Networks are amongst the central building blocks of many systems. Given a graph of a network, methods from graph theory enable a precise investigation of its properties. Software for the analysis of graphs is widely available and has been applied to study various types of networks. In some applications, graph acquisition is relatively simple. However, for many networks data collection relies on images where graph extraction requires domain-specific solutions. Here we introduce NEFI, a tool that extracts graphs from images of networks originating in various domains. Regarding previous work on graph extraction, theoretical results are fully accessible only to an expert audience and ready-to-use implementations for non-experts are rarely available or insufficiently documented. NEFI provides a novel platform allowing practitioners to easily extract graphs from images by combining basic tools from image processing, computer vision and graph theory. Thus, NEFI constitutes an alternative to tedious manual graph extraction and special purpose tools. We anticipate NEFI to enable time-efficient collection of large datasets. The analysis of these novel datasets may open up the possibility to gain new insights into the structure and function of various networks. NEFI is open source and available at http://nefi.mpi-inf.mpg.de.
We built and characterised a macroscopic self-assembly reactor that agitates magnetic, centimeter-sized particles with a turbulent water flow. By scaling up the self-assembly processes to the centimeter-scale, the characteristic time constant scale also drastically increases. This makes the system a physical simulator of microscopic self-assembly, where the interaction of inserted particles are easily observable. Trajectory analysis of single particles reveals their velocity to be a Maxwell-Boltzmann distribution and it shows that their average squared displacement over time can be modelled by a confined random walk model, demonstrating a high level of similarity to Brownian motion. The interaction of two particles has been modelled and verified experimentally by observing the distance between two particles over time. The disturbing energy (analogue to temperature) that was obtained experimentally increases with sphere size, and differs by an order of magnitude between single-sphere and two-sphere systems (approximately 80 µJ versus 6.5 µJ, respectively). arXiv:1709.04978v1 [cond-mat.soft]
We introduce the Slime Mold Graph Repository, a novel data collection promoting the visibility, accessibility and reuse of experimental data revolving around network-forming slime molds. By making data instantly available for researchers across multiple disciplines, the SMGR promotes novel research as well as the reproduction of original results. While SMGR data may take various forms, we stress the importance of graph representations of slime mold networks due to their ease of handling and their large potential for reuse. Data added to the SMGR stands to gain impact beyond initial publications or even beyond its domain of origin. We initiate the SMGR with the comprehensive KIST Europe data set focused on the slime mold Physarum polycephalum. It contains sequences of images documenting growth and network formation of the organism under constant conditions. Suitable image sequences depicting the typical P. polycephalum network structures are used to compute sequences of graphs faithfully capturing them. Given such sequences, node identities are computed, tracking the development of nodes over time. The entire data set is well-documented, self-contained and ready for inspection via the SMGR at http://smgr.mpi-inf.mpg.de.
Physarum polycephalum is a slime mold that is apparently able to solve shortest path problems. A mathematical model for the slime's behavior in the form of a coupled system of differential equations was proposed by Tero, Kobayashi and Nakagaki [TKN07]. We prove that a discretization of the model (Euler integration) computes a (1 + )approximation of the shortest path in O(mL(log n + log L)/ 3 ) iterations, with arithmetic on numbers of O(log(nL/ )) bits; here, n and m are the number of nodes and edges of the graph, respectively, and L is the largest length of an edge. We also obtain two results for a directed Physarum model proposed by Ito et al. [IJNT11]: convergence in the general, nonuniform case and convergence and complexity bounds for the discretization of the uniform case.
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