Many problems in industry — and in the social, natural, information, and medical sciences — involve discrete data and benefit from approaches from subjects such as network science, information theory, optimization, probability, and statistics. Because the study of networks is concerned explicitly with connectivity between different entities, it has become very prominent in industrial settings, and this importance has been accentuated further amidst the modern data deluge. In this article, we discuss the role of network analysis in industrial and applied mathematics, and we give several examples of network science in industry.
The Role of Network Analysis in Industrial and Applied Mathematics
Mason A. Porter, Sam D. Howison
The spider silk is one of the most interesting bio-materials investigated in the last years. One of the main reasons that brought scientists to study this organized system is its high level of resistance if compared to other artificial materials characterized by higher density. Subsequently, researchers discovered that the spider silk is a complex system formed by different kinds of proteins, organized (or disorganized) to guarantee the required resistance, which is function of the final application and of the environmental conditions. Some spider species are able to make different silks, up to twelve, having a composition that seems to be function of the final use (i.e. dragline web, capture web, etc). The aim of this paper is to analyze the properties of the spider silk by means of a thermodynamic approach, taking advantage of the well-known theories applied to polymers, and to try to underline and develop some intriguing considerations. Moreover, this study can be taken as an example to introduce and discuss the importance of the concept of optionality and of the anti-fragile systems proposed by N. N. Thaleb in his book “Antifragile: Things that gain from disorder”.
A thermodynamic analysis of the spider silk and the importance of complexity
S.Ripandelli, D.Pugliese, U.Lucia
Collective phenomena emerge from the interaction of natural or artificial units with a complex organization. The interplay between structural patterns and dynamics might induce functional clusters that, in general, are different from topological ones. In biological systems, like the human brain, the overall functionality is often favored by the interplay between connectivity and synchronization dynamics, with functional clusters that do not coincide with anatomical modules in most cases. In social, sociotechnical, and engineering systems, the quest for consensus favors the emergence of clusters. Despite the unquestionable evidence for mesoscale organization of many complex systems and the heterogeneity of their interconnectivity, a way to predict and identify the emergence of functional modules in collective phenomena continues to elude us. Here, we propose an approach based on random walk dynamics to define the diffusion distance between any pair of units in a networked system. Such a metric allows us to exploit the underlying diffusion geometry to provide a unifying framework for the intimate relationship between metastable synchronization, consensus, and random search dynamics in complex networks, pinpointing the functional mesoscale organization of synthetic and biological systems.
Diffusion Geometry Unravels the Emergence of Functional Clusters in Collective Phenomena
Manlio De Domenico
Phys. Rev. Lett. 118, 168301
Natural evolution has produced a tremendous diversity of functional organisms. Many believe an essential component of this process was the evolution of evolvability, whereby evolution speeds up its ability to innovate by generating a more adaptive pool of offspring. One hypothesized mechanism for evolvability is developmental canalization, wherein certain dimensions of variation become more likely to be traversed and others are prevented from being explored (e.g. offspring tend to have similarly sized legs, and mutations affect the length of both legs, not each leg individually). While ubiquitous in nature, canalization almost never evolves in computational simulations of evolution. Not only does that deprive us of in silico models in which to study the evolution of evolvability, but it also raises the question of which conditions give rise to this form of evolvability. Answering this question would shed light on why such evolvability emerged naturally and could accelerate engineering efforts to harness evolution to solve important engineering challenges. In this paper we reveal a unique system in which canalization did emerge in computational evolution. We document that genomes entrench certain dimensions of variation that were frequently explored during their evolutionary history. The genetic representation of these organisms also evolved to be highly modular and hierarchical, and we show that these organizational properties correlate with increased fitness. Interestingly, the type of computational evolutionary experiment that produced this evolvability was very different from traditional digital evolution in that there was no objective, suggesting that open-ended, divergent evolutionary processes may be necessary for the evolution of evolvability.
The Emergence of Canalization and Evolvability in an Open-Ended, Interactive Evolutionary System
Joost Huizinga, Kenneth O. Stanley, Jeff Clune