- Further Info
1. The Physics of Information in Complex Systems
Information transmission, chaos, and predictability in complex systems. Information is a fundamental quantity. In thermodynamic systems, information has been shown to be more than just an abstract concept, complementing the set of macroscopic quantities (e.g., entropy, energy, work). It can be converted into work, and vice-versa. Currently, there is a great interest in the scientific community to understand the relationship among all these fundamental quantities. The hope is to better understand how to model and do predictions in a large class of systems, ranging from particles that move in harmonic potential wells to the stellar cycle, and the creation of the universe. Our group at the ICSMB works to establish the dynamical foundations for the entropy production and the transfer of information in complex and Hamiltonian systems. We show how to link entropy and information transfer with dynamical quantities (correlation decay and Lyapunov exponents) and behavioural signatures (synchronisation). This knowledge is being applied to infer how elements in a complex network interact among themselves from the way they exchange information, and to show how chaos mediates the transfer of energy and information in Hamiltonian systems.
2. Stability, Observability, and Controllability.
Stability and control of complex systems. Elements in many complex systems need to operate in synchrony and be stable to function well. They must have the ability to regain an initial synchronous state of operation when system is subject to physical disturbances, attacks, or suffers time-varying changes. Control provides a solution for the stability problem. For linear time-invariant complex networks, a minimal set of nodes in a network can be shown to be sufficient to control the entire network. However, complex systems are in general highly heterogeneous, non -autonomous, and evolve in time. In the particular case of the modern power-grid, power outages are often caused by misusage of equipment or human operation error. Our group at the ICSMB is working to design complex systems (such as the power-grid) whose structure naturally provides stability and optimal observability, a simple strategy to turning the system "smart", but with reduced active control.
3. Technological Applications
Secure wireless communication with chaos. The modern world fully relies on wireless communication. Because of intrinsic physical constraints of the wireless physical media (multipath, damping, and filtering), signals carrying information are strongly modified, preventing information from being transmitted with a high bit rate. Often, communication must happen in a secure environment. Our group at the ICSMB is showing how to use chaos and chaotic networks to circumvent the limitation imposed by the wireless media, and to improve the security and the speed of smartphone and tablet communication.
4. Graphs and Networks
Social networks. The description of society and many other complex systems by the approaches of the network theory has successfully identified in these systems unknown structural patterns, characterizing statistical signatures, expected and unexpected leaders (hubs) and relevant links between communities (clusters). Our interest in the ICSMB is to use the approaches from graphs and network theories to unravel the hidden patterns and the statistical signatures of literacy and online social networks [Baptista].
Supply-demand networks. The ability to design a transport network such that commodities are brought from suppliers to consumers in a steady, optimal, and stable way is of great importance for nowadays distribution systems. Our group is working to calculate the maximal value of loads that can be transported between two nodes in a supply-demand network, when the system evolves (nodes are added or removed, connecting topology is varying), hub sources or sinks become decentralized, and suppliers and consumers have intermittent characteristics. Two examples of applications of this work are to understand how fractures happen in materials and how power can be optimally distributed in power-grid networks.
5. Data based Modeling
Markov models of complex systems. In many instances, the “equations of motion” of a complex system are unknown. A simple but general strategy to model such a system is by constructing Markov chain models of lower-dimensional projections of it. These models provide a statistical description of the system that captures almost all the relevant information of it with additional advantages. They can be low-dimensional, simple to handle, but still providing accurate information about the dynamics and main features of the system being studied. Our group at the ICSMB is currently employing such models to construct a network representation of the grammar of the DNA, to model the brain, to characterize the dynamics of turbulence in heating cells, and to model the stock market.
6. System Biology and Model Based Data Analysis
Time-delay models of cancer-imuno-chemiotherapy system. An intrinsic property of biological systems is the existence of variables with time-delays. Our goal is to model biological systems such as the cancer-imuno-chemioteraphy system and neural networks, with time-delay ODEs. The model for cancer growth under therapy is being used to predict the development of cancer drugs being currently used to treat cancer.
7. Collective Phenomena
Weak coupling in complex networks. Spontaneous emergence of collective behaviour is common in nature. Of special interest is the manifestation of collective behavior when nodes are weakly connected. The interest in this area ranges from theories of phase transition up to application in social networks, information flow in the brain, cryptography, and communication networks. In the brain, one wishes to understand the conditions that neurons belonging to a sub-network are sufficiently independent (desynchronous) to achieve independent computations, but the sub-networks are sufficiently connected (synchronous) such that information can be transmitted between sub-networks and integrated into coherent patterns. Our group at the ICSMB is working to decipher the dynamical behavior of networks formed by weak coupled elements, in order to better understand the brain and to construct better cryptographic systems.