We are interested in understanding how the interactions of relatively simple components at different temporal and spatial scales can lead to the observation of emergent phenomena. Our approach is three-fold:
1. Biological. We study animal behavior, in particular, vocal communication, as an example of emergent phenomena. Our aim is to understand the ethogenesis of vocal interaction, i.e., to understand the evolutionary, developmental, physiological and biomechanical processes that shape the animal vocal communication. The significant interaction of all these processes at different spatial and temporal scales makes vocal communication a truly fascinating behavior.
2. Statistical. We develop rigorous statistical and computational methods to infer and interpret the interaction between different components of the nervous system at several temporal and spatial scales. Our aim is not only to expand the set of tools available to study interactions but also to understand what are the limitations of each method and conceptual framework. It is only through understanding the limits of our methods that we can properly interpret their results.
3. Mathematical. We study stochastic chains with unbounded memories (SCUMs) as an example of a mathematical object that can exhibit emergent phenomena like phase transition and intermittency. Our aim is to understand how non-Markovian dependency in time can lead to the appearance of non-trivial stochastic phenomena. SCUMs allow us to obtain a precise understanding of emergent phenomena in several cases.
Each approach gives us insights into the other and helps us understand the deeper facets of the emergence of complex phenomena.