Skip to content

Commit a03ae1e

Browse files
committed
Update tutorial_5.html
fix inline math display in tutorial 5
1 parent 2d2282c commit a03ae1e

1 file changed

Lines changed: 6 additions & 6 deletions

File tree

tutorial_5.html

Lines changed: 6 additions & 6 deletions
Original file line numberDiff line numberDiff line change
@@ -347,14 +347,14 @@ <h1>Single-component cosinor<a class="headerlink" href="#single-component-cosino
347347
</div>
348348
</div>
349349
<p>Single-component cosinor analysis models rhythmic biological signals by fitting a sinusoidal function to time-series data (e.g., activity, light exposure, or temperature). This approach enables the quantitative estimation of key rhythm parameters. The regression model is expressed as:</p>
350-
<p>$$Y(t) = M + A \cos!\left(\frac{2\pi t}{\tau} + \phi\right) + \varepsilon(t)$$</p>
350+
<p>$$Y(t) = M + A \cos\left(\frac{2\pi t}{\tau} + \phi\right) + \varepsilon(t)$$</p>
351351
<p>Where:</p>
352352
<ul class="simple">
353-
<li><p>M is the MESOR (Midline Estimating Statistic Of Rhythm), representing the rhythm-adjusted mean,</p></li>
354-
<li><p>A is the amplitude, defined as the half the peak-to-trough variation of the fitted curve,</p></li>
355-
<li><p>$\tau$ is the assumed period (the duration of one cycle, typically ~24h),</p></li>
356-
<li><p>$\phi$ is the acrophase, representing the timing of the peak of the fitted rhythm within each cycle,</p></li>
357-
<li><p>$\varepsilon(t)$ is the residual error term.</p></li>
353+
<li><p><em>M</em> is the MESOR (Midline Estimating Statistic Of Rhythm), representing the rhythm-adjusted mean,</p></li>
354+
<li><p><em>A</em> is the amplitude, defined as the half the peak-to-trough variation of the fitted curve,</p></li>
355+
<li><p><em>τ</em> is the assumed period (the duration of one cycle, typically ~24h),</p></li>
356+
<li><p><em>φ</em> is the acrophase, representing the timing of the peak of the fitted rhythm within each cycle,</p></li>
357+
<li><p><em>ε</em>(<em>t</em>) is the residual error term.</p></li>
358358
</ul>
359359
<p>In <code class="docutils literal notranslate"><span class="pre">circStudio</span></code>, the cosinor model is implemented following the same principles as in <code class="docutils literal notranslate"><span class="pre">pyActigraphy</span></code> and is consistent with the general design philosophy of other circadian models in the package. Specifically, the workflow involves instantiating a cosinor model and fitting it to an actigraphy-derived time series:</p>
360360
<div class="cell docutils container">

0 commit comments

Comments
 (0)