Research

OverviewEarly warning signalsGene networksCorrelation networksTemporal network dataTemporal network theoryEnergy landscapesPublic healthEvolutionary dynamicsAnimal behavior

Overview

My main research interests are network science and mathematical biology. In mathematical biology, I am mostly working on network-related topics: network science applied to biology and medicine. However, this is very often not mere applications of ready-to-use methods; the work often involves method development and validation. In network science, I am working on both non-bio things and bio-related things. I occasionally work on non-network research (evolutionary game theory unrelated to networks, science of science) but only a little. Below is a brief overview of each topic, with more recent ones coming first.

Early warning signals and sentinel nodes in network dynamics

Many complex systems — ecosystems, power grids, the brain, financial markets — can change abruptly, jumping from one state to a very different one once they are pushed past a so-called tipping point. Can we see such a jump coming before it happens? Often we can: as a system approaches a tipping point, its fluctuations tend to grow larger and to change more slowly over time, and these trends can serve as early warning signals. This has been studied since at least early 2000s. In fact, many systems for which we want to anticipating a tipping point are networks composed of many interacting parts: e.g., species in an ecosystem, regions of the brain, firms in a market. In network systems, we often cannot watch every part, and some part may give more informative early warning signals than others. So, which handful of nodes we monitor makes a big difference. We developed early warning signals tailored to network dynamics and ways to choose a small set of especially informative “sentinel” nodes that give the clearest advance warning. A closely related theme is dimension reduction: describing the collective behavior of a whole network with just a few variables, which helps explain why watching a few well-chosen nodes can work and keeps the mathematics manageable. The papers below build algorithms and theory behind these and related ideas and test them on both model and real-world networks.

Multilayer gene networks

I bring network science and data analysis to genetics, in collaboration with genome biologists. The tens of thousands of genes in our cells act in a coordinated way: genes that co-vary can be joined into a gene co-expression network. For example, looking at the “communities” of such a network — and how they change from one tissue to another — helps reveal which groups of genes work as a team. Using related ideas and methods, we also study, e.g., why some genes behave in a switch-like, all-or-nothing way that can raise or lower disease risk, how large duplicated stretches of DNA differ across animal species, and how structural differences in DNA vary among human populations. The common thread is using mathematics and computation to find meaningful patterns in multilayer genomic datasets.

Correlation networks

In many fields, we begin not with a network but with a big table of measurements — say, the activity of many brain regions over time, the price movements of many stocks, or the expression levels of many genes. A common way to turn such data into a network is to measure how strongly each pair of variables is correlated and to treat strong correlations as connections; the result is a correlation network. Building one well is in fact subtle: simply keeping the correlations above a chosen cutoff can create misleading structure. So, we develop more principled ways to construct correlation networks. In contrast to methods in statistics and machine learning, such as graphical lasso and covariance shrinkage, my main focus is to extract structures and numbers that network science proposed and have been useful (e.g., multilayer communities, clustering coefficient), but without transforming the original data into networks (because doing so introduces bias). I am also doing applications to genomics. The Physics Report paper below is a review of the whole area.

Temporal network data analytics

Many networks are not fixed: the links between people, animals, neurons, or devices switch on and off over time, and the exact timing of contacts can matter as much as who is connected to whom. Networks that keep this timing information are called temporal networks. As data with precise time stamps become widely available, we need good ways to represent, summarize, and compare them. We develop such tools — for example, methods that turn an evolving network into a trajectory or a low-dimensional embedding so that its changes can be visualized and analyzed, and techniques for detecting recurring states or activity patterns in a network that changes over time.

Temporal network theory

A question complementary to temporal network data analytics is what temporal structure actually does: how the timing of connections changes processes that unfold on a network, such as the spread of an epidemic or a rumor, the evolution of cooperation, or the formation of opinions. Real-world contacts tend to be bursty and correlated rather than smooth and random, and this can speed up, slow down, or even qualitatively change such dynamics compared with a static network. We build and analyze mathematical and computational models — for instance, of how concurrent (overlapping) partnerships affect contagion, how evolutionary games play out when the network keeps switching, and how to simulate bursty, non-Markovian dynamics efficiently — and use them to understand, and sometimes control, what happens on temporal networks.

Energy landscape analysis

Energy landscape analysis is a method we have been developing to make sense of multichannel dynamical data — many time series recorded together, such as brain signals from multiple regions of interest (but the data need not be biological). The idea is to picture the system as a ball rolling on a landscape of hills and valleys: each valley is a relatively stable pattern of activity that the system tends to settle into, and the hills are barriers it must cross to reach another. From the data alone we estimate this landscape and read off how many stable states there are, how they connect, and how the system moves among them — turning a high-dimensional recording into an intuitive map of a few states, which we apply mainly to neuroimaging. Differences in the energy landscape between patients and healthy people can be useful biomarkers, which various research (mostly done by other people using this method) is supporting. Below, PLoS Complex Systems (2025) and Phil. Trans. R. Soc. A (2017) papers are review papers.

Schematics of brain dynamics during bistable perception
Fig: Schematics of brain dynamics during bistable perception. Magenta: visual-area state. Blue: frontal-area state. Yellow: intermediate state. A colored circle represents activity of regions of interest in each of the three attractive basins (red: high, blue: low). The green curve represents brain dynamics.

Networks in public health

Network thinking is useful across many public-health problems. In this line of work, I mostly apply network methods, often in collaboration with public-health specialists. Examples include mapping the “journeys” that people take during opioid overdose behavior, studying online social networks of people affected by adverse childhood experiences or expressing suicidal thoughts, and using medical record data from a hospital to help limit infections that spread within a hospital contact network.

Evolutionary dynamics on networks

How does the structure of a population shape which behaviors or traits spread and eventually take over? In evolutionary dynamics on networks, individuals sit on the nodes of a network and interact with their neighbors, and we ask questions such as how likely a new mutant or strategy is to spread to the whole population (its fixation probability) and how fast this happens. A central case is evolutionary games on networks, in which individuals play social-dilemma games such as the prisoner’s dilemma game with their neighbors; here the network structure can strongly affect whether cooperation survives. We study these questions on ordinary networks and on richer structures — weighted, multilayer, temporal, and higher-order (hypergraph) networks — and consider effects such as committed “zealots” and feedback between individuals and their environment, for example.

Modeling and data analysis of animal behavior

Animals in a group interact with one another to accomplish collective tasks — ants selecting and moving to a new nest, sharing information during an emigration, or forming dominance hierarchies, and homing pigeons settling on a route as a flock. I study such collective animal behavior by combining mathematical modeling with data analysis, usually together with biologists: building models of how group-level decisions emerge from simple rules that individuals follow, and sometimes using network analysis to describe who interacts with whom and how information and influence flow through a group.