Global structural stability and the role of cooperation in mutualistic systems.

Dynamical systems on graphs allow to describe multiple phenomena from different areas of Science. In particular, many complex systems in Ecology are studied by this approach. In this paper we analize the mathematical framework for the study of the structural stability of each stationary point, feasible or not, introducing a generalization for this concept, defined as Global Structural Stability. This approach would fit with the proper mathematical concept of structural stability, in which we find a full description of the complex dynamics on the phase space due to nonlinear dynamics. This fact can be analyzed as an informational field grounded in a global attractor whose structure can be completely characterized. These attractors are stable under perturbation and suppose the minimal structurally stable sets. We also study in detail, mathematically and computationally, the zones characterizing different levels of biodiversity in bipartite graphs describing mutualistic antagonistic systems of population dynamics. In particular, we investigate the dependence of the region of maximal biodiversity of a system on its connectivity matrix. On the other hand, as the network topology does not completely determine the robustness of the dynamics of a complex network, we study the correlation between structural stability and several graph measures. A systematic study on synthetic and biological graphs is presented, including 10 mutualistic networks of plants and seed-dispersal and 1000 random synthetic networks. We compare the role of centrality measures and modularity, concluding the importance of just cooperation strength among nodes when describing areas of maximal biodiversity. Indeed, we show that cooperation parameters are the central role for biodiversity while other measures act as secondary supporting functions.

A network approach to analyze neuronal lineage and layer innervation in the Drosophila optic lobes.

The optic lobes of the fruit fly Drosophila melanogaster form a highly wired neural network composed of roughly 130.000 neurons of more than 80 different types. How neuronal diversity arises from very few cell progenitors is a central question in developmental neurobiology. We use the optic lobe of the fruit fly as a paradigm to understand how neuroblasts, the neural stem cells, generate multiple neuron types. Although the development of the fly brain has been the subject of extensive research, very little is known about the lineage relationships of the cell types forming the adult optic lobes. Here we perform a large-scale lineage bioinformatics analysis using the graph theory. We generated a large collection of cell clones that genetically label the progeny of neuroblasts and built a database to draw graphs showing the lineage relationships between cell types. By establishing biological criteria that measures the strength of the neuronal relationships and applying community detection tools we have identified eight clusters of neurons. Each cluster contains different cell types that we pose are the product of eight distinct classes of neuroblasts. Three of these clusters match the available lineage data, supporting the predictive value of the analysis. Finally, we show that the neuronal progeny of a neuroblast do not have preferential innervation patterns, but instead become part of different layers and neuropils. Here we establish a new methodology that helps understanding the logic of Drosophila brain development and can be applied to the more complex vertebrate brains.

Informational structures: A dynamical system approach for integrated information.

Integrated Information Theory (IIT) has become nowadays the most sensible general theory of consciousness. In addition to very important statements, it opens the door for an abstract (mathematical) formulation of the theory. Given a mechanism in a particular state, IIT identifies a conscious experience with a conceptual structure, an informational object which exists, is composed of identified parts, is informative, integrated and maximally irreducible. This paper introduces a space-time continuous version of the concept of integrated information. To this aim, a graph and a dynamical systems treatment is used to define, for a given mechanism in a state for which a dynamics is settled, an Informational Structure, which is associated to the global attractor at each time of the system. By definition, the informational structure determines all the past and future behavior of the system, possesses an informational nature and, moreover, enriches all the points of the phase space with cause-effect power by means of its associated Informational Field. A detailed description of its inner structure by invariants and connections between them allows to associate a transition probability matrix to each informational structure and to develop a measure for the level of integrated information of the system.

Experimental fully contextual correlations.

Quantum correlations are contextual yet, in general, nothing prevents the existence of even more contextual correlations. We identify and test a noncontextuality inequality in which the quantum violation cannot be improved by any hypothetical postquantum theory, and use it to experimentally obtain correlations in which the fraction of noncontextual correlations is less than 0.06. Our correlations are experimentally generated from the results of sequential compatible tests on a four-state quantum system encoded in the polarization and path of a single photon.