Motif-h: a novel functional backbone extraction for directed networks

Dense networks are very pervasive in social analytics, biometrics, communication, architecture, etc. Analyzing and visualizing such large-scale networks are significant challenges, which are generally met by reducing the redundancy on the level of nodes or edges. Motifs, patterns of the higher order organization compared with nodes and edges, are recently found to be the novel fundamental unit structures of complex networks. In this work, we proposed a novel motif h-backbone (Motif-h) method to extract functional cores of directed networks based on both motif strength and h-bridge. Compared with the state-of-the-art method Motif-DF and Entropy, our method solves two main issues which are often found in existing methods: the Motif-h reconsiders weak ties into our candidate set, and those weak ties often have critical functions of bridges in networks; moreover, our method provides a trade-off between the motif size and the edge strength, which quantifies the core edges accordingly. In the simulations, we compare our method with Motif-DF in four real-world networks and found that Motif-h can streamline the extraction of crucial structures compared with the others with limited edges.

Edge irregular reflexive labeling on sun graph and corona of cycle and null graph with two vertices

<p>Let <em>G</em>(<em>V</em>,<em>E</em>) be a simple and connected graph which set of vertices is <em>V</em> and set of edges is <em>E</em>. Irregular reflexive <em>k</em>-labeling f on <em>G</em>(<em>V</em>,<em>E</em>) is assignment that carries the numbers of integer to elements of graph, such that the positive integer {1,2, 3,...,<em>k</em>_e} assignment to edges of graph and the even positive integer {0,2,4,...,2<em>k</em>_v} assignment to vertices of graph. Then, we called as edge irregular reflexive <em>k</em>-labelling if every edges has different weight with <em>k</em> = max{<em>k</em>_e,2<em>k</em>_v}. Besides that, there is definition of reflexive edge strength of <em>G</em>(<em>V</em>,<em>E</em>) denoted as <em>res</em>(<em>G</em>), that is a minimum <em>k</em> that using for labeling <em>f</em> on <em>G</em>(<em>V</em>,<em>E</em>). This paper will discuss about edge irregular reflexive <em>k</em>-labeling for sun graph and corona of cycle and null graph, denoted by <em>C</em>_n ⨀ <em>N</em>₂ and make sure about their reflexive edge strengths.</p>

Community detection in social networks based on information propagation and user engagement

The iterative propagation of information between nodes will strengthen the connection strength between nodes, and the network can evolve into different groups according to difference edge strength. Based on this observation, we present the user engagement to quantify the influences of users different propagation modes to network propagation, and construct weight network to simulate real social network, and proposed the community detection method in social networks based on information propagation and user engagement. Our method can produce different scale communities and overlapping community. We also applied our method to real-world social networks. The experiment proved that the network spread and the community division interact with each other. The community structure is significantly different in the network propagation of different scales.

Edge strength of core drilled and waterjet cut holes in architectural glass

In structural glass design, an often-applied connection is a bolted connection subjected to in-plane tensile loads. Traditionally, the hole in the glass pane is manufactured by core drilling and conical edge finishing. An alternative method is by waterjet cutting the holes, resulting in cylindrically shaped holes. This research compares the edge strength of core drilled and waterjet cut holes. It focuses on in-plane tensile tests and consists of an experimental part in combination with a numerical part. In the in-plane tensile tests, peak stresses occur perpendicular to the load direction. These stresses are found to be higher for waterjet cut holes (+ 13%) compared to core drilled holes. As a result, the characteristic ultimate load is lower for waterjet cut holes (− 16%). Furthermore, the influence of thermally toughening the glass is found to be more favourable for the characteristic ultimate load of specimens containing core drilled holes than it is for waterjet cut holes. Next to that, it was found that the ultimate load linearly increases with the panel thickness. Eccentric loading, caused by insufficient bushing material or rotation of the bolt, only slightly decreases the ultimate load, provided that no hard contact between bolt and glass occurs. In addition, coaxial double ring tests were performed in the hole area, showing that waterjet cut holes result in larger stresses near the hole edge than core drilled holes. Furthermore, waterjet cut holes are found not to be perfectly round, while drilled holes are. This un-roundness negatively influences the ultimate load and the stresses in the glass; the larger the extent of un-roundness, the higher the stresses and the lower the ultimate load. Also, the orientation of the un-round hole is of influence on the stresses and ultimate load for the tensile test. It is concluded that waterjet cut holes result in lower characteristic ultimate loads and higher stresses. Due to the different edge finishing, the ultimate load still is lower compared to core drilled holes, even if the waterjet cut holes are perfectly round.

Edge irregular reflexive labeling for the $ r $-th power of the path

<abstract><p>Let $ G(V, E) $ be a graph, where $ V(G) $ is the vertex set and $ E(G) $ is the edge set. Let $ k $ be a natural number, a total k-labeling $ \varphi:V(G)\bigcup E(G)\rightarrow \{0, 1, 2, 3, ..., k\} $ is called an edge irregular reflexive $ k $-labeling if the vertices of $ G $ are labeled with the set of even numbers from $ \{0, 1, 2, 3, ..., k\} $ and the edges of $ G $ are labeled with numbers from $ \{1, 2, 3, ..., k\} $ in such a way for every two different edges $ xy $ and $ x^{'}y^{'} $ their weights $ \varphi(x)+\varphi(xy)+\varphi(y) $ and $ \varphi(x^{'})+\varphi(x^{'}y^{'})+\varphi(y^{'}) $ are distinct. The reflexive edge strength of $ G $, $ res(G) $, is defined as the minimum $ k $ for which $ G $ has an edge irregular reflexive $ k $-labeling. In this paper, we determine the exact value of the reflexive edge strength for the $ r $-th power of the path $ P_{n} $, where $ r\geq2 $, $ n\geq r+4 $.</p></abstract>

Multi-Modal Medical Image Fusion Algorithm Based On Spatial Frequency Motivated PA-PCNN In NSST Domain

Background: Image fusion has been grown as an effectual method in diseases related diagnosis schemes. Methods: In this paper, a new method for combining multimodal medical images using spatial frequency motivated parameter-adaptive PCNN (SF-PAPCNN) is suggested. The multi-modal images are disintegrated into frequency bands by using decomposition NSST. The coefficients of low frequency bands are selected using maximum rule. The coefficients of high frequency bands are combined by SF-PAPCNN. Results: The fused medical images is obtained by applying INSST to above coefficients. Conclusion: The quality metrics such as entropy ENT, fusion symmetry FS, deviation STD, mutual information QMI and edge strength QAB/F are used to validate the efficacy of suggested scheme.