From 4b490020b1930cdfa1b2b1f473aa6e9b99eec870 Mon Sep 17 00:00:00 2001 From: Michiel Stock Date: Mon, 26 Jul 2021 11:48:07 +0200 Subject: [PATCH] =?UTF-8?q?=E2=9C=8Ffix=20equations=20information=20docs?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Equations were not processed correctly. Quick fix --- docs/src/properties/information.md | 14 ++++---------- 1 file changed, 4 insertions(+), 10 deletions(-) diff --git a/docs/src/properties/information.md b/docs/src/properties/information.md index 678d5a1d..b4fab8d5 100644 --- a/docs/src/properties/information.md +++ b/docs/src/properties/information.md @@ -4,17 +4,11 @@ Indices based on information theory, such as entropy, mutual information etc, ca One can compute individual indices or use the function `information_decomposition` which performs the entire decomposition at once. This decomposition yields for a given network the deviation of the marginal distributions of the species with the uniform distribution (quantifying the evenness), the mutual information (quantifying the specialisation) and the variance of information (quantifying the freedom and stability of the interactions). These indices satisfy the following balance equation for the top ($T$) and bottom ($B$) throphic level: -$$ -\log(nm) = D(B,T) + 2 I(B;T) + V(B;T) -$$ +$$\log(nm) = D(B,T) + 2 I(B;T) + V(B;T)$$ -$$ -\log(n) = D(B) + I(B;T) + H(B|T) -$$ +$$\log(n) = D(B) + I(B;T) + H(B|T)$$ -$$ -\log(m) = D(T) + I(B;T) + H(T|B) -$$ +$$\log(m) = D(T) + I(B;T) + H(T|B)$$ Here, $n$ and $m$ are number of bottom and top species, respectively. @@ -52,4 +46,4 @@ convert2effective ## References Stock, M.; Hoebeke, L.; De Baets, B. « Disentangling the Information in Species Interaction Networks ». -Entropy 2021, 23, 703. https://doi.org/10.3390/e23060703 \ No newline at end of file +Entropy 2021, 23, 703. https://doi.org/10.3390/e23060703