Weak percolation on multiplex networks

peer-reviewedBootstrap percolation is a simple but nontrivial model. It has applications in many areas of science and has been explored on random networks for several decades. In single-layer (simplex) networks, it has been recently observed that bootstrap percolation, which is defined as an incremental process, can be seen as the opposite of pruning percolation, where nodes are removed according to a connectivity rule. Here we propose models of both bootstrap and pruning percolation for multiplex networks. We collectively refer to these two models with the concept of "weak" percolation, to distinguish them from the somewhat classical concept of ordinary ("strong") percolation. While the two models coincide in simplex networks, we show that they decouple when considering multiplexes, giving rise to a wealth of critical phenomena. Our bootstrap model constitutes the simplest example of a contagion process on a multiplex network and has potential applications in critical infrastructure recovery and information security. Moreover, we show that our pruning percolation model may provide a way to diagnose missing layers in a multiplex network. Finally, our analytical approach allows us to calculate critical behavior and characterize critical clusters.PUBLISHEDpeer-reviewe

Adaptable Security in Wireless Sensor Networks by Using Reconfigurable ECC Hardware Coprocessors

Specific features of Wireless Sensor Networks (WSNs) like the open accessibility to nodes, or the easy observability of radio communications, lead to severe security challenges. The application of traditional security schemes on sensor nodes is limited due to the restricted computation capability, low-power availability, and the inherent low data rate. In order to avoid dependencies on a compromised level of security, a WSN node with a microcontroller and a Field Programmable Gate Array (FPGA) is used along this work to implement a state-of-the art solution based on ECC (Elliptic Curve Cryptography). In this paper it is described how the reconfiguration possibilities of the system can be used to adapt ECC parameters in order to increase or reduce the security level depending on the application scenario or the energy budget. Two setups have been created to compare the software- and hardware-supported approaches. According to the results, the FPGA-based ECC implementation requires three orders of magnitude less energy, compared with a low power microcontroller implementation, even considering the power consumption overhead introduced by the hardware reconfiguratio

On the Role of Expander Graphs in Key Predistribution Schemes for Wireless Sensor Networks

Providing security for a wireless sensor network composed of small sensor nodes with limited battery power and memory can be a non-trivial task. A variety of key predistribution schemes have been proposed which allocate symmetric keys to the sensor nodes before deployment. In this paper we examine the role of expander graphs in key predistribution schemes for wireless sensor networks. Roughly speaking, a graph has good expansion if every `small\u27 subset of vertices has a `large\u27 neighbourhood, and intuitively, expansion is a desirable property for graphs of networks. It has been claimed that good expansion in the product graph is necessary for `optimal\u27 networks. We demonstrate flaws in this claim, argue instead that good expansion is desirable in the intersection graph, and discuss how this can be achieved. We then consider key predistribution schemes based on expander graph constructions and compare them to other schemes in the literature. Finally, we propose the use of expansion and other graph-theoretical techniques as metrics for assessing key predistribution schemes and their resulting wireless sensor networks

Poly[ethyl­enediammonium [tris­[μ3-hydrogenphosphato(2−)]dicadmium] monohydrate]

The title compound, {(C2H10N2)[Cd2(HPO4)3]·H2O}n, was synthesized under hydro­thermal conditions. The structure of this hybrid compound consists of CdO6, CdO5 and PO4 polyhedra arranged so as to build an anionic inorganic layer, namely [Cd2(HPO4)3]2−, parallel to the ab plane. The edge-sharing CdO6 octa­hedra form infinite chains running along the a axis and are linked by CdO5 and PO4 polyhedra. The ethyl­ene­diammonium cation and the water mol­ecule are located between two adjacent inorganic layers and ensure the cohesion of the structure via N—H⋯O and O—H⋯O hydrogen bonds