natural fractals

We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes with which we cover the network when determining its box dimension. This approach-grounded in both scaling theory of phase transitions and renormalization group theory-leads to the consistent scaling theory of fractal complex networks, which complements the collection of scaling exponents with several new ones and reveals various relationships between them...

Comprehensive visualization and accurate extraction of tumor vasculature are essential to study the nature of glioma. Nowadays, tissue clearing technology enables 3D visualization of human glioma vasculature at micron resolution, but current vessel extraction schemes cannot well cope with the extraction of complex tumor vessels with high disruption and irregularity under realistic conditions. Here, we developed a framework, FineVess, based on deep learning to automatically extract glioma vessels in confocal microscope images of cleared human tumor tissues...

Protein dynamics involves a myriad of mechanical movements happening at different time and space scales, which make it highly complex. One of the less understood features of protein dynamics is subdiffusivity, defined as sublinear dependence between displacement and time. Here, we use all-atoms molecular dynamics (MD) simulations to directly interrogate an already well-established theory and demonstrate that subdiffusivity arises from the fractal nature of the network of metastable conformations over which the dynamics, thought of as a diffusion process, takes place...

In this study, fast-growing poplar reclaimed from abandoned homestead in Xixian New District, Xi'an City, Shaanxi Province, was used as the research object to explore the multi-fractal characteristics of soil particle size distribution under different management modes of abandoned land (control), irrigation, fertilizer irrigation and mixed fertilizer irrigation. The results showed that the mean values of soil clay, silt and sand in abandoned land were 14.58%, 81.21% and 4.22% respectively, 14.08%, 79.92% and 5...

We theoretically study topological features, band structure, and localization properties of a dimerized two-leg ladder with an oscillating on-site potential. The periodicity of the on-site potential can take either rational or irrational values. We consider two types of dimerized configurations; symmetric and asymmetric models. For rational values of the periodicity as long as inversion symmetry is preserved both symmetric and asymmetric ladders can host topological phases. Additionally, the energy spectrum of the models exhibits a fractal structure known as the Hofstadter butterfly spectrum, dependent on the dimerization of the hopping and the strength of the on-site potential...

This paper presents the investigation of the dynamic mechanical properties of coal rock under complex stress conditions at depth, based on the improved Separate Hopkinson Pressure Bar Test System. A total of 15 groups of coal samples were used to perform dynamic impact tests under different conditions. The changing rules of dynamic strength, crushing, fractal dimension and damage modes of coal under different stress conditions were analyzed. A total of nine groups of coal samples were selected for numerical simulation using ANSYS/LS-DYNA...

Fractals are patterns that are self-similar across multiple length-scales1 . Macroscopic fractals are common in nature2-4 ; however, so far, molecular assembly into fractals is restricted to synthetic systems5-12 . Here we report the discovery of a natural protein, citrate synthase from the cyanobacterium Synechococcus elongatus, which self-assembles into Sierpiński triangles. Using cryo-electron microscopy, we reveal how the fractal assembles from a hexameric building block. Although different stimuli modulate the formation of fractal complexes and these complexes can regulate the enzymatic activity of citrate synthase in vitro, the fractal may not serve a physiological function in vivo...

Accumulation of bioavailable heavy metals in aquatic environment poses a serious threat to marine communities and human health due to possible trophic transfers through the food chain of toxic, non-degradable, exogenous pollutants. Copper (Cu) is one of the most spread heavy metals in water, and can severely affect primary producers at high doses. Here we show a novel imaging test to assay the dose-dependent effects of Cu on live microalgae identifying stress conditions when they are still capable of sustaining a positive growth...

Over the past two decades, the study of self-similarity and fractality in discrete structures, particularly complex networks, has gained momentum. This surge of interest is fueled by the theoretical developments within the theory of complex networks and the practical demands of real-world applications. Nonetheless, translating the principles of fractal geometry from the domain of general topology, dealing with continuous or infinite objects, to finite structures in a mathematically rigorous way poses a formidable challenge...

In this paper, we propose a fractional-order mathematical model to explain the role of glucagon in maintaining the glucose level in the human body by using a generalised form of a fractal fractional operator. The existence, boundedness, and positivity of the results are constructed by fixed point theory and the Lipschitz condition for the biological feasibility of the system. Also, global stability analysis with Lyapunov's first derivative functions is treated. Numerical simulations for fractional-order systems are derived with the help of Lagrange interpolation under the Mittage-Leffler kernel...

Very recently, a fundamental observable has been introduced and analyzed to quantify the exploration of random walks: the time τ_{k} required for a random walk to find a site that it never visited previously, when the walk has already visited k distinct sites. Here, we tackle the natural issue of the statistics of M_{n}, the longest duration out of τ_{0},…,τ_{n-1}. This problem belongs to the active field of extreme value statistics, with the difficulty that the random variables τ_{k} are both correlated and nonidentically distributed...

Colonoscopy is accurate but inefficient for colorectal cancer (CRC) prevention due to the low (~ 7 to 8%) prevalence of target lesions, advanced adenomas. We leveraged rectal mucosa to identify patients who harbor CRC field carcinogenesis by evaluating chromatin 3D architecture. Supranucleosomal disordered chromatin chains (~ 5 to 20 nm, ~1 kbp) fold into chromatin packing domains (~ 100 to 200 nm, ~ 100 to 1000 kbp). In turn, the fractal-like conformation of DNA within chromatin domains and the folding of the genome into packing domains has been shown to influence multiple facets of gene transcription, including the transcriptional plasticity of cancer cells...

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The disintegration of red-bed soft rock exhibits a strong correlation with various geological disasters. However, the investigation into the evolutionary mechanisms underlying disintegration breakage has not yet received extensive exploration. In order to comprehensively examine the disintegration characteristics of red-bed soft rock, the slake durability tests were conducted to red-bed soft rocks of varying burial depths. Subsequently, an investigation was carried out to examine the disintegration characteristics and the evolution of disintegration parameters, including the coefficient of uniformity (Cu), coefficient of curvature (Cc), disintegration rate (DRE), disintegration ratio (Dr), and fractal dimension (D), throughout the disintegration process...

Mud flocculation and settling play key role in understanding sediment transport cycle and affect water quality in estuaries and coastal seas. However, the morphological irregularity and structural instability of fragile mud flocs set huge obstacles for quantifying geometric property accurately and establishing reliable predicting tools in settling dynamics via previous observing strategies based on instant measured and 2-dimensional imagery floc parameterizations. Here we designed a multi-camera apparatus targeting capturing multiple angles of individual flocs, and developed a multi-view segmentation algorithm on floc images analysis...

Coal-series diatomite (CSD) is widely distributed in China and has poor functional and structural properties and exhibits limited utilization of high value-added materials, resulting in a serious waste of resources and tremendous pressure on the environment. Moreover, due to differences in the mineralogical characteristics of CSD, different particle size scales (PSSs) have different functional structures and exhibit different self-similarities. In this study, we took CSD as the research object and PSS as the entry point and carried out a self-similarity study based on gas adsorption and an image processing method to illustrate the microstructures and self-similarities of different PSSs...

Investigating the impact of train-induced vibration loads on soil hydraulic properties, this study conducted experiments using a self-designed indoor soil seepage platform that incorporates vibration loads. The experiments were complemented with scanning electron microscopy to analyze the influence of train-induced vibration loads on soil hydraulic conductivity and its evolutionary characteristics under different vibration frequencies. The experimental results indicated that as the vibration frequency increases from no vibration (0 Hz) to 20 Hz, the time required for the soil volumetric moisture content to reach its peak and stabilize decreases rapidly...

In this work, a novel adsorbent called magnetite/MXene (Fe3 O4 /Ti3 C2 ) nanocomposite was prepared, characterized, and applied for the removal of organic dye, malachite green dye (MG), from both real water and model solutions. Numerous techniques were used to characterize the prepared Fe3 O4 /Ti3 C2 nanocomposite: XRD, SEM, TEM, FTIR, and surface area analysis. The outcomes showed that the Al layer had been selectively etched, that the MAX phase (Ti3 AlC2 ) had been transformed into layered Ti3 C2 MXene, that the cubic Fe3 O4 phase had been prepared, and that the prepared Fe3 O4 NPs had been evenly distributed on the MXene surface...

The dynamic compression test of geopolymer concrete (GC) before and after water saturation was carried out by the split Hopkinson pressure bar (SHPB). And the effects of water saturation and strain rate on impact toughness of GC were studied. Based on Weibull statistical damage distribution theory, the dynamic constitutive model of GC after water saturation was constructed. The results show that the dynamic peak strain and specific energy absorption of GC have strain rate strengthening effect before or after water saturation...

Due to the intricate relationship between the small non-coding ribonucleic acid (miRNA) sequences, the classification of miRNA species, namely Human, Gorilla, Rat, and Mouse is challenging. Previous methods are not robust and accurate. In this study, we present AtheroPoint's GeneAI 3.0, a powerful, novel, and generalized method for extracting features from the fixed patterns of purines and pyrimidines in each miRNA sequence in ensemble paradigms in machine learning (EML) and convolutional neural network (CNN)-based deep learning (EDL) frameworks...