From dfb3531e89dedaac2646a09853e85805002f43de Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Tue, 9 Sep 2025 10:58:46 +0200
Subject: Small edits

---
 figs/folena_new.pdf | Bin 0 -> 32084 bytes
 figs/walk.pdf       | Bin 0 -> 176405 bytes
 zif.bib             |  12 ++++++++++--
 zif.tex             |  25 +++++++++++++++++++++++--
 4 files changed, 33 insertions(+), 4 deletions(-)
 create mode 100644 figs/folena_new.pdf
 create mode 100644 figs/walk.pdf

diff --git a/figs/folena_new.pdf b/figs/folena_new.pdf
new file mode 100644
index 0000000..0da889a
Binary files /dev/null and b/figs/folena_new.pdf differ
diff --git a/figs/walk.pdf b/figs/walk.pdf
new file mode 100644
index 0000000..b04b96e
Binary files /dev/null and b/figs/walk.pdf differ
diff --git a/zif.bib b/zif.bib
index f8d9818..d1b87c2 100644
--- a/zif.bib
+++ b/zif.bib
@@ -45,9 +45,7 @@
  author = {JK-D},
  title = {Algorithm-independent bounds on complex optimization through the statistics of marginal optima},
  year = {2024},
- month = {July},
  url = {https://arxiv.org/abs/2407.02092},
- note = {arXiv preprint},
  archiveprefix = {arXiv},
  eprint = {2407.02092},
  primaryclass = {cond-mat.dis-nn}
@@ -126,3 +124,13 @@
  issn = {1063-5203}
 }
 
+@unpublished{Kent-Dobias_2025_Very,
+ author = {JK-D},
+ title = {Very persistent random walkers reveal transitions in landscape topology},
+ year = {2025},
+ url = {http://arxiv.org/abs/2505.16653},
+ eprint = {2505.16653},
+ eprintclass = {cond-mat.dis-nn},
+ eprinttype = {arxiv}
+}
+
diff --git a/zif.tex b/zif.tex
index 50f083f..38aa2c4 100644
--- a/zif.tex
+++ b/zif.tex
@@ -158,9 +158,11 @@
         \#_\text{points}
         &=\int_\Omega d\boldsymbol x\,\delta\big(\nabla H(\boldsymbol x)\big)\,\big|\det\operatorname{Hess}H(\boldsymbol x)\big|
       \end{align*}
-      Note absolute value of the determinant: want to account for curvature but not add $-1$
 
-      \bigskip
+      Typically exponential in dimension $N$, with \emph{complexity} defined by
+      \[
+        \Sigma=\frac1N\log\#_\text{points}
+      \]
 
       Can specify properties of points by inserting $\delta$-functions:
       \begin{align*}
@@ -1193,6 +1195,25 @@
   \end{columns}
 \end{frame}
 
+\begin{frame}
+  \frametitle{Other landscape applications without RMT}
+
+  \begin{columns}
+    \begin{column}{0.5\textwidth}
+      \includegraphics[width=\textwidth]{figs/folena_new.pdf}
+
+      \tiny\fullcite{Kent-Dobias_2025_On}
+    \end{column}
+    \begin{column}{0.5\textwidth}
+      \vspace{2.5em}
+
+      \includegraphics[width=\textwidth]{figs/walk.pdf}
+
+      \tiny\fullcite{Kent-Dobias_2025_Very}
+    \end{column}
+  \end{columns}
+\end{frame}
+
 \begin{frame}
   \frametitle{Understanding the flat parts of random landscapes}
   \begin{columns}
-- 
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