The Shape of Randomness

Kendra Redmond over at The Physics Buzz blog:

We often rely on shapes and patterns when navigating the world. Poison ivy or an innocent plant? A nasty rash or the imprint of the textured wall you were leaning against? Similarly, scientists often use shapes and patterns to interpret datasets. Do the points follow a straight line? Appear in clusters? On the street and in the lab, shapes help us organize information, interpret data, and even make predictions.

While some sets of data are relatively straightforward to interpret, others get messy quickly. It can be difficult to extract useful information from maps of complicated situations like the relationship between diseases and their associated genes. This is because the structures that emerge often depend on parameters chosen by researchers through a somewhat arbitrary process, making it difficult to tell when a structure is really significant. In new research recently published in the American Physical Society’s journal Physical Review E, a team of scientists from Université Laval in Canada, the Politecnico di Torino and the ISI Foundation in Italy introduce a valuable tool for determining whether the shape of a complex dataset is actually significant.

This map represents the complex relationship between crimes and individuals in St. Louis. The blue shapes correspond to criminal cases; the orange dots represent involved individuals (criminals, victims, and witnesses). The system is highly organized, according to the simplicial configuration model.
Image Credit: Alice Patania, Giovanni Petri, Francesco Vaccarino, and Jean-Gabriel Young.

Diseases and their associated genes are just one example of what scientists classify as a complex system. Many other systems fall into this category too—the Earth’s climate, living cells, the human brain, social structures—really any system that is difficult to describe because it contains so many moving, interacting pieces. Of course, understanding these same systems can have a profound effect on our quality of life, enabling early warning systems, targeted treatments, and effective interventions.

A common way of studying these systems is with complex networks, a way of visually representing components and their interactions and looking at the structures that emerge. For example, the traditional network approach considers each component to be a node and each interaction between two components as a line linking them together. Research shows that the network approach is effective in helping us understand many systems. However, you can lose important information by applying it to a complex system that can’t be broken down into a set of clean interactions between two components.

More here.