An artificial intelligence-integrated analysis of the effect of drought stress on root traits of "modern" and "ancient" wheat varieties.

Due to drought stress, durum wheat production in the Mediterranean basin will be severely affected in the coming years. Durum wheat cultivation relies on a few genetically uniform "modern" varieties, more productive but less tolerant to stresses, and "traditional" varieties, still representing a source of genetic biodiversity for drought tolerance. Root architecture plasticity is crucial for plant adaptation to drought stress and the relationship linking root structures to drought is complex and still largely under-explored. In this study, we examined the effect of drought stress on the roots' characteristics of the "traditional" Saragolla cultivar and the "modern" Svevo. By means of "SmartRoot" software, we demonstrated that drought stress affected primary and lateral roots as well as root hair at different extents in Saragolla and Svevo cultivars. Indeed, we observed that under drought stress Saragolla possibly revamped its root architecture, by significantly increasing the length of lateral roots, and the length/density of root hairs compared to the Svevo cultivar. Scanning Electron Microscopy analysis of root anatomical traits demonstrated that under drought stress a greater stele area and an increase of the xylem lumen size vessel occurred in Saragolla, indicating that the Saragolla variety had a more efficient adaptive response to osmotic stress than the Svevo. Furthermore, for the analysis of root structural data, Artificial Intelligence (AI) algorithms have been used: Their application allowed to predict from root structural traits modified by the osmotic stress the type of cultivar observed and to infer the relationship stress-cultivar type, thus demonstrating that root structural traits are clear and incontrovertible indicators of the higher tolerance to osmotic stress of the Saragolla cultivar. Finally, to obtain an integrated view of root morphogenesis, phytohormone levels were investigated. According to the phenotypic effects, under drought stress,a larger increase in IAA and ABA levels, as well as a more pronounced reduction in GA levels occurred in Saragolla as compared to Svevo. In conclusion, these results show that the root growth and hormonal profile of Saragolla are less affected by osmotic stress than those of Svevo, demonstrating the great potential of ancient varieties as reservoirs of genetic variability for improving crop responses to environmental stresses.

Canonical Divergence for Measuring Classical and Quantum Complexity.

A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both classical and quantum systems. On the simplex of probability measures, it is proved that the new divergence coincides with the Kullback-Leibler divergence, which is used to quantify how much a probability measure deviates from the non-interacting states that are modeled by exponential families of probabilities. On the space of positive density operators, we prove that the same divergence reduces to the quantum relative entropy, which quantifies many-party correlations of a quantum state from a Gibbs family.

Information geometric methods for complexity.

Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and, whenever available, quantum physical settings. A paradigmatic example of a dramatic change in complexity is given by phase transitions (PTs). Hence, we review both global and local aspects of PTs described in terms of the scalar curvature of the parameter manifold and the components of the metric tensor, respectively. We also report on the behavior of geodesic paths on the parameter manifold used to gain insight into the dynamics of PTs. Going further, we survey measures of complexity arising in the geometric framework. In particular, we quantify complexity of networks in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. We are also concerned with complexity measures that account for the interactions of a given number of parts of a system that cannot be described in terms of a smaller number of parts of the system. Finally, we investigate complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information. The Kullback-Leibler divergence, the distance to an exponential family and volumes of curved parameter manifolds, are examples of essential IG notions exploited in our discussion of complexity. We conclude by discussing strengths, limits, and possible future applications of IG methods to the physics of complexity.

The Volume of Two-Qubit States by Information Geometry.

Using the information geometry approach, we determine the volume of the set of two-qubit states with maximally disordered subsystems. Particular attention is devoted to the behavior of the volume of sub-manifolds of separable and entangled states with fixed purity. We show that the usage of the classical Fisher metric on phase space probability representation of quantum states gives the same qualitative results with respect to different versions of the quantum Fisher metric.

Riemannian-geometric entropy for measuring network complexity.

A central issue in the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate with a-in principle, any-network a differentiable object (a Riemannian manifold) whose volume is used to define the entropy. The effectiveness of the latter in measuring network complexity is successfully proved through its capability of detecting a classical phase transition occurring in both random graphs and scale-free networks, as well as of characterizing small exponential random graphs, configuration models, and real networks.