/main.tex b/main.tex index 33b0910..fa64d5b 100644 --- a/main.tex +++ b/main.tex @@ -309,26 +309,32 @@ $c_i(t)$ exceeds the threshold value $\thr$ during the corresponding averaging interval $\tlp$ \textbf{Implication for intensity invariance:}\\ -- Convolution output $c_i(t)$ = amplitude-based quantity\\ -$\rightarrow$ Values indicate correspondence between template waveform and signal\\ +- Convolution output $c_i(t)$ quantifies temporal similarity between amplitudes of +template waveform $k_i(t)$ and signal $\adapt(t)$ centered at time point $t$\\ +$\rightarrow$ Based on amplitudes on a graded scale -$\rightarrow$ Values indicate correspondence between a template waveform $k_i(t)$ -matches -the waveform of the pre-processed signal $\adapt(t)$ at a given time point $t$ +- Feature $\feat(t)$ quantifies the probability that amplitudes of $c_i(t)$ +exceed threshold value $\thr$ within interval $\tlp$ around time point $t$\\ +$\rightarrow$ Based on binned amplitudes corresponding to one of two categorical states +$\rightarrow$ Deliberate loss of precise amplitude information\\ +$\rightarrow$ Emphasis on temporal structure (ratio of $T_1$ over $\tlp$) -- Feature $\feat(t)$ = duty cycle-based quantity\\ -$\rightarrow$ Values indicate the ratio of two temporal quantities\\ -$\rightarrow$ Values indicate the ratio of time, or probability, that $c_i(t)$ -exceeds threshold value $\thr$ within +- Thresholding of $c_i(t)$ and subsequent temporal averaging of $\bi(t)$ to +obtain $\feat(t)$ constitutes a remapping of an amplitude-encoding quantity into a +duty cycle-encoding quantity, mediated by threshold function $\nl$ +- Different scales of $c_i(t)$ can result in similar $T_1$ segments depending +on the magnitude of the derivative of $c_i(t)$ in temporal proximity to time +points at which $c_i(t)$ crosses threshold value $\thr$\\ +$\rightarrow$ The steeper the slope of $c_i(t)$, the less $T_1$ changes with scale variations\\ +$\rightarrow$ Extreme amplitudes of $c_i(t)$ (peaks/troughs) +$\rightarrow$ Only amplitudes of \\ +$\rightarrow$ Absolute amplitudes of peaks/troughs of $c_i(t)$ \\ +$\rightarrow$ Acuity of peaks/troughs in $c_i(t)$ matters, not their absolute amplitude +- From graded stimulus to categorical behavioral decision:\\ -- Feature $\feat(t)$ = duty cycle-based quantity\\ -$\rightarrow$ Values indicate how often $c_i(t)$ exceeds threshold value $\thr$ - -- Thresholding of $c_i(t)$ and subsequent temporal averaging of $\bi(t)$ to obtain $\feat(t)$ -constitutes a remapping of an amplitude-based quantity (values indicating the match between) into a duty cycle-based quantity\\ \section{Discriminating species-specific song\\patterns in feature space}