The use of experimental data from biological systems to infer the parameters of a reasonable underlying model is now a standard practice. However, due to the noise in the experimental data, for simplicity the interaction network to be inferred is often assumed to be symmetric and homogeneous, with just pairwise interactions and important differences involving peripheral nodes are just ignored.
In this project, we will apply methods and techniques commonly used in inference problems, such as Monte Carlo simulations or neural-networks to go beyond the state of the art and achieve a more detailed characterization of the interaction network in living systems to unveil new behavioral traits.
In particular we want to verify if the introduction of possible asymmetries in the iteraction networks is responsible for collective changes of state in response to noise or external reasons, like the presence of a predator. We also want to better understand the role of external individuals.
In the last twenty years much advance has been achieved in the understanding and description of active matter behavior. Active matter refers to systems where individual units are endowed with self-propulsion: they have an internal source of energy, which is transformed into motion. Contrary to the `passive particles¿ usually studied in condensed matter, these systems are intrinsically out of equilibrium. As a consequence they display novel behavior and - in the interacting case - non-trivial collective patterns. Examples from the living world are flocking, swarming and collective movements in cellular assemblies. Several seminal studies, both theoretical and experimental, led to a general framework for the description of these systems [1]. Still, there are several important aspects that need to be addressed. As mentioned before, most theoretical analysis makes assumptions on the structure of the interaction network between individuals. Homogeneity is one of them. Even though this is most of the time reasonable, there are important features that require going beyond this state of the art.
In particular, the role of heterogeneities, either related to individual perceptual differences, or due to positional collocations within the group (e.g. boundary vs internal individuals) is likely to play a crucial role in the way response is elicited in the system. In terms of the interaction matrix describing mutual coordination, such heterogeneities can determine links with different intensities, different number of connections per node, and asymmetric interactions (i.e. a directed interaction graph). Both the directed structure of the adjacency matrix, and the variability of the interaction strengths determine the way information propagates and therefore the features of the collective response function, a primary issue in many living systems where an efficient anti predatory behavior is crucial to survival. This topic is still largely unexplored. On the one hand it is important to understand at theoretical level what could be the effect of given classes of asymmetries and heterogeneities, on the other hand it is crucial to extract from the data as much information as possible about their role, in order to guide theoretical analysis.
[1] Marchetti, M. Cristina, et al. "Hydrodynamics of soft active matter." Reviews of Modern Physics 85 1143 (2013)