diff --git a/papers/matthew_feickert/full_text.pdf b/papers/matthew_feickert/full_text.pdf index 8192c2de4b..8a17bb8451 100644 Binary files a/papers/matthew_feickert/full_text.pdf and b/papers/matthew_feickert/full_text.pdf differ diff --git a/papers/matthew_feickert/meca.zip b/papers/matthew_feickert/meca.zip index 98f5778a7c..f9d56564c2 100644 Binary files a/papers/matthew_feickert/meca.zip and b/papers/matthew_feickert/meca.zip differ diff --git a/papers/sam_morley/full_text.pdf b/papers/sam_morley/full_text.pdf new file mode 100644 index 0000000000..36ca2df9f3 Binary files /dev/null and b/papers/sam_morley/full_text.pdf differ diff --git a/papers/sam_morley/main.md b/papers/sam_morley/main.md index ebaf99b0fd..99828aecaa 100644 --- a/papers/sam_morley/main.md +++ b/papers/sam_morley/main.md @@ -539,10 +539,10 @@ RoughPy streams cache the result of log-signature queries over dyadic intervals so they can be reused in later calculations. To compute the log-signature over any interval $I$, we granularise at a fixed stream resolution $n$ to obtain the interval $\tilde I = [k_1/2^n, k_2/2^n)$, and then compute -:::{math} -\mathrm{LogSig}(\tilde I) = \log\biggl(\prod\_{k=k_1}^{k_2-1} +```{math} +\mathrm{LogSig}(\tilde{I}) = \log\biggl(\prod_{k=k_1}^{k_2-1} \exp(\mathrm{LogSig}(D_k^n))\biggr). -::: +``` The $\mathrm{LogSig}(D_k^n)$ terms on the right-hand-side are either retrieved from the cache, or computed from the underlying source. This is essentially the Campbell-Baker-Hausdorff formula applied to the log-signatures at the finest diff --git a/papers/sam_morley/meca.zip b/papers/sam_morley/meca.zip new file mode 100644 index 0000000000..c4339bb96e Binary files /dev/null and b/papers/sam_morley/meca.zip differ