Abstract: The origin and consequences of the nested structure of mutualistic ecosystems is a matter of strong debate in the ecological community. The relationship between the structure of mutualistic ecosystems and the dynamics that led to this structure is still an open problem. In the seminal paper of May[1], the ecosystem is described by a dynamical linear model, with a random matrix interaction. His results show that a large ecosystem with high connectivity is unstable. Since then, special attention has been paid to the structure of the interaction matrix. Bastolla et. al [2] study a population dynamics model that includes plant-animal mutualistic interactions and animal-animal and plant-plant competing interactions, in the mean field approach, except for the weak mutualism regime, where a more realistic mutualistic term is included. They conclude that the nestedness minimizes competition, allowing for an increase of biodiversity. A recent article [3] discusses the importance of structural stability of mutualistic ecosystems. In this work we investigate the influence of the network structure on the persistence of species of a mutualistic ecosystem. We study a non-linear population dynamics model where we take into account the structure of interactions both, in mutualistic and competition terms. In fact, the observed networks contain more information than just the plant-pollinator interactions. The ecosystem may be treated as a two layers of competing agents, one for plants and another for animals, coupled by the mutualistic interactions. This information can be then used to model the competition term beyond the mean-field approach. Our results show the existence of a trade-off between mutualism and competition, so that the largest biodiversity is achieved with a non-trivial combination of both mechanisms. [1] RM. May. Nature. 238, 413 (1972) [2] U. Bastolla et al. Nature. 458, 1018 (2009) [3] R.P. Rohr, S. Saavedra, J. Bascompte, Science 345, 416 (2014)

Abstract: The albatross was the first example of levy walk in animals, leading to the development of optimal foraging theories in levy walks. Other pelagic birds like the shearwaters presents a range of displacement distributed as a power law, but with an exponent different to the optimal foraging one, challenging the scientific community for a while. In this talk we show how the exponent of the power law in the pdf of displacement is simply the result of the law of first passage, related to the olfactory­cued navigation in shearwaters birds. Olfactory­cued navigation was proposed for a great variety of animals especially those one that navigate in featureless environment. We present the first mechanistic proof of olfactory­cued navigation showing the relation between the cut off of the pdf and the wind turbulence intensity.

Abstract: In this work we use belief-propagation techniques to study the equilibrium behaviour of a minimal model for the immune system comprising interacting T and B clones. We investigate the effect of the so-called idiotypic interactions among complementary B clones on the system's activation. Our result shows that B-B interactions increase the system's resilience to noise, making clonal activation more stable, while increasing the cross-talk between different clones. We derive analytically the noise level at which a B clone gets activated, in the absence of cross-talk, and find that this increases with the strength of idiotypic interactions and with the number of T cells signalling the B clone. We also derive, analytically and numerically, via population dynamics, the critical line where clonal cross-talk arises. Our approach allows us to derive the B clone size distribution, which can be experimentally measured and gives important information about the adaptive immune system response to antigens and vaccination.

Abstract: Healthy life is maintained through a complex regulating system in our bodies that ensure our dynamic functioning and keep vital physical and mental parameters within safe limits despite environmental challenges. Systemic resilience is the capacity of our complex systems to bounce back to normal functioning upon disturbances, ultimately determining our chances of survival and quality of life. As they age, humans gradually lose resilience which often remains unnoticed until confronted with a health crisis that is often detrimental to well-being and costly to society. We currently still lack valid methods to dynamically measure resilience for upcoming stressors. Emerging insights in other complex dynamical systems such as ecological networks, the climate and financial markets are uncovering generic empirical indicators that may be used to quantify systemic resilience dynamically: these early warning signals comprise changes in the dynamics of a system that are most clearly observed when the system recovers from a disturbance, which slows down upon decreasing resilience. Here we present integrative research in which we asked whether we can rank humans from resilient to frail by looking at differences in these dynamical characteristics in empirical data collected over time. We analysed time series of daily self-reported physical and mental health during 100 days in 22 elderly people ranging from frail to resilient as determined by a frailty index. The dynamics of the time series of a less resilient human system indeed turned out to be characterised by elevated variance and temporal autocorrelation. Additionally, as network theory predicts, as the different elements in a network of fluctuating elements lose resilience, deviations in the physical and mental domains of the system became more correlated. This contribution to the empirical evidence for the use of dynamical characteristics to quantify resilience across complex systems brings hope of foreseeing and preventing catastrophic failures in health.

Abstract: Protein-protein interactions are important in various areas of cell biology, including drug development for several diseases. Many therapeutic methods are based on complex algorithms supported by protein-protein interaction networks. Using a known mathematical model of the cell (from membrane computing), as well as a new abstract measure of complexity provided by proteins length, we study the computational power of protein-protein interaction systems involving a minimal number of cells/membranes with respect to the movement provided by endocytosis and exocytosis operations that are supported by proteins of different lengths. We proved that such protein-protein interaction networks can simulate all computable functions, and thus can be effectively used in designing efficient therapeutic algorithms for numerous diseases. We study the computational power of a pair of certain forms of endocytosis and exocytosis (namely pino and exo operations), and prove their universality by using at most three cells/membranes using proteins for both (pino) and (exo) operations of length at most two. We also study the computational power of the pair (phago) and (exo) operations, and prove their universality by using at most four cells/membranes, while the length of proteins of are at most two. The higher number of cells/membranes here is triggered by the use of the (phago) operation. These universality results means that the corresponding protein-protein interaction networks have the same computational power as a Turing machine, and so able to support all the complex algorithms (describing computable functions).