Fix forecasting slides

forecasting/slides.html

@@ -91,19 +91,20 @@ <h3>Nonlinear forecasting</h3>
 				</section>
 
 				<section>
-					<h3>Complex attractors</h3>
+					<h3>Dynamics may be chaotic</h3>
 					<img class="stretch" src="images/lorenz.png">
 				</section>
 
 				<section>
-					<h3>Why short-term?</h3>
+					<h3>Predictions with chaos: short shelf life</h3>
 					<p>Trajectories in chaotic attractors diverge
 					<p> $$ \lvert \delta \textbf{Z}(t)\rvert \approx e^{\lambda t}\lvert\delta\textbf{Z}_0\rvert$$
 					<p> $\lambda$ is the Lyapunov exponent
 					<p> (so with chaos, $\lambda>0$)
 				</section>
 
 				<section>
+					<section>
 					<h3>How to forecast</h3>
 					<ul>
 						<li>Choose an embedding dimension $E$ and lag $\tau$</li>
@@ -113,9 +114,9 @@ <h3>How to forecast</h3>
 						<li>See where predictee's $E+1$ nearest neighbors wind up $t$ steps into the future</li>
 						<li>Measure correlations $\rho$ between predictee's observed future state and neighbors' weighted predictions</li>
 					</ul>
-				</section>
+					</section>
 
-				<section>
+					<section>
 					<h3>Choosing $E$ and $\tau$</h3>
 					<p>An unsolved problem
 					<p>Use $E$ (and $\tau$) that yield best predictions</p>
@@ -124,6 +125,9 @@ <h3>Choosing $E$ and $\tau$</h3>
 							<a href="http://www.nature.com/nature/journal/v344/n6268/abs/344734a0.html">Sugihara and May 1990</a>
 						</div>
 						</section>
+				</section>
+
+
 
 				<section>
 					<h3>Observational noise v. chaos</h3>
@@ -246,7 +250,7 @@ <h3>Predictive fitness models</h3>
 					<br>
 					<p>A simple predictive model estimates the fitness $f$ of virus $i$ as</p>
 					<p>$$\hat{f}_i = \beta^\mathrm{ep} \, f_i^\mathrm{ep} + \beta^\mathrm{ne} \, f_i^\mathrm{ne}$$</p>
-					<p>where $f_i^\mathrm{ep}$ measures cross-immunity via substitutions at epitope sites and $f_i^\mathrm{ep}$ measures mutational load via substitutions at non-epitope sites</p>
+					<p>where $f_i^\mathrm{ep}$ measures cross-immunity via substitutions at epitope sites and $f_i^\mathrm{ne}$ measures mutational load via substitutions at non-epitope sites</p>
 					<div class="citation">
 						<a href="http://www.nature.com/nature/journal/v507/n7490/full/nature13087.html">&#321;uksza and L&auml;ssig 2014</a>
 					</div>	
@@ -257,7 +261,7 @@ <h3>Model selection</h3>
 					<img src="images/luksza_models.png">
 						<div class="citation">
 							<a href="https://www.google.com/?ion=1&espv=2#q=predictive%20fitness%20luksza">
-								Luksza and Lassig 2014
+								&#321;uksza and L&auml;ssig 2014
 							</a>
 						</div>
 				</section>
@@ -267,7 +271,7 @@ <h3>Performance</h3>
 					<img class="stretch" src="images/prediction_ll.jpg">	
 					<div class="citation">
 						<a href="https://www.google.com/?ion=1&espv=2#q=predictive%20fitness%20luksza">
-							Luksza and Lassig 2014
+							&#321;uksza and L&auml;ssig 2014
 						</a>
 					</div>
 				</section>