My scientific research focuses on complex systems, one of the most exciting new frontiers in fundamental and applied research. I believe we are living in the era of complexity, when massive increases in computational capabilities, data collection, and distributed technologies facilitate a novel understanding of the amazing level of self-organization that can emerge from evolving systems that are far from equilibrium, nonlinear, and self-driven. As a physicist, I am inspired by parallels to the golden era of physics, about a century ago, when the discovery of quantum mechanics and relativity led to fundamental developments with long-lasting impact on humanity, ranging from technological applications to our philosophical view of the world.
Research on complex systems spans multiple fields, including physics, biology, technology, and even sociology or the arts. Like physics in its golden era, it is simultaneously affecting everyday life and our deepest philosophical views. Complex systems have also gathered great public interest, especially when they relate to human dynamics, as shown by the media attention generated by some of our work. For example, this piece in The Rachel Maddow Show (a cable-news political program) explains our work on opinion-formation networks and this collage shows the media response to our paper on networks and locus swarms, which is summarized in this video abstract.
I describe below my current research themes and projects.
1. Collective Motion, Active Matter, Self-Organization, and the Emergence of Structure
Collective motion is one of the simplest forms of self-organization that is observed in various animal groups such as bird flocks or fish schools, in microscopic organisms such as cell colonies, in swarms of autonomous robots, and even in groups of pedestrians. In these systems, groups of self-propelled agents achieve coherent dynamics through simple interactions and without any centralized control. In recent years, the study of collective motion has expanded to include a broader range of systems defined as active matter: Groups of multiple components that inject mechanical energy at the smallest scales considered, which must then self-organize to produce coherent work at larger scales. Active matter systems include developing tissue, active actin polymerization and depolymerization networks within cells, fluids of swimming bacteria, materials with embedded micromotors, etc.
I was fortunate to start working on this field over a decade ago, when very few scientists had identified it as a relevant problem, and have seen it rapidly grow into a very active research area. I have studied many questions within the field with multiple collaborators and from different perspectives, including the statistical mechanics, fluid dynamics, material science, control theory, collective decision making, distributed computations, and swarm intelligence perspectives. The field addresses a number of deep questions, such as the origin of self-organizing collectives in biology, while also leading to a variety of applications, such controlling robot swarms or understanding the process that leads to the collective migration of cancer cells.
Some of the efforts in which I am currently involved are described below.
1.1. Active elastic systems
The main aspects of this work appear in this video abstract of one of our papers. A more detailed description can be found in my talk at the Kavli Institute for Theoretical Physics.
Up to now, the dynamics of collective motion has been largely understood as based on alignment interactions, where agents turn to reach a consensus on their heading direction. In recent work inspired by robotic control algorithms, I collaborated with engineers to show that collective motion can also emerge from agents that only exchange information on their relative positions through interactions similar to attraction-repulsion. This can be viewed as an active elastic system, where agents are self-propelled masses connected by springs. The self-organizing mechanism is driven here by an inverse energy cascade (from smaller to larger scales) that produces growing regions of coherent motion. This mechanism is similar to the dampening of higher harmonics on a string, but where self-propulsion yields persistent self-organized dynamics. It is archetypical of living systems, where energy is generated at small scales and must self-organize to produce work at larger scales.
This work opens a new perspective in the study of active matter, serving as a starting point for various future projects. For example, active elastic structures could be used to represent agents in artificial-life simulations, where evolutionary algorithms could lead to different self-organized dynamics and to the emergence of the modular-hierarchical structures described below and in this short proposal. Another interesting project could use 3d-printed sheets of bead-like bristlebots linked by springs to represent mechanically an active elastic system. These would first self-align and then start advancing when placed on any vibrating surface, which could make for an interesting toy or educational tool.
1.2. Inverse Energy cascades
The inverse energy cascades discussed is a novel self-organizing mechanism, with yet unexplored features. Rather than relying on a consensus process between agents, it results from mode selection, where small disordered modes decay and large ordered structures are amplified. In order to further study this mechanism in a minimal model, we are analyzing with Prof. Rodrigo Soto (University of Chile) a system of springs and masses that becomes naturally active simply due to a lack of action-reaction principle. This type of dynamics can occur in nonequilibrium systems. In a month-long project in Chile last October, we found preliminary evidence with Prof. Soto that the inverse energy cascade we observed in our active elastic model is a generic mechanism that can lead to self-organization in a broad range of systems.
1.3. Analysis of swarm data
I recently completed a project with the experimental group of Prof. Iain Couzin (Princeton University), where we set up a shallow fish tank with up to 1000 golden shiners and tracked in detail their motion. We understood a number of properties of their individual motion rules and collective dynamics that I continue to analyze in other experimental systems (see, for example, our paper on PNAS).
I am currently studying data from groups of pigeons and of midges. Together with Prof. Thomas Ihle (North Dakota State University), we are using statistical physics tools to deduce how important complex biological components such as memory or trajectory prediction are for maintaining the highly coherent dynamics observed in many swarms.
1.4. Experiments with slime molds
I am one of the three PI’s in this international proposal that aims to understand the viscoelastic active dynamics of the slime mold Physarum Polycephalum (PP), a macroscopic unicellular organism without central control, where local biomechanical activity leads to sophisticated behaviors such as choosing the best food source or solving complex mazes. In this project, Prof. Simon Garnier (NJIT) will analyze experimentally the detailed dynamics of PP while Dr. Silke Henkes (University of Aberdeen) and I will develop active elastic and viscoelastic models.
We aim to understand the connection between mechanisms that produce self-organizing coherent dynamics within PP and the emergence of organism-level behavior that benefits survival. This is an ideal system to understand how physical self-organization and evolution can lead to the emergence of structure in biology.
1.5. Minimal robotic swarm experiments
The concepts of self-organizing collective motion and active matter described above can be applied to the design of swarm robotic systems and engineering of active smart materials. In two different projects, we are working with Prof. Ali Emre Turgut (Middle Eastern Technical University, Ankara, Turkey) and Prof. Claudio Falcon (University of Chile) to develop minimal swarm robotic systems.
In both robotic experiments, simple small self-propelled robots with light sensors are coupled to a tracking system, an external computer, and a projector. This allows us to capture the agent positions and implement in the external computer any desired motion control algorithm, by encoded it on the light shone over each agent and captured by their sensors. This setup will allow us to rapidly explore a diversity of collective dynamics that may lead to self-organization, and could serve as a prototype of future active (e.g. self-healing) materials based on micromotors.
2. Modular hierarchical structures in natural & engineered systems
Multi-scale modular hierarchical (MH) structures are a distinctive feature of biological systems and other complex evolving self-organized systems. They consist of relatively autonomous modules that interact more strongly internally than with other modules. These can come together to build higher level modules, which can in turn be part of even higher-level modules, etc., producing a multi-level hierarchy of structures. Such MH organization is often present in biological interaction networks such as genetic networks, metabolic networks, neural networks, or ecological networks. Intracellular interaction networks organize to produce actions at the cell level, cells assemble to produce functioning organs, and these in turn organize to produce individuals. This view can even be extended to communities and ecologies.
A similar set of design, structuring, and self-organizing principles are starting to emerge in technological systems, as they become more complex and decentralized. Examples can be found in a new generation of engineering solutions, including sensor networks, smart grids, highly distributed web-based computations, and swarm robotic systems.
Despite this apparent ubiquity and potential applicability of multi-scale MH structures, there is little fundamental understanding of the types of processes that can lead to their emergence or of the dynamical properties that can be expected from them. In this research theme, I am analyzing in a variety of contexts the evolutionary origins and dynamical consequences of a MH organization. My objective is to develop the theory of MH structures and dynamics in natural and artificial systems, while exploring a number of diverse applications in Biology and Engineering.
2.1. Modular-hierarchical complex networks
I am collaborating in this project with Prof. Dirk Brockmann (Robert Koch Institute and Humboldt University – Berlin, Germany). We to develop a strong theoretical understanding of the topology and dynamics that characterize MH interaction networks, in order to have effective tools to analyze and model biological experiments and other data on MH systems.
We are currently analyzing our recently developed random MH network growth model, which mimics natural MH structures. We are characterizing MH topologies, studying their node state dynamics, and implementing evolutionary algorithms and simple artificial-life simulations on MH systems, to understand how MH structures affect fitness. Our ultimate objective is to relate the theoretical properties of MH systems to their experimental manifestations, facilitating model-based predictions. We aim to address the key questions 1) what dynamics are supported by MH structures, 2) do MH structures improve fitness and 3) how do MH structures emerge and evolve?
2.2. Synthetic engineering of modular-hierarchical structures
This project is a collaboration with Prof. Joshua Leonard (Northwestern University) and aims to relate concepts on the origin and function of MH biological structures to ongoing experiments in his lab. We will study existing biological networks and construct new ones in living cells using synthetic biology approaches, aiming to uncover universal rules that govern the role of such MH dynamics and their underlying structures in biological genetic networks. We seek to answer the same types of questions listed in Section 2.1 above in an experimental context.
Prof. Leonard is artificially building biological MH networks by genetically manipulating intracellular and extracellular interactions in order to directly study their functioning dynamics and adaptability. We have identified specific questions on which MH theory may shed new light and where experimental tests derived from theoretical work that can be implemented.
2.3. Visualizing modular-hierarchical dynamics and architectures
In this project, we are combining the analysis of MH structures in living systems with the know-how of Prof. Luis Amaral (Northwestern University) and his group in analyzing the biomass production metabolic network data of dozens of organisms. This network describes the process through which cells use nutrients in their environment to grow.
In previous work, Prof. Amaral had developed an algorithm that extracts hierarchies of modules in the biomass production network of cells. I am currently combining these results with a novel visualization code that allows us to view the network in 3 dimension, where the z-axis indicates the hierarchical level. This approach, together with a Flux Balance Analysis will allow us to view in a manner that directly corresponds to our physical intuition of the fluid flow through a network of channels, how the Carbon molecules required to produce biomass are used by different processes and sub-processes. It will allow us to relate how the modular and hierarchical structure of metabolic processes to functional hierarchies.
Interestingly, due to the conservation of Carbon across biochemical processes in the cell, this network representation can actually be built as a set of physical channels. We plan to use either a 3d printer, 3d laser glass engraving, or a microfluidic array to build this network of channels. In addition to helping develop intuition, this visualization of the flow of carbon through processes and sub-processes as a fluid flow has clear artistic appeal.
2.4. Towards a theory of modular-hierarchical structures in natural & engineered systems
The different explorations described above have the ambitious aim of establishing the basic building blocks of a unified theory of MH structures in natural and engineered systems. I recently developed a project that plans to integrate and advance current knowledge on MH systems, such as network growth algorithms that yield MH topologies or the emergence of modular structures under alternating fitness constraints.
I am developing this work with multiple collaborators, who will provide insights from various specific biological systems and archetypical MH structures for theoretical analysis. These include groups that (1) engineer intracellular and extracellular interaction networks with different degrees of MH organization using synthetic biology, (2) analyze MH properties of metabolic biomass production networks, (3) study the symbiotic coupling of modular structures in certain squids and their microbiota, and (4) consider the role of MH structures in tumor development. These diverse systems will help unveil universal MH features while grounding our studies with concrete example.