Graph product multilayer networks: spectral properties and applications

This article aims to establish theoretical foundations of graph product multilayer networks (GPMNs), a family of multilayer networks that can be obtained as a graph product of two or more factor networks. Cartesian, direct (tensor), and strong product operators are considered, and then generalized. We first describe mathematical relationships between GPMNs and their factor networks regarding their degree/strength, adjacency, and Laplacian spectra, and then show that those relationships can still hold for non-simple and generalized GPMNs. Applications of GPMNs are discussed in three areas: predicting epidemic thresholds, modelling propagation in non-trivial space and time, and analysing higher-order properties of self-similar networks. Directions of future research are also discussed

Mapping the Curricular Structure and Contents of Network Science Courses

As network science has matured as an established field of research, there are already a number of courses on this topic developed and offered at various higher education institutions, often at postgraduate levels. In those courses, instructors adopted different approaches with different focus areas and curricular designs. We collected information about 30 existing network science courses from various online sources, and analyzed the contents of their syllabi or course schedules. The topics and their curricular sequences were extracted from the course syllabi/schedules and represented as a directed weighted graph, which we call the topic network. Community detection in the topic network revealed seven topic clusters, which matched reasonably with the concept list previously generated by students and educators through the Network Literacy initiative. The minimum spanning tree of the topic network revealed typical flows of curricular contents, starting with examples of networks, moving onto random networks and small-world networks, then branching off to various subtopics from there. These results illustrate the current state of consensus formation (including variations and disagreements) among the network science community on what should be taught about networks and how, which may also be informative for K--12 education and informal education.Comment: 17 pages, 11 figures, 2 tables; to appear in Cramer, C. et al. (eds.), Network Science in Education -- Tools and Techniques for Transforming Teaching and Learning (Springer, 2017, in press

The Effect of Sensory Blind Zones on Milling Behavior in a Dynamic Self-Propelled Particle Model

Emergent pattern formation in self-propelled particle (SPP) systems is extensively studied because it addresses a range of swarming phenomena which occur without leadership. Here we present a dynamic SPP model in which a sensory blind zone is introduced into each particle's zone of interaction. Using numerical simulations we discovered that the degradation of milling patterns with increasing blind zone ranges undergoes two distinct transitions, including a new, spatially nonhomogeneous transition that involves cessation of particles' motion caused by broken symmetries in their interaction fields. Our results also show the necessity of nearly complete panoramic sensory ability for milling behavior to emerge in dynamic SPP models, suggesting a possible relationship between collective behavior and sensory systems of biological organisms.Comment: 12 pages, 4 figure

Cervical spine metastases: techniques for anterior reconstruction and stabilization

pre-printThe surgical management of cervical spine metastases continues to evolve and improve. The authors provide an overview of the various techniques for anterior reconstruction and stabilization of the subaxial cervical spine after corpectomy for spinal metastases. Vertebral body reconstruction can be accomplished using a variety of materials such as bone autograft/allograft, polymethylmethacrylate, interbody spacers, and/or cages with or without supplemental anterior cervical plating. In some instances, posterior instrumentation is needed for additional stabilization

Formation of regular spatial patterns in ratio-dependent predator-prey model driven by spatial colored-noise

Results are reported concerning the formation of spatial patterns in the two-species ratio-dependent predator-prey model driven by spatial colored-noise. The results show that there is a critical value with respect to the intensity of spatial noise for this system when the parameters are in the Turing space, above which the regular spatial patterns appear in two dimensions, but under which there are not regular spatial patterns produced. In particular, we investigate in two-dimensional space the formation of regular spatial patterns with the spatial noise added in the side and the center of the simulation domain, respectively.Comment: 4 pages and 3 figure

Local Susceptibility Against Soft Errors in Dynamic Random Access Memories (DRAMs) Analyzed by Nuclear Microprobes

A novel evaluation technique for soft errors in Mbit DRAMs (dynamic random access memories) has been developed using a 400 keV proton microprobe system. This technique, which is called soft error mapping, consists of a bit-state mapping image and a secondary electron mapping image, and can reveal the correlation between the incident position of protons and susceptibility against soft errors in DRAMs. Soft errors are found to be induced by proton incidence at 400 keV within about 6 μm around the memory cell in the case of DRAMs with a conventional well. The susceptible area against proton incidence is much larger than the memory cell size. It is found that the area within 4 μm around the memory cell is, in particular, highly sensitive to 400 keV protons. A threshold dose to radiation hardness is estimated by deterioration of the DRAMs during soft error mapping. A buried barrier layer, formed by high-energy ion-implantation, was found to control the charge collection of induced carriers and to suppress soft errors by 400 keV proton microprobes

Complexity, Development, and Evolution in Morphogenetic Collective Systems

Many living and non-living complex systems can be modeled and understood as collective systems made of heterogeneous components that self-organize and generate nontrivial morphological structures and behaviors. This chapter presents a brief overview of our recent effort that investigated various aspects of such morphogenetic collective systems. We first propose a theoretical classification scheme that distinguishes four complexity levels of morphogenetic collective systems based on the nature of their components and interactions. We conducted a series of computational experiments using a self-propelled particle swarm model to investigate the effects of (1) heterogeneity of components, (2) differentiation/re-differentiation of components, and (3) local information sharing among components, on the self-organization of a collective system. Results showed that (a) heterogeneity of components had a strong impact on the system's structure and behavior, (b) dynamic differentiation/re-differentiation of components and local information sharing helped the system maintain spatially adjacent, coherent organization, (c) dynamic differentiation/re-differentiation contributed to the development of more diverse structures and behaviors, and (d) stochastic re-differentiation of components naturally realized a self-repair capability of self-organizing morphologies. We also explored evolutionary methods to design novel self-organizing patterns, using interactive evolutionary computation and spontaneous evolution within an artificial ecosystem. These self-organizing patterns were found to be remarkably robust against dimensional changes from 2D to 3D, although evolution worked efficiently only in 2D settings.Comment: 13 pages, 8 figures, 1 table; submitted to "Evolution, Development, and Complexity: Multiscale Models in Complex Adaptive Systems" (Springer Proceedings in Complexity Series