eGHWT: The Extended Generalized Haar–Walsh Transform

Extending computational harmonic analysis tools from the classical setting of regular lattices to the more general setting of graphs and networks is very important, and much research has been done recently. The generalized Haar–Walsh transform (GHWT) developed by Irion and Saito (2014) is a multiscale transform for signals on graphs, which is a generalization of the classical Haar and Walsh–Hadamard transforms. We propose the extended generalized Haar–Walsh transform (eGHWT), which is a generalization of the adapted time–frequency tilings of Thiele and Villemoes (1996). The eGHWT examines not only the efficiency of graph-domain partitions but also that of “sequency-domain” partitions simultaneously. Consequently, the eGHWT and its associated best-basis selection algorithm for graph signals significantly improve the performance of the previous GHWT with the similar computational cost, $$O(N \log N)$$ O ( N log N ) , where N is the number of nodes of an input graph. While the GHWT best-basis algorithm seeks the most suitable orthonormal basis for a given task among more than $$(1.5)^N$$ ( 1.5 ) N possible orthonormal bases in $$\mathbb {R}^N$$ R N , the eGHWT best-basis algorithm can find a better one by searching through more than $$0.618\cdot (1.84)^N$$ 0.618 · ( 1.84 ) N possible orthonormal bases in $$\mathbb {R}^N$$ R N . This article describes the details of the eGHWT best-basis algorithm and demonstrates its superiority using several examples including genuine graph signals as well as conventional digital images viewed as graph signals. Furthermore, we also show how the eGHWT can be extended to 2D signals and matrix-form data by viewing them as a tensor product of graphs generated from their columns and rows and demonstrate its effectiveness on applications such as image approximation.

Direct Pore-Scale Simulations of Fully Periodic Unit Cells of Different Regular Lattices

Open-cell metal foams are known for their superior heat dissipation capabilities. The morphological, pressure-drop and heat transfer characteristics of stochastic metal foams manufactured through traditional 'foaming' process are well established in the literature. Employment of stochastic metal foams in next generation heat exchangers, is however, challenged by the irregularity in the pore-and fiber-geometries, limited control on the pore-volume, and an inherent necessity of a bonding agent between foam and heat source. On the other hand, additive manufacturing is an emerging technology that is capable of printing complex user-defined unit cell topologies with customized fiber shapes directly on the heated substrates. Moreover, the user-defined regular lattices are capable of exhibiting better thermal and mechanical properties than stochastic metal foams. In this paper, we present a numerical investigation on fully periodic unit-cells of three different topologies, viz. Tetrakaidecahedron (TKD), Rhombic-dodecahedron (DDC), and Octet with air as the working fluid. Pressure gradient, interfacial heat transfer coefficient, friction factor, and Nusselt number are reported for each topology. Rhombic-dodecahedron yielded in the highest average interfacial heat transfer coefficient whereas Octet incurred the highest flow losses. Pore diameter, defined as the maximum diameter of a sphere passing through the polygonal openings of the structures, when used as the characteristics length scale for the presentation of Nusselt number and Reynolds number, resulted in a single trendline for all the three topologies.

Lattice-Based 3-Dimensional Wireless Sensor Deployment

With the wide application of wireless sensor networks (WSNs) in real space, there are numerous studies on 3D sensor deployments. In this paper, the k -connectivity theoretical model of fixed and random nodes in regular lattice-based deployment was proposed to study the coverage and connectivity of sensor networks with regular lattice in 3D space. The full connectivity range and cost of the deployment with sensor nodes fixed in the centers of four regular lattices were quantitatively analyzed. The optimal single lattice coverage model and the ratio of the communication range to the sensing range r c / r s were investigated when the deployment of random nodes satisfied the k -connectivity requirements for full coverage. In addition, based on the actual sensing model, the coverage, communication link quality, and reliability of different lattice-based deployment models were determined in this study.

Evaluation of Serpent Capabilities for Hyperfidelity Depletion of Pebble Bed Cores

Accurate burnup calculation in pebble bed reactor cores is today necessary but challenging. The continuous advancement in computing capabilities make the use of Monte Carlo transport codes possible to efficiently study individual pebbles depletion without making strong assumptions. The purpose is to eliminate unnecessary typical assumptions made in existing codes, while being flexible and suitable for commonly available computing machines. Among the available codes, Serpent 2 provides extremely useful tools to make pebble beds modeling and simulation efficient. The explicit stochastic geometry definition handles irregular pebble beds with comparable performances to regular lattices. Optimization modes controlling the use of unionized energy grids, cross-sections pre-calculation and flux calculation through spectrum collapse or direct tally lead to high flexibility and optimal memory usage while limiting calculation time. Automated burnable materials division is a useful tool to lower the memory requirements while quickly generating the geometry and materials. Finally, parallelization and domain decomposition allow for decreasing unreasonable memory constraints for large cores. This work thus explores the possibilities of Serpent 2 when applying depletion in pebble beds, compares the optimization modes and quantifies the simulation time and memory usage depending on the conditions of the calculation. Overall, the results show that Serpent 2 is well adapted to the use of small to large cores calculations with commonly available resources.

A 3-D FINITE ELEMENT FEW-GROUP DIFFUSION CODE AND ITS APPLICATION TO GENERATION IV REACTOR CONCEPTS

In this paper, a recently developed 3-d few-group finite element-based diffusion code is de-scribed. Its geometrical flexibility allows future modeling of complex and irregular geometries of (very) small and medium size reactor concepts –(v)SMRs –being in the spotlight for energy provision in remote residential and industrial regions or for space applications, and also liquid metal cooled Generation IV reactors where thermally induced core deformation results in localized assembly lattice distortions which cannot be treated by traditional 3-d neutron kinetics codes devoted to the regular lattices of LWR and Generation IV systems. The description of the implemented FEM solution method is followed by first applications to a prismatic (or block type) high-temperature reactor MHTGR-350MW within an OECD/NEA benchmark activity and to the sodium cooled fast reactor concept ASTRID within the past EU project ESNII+. Finally, an outlook to planned further code development activities is given.

Optimization processes of tangible and intangible networks through the Laplace problems for regular lattices with multiple obstacles along the way

A systematic approach is proposed to the theme of safety, reliabil-ity and global quality of complex networks (material and immaterial) bymeans of special mathematical tools that allow an adequate geometriccharacterization and study of the operation, even in the presence of mul-tiple obstacles along the path. To that end, applying the theory of graphsto the problem under study and using a special mathematical model basedon stochastic geometry, in this article we consider some regular latticesin which it is possible to schematize the elements of the network, withthe fundamental cell with six, eight or 2(n + 2) obstacles, calculating theprobability of Laplace. In this way it is possible to measure the "degree ofimpedance" exerted by the anomalies along the network by the obstaclesexamined. The method can be extended to other regular or irregular ge-ometric gures, whose union together constitutes the examined network,allowing to optimize the functioning of the complex system considered.

Graph representation learning: a survey

Research on graph representation learning has received great attention in recent years since most data in real-world applications come in the form of graphs. High-dimensional graph data are often in irregular forms. They are more difficult to analyze than image/video/audio data defined on regular lattices. Various graph embedding techniques have been developed to convert the raw graph data into a low-dimensional vector representation while preserving the intrinsic graph properties. In this review, we first explain the graph embedding task and its challenges. Next, we review a wide range of graph embedding techniques with insights. Then, we evaluate several stat-of-the-art methods against small and large data sets and compare their performance. Finally, potential applications and future directions are presented.