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Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from the high computational cost and excessive memory requirements associated with the high-dimensionality and heterogeneous characteristics of industrial size networks. Graph embedding techniques can be effective in converting high-dimensional sparse graphs into low-dimensional, dense, and continuous vector spaces, preserving maximally the graph structure properties. Another type of emerging graph embedding employs Gaussian distribution--based graph embedding with important uncertainty estimation. The main goal of graph embedding methods is to pack every node's properties into a vector with a smaller dimension; hence, node similarity in the original complex irregular spaces can be easily quantified in the embedded vector spaces using standard metrics. The nonlinear and highly informative graph embeddings generated in the latent space can be conveniently used to address different downstream graph analytics tasks (e.g., node classification, link prediction, community detection, visualization, etc.). In this review, we present some fundamental concepts in graph analytics and graph embedding methods, focusing in particular on random walk--based and neural network--based methods. We also discuss the emerging deep learning--based dynamic graph embedding methods. We highlight the distinct advantages of graph embedding methods in four diverse applications, and we present implementation details and references to open-source software as well as available databases in the supplementary material to help interested readers start their exploration into graph analytics. [ABSTRACT FROM AUTHOR]

Permutation entropy (PE) is a novel measure to quantify the complexity of nonlinear time series. In this paper, we propose a generalized permutation entropy (PEq,δ) based on the recently postulated entropic form, Sq,δ, which was proposed as an unification of the well-known Sq of nonextensivestatistical mechanics and Sδ, a possibly appropriate candidate for the black-hole entropy. We find that PEq,δ with appropriate parameters can amplify minor changes and trends of complexities in comparison to PE. Experiments with this generalized permutation entropy method are performed with both synthetic and stock data showing its power. Results show that PEq,δ is an exponential function of q and the power (k(δ) is a constant if δ is determined. Some discussions about k(δ) are provided. Besides, we also find some interesting results about power law. [ABSTRACT FROM AUTHOR]

In this study, we develop a new algorithm based on fractional operators of variable-order in order to enhance image quality. First, three kinds of popular high-order discrete formulas are adopted to obtain the coefficients, and subsequently, a mask optimization method for selecting the fractional order adaptively is applied to construct a variable-order fractional differential mask along with the coefficients generated from the first step. We carry out experiments on OCT thoracic aorta images and some nature images with low contrast and noise, demonstrating that the high-order discrete method leads to significantly better performance in enhancing the edge information nonlinearly compared to the standard first-order discrete method. Moreover, the optimized mask with variable-order of the fractional derivative not only can preserve the edge information of the processed images adequately, but it also effectively suppresses the noise in the smooth area. [ABSTRACT FROM AUTHOR]

The light chains (KLCs) of the microtubule motor kinesin-1 bind cargoes and regulate its activity. Through their tetratricopeptide repeat domain (KLCTPR), they can recognize short linear peptide motifs found in many cargo proteins characterized by a central tryptophan flanked by aspartic/glutamic acid residues (W-acidic). Using a fluorescence resonance energy transfer biosensor in combination with X-ray crystallographic, biochemical, and biophysical approaches, we describe how an intramolecular interaction between the KLC2TPR domain and a conserved peptide motif within an unstructured region of the molecule, partly occludes the W-acidic binding site on the TPR domain. Cargo binding displaces this interaction, effecting a global conformational change in KLCs resulting in a more extended conformation. Thus, like the motor-bearing kinesin heavy chains, KLCs exist in a dynamic conformational state that is regulated by self-interaction and cargo binding. We propose a model by which, via this molecular switch, W-acidic cargo binding regulates the activity of the holoenzyme. [ABSTRACT FROM AUTHOR]

Traditional Hessian multiscale filter consider only the local geometric feature but not the global grayscale information. In medical image analysis, Hessian filter is usually used to enhance the blood vessels. However, it also produces some pseudo vascular structures or some isolate noise points, such as the nasal soft tissues that have the similar shape with the vessels in MRA data, which will increase the difficulty of cerebrovascular segmentation. To resolve this issue, an improved Hessian multiscale filter is proposed in this paper. An image grayscale factor is added to the vascular similarity function computed by Hessian matrix eigenvalue. This method is experimented on brain MRA data and lung CTA data. Experimental results show that this method can enhance vascular structures, and simultaneously reduce the appearance of the pseudo vascular structures and the isolated noise points. [ABSTRACT FROM AUTHOR]