Optimally-balanced Hash Tree Generation in Ad Hoc Networks

Ideally a hash tree is a perfect binary tree with leaves equal to power of two. Each leaf node in this type of tree can represent a mobile node in an ad hoc network. Each leaf in the tree contains hash value of mobile node’s identification (ID) and public key (PK). Such a tree can be used for authenticating PK in ad hoc networks. Most of the previous works based on hash tree assumed perfect hash tree structures, which can be used efficiently only in networks with a specific number of mobile nodes. Practically the number of mobile nodes may not be always equal to a power of two and the conventional algorithms may result in an inefficient tree structure. In this paper the issue of generating a hash tree is addressed by proposing an algorithm to generate an optimally-balanced structure for a complete hash tree. It is demonstrated through both the mathematical analysis and simulation that such a tree is optimally-balanced and can efficiently be used for public key authentication in ad hoc networks

Random sum-product networks: A simple and effective approach to probabilistic deep learning

Sum-product networks (SPNs) are expressive probabilistic models with a rich set of exact and efficient inference routines. However, in order to guarantee exact inference, they require specific structural constraints, which complicate learning SPNs from data. Thereby, most SPN structure learners proposed so far are tedious to tune, do not scale easily, and are not easily integrated with deep learning frameworks. In this paper, we follow a simple “deep learning” approach, by generating unspecialized random structures, scalable to millions of parameters, and subsequently applying GPU-based optimization. Somewhat surprisingly, our models often perform on par with state-of-the-art SPN structure learners and deep neural networks on a diverse range of generative and discriminative scenarios. At the same time, our models yield well-calibrated uncertainties, and stand out among most deep generative and discriminative models in being robust to missing features and being able to detect anomalies

BN-Doped Metal–Organic Frameworks: Tailoring 2D and 3D Porous Architectures through Molecular Editing of Borazines

Building on the MOF approach to prepare porous materials, herein we report the engineering of porous BN-doped materials using tricarboxylic hexaarylborazine ligands, which are laterally decorated with functional groups at the full-carbon ‘inner shell’. Whilst an open porous 3D entangled structure could be obtained from the double interpenetration of two identical metal frameworks derived from the methyl substituted borazine, the chlorine-functionalised linker undergoes formation of a porous layered 2D honeycomb structure, as shown by single-crystal X-ray diffraction analysis. In this architecture, the borazine cores are rotated by 60° in alternating layers, thus generating large rhombohedral channels running perpendicular to the planes of the networks. An analogous unsubstituted full-carbon metal framework was synthesised for comparison. The resulting MOF revealed a crystalline 3D entangled porous structure, composed by three mutually interpenetrating networks, hence denser than those obtained from the borazine linkers. Their microporosity and CO2 uptake were investigated, with the porous 3D BN-MOF entangled structure exhibiting a large apparent BET specific surface area (1091 m2 g−1) and significant CO2 reversible adsorption (3.31 mmol g−1) at 1 bar and 273 K