Finding the optimal nets for self-folding Kirigami

Three-dimensional shells can be synthesized from the spontaneous self-folding of two-dimensional templates of interconnected panels, called nets. However, some nets are more likely to self-fold into the desired shell under random movements. The optimal nets are the ones that maximize the number of vertex connections, i.e., vertices that have only two of its faces cut away from each other in the net. Previous methods for finding such nets are based on random search and thus do not guarantee the optimal solution. Here, we propose a deterministic procedure. We map the connectivity of the shell into a shell graph, where the nodes and links of the graph represent the vertices and edges of the shell, respectively. Identifying the nets that maximize the number of vertex connections corresponds to finding the set of maximum leaf spanning trees of the shell graph. This method allows not only to design the self-assembly of much larger shell structures but also to apply additional design criteria, as a complete catalog of the maximum leaf spanning trees is obtained.Comment: 6 pages, 5 figures, Supplemental Material, Source Cod

When is a Network a Network? Multi-Order Graphical Model Selection in Pathways and Temporal Networks

We introduce a framework for the modeling of sequential data capturing pathways of varying lengths observed in a network. Such data are important, e.g., when studying click streams in information networks, travel patterns in transportation systems, information cascades in social networks, biological pathways or time-stamped social interactions. While it is common to apply graph analytics and network analysis to such data, recent works have shown that temporal correlations can invalidate the results of such methods. This raises a fundamental question: when is a network abstraction of sequential data justified? Addressing this open question, we propose a framework which combines Markov chains of multiple, higher orders into a multi-layer graphical model that captures temporal correlations in pathways at multiple length scales simultaneously. We develop a model selection technique to infer the optimal number of layers of such a model and show that it outperforms previously used Markov order detection techniques. An application to eight real-world data sets on pathways and temporal networks shows that it allows to infer graphical models which capture both topological and temporal characteristics of such data. Our work highlights fallacies of network abstractions and provides a principled answer to the open question when they are justified. Generalizing network representations to multi-order graphical models, it opens perspectives for new data mining and knowledge discovery algorithms.Comment: 10 pages, 4 figures, 1 table, companion python package pathpy available on gitHu

Experimental characterization of the structural response of adobe arches

Earth was one of the first construction materials used by mankind and has been used as a building material since ancient times until the present days. Its qualities related to thermal comfort, low cost or simple construction techniques have contributed to such a long tradition throughout the world with several different architectural expressions, integrating the culture and history of each region. With the wide propagation of steel and concrete structures, there has been a general loss of the traditional knowledge in earth construction. This type of construction presents important structural fragilities and requires a special maintenance to preserve its qualities. In order to understand the structural behaviour of this type of structures, the associated construction methods and processes have to be considered. Aveiro University has been developing studies on adobe constructions, with research on the material mechanical characterization, experimental study of the structural behaviour of adobe masonry walls and, more recently, in the development of a detailed survey methodology for the characterization of buildings in Aveiro district. Integrated in these studies, arches with different geometries were built using adobe blocks and traditional construction methods. These arches were tested under different types of vertical loading (distributed symmetrical, distributed non-symmetrical and point load) until collapse. The experimental tests performed reproduce the typical loading conditions of these structures during construction and use. The tests conducted, the results obtained and the main conclusions attained are described in this paper