Skeleton and fractal scaling in complex networks

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in-silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.Comment: 4 pages, 2 figures, final version published in PR

The impact of pre- and post-image processing techniques on deep learning frameworks: A comprehensive review for digital pathology image analysis

Recently, deep learning frameworks have rapidly become the main methodology for analyzing medical images. Due to their powerful learning ability and advantages in dealing with complex patterns, deep learning algorithms are ideal for image analysis challenges, particularly in the field of digital pathology. The variety of image analysis tasks in the context of deep learning includes classification (e.g., healthy vs. cancerous tissue), detection (e.g., lymphocytes and mitosis counting), and segmentation (e.g., nuclei and glands segmentation). The majority of recent machine learning methods in digital pathology have a pre- and/or post-processing stage which is integrated with a deep neural network. These stages, based on traditional image processing methods, are employed to make the subsequent classification, detection, or segmentation problem easier to solve. Several studies have shown how the integration of pre- and post-processing methods within a deep learning pipeline can further increase the model's performance when compared to the network by itself. The aim of this review is to provide an overview on the types of methods that are used within deep learning frameworks either to optimally prepare the input (pre-processing) or to improve the results of the network output (post-processing), focusing on digital pathology image analysis. Many of the techniques presented here, especially the post-processing methods, are not limited to digital pathology but can be extended to almost any image analysis field

Automatic segmentation and classification methods using optical coherence tomography angiography (Octa): A review and handbook

Optical coherence tomography angiography (OCTA) is a promising technology for the non-invasive imaging of vasculature. Many studies in literature present automated algorithms to quantify OCTA images, but there is a lack of a review on the most common methods and their comparison considering multiple clinical applications (e.g., ophthalmology and dermatology). Here, we aim to provide readers with a useful review and handbook for automatic segmentation and classification methods using OCTA images, presenting a comparison of techniques found in the literature based on the adopted segmentation or classification method and on the clinical application. Another goal of this study is to provide insight into the direction of research in automated OCTA image analysis, especially in the current era of deep learning

Scale-free random branching tree in supercritical phase

We study the size and the lifetime distributions of scale-free random branching tree in which $k$ branches are generated from a node at each time step with probability $q_k\sim k^{-\gamma}$. In particular, we focus on finite-size trees in a supercritical phase, where the mean branching number $C=\sum_k k q_k$ is larger than 1. The tree-size distribution $p(s)$ exhibits a crossover behavior when $2 < \gamma < 3$; A characteristic tree size $s_c$ exists such that for $s \ll s_c$, $p(s)\sim s^{-\gamma/(\gamma-1)}$ and for $s \gg s_c$, $p(s)\sim s^{-3/2}\exp(-s/s_c)$, where $s_c$ scales as $\sim (C-1)^{-(\gamma-1)/(\gamma-2)}$. For $\gamma > 3$, it follows the conventional mean-field solution, $p(s)\sim s^{-3/2}\exp(-s/s_c)$ with $s_c\sim (C-1)^{-2}$. The lifetime distribution is also derived. It behaves as $\ell(t)\sim t^{-(\gamma-1)/(\gamma-2)}$ for $2 < \gamma < 3$, and $\sim t^{-2}$ for $\gamma > 3$ when branching step $t \ll t_c \sim (C-1)^{-1}$, and $\ell(t)\sim \exp(-t/t_c)$ for all $\gamma > 2$ when $t \gg t_c$. The analytic solutions are corroborated by numerical results.Comment: 6 pages, 6 figure

ENHANCED GRAVITROPISM 2 coordinates molecular adaptations to gravistimulation in the elongation zone of barley roots

Root gravitropism includes gravity perception in the root cap, signal transduction between root cap and elongation zone, and curvature response in the elongation zone. The barley (Hordeum vulgare) mutant enhanced gravitropism 2 (egt2) displays a hypergravitropic root phenotype. We compared the transcriptomic reprogramming of the root cap, the meristem, and the elongation zone of wild-type (WT) and egt2 seminal roots upon gravistimulation in a time-course experiment and identified direct interaction partners of EGT2 by yeast-two-hybrid screening and bimolecular fluorescence complementation validation. We demonstrated that the elongation zone is subjected to most transcriptomic changes after gravistimulation. Here, 33% of graviregulated genes are also transcriptionally controlled by EGT2, suggesting a central role of this gene in controlling the molecular networks associated with gravitropic bending. Gene co-expression analyses suggested a role of EGT2 in cell wall and reactive oxygen species-related processes, in which direct interaction partners of EGT2 regulated by EGT2 and gravity might be involved. Taken together, this study demonstrated the central role of EGT2 and its interaction partners in the networks controlling root zone-specific transcriptomic reprogramming of barley roots upon gravistimulation. These findings can contribute to the development of novel root idiotypes leading to improved crop performance