Making sense of complex systems through resolution, relevance, and mapping entropy

Abstract

Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those degrees of freedom that mostly determine the behaviour of the system and separate them from less prominent players. Here, we propose an analysis pipeline that integrates three measures of statistical information: resolution, relevance, and mapping entropy. This approach allows one first to identify, in a quantitative manner, the number of degrees of freedom of the system that preserve the largest information content about the generative process that governs it, then to select the specific subset of constituents that optimally provide a synthetic, yet informative reduced representation of the whole. The method, which is implemented in a freely available software, is fully general, as it is shown through the application to three very diverse systems, namely a toy model of independent binary spins, a coarse-grained representation of the financial stock market, and a fully atomistic simulation of a protein.

In Search of a Dynamical Vocabulary: A Pipeline to Construct a Basis of Shared Traits in Large-Scale Motions of Proteins

“…Distance in dynamics After all the pairwise alignments between the elements of the dataset are performed, a distance matrix that expresses differences in the large-scale dynamics is obtained (Figure 1c); then, the dataset undergoes hierarchical clustering [52] based on this distance matrix, in order to identify groups of dynamics-related proteins (Figure 1d). The optimal number of clusters is identified from the interplay between resolution and relevance [53][54][55][56][57]. These two quantities are entropies that are related to each other and depend on the clusterization procedure adopted.…”

In search of a dynamical vocabulary: a pipeline to construct a basis of shared traits in large-scale motions of proteins

“…After all the pairwise alignments between the elements of the dataset are performed, a distance matrix that expresses differences in the large-scale dynamics is obtained; then the dataset undergoes hierarchical clustering [46] based on this distance matrix, in order to identify groups of dynamics-related proteins. The optimal number of clusters is identified from the interplay between resolution and relevance [47][48][49][50][51]. These two quantities, which are defined in more detail in the Methods section, are entropies that are related to each other and depend on the clusterization procedure adopted.…”