Little changes made on the train

1 files changed, 13 insertions, 7 deletions

diff --git a/zif.tex b/zif.tex
index 1680d0c..50f083f 100644
--- a/zif.tex
+++ b/zif.tex
@@ -187,7 +187,7 @@
         \mu=\frac1N\operatorname{Tr}\operatorname{Hess} H(\boldsymbol x)
       \]
 
-      \bigskip
+      \smallskip
 
       Condition on marginal minima by inserting
       \[
@@ -506,7 +506,7 @@
 
       \medskip
 
-      Jamming of disks in $d$ dimensions:
+      Rectified activations or jamming of disks:
       \[
         \|\boldsymbol x^i-\boldsymbol x^j\|\geq 2R\qquad i,j=1,\ldots,P
       \]
@@ -697,7 +697,8 @@
     \begin{column}{0.5\textwidth}
       $M$ data points, $N$ parameters, $\alpha=M/N$, $y^\mu=V_0$, $\boldsymbol a^\mu$ spherical $p$-spin coefficients,
       \[
-        f_{\boldsymbol x}(\boldsymbol a^\mu)
+        V_0
+        =f_{\boldsymbol x}(\boldsymbol a^\mu)
         =H^{(\mu)}_p(\boldsymbol x)
       \]
       Average Euler characteristic reduced to integral over $m=\frac1N\boldsymbol x\cdot\boldsymbol x_0$,
@@ -726,7 +727,8 @@
     \begin{column}{0.5\textwidth}
       $M$ data points, $N$ parameters, $\alpha=M/N$, $y^\mu=V_0$, $\boldsymbol a^\mu$ spherical $p$-spin coefficients,
       \[
-        f_{\boldsymbol x}(\boldsymbol a^\mu)
+        V_0
+        =f_{\boldsymbol x}(\boldsymbol a^\mu)
         =H^{(\mu)}_p(\boldsymbol x)
       \]
       Simplest case: $p=1$, $\Omega$ is intersection of random hyperplanes with the sphere
@@ -764,7 +766,7 @@
         f_{\boldsymbol x}(\boldsymbol a^\mu)
         =H^{(\mu)}_p(\boldsymbol x)
       \]
-      For $p>1$, new phases possible
+      For $p>1$, new phases are possible
 
       \medskip
 
@@ -1048,6 +1050,10 @@
   \frametitle{Practical considerations: treating the sum over subsets}
   \begin{columns}
     \begin{column}{0.9\textwidth}
+      Annealed count can be made with or without this trick
+
+      \bigskip
+
       \includegraphics[width=\textwidth]{figs/annealed_compare.pdf}
     \end{column}
   \end{columns}
@@ -1077,12 +1083,12 @@
 
       \bigskip
 
-      $N\to\infty$ gives asymptotically zero curvature for all $\kappa$
+      \alert<5>{$N\to\infty$ gives asymptotically zero curvature for all $\kappa$}
     \end{column}
     \begin{column}{0.27\textwidth}
       \begin{overprint}
         \onslide<1-2>\includegraphics[width=\textwidth]{figs/curvature_demo_1.pdf}
-        \onslide<3>\includegraphics[width=\textwidth]{figs/curvature_demo_2.pdf}
+        \onslide<3,5>\includegraphics[width=\textwidth]{figs/curvature_demo_2.pdf}
         \onslide<4>\includegraphics[width=\textwidth]{figs/curvature_demo_3.pdf}
       \end{overprint}
     \end{column}