edge weight
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The graph transitivity measures the probability that adjacent vertices in a network are interconnected, thus revealing the existence of tightly connected neighborhoods playing a role in information and pathogen circulation. The graph transitivity is usually computed for dichotomized networks, therefore focusing on whether triangular relationships are closed or open. But when the connections vary in strength, focusing on whether the closing ties exist or not can be reductive. I score the weighted transitivity according to the similarity between the weights of the three possible links in each triad. In a simulation, that new technique correctly diagnosed excesses of balanced or imbalanced triangles, for example, strong triplets closed by weak links. I illustrate the biological relevance of that information with two reanalyses of animal contact networks. In the rhesus macaque Macaca mulatta, a species in which kin relationships strongly predict social relationships, the new metrics revealed striking similarities in the configuration of grooming networks in captive and free-ranging groups, but only as long as the matrilines were preserved. In the barnacle goose Branta leucopsis, in an experiment designed to test the long-term effect of the goslings' social environment, the new metrics uncovered an excess of weak triplets closed by strong links, particularly pronounced in males, and consistent with the triadic process underlying goose dominance relationships.

Gene co-expression networks can be used to determine gene regulation and attribute gene function to biological processes. Different high throughput technologies, including one and two-channel microarrays and RNA-sequencing, allow evaluating thousands of gene expression data simultaneously, but these methodologies provide results that cannot be directly compared. Thus, it is complex to analyze coexpression relations between genes, especially when there are missing values arising for experimental reasons. Networks are a helpful tool for studying gene co-expression, where nodes represent genes and edges represent co-expression of pairs of genes. In this paper, we propose a method for constructing a gene co-expression network for the Anopheles gambiae transcriptome from 257 unique studies obtained with different methodologies and experimental designs. We introduce the sliding threshold approach to select node pairs with high Pearson correlation coefficients. The robustness of the method was verified by comparing edge weight distributions under random removal of conditions. The properties of the constructed network are studied in this paper, including node degree distribution, coreness, and community structure. The network core is largely comprised of genes that encode components of the mitochondrial respiratory chain and the ribosome, while different communities are enriched for genes involved in distinct biological processes. This suggests that the overall network structure is driven to maximize the integration of essential cellular functions, possibly allowing the flexibility to add novel functions.

AbstractStar identification is the foundation of star trackers, which are used to precisely determine the attitude of spacecraft. In this paper, we propose a novel star identification approach based on spectral graph matching. In the proposed approach, we construct a feature called the neighbor graph for each main star, transforming the star identification to the problem of finding the most similar neighbor graph. Then the rough search and graph matching are cooperated to form a dynamic search framework to solve the problem. In the rough search stage, the total edge weight in the minimum spanning tree of the neighbor graph is selected as an indicator, then the k-vector range search is applied for reducing the search scale. Spectral graph matching is utilized to achieve global matching, identifying all stars in the neighbor circle with good noise-tolerance ability. Extensive simulation experiments under the position noise, lost-star noise, and fake-star noise show that our approach achieves higher accuracy (mostly over 99%) and better robustness results compared with other baseline algorithms in most cases.

AbstractHere, we combine network neuroscience and machine learning to reveal connections between the brain’s network structure and the emerging network structure of an artificial neural network. Specifically, we train a shallow, feedforward neural network to classify hand-written digits and then used a combination of systems neuroscience and information-theoretic tools to perform ‘virtual brain analytics’ on the resultant edge weights and activity patterns of each node. We identify three distinct phases of network reconfiguration across learning, each of which are characterized by unique topological and information-theoretic signatures. Each phase involves aligning the connections of the neural network with patterns of information contained in the input dataset or preceding layers (as relevant). We also observe a process of low-dimensional category separation in the network as a function of learning. Our results offer a systems-level perspective of how artificial neural networks function—in terms of multi-stage reorganization of edge weights and activity patterns to effectively exploit the information content of input data during edge-weight training—while simultaneously enriching our understanding of the methods used by systems neuroscience.

Among the inorganic compounds, there are many influential crystalline structures, and magnesium iodide is the most selective. In the making of medicine and its development, magnesium iodide is considered a multipurpose and rich compound. Chemical structures and networks can be studied by given tools of molecular graph theory. Given tools of molecular graph theory can be studied for chemical structures and networks, which are considered economical with simple methodology. Edge weight-based entropy is a recent advent tool of molecular graph theory to study chemical networks and structures. It provides the structural information of chemical networks or their related build-up graphs and highlights the molecular properties in the form of a polynomial function. In this work, we provide the edge weight-based entropy of magnesium iodide structure and compute different entropies, such as Zagreb and atom bond connectivity entropies.

Abstract Convolutional neural network is an important neural network model in deep learning and a common algorithm in computer vision problems. From the perspective of practical application scenarios, this paper studies whether padding in convolutional neural network convolution layer weakens the image edge information. In order to eliminate the background factor, this paper select MNIST dataset as the research object, move the 0-9 digital image to the specified image edge by clearing the white area pixels in the specified direction, and use OpenCV to realize bilinear interpolation to scale the image to ensure that the image dimension is 28×28. The convolution neural network is built to train the original dataset and the processed dataset, and the accuracy rates are 0.9892 and 0.1082 respectively. In the comparative experiment, padding cannot solve the problem of weakening the image edge weight well. In the actual digital recognition scene, it is necessary to consider whether the core recognition area in the input image is at the edge of the image.

Abstract Network embedding has attracted a surge of attention recently. In this field, how to preserve high-order proximity has long been a difficult task. Graph convolutional network (GCN) and random walk-based approaches can preserve high-order proximity to a certain extent. However, they partially concentrate on the aggregation process and sampling process respectively. Path aggregation methods combine the merits of GCN and random walk, and thus can preserve more high-order information and achieve better performance. However, path aggregation framework has not been applied in attributed network embedding yet. In this paper, we propose a path aggregation model for attributed network embedding, with two main contributions. First, we claim that there always exists implicit edge weight in networks, and design a tweaked random walk algorithm to sample paths accordingly. Second, we propose a path aggregation framework dealing with both nodes and attributes. Extensive experimental results show that our proposal outperforms the cutting-edge baselines on downstream tasks, such as node clustering, node classification, and link prediction.

Hyperspectral images contain distinguishing spectral information and show great potential in the anomaly detection (AD) task which aims to extract discrepant targets from the background. However, most of the popular hyperspectral AD techniques are time consuming and suffer from poor detection performance due to noise disturbance. To address these issues, we propose an efficient and robust AD method for hyperspectral images. In our framework, principal component analysis (PCA) is adopted for spectral dimensionality reduction and to enhance the anti-noise ability. An improved guided filter with edge weight is constructed to purify the background and highlight the potential anomalies. Moreover, a diagonal matrix operation is designed to quickly accumulate the energy of each pixel and efficiently locate the abnormal targets. Extensive experiments conducted on the real-world hyperspectral datasets qualitatively and quantitatively demonstrate that, compared with the existing state-of-the-art approaches, the proposed method achieves higher detection accuracy with faster detection speed which verifies the superiority and effectiveness of the proposed method.