Socioeconomic characterization of regions through the lens of individual financial transactions.

People are increasingly leaving digital traces of their daily activities through interacting with their digital environment. Among these traces, financial transactions are of paramount interest since they provide a panoramic view of human life through the lens of purchases, from food and clothes to sport and travel. Although many analyses have been done to study the individual preferences based on credit card transaction, characterizing human behavior at larger scales remains largely unexplored.

Charting molecular free-energy landscapes with an atlas of collective variables.

Collective variables (CVs) are a fundamental tool to understand molecular flexibility, to compute free energy landscapes, and to enhance sampling in molecular dynamics simulations. However, identifying suitable CVs is challenging, and is increasingly addressed with systematic data-driven manifold learning techniques. Here, we provide a flexible framework to model molecular systems in terms of a collection of locally valid and partially overlapping CVs: an atlas of CVs.

Topological obstructions in the way of data-driven collective variables.

Nonlinear dimensionality reduction (NLDR) techniques are increasingly used to visualize molecular trajectories and to create data-driven collective variables for enhanced sampling simulations. The success of these methods relies on their ability to identify the essential degrees of freedom characterizing conformational changes. Here, we show that NLDR methods face serious obstacles when the underlying collective variables present periodicities, e.

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables.

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior.