Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web

We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology, they extend the information beyond conventional cosmological studies of topology in terms of genus and Euler characteristic. The richer information content of Betti numbers goes along the availability of fast algorithms to compute them. For continuous density fields, we determine the scale-dependence of Betti numbers by invoking the cosmologically familiar filtration of sublevel or superlevel sets defined by density thresholds. For the discrete galaxy distribution, however, the analysis is based on the alpha shapes of the particles. These simplicial complexes constitute an ordered sequence of nested subsets of the Delaunay tessellation, a filtration defined by the scale parameter, $\alpha$. As they are homotopy equivalent to the sublevel sets of the distance field, they are an excellent tool for assessing the topological structure of a discrete point distribution. In order to develop an intuitive understanding for the behavior of Betti numbers as a function of $\alpha$, and their relation to the morphological patterns in the Cosmic Web, we first study them within the context of simple heuristic Voronoi clustering models. Subsequently, we address the topology of structures emerging in the standard LCDM scenario and in cosmological scenarios with alternative dark energy content. The evolution and scale-dependence of the Betti numbers is shown to reflect the hierarchical evolution of the Cosmic Web and yields a promising measure of cosmological parameters. We also discuss the expected Betti numbers as a function of the density threshold for superlevel sets of a Gaussian random field.Comment: 42 pages, 14 figure

Born to learn: The inspiration, progress, and future of evolved plastic artificial neural networks

Biological plastic neural networks are systems of extraordinary computational capabilities shaped by evolution, development, and lifetime learning. The interplay of these elements leads to the emergence of adaptive behavior and intelligence. Inspired by such intricate natural phenomena, Evolved Plastic Artificial Neural Networks (EPANNs) use simulated evolution in-silico to breed plastic neural networks with a large variety of dynamics, architectures, and plasticity rules: these artificial systems are composed of inputs, outputs, and plastic components that change in response to experiences in an environment. These systems may autonomously discover novel adaptive algorithms, and lead to hypotheses on the emergence of biological adaptation. EPANNs have seen considerable progress over the last two decades. Current scientific and technological advances in artificial neural networks are now setting the conditions for radically new approaches and results. In particular, the limitations of hand-designed networks could be overcome by more flexible and innovative solutions. This paper brings together a variety of inspiring ideas that define the field of EPANNs. The main methods and results are reviewed. Finally, new opportunities and developments are presented

Material properties affect evolution's ability to exploit morphological computation in growing soft-bodied creatures

The concept of morphological computation holds that the body of an agent can, under certain circumstances, exploit the interaction with the environment to achieve useful behavior, potentially reducing the computational burden of the brain/controller. The conditions under which such phenomenon arises are, however, unclear. We hypothesize that morphological computation will be facilitated by body plans with appropriate geometric, material, and growth properties, while it will be hindered by other body plans in which one or more of these three properties is not well suited to the task. We test this by evolving the geometries and growth processes of soft robots, with either manually-set softer or stiffer material properties. Results support our hypothesis: we find that for the task investigated, evolved softer robots achieve better performances with simpler growth processes than evolved stiffer ones. We hold that the softer robots succeed because they are better able to exploit morphological computation. This four-way interaction among geometry, growth, material properties and morphological computation is but one example phenomenon that can be investigated using the system here introduced, that could enable future studies on the evolution and development of generic soft-bodied creatures

Evolving soft locomotion in aquatic and terrestrial environments: effects of material properties and environmental transitions

Designing soft robots poses considerable challenges: automated design approaches may be particularly appealing in this field, as they promise to optimize complex multi-material machines with very little or no human intervention. Evolutionary soft robotics is concerned with the application of optimization algorithms inspired by natural evolution in order to let soft robots (both morphologies and controllers) spontaneously evolve within physically-realistic simulated environments, figuring out how to satisfy a set of objectives defined by human designers. In this paper a powerful evolutionary system is put in place in order to perform a broad investigation on the free-form evolution of walking and swimming soft robots in different environments. Three sets of experiments are reported, tackling different aspects of the evolution of soft locomotion. The first two sets explore the effects of different material properties on the evolution of terrestrial and aquatic soft locomotion: particularly, we show how different materials lead to the evolution of different morphologies, behaviors, and energy-performance tradeoffs. It is found that within our simplified physics world stiffer robots evolve more sophisticated and effective gaits and morphologies on land, while softer ones tend to perform better in water. The third set of experiments starts investigating the effect and potential benefits of major environmental transitions (land - water) during evolution. Results provide interesting morphological exaptation phenomena, and point out a potential asymmetry between land-water and water-land transitions: while the first type of transition appears to be detrimental, the second one seems to have some beneficial effects.Comment: 37 pages, 22 figures, currently under review (journal