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| -rw-r--r-- | figs/folena_new.pdf | bin | 0 -> 32084 bytes | |||
| -rw-r--r-- | figs/walk.pdf | bin | 0 -> 176405 bytes | |||
| -rw-r--r-- | zif.bib | 12 | ||||
| -rw-r--r-- | zif.tex | 25 |
4 files changed, 33 insertions, 4 deletions
diff --git a/figs/folena_new.pdf b/figs/folena_new.pdf Binary files differnew file mode 100644 index 0000000..0da889a --- /dev/null +++ b/figs/folena_new.pdf diff --git a/figs/walk.pdf b/figs/walk.pdf Binary files differnew file mode 100644 index 0000000..b04b96e --- /dev/null +++ b/figs/walk.pdf @@ -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= {arXiv}, eprint = {2407.02092}, primaryclass = {cond-mat.dis-nn} @@ -126,3 +124,13 @@ issn = {1063-5203} } +@unpublished{Kent-Dobias_2025_Very, + author = {JK-D}, + title = {Very persistent random walkers reveal transitions in landscape topology}, + year = {2025}, + url =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} +} + @@ -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*} @@ -1194,6 +1196,25 @@ \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} \begin{column}{0.33\textwidth} |