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Ferroelastic textures called star patterns are transformable into grilles whose rigid bars replace domain boundaries and are connected with hinges at their junctions. The grilles show several levels of self‐similarity. Exact formulae for the scaling factors as functions of the shape and number N of the arms are provided. The minimal dynamic model of such systems involves force constants at only one level (generation) of self‐similarity. The minimal set of force constants ensures stability of the stars with N = 2 and N = 3. At N = 4 the minimal model exhibits exactly one mode of zero frequency. The reaction of the four‐arm star to a tensile stress applied at the level of the force constants depends on the self‐similarity scaling factor and on the separation between the applied stress and the generation where the observation is made. In some regions of these parameters the reaction is analogous to auxetics but it also shows negative tensile characteristics, that is, a shrinking in the direction of the stress axis. With increasing distance from the external perturbation toward outer generations of self‐similarity the system shows a surprisingly fast restoration of the symmetry broken by the stress. [ABSTRACT FROM AUTHOR]

A painting, like human skin, develops cracks on the surface as it dries and ages. The painting cracks, also known as craquelure, are often considered analogous to human fingerprints; these have been regarded as a unique signature reflective of the painting’s characteristics and are important in art authentication. Intriguingly, studies in other fields, such as geology, have observed the presence of distinctive characteristics in soil desiccation cracks. These cracks exhibit self-similarity, forming patterns that suggest broader geological processes at work. In light of this connection, the primary objective of this study is to investigate whether the painting cracks also exhibit a self-similar nature. By delving into this, we seek to shed light on the underlying properties of the painting cracks. This study also aims to investigate whether the characteristic self-similar trait of the cracks can serve as an identifier in relation to the provenances of the paintings. To this end, this study adopts the methodology originally designed to characterize the phenotypic traits of 3D particle geometries in granular materials research. This study develops a 2D equivalent concept, focusing on the phenotypic traits of the individual islands enclosed by cracks within paintings. The results successfully demonstrate that the phenotypic trait of painting cracks exhibits a self-similar nature, which can reveal characteristics associated with the provenances of paintings. The findings will offer valuable insights into the scientific examination of artworks based on painting cracks. [ABSTRACT FROM AUTHOR]

Summary: In this work, an improved analytical model of fractal memelement in which the pinched point shifting has been considered and the original analytical model of fractal inverse memelement have been proposed. These fractal circuit elements are the memelement, and inverse memelement operates based on the principle of electromagnetic in fractal time/space, which must be applied whenever the current flows through fractal media. These models are important because these memory elements can be realized based on the porous material, which is a fractal media. In addition, they can employ self‐similarity, which is hard to be simulated by using the traditional models. This is because such self‐similarity can be well explained by the fractal set‐based model, yet those traditional models are based on the set of real values. Therefore, for deriving the proposed models, the fractal calculus, which is oriented to the fractal set, has been adopted as the mathematical basis. From the analytical and numerical analyses based on the derived models, it has been found that both memelement and inverse memelement can retain their unique frequency characteristics despite being operated based on the abovementioned principle. In addition, their input–output relationships are mathematically differentiable albeit the inputs and outputs themselves are not. [ABSTRACT FROM AUTHOR]

The stiffness matrix of a structural Sierpiński triangle under conditions of transversal bending is presented. The derivation is based exclusively on considerations of symmetry, equilibrium, and self-similarity. As a result, the stiffness matrix is shown to depend on a single material parameter. An illustrative numerical example is presented on the basis of an ad hoc computer code for the assembled stiffness of an overall structure consisting of a grid of fractal elements. [ABSTRACT FROM AUTHOR]

This article focuses on characterizing a class of quasi-periodic metamaterials created through the repeated arrangement of an elementary cell in a fixed direction. The elementary cell consists of two building blocks made of elastic materials and arranged according to the generalized Fibonacci sequence, giving rise to a quasi-periodic finite microstructure, also called Fibonacci generation. By exploiting the transfer matrix method, the frequency band structure of selected periodic approximants associated with the Fibonacci superlattice, i.e. the layered quasi-periodic metamaterial, is determined. The self-similarity of the frequency band structure is analysed by means of the invariants of the symplectic transfer matrix as well as the transmission coefficients of the finite clusters of Fibonacci generations. A high-frequency continualization scheme is then proposed to identify integral-type or gradient-type non-local continua. The frequency band structures obtained from the continualization scheme are compared with those derived from the Floquet–Bloch theory to validate the proposed scheme. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1).' [ABSTRACT FROM AUTHOR]

Past efforts to identify and characterize minimally monophyletic groups (microgenera) by deconstructing larger bryophyte genera successfully determined 10 microgenera comprising the moss family Streptotrichaceae. Thirty other microgenera have also been found in the moss family Pottiaceae. A microgenus consists of one ancestral species and, optimally, four immediate descendant species, each of which shares exactly the same ancestral traits. To determine if microgenera were common, evidence of these in larger genera was garnered from published estimates of species per genus in other groups and from molecular cladograms in the moss family Pottiaceae. Both classical mesogenera and cladistically enlarged macrogenera exhibited an internal granularity of one to five species, either as multiple species below the inflection point in the hollow curve of logarithmic graphs of species per genus or as small groups of molecular cladogram branches. Microgenera are basic units of evolution. The constancy of size and monothecy of traits in microgenera give them properties that larger taxonomic groups lack. Sequences of microgenera monophyletic are easily concatenated, adaptational changes may be directly determined, self-similarity across scale allows extended scientific inferences, and traits can be associated with survival across millions of years of environmental perturbation. [ABSTRACT FROM AUTHOR]

Image itself information is naturally robust to image reconstruction, yet most current super-resolution methods do not fully utilize global feature information. This study proposes a new image super-resolution model mixing multiple and multi-scale attentions, including two new modules: Multi-scale hybrid non-local attention upsampling module and residual dense attention block. Different from previous nonlocal methods, multi-scale hybrid non-local attention upsampling module mixes pixel-based and patch-based nonlocal attention and establishes patch-level upsampling mapping relationships at multiple scales, which enables a wider global search space. The residual dense attention block establishes attention associations in channel and spatial dimensions, which enhances the transfer and fusion of front-to-back attention information through dense connections. In this study, quantitative and qualitative evaluations are conducted on several benchmark datasets, and the experimental results show that the model outperforms similar super-resolution models in terms of performance and reconstruction quality. [ABSTRACT FROM AUTHOR]

This paper studies the existence of local and global self-similar solutions for a Boussinesq system with fractional memory and fractional diffusions u t + u · ∇ u + ∇ p + ν (− Δ) β u = θ f , x ∈ R n , t > 0 , θ t + u · ∇ θ + g α ∗ (− Δ) γ θ = 0 , x ∈ R n , t > 0 , div u = 0 , x ∈ R n , t > 0 , u (x , 0) = u 0 , θ (x , 0) = θ 0 , x ∈ R n , where g α (t) = t α − 1 Γ (α) . The existence results are obtained in the framework of pseudo-measure spaces. We find that the existence and self-similarity of global solutions is strongly influenced by the relationship among the memory and the fractional diffusions. Indeed, we obtain the existence and self-similarity of global solutions only when γ = (α + 1) β. Moreover, we prove a stability result for the global solutions and the existence of asymptotically self-similar solutions. [ABSTRACT FROM AUTHOR]

We embed an object with a singular horizon structure, reminiscent of (but fundamentally different from, except in a limiting case) a black hole event horizon, in an expanding, spherically symmetric, homogeneous, Universe that has a positive cosmological constant. Conformal representation is discussed. There is a temperature/pressure singularity and a corresponding scalar curvature singularity at the horizon. The expanding singular horizon ultimately bounds the entire spacetime manifold. It is is preceded by an expanding light front, which separates the spacetime affected by the singularity from that which is not yet affected. An appropriately located observer in front of the light front can have a Hubble–Lemaître constant that is consistent with that currently observed. [ABSTRACT FROM AUTHOR]

We embed an object with a singular horizon structure, reminiscent of (but fundamentally different from, except in a limiting case) a black hole event horizon, in an expanding, spherically symmetric, homogeneous, Universe that has a positive cosmological constant. Conformal representation is discussed. There is a temperature/pressure singularity and a corresponding scalar curvature singularity at the horizon. The expanding singular horizon ultimately bounds the entire spacetime manifold. It is is preceded by an expanding light front, which separates the spacetime affected by the singularity from that which is not yet affected. An appropriately located observer in front of the light front can have a Hubble–Lemaître constant that is consistent with that currently observed.

We consider the spherical piston problem in relativistic fluid dynamics. When the spherical piston expands at a constant speed, we show that the self-similar solution with a shock front exists under the relativistic principle that all velocities are bounded by the light speed. The equation of state is given by P= \sigma ^2 \rho, where \sigma, the sound speed, is a constant. It is an important model describing the evolution of stars. Also, we present the global existence of BV solutions for the relativistic Euler system given that the piston speed is perturbed around a constant in a finite time interval. The analysis is based on the modified Glimm scheme and the smallness assumption is required on the initial data. [ABSTRACT FROM AUTHOR]

Abstract In order to retain the characteristics and style of traditional settlements and respect their layout and structure, it is necessary to carry out original planning and expansion of traditional settlements. This model of planning and expansion aims to protect the unique character of the settlement, maintain its original historical and cultural value, and integrate with the surrounding environment. Early research on the space complexity of settlements was dominated by qualitative analysis, and the depth of quantitative research on the spatial form of traditional settlements was insufficient. This article takes Xiaoliangjiang Village in Jingxing County, Shijiazhuang City, Hebei Province, which entered the fifth batch of the list of Chinese traditional villages list, as the research object. The spatial relationship of the settlement was obtained through field surveys and drone oblique photography, and the spatial morphological elements of Xiaoliangjiang Village were analyzed and extracted. Based on three quantitative theories of spatial form, namely topology theory, fractal theory, and space syntax, the self-similarity of settlements is analyzed from the perspectives of buildings, streets, and spaces. The research uses Matlab and DepthMap software to quantitatively analyze the spatial form of Xiaoliangjiang Village and obtains data. Through the analysis of data, it was found that Xiaoliangjiang Village has self-similarity at three levels: buildings, roads and settlement spaces. The buildings iteratively generate various forms of architectural courtyards through the basic “L”-shaped pattern. The spatial structures at all levels of roads and settlement space in Xiaoliangjiang Village are relatively similar, in line with the bottom-up traditional settlement evolutionary law. By studying settlement self-similarity, people can better understand the formation mechanism of traditional settlement space structure and its evolution law. At the same time, it enriches the research perspective of traditional settlements and provides technical support for analyzing the self-similarity of traditional settlements and settlement protection planning.

We prove that the lattice of ideals of an arbitrary L-algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. the set of prime ideals) of L-algebras and characterize prime ideals in topological terms. [ABSTRACT FROM AUTHOR]

Super-resolution is an ill-posed inverse problem. It needs a self-similarity regularization term in its formulation to solve the issue. Researchers have studied self-similarity in natural images thoroughly and extended the results to medical data. This paper investigates the self-similarity property using a general affine model and the SSIM, PSNR, matrix rank, and mutual information measures. We study variations of self-similarity with image modality, inter/intra-resolution, tissue types, and acquisition phase. Based on our experiments, super-resolution algorithms that use self-similarity property achieve better results in CT images than MR data. Some organs, including the liver, have a stronger self-similarity compared to the brain and lung. The extension of our study prepares a comprehensive guide map to employ self-similarity properties in medical image processing algorithms. [ABSTRACT FROM AUTHOR]

Industrial internet traffic prediction is not only an academic problem, but also a concern of industry and network performance department. Efficient prediction of industrial internet traffic is helpful for protocol design, traffic scheduling, detection of network attacks, etc. This paper proposes an industrial internet traffic prediction method based on the Echo State Network. In the first place this paper proves that the industrial internet traffic data are self-similar by means of the calculation of Hurst exponent of each traffic time series. It indicates that industrial internet traffic can be predicted utilizing nonlinear time series models. Then Echo State Network is applied for industrial internet traffic forecasting. Furthermore, to avoid the weak-conditioned problem, grid search algorithm is used to optimize the reservoir parameters and coefficients. The dataset this paper perform experiments on are large-scale industrial internet traffic data at different time scale. They come from Industrial Internet in three regions and are provided by ZTE Corporation. The result shows that our approach can predict industrial internet traffic efficiently, which is also a verification of the self-similarity analysis. [ABSTRACT FROM AUTHOR]

We explicitly calculate the Hausdorff dimension of the graph and range of an isotropic stable Lévy process X plus deterministic drift function f. For that purpose we use a restricted version of the genuine Hausdorff dimension, which is called the parabolic Hausdorff dimension. It turns out that covers by parabolic cylinders are optimal for treating self-similar processes, since their distinct non-linear scaling between time and space geometrically matches the self-similarity of the processes. We provide explicit formulas for the Hausdorff dimension of the graph and the range of X + f. In sum, the parabolic Hausdorff dimension of the drift term f alone contributes to the Hausdorff dimension of X + f. Furthermore, we derive some formulas and bounds for the parabolic Hausdorff dimension. [ABSTRACT FROM AUTHOR]

In recent years, patch-based image restoration approaches have demonstrated superior performance compared to conventional variational methods. This paper delves into the mathematical foundations underlying patch-based image restoration methods, with a specific focus on establishing restoration guarantees for patch-based image inpainting, leveraging the assumption of self-similarity among patches. To accomplish this, we present a reformulation of the image inpainting problem as structured low-rank matrix completion, accomplished by grouping image patches with potential overlaps. By making certain incoherence assumptions, we establish a restoration guarantee, given that the number of samples exceeds the order of r log²(N ), where N×N denotes the size of the image and r > 0 represents the sum of ranks for each group of image patches. Through our rigorous mathematical analysis, we provide valuable insights into the theoretical foundations of patch-based image restoration methods, shedding light on their efficacy and offering guidelines for practical implementation. [ABSTRACT FROM AUTHOR]

The scale and shape of objects in remote sensing images varies greatly, and thus the object detection of remote sensing image has always been a relatively challenging task. Focusing on the problem of multi-scale and extreme aspect ratio object detection, this paper proposes the extreme object detection net (EODNet). Firstly, we design a fractal-based feature fusion network (FFFN) by stacking different multilayer elementary convolutional blocks based on the self-similarity feature of fractals, so that the fused feature maps can fully retain the original features to facilitate the extraction of objects of different sizes. The parallel and serial asymmetric convolution block is fitted objects by forming receptive fields that approximate the shape of the object for feature maps used to detect large-sized objects. Following this, the width-height sensitive loss function is designed, which adapts to multi-scale objects and is sensitive to shape. Finally, the Extreme-soft- non maximum suppression (NMS) realizes the removal of extreme overlapping boxes and avoids the accidental deletion of dense object prediction boxes. The proposed method is tested on the NWPU VHR-10 and RSOD datasets, and the results are compared with mainstream object detection algorithms, verifying the effectiveness of the proposed method, as the mAP on the two datasets is 96.1% and 95.4%, respectively. [ABSTRACT FROM AUTHOR]

Particle breakage at coral sands–structure interface is common in marine geological environments and is critical to the stability of geotechnical structures. However, due to the knowledge gap regarding the relationship between structure roughness and coral sand particle breakage, previous studies have not provided a clear understanding of this phenomenon. To address this gap, we conducted ring shear tests to investigate the evolution of the fractal dimension of particle breakage and its dependence on structure surface roughness and vertical stress based on fractal theory. The results show that both the roughness of the steel plate simulating the structure surface in the ring shear test and the particle size of coral sand have significant impacts on the evolutions of particle breakage and morphology at the contact interface. In detail, the particle size distributions (PSDs) of coral sands after shearing have obvious self-similarity and converge to the limit distribution state, especially when the sands contain more large particles. When the steel plate is smooth, the fractal dimension of the broken coral sand is relatively low, which indicates an early stage of fractal dimension development. Moreover, the relationship between the fractal dimension and vertical stress exerted on a rough steel plate can be approximately described using a second-order polynomial function. Moreover, there exists a critical vertical stress that corresponds to the maximum fractal dimension for each kind of coral sand in our tests. The particle breakage rates of coral sand samples on smooth steel plates are substantially lower than those on rough steel plates. [ABSTRACT FROM AUTHOR]

The segmentation analysis of the Golding–Cox mRNA dataset clarifies the description of these trajectories as a Fractional Lévy Stable Motion (FLSM). The FLSM method has several important advantages. Using only a few parameters, it allows for the detection of jumps in segmented trajectories with non-Gaussian confined parts. The value of each parameter indicates the contribution of confined segments. Non-Gaussian features in mRNA trajectories are attributed to trajectory segmentation. Each segment can be in one of the following diffusion modes: free diffusion, confined motion, and immobility. When free diffusion segments alternate with confined or immobile segments, the mean square displacement of the segmented trajectory resembles subdiffusion. Confined segments have both Gaussian (normal) and non-Gaussian statistics. If random trajectories are estimated as FLSM, they can exhibit either subdiffusion or Lévy diffusion. This approach can be useful for analyzing empirical data with non-Gaussian behavior, and statistical classification of diffusion trajectories helps reveal anomalous dynamics. [ABSTRACT FROM AUTHOR]

We present here more general concepts of Hausdorff derivatives (structural Nabla derivatives) on a timescale. We examine structural Nabla integration on temporal scales. Using the fixed-point theorem, we establish adequate criteria for the question of existence and uniqueness of the solution to an initial value problem characterized by structural Nabla derivatives on timescales. Furthermore, some features of the new operator are proven and illustrated by using concrete examples. [ABSTRACT FROM AUTHOR]

Numerical simulation is applied to investigate the outflow of an incompressible three-dimensional turbulent swirled wall jet. The purpose of the study is to determine the jet flow structure and to compare the characteristics of swirled and nonswirled jets. The numerical solution of the equations of motion is obtained using large eddy simulation with wall resolution (WRLES). The results of the modeling are compared with the data of a unique published study devoted to experimental investigation of swirled wall jets. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the type of monadic bounded L-algebras as L-algebras equipped with two monadic operators, named universal quantifier "∀" and existential quantifier "∃", respectively. First, we investigate the properties of pre-ideals on L-algebras and the pre-ideal generated by a nonempty subset of an L-algebra is defined. Second, we investigate monadic bounded L-algebras and monadic pre-ideals in monadic bounded L-algebras. Moreover, the relation between monadic bounded L-algebras and monadic quantum B-algebras is discussed. Finally, the relations among monadic self-similar L-algebras and other monadic structures are discussed, such as monadic (left) hoops, monadic Wajsberg hoops and monadic MV-algebras. Moreover, we obtain a characterization of monadic bounded L-algebras and monadic bounded self-similar L-algebras by relatively complete subalgebras and m-relatively complete subalgebras, respectively. These results are important to the further study of logical system with monadic operators. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Shanghai Jiaotong University (Science) is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Spectral response functions are central quantities in the analysis of quantum many-body states, since they describe the response of many-body systems to external perturbations and hence directly correspond to observables in experiments. In this paper, we evaluate a momentum-averaged dynamical density structure factor for the fermionic ν = 1 / 3 fractional quantum Hall (FQH) state on a torus, using the continued fraction method to compute the dynamical correlation function. We establish the scaling behaviour of the screened Coulomb structure factor with respect to interaction range, and expose an inherent self-similarity of structure factors in the frequency domain. These results highlight the statistical properties of spectral response functions for FQH states and show how they can be efficiently approximated in numerical models.

A problem has been solved on electrovortex flow between two cylinders in a self-similar formulation within the framework of Stokes approximation implying a rather low velocity of the flow and its fast entry into a stationary mode, which makes it possible to significantly simplify the solution of the Navier–Stokes equation and to establish the relation between different flow parameters. Results of an analytical solution of the problem supported by numerical assessments are presented. [ABSTRACT FROM AUTHOR]

Hox gene clusters are crucial in embryogenesis. It was observed that some Hox genes are located in order along the telomeric to centromeric direction of the DNA sequence: Hox1, Hox2, Hox3.... These genes are expressed in the same order in the ontogenetic units of the Drosophila embryo along the anterior–posterior axis. The two entities (genome and embryo) differ significantly in linear size and in-between distance. This strange phenomenon was named spatial collinearity (SP). Later, it was observed that, particularly in the vertebrates, a temporal collinearity (TC) coexists: first Hox1 is expressed, later Hox2, and later on Hox3.... According to a biophysical model (BM), pulling forces act at the anterior end of the cluster while a cluster fastening applies at the posterior end. Hox clusters are irreversibly elongated along the force direction. During evolution, the elongated Hox clusters are broken at variable lengths, thus split clusters may be created. An empirical rule was formulated, distinguishing development due to a complete Hox cluster from development due to split Hox clusters. BM can explain this empirical rule. In a spontaneous mutation, where the cluster fastening is dismantled, a weak pulling force automatically shifts the cluster inside the Hox activation domain. This cluster translocation can probably explain the absence of temporal collinearity in Drosophila. [ABSTRACT FROM AUTHOR]

A steady three-dimensional laminar wall jet of a viscous incompressible fluid flowing out into a space submerged with the same fluid was studied numerically and experimentally in I. I. But, A. M. Gailfullin, and V. V. Zhvick, Fluid Dyn. 56, 812–823 (2021) and K. F. Adane and M. F. Tachie, ASME J. Fluids Eng. 132 (10), 1 (2010). It was found that the flow reaches a self-similar state at large values of the longitudinal coordinate with the self-similarity exponent value close to . The goal of this article is to solve this problem exploiting the fact that its dimensionality can be reduced by one. The problem is solved by means of a physically-informed neural network (PINN) implemented via PyTorch framework. [ABSTRACT FROM AUTHOR]

Understanding the long-range dependence and self-similarity of global sea surface chlorophyll concentration (SSCC) will enrich its characteristics description and analysis with global change patterns. The satellite SSCC products were collected from the European Space Agency during the period from 29 July 1998 to 31 December2020. After resampling the SSCC products into the spatial resolution of 1°, the missing values were interpolated by Bayesian maximum entropy with mean absolute error of cross validation equaling to 0.1295 mg/m[sup 3]. Generalized Cauchy model was employed to quantitatively determine the long-range dependence and self-similarity of SSCC at a global scale by using the Hurst parameter and fractal dimension. Good fitted results were achieved with an averaged R[sup 2] of 0.9141 and a standard deviation of 0.0518 across the 32,281 spatial locations of the entire ocean; the averaged values of Hurst parameter and fractal dimension were 0.8667 and 1.2506, respectively, suggesting strong long-range dependence and weak self-similarity of SSCC in the entire oceans. Univariate and multivariate generalized addictive models (GAM) were introduced to depict the influence of sea surface height anomaly, sea surface salinity, sea surface temperature and sea surface wind on the Hurst parameter and fractal dimension of SSCC; and smaller mean absolute error were achieved for the GAM of Hurst parameter than that of fractal dimension. Sea surface height anomaly showed the strongest influence for the Hurst parameter than the other three factors, and sea surface wind depicted similar influence; the sea surface temperature owned opposite influence on Hurst parameter compared to sea surface salinity. [ABSTRACT FROM AUTHOR]

GPE-algebras were introduced by Dvurečenskij and Vetterlein as unbounded pseudo-effect algebras. Recently, they have been characterized as partial L-algebras with local duality. In the present paper, GPE-algebras with an everywhere defined L-algebra operation are investigated. For example, linearly ordered GPE-algebra are of that type. They are characterized by their self-similar closures which are represented as negative cones of totally ordered groups. More generally, GPE-algebras with an everywhere defined multiplication are identified as negative cones of directed groups. If their partial L-algebra structure is globally defined, the enveloping group is lattice-ordered. For any self-similar L-algebra A, exponent maps are introduced, generalizing conjugation in the structure group. It is proved that the exponent maps are L-algebra automorphisms of A if and only if A is a GPE-algebra. As an application, a new characterization of cone algebras is obtained. Lattice GPE-algebras are shown to be equivalent to ∧-closed L-algebras with local duality. [ABSTRACT FROM AUTHOR]

Copyright of Environmental & Social Management Journal / Revista de Gestão Social e Ambiental is the property of Environmental & Social Management Journal and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Canopy structural complexity is a key emergent property of forest ecosystems that directly relates to their ability to store carbon, cycle water and nutrients, and provide habitat for biodiversity. However, we lack a general framework for quantifying the structural complexity of forest canopies, and it remains to be seen if there are simple rules that explain the huge variation in canopy structure that we observe across the world's forests.A leading candidate for characterizing differences in structural complexity among forest ecosystems are fractal scaling laws, or measures of statistical self‐similarity. If forest canopies were fractal in nature, their structural attributes could be distilled into a single coefficient—their fractal dimension—which could then be used to directly compare structural differences within and across biomes.To test this idea, we used airborne laser scanning (ALS) data acquired across nine landscapes in Australia that span a huge environmental gradient and include everything from dry shrublands, tropical savannas, dense rainforests, to 90 m tall Mountain Ash forests. Using the ALS data, we built high‐resolution 3D canopy height models of each landscape so that we could quantify how closely they followed fractal scaling laws, based on a comprehensive set of fractal dimension estimators.Across all ecosystem types, fractal scaling assumptions were consistently violated, with clear and systematic differences between real‐world forest canopies and simulated fractal surfaces. However, deviations from fractality did vary predictably among sites, with forests in less arid environments, dominated by tall trees with large crowns, exhibiting a higher degree of self‐similarity across scales.Synthesis: Our study conclusively shows that canopy surfaces are not fractal beyond the scale of individual tree crowns. Nevertheless, we still observed ecologically meaningful and generalisable patterns in forest structure across scales, which closely reflect biophysical and physiological constraints on tree size and architecture. These patterns point the way towards a more general framework for characterizing ecological complexity. [ABSTRACT FROM AUTHOR]

Decreased long‐range temporal correlations (LRTC) in brain signals can be used to measure cognitive effort during task execution. Here, we examined how learning a motor sequence affects long‐range temporal memory within resting‐state functional magnetic resonance imaging signal. Using the Hurst exponent (HE), we estimated voxel‐wise LRTC and assessed changes over 5 consecutive days of training, followed by a retention scan 12 days later. The experimental group learned a complex visuomotor sequence while a complementary control group performed tightly matched movements. An interaction analysis revealed that HE decreases were specific to the complex sequence and occurred in well‐known motor sequence learning associated regions including left supplementary motor area, left premotor cortex, left M1, left pars opercularis, bilateral thalamus, and right striatum. Five regions exhibited moderate to strong negative correlations with overall behavioral performance improvements. Following learning, HE values returned to pretraining levels in some regions, whereas in others, they remained decreased even 2 weeks after training. Our study presents new evidence of HE's possible relevance for functional plasticity during the resting‐state and suggests that a cortical subset of sequence‐specific regions may continue to represent a functional signature of learning reflected in decreased long‐range temporal dependence after a period of inactivity. [ABSTRACT FROM AUTHOR]

Multi-scale coherent structures have been observed in ocean currents, which are induced by the interaction of shear flows with different velocities. Understanding the spatial configuration and scale characteristics of coherent structures will promote the explanation of physical ocean phenomena. Considering the self-similarity, we propose a spatial correlation identification model for coherent structure extraction and three-dimensional visualization based on the wavelet transform and time-dependent intrinsic correlation method. The spatial and scale distributions of coherent structures are related to the dissipation rate variation. Most large-scale coherent structures, with the largest length scale of 13 m, are found to exist in stable fluid, such as the water column below 50 m. However, small-scale structures are found in chaotic fluids, such as the upper layer. Furthermore, we found that coherent structures of different scales coexist simultaneously in the same depth range, indicating a simultaneous multi-scale structure pattern for turbulent flow investigations. [ABSTRACT FROM AUTHOR]

Supervisory Control and Data Acquisition (SCADA) systems are crucial for modern industrial processes and securing them against increasing cyber threats is a significant challenge. This study presents an advanced method for bolstering SCADA security by employing a modified hybrid deep learning model. A key innovation in this work is integrating the Self-similarity Hurst parameter into the dataset alongside a CNN-LSTM model, significantly boosting the Intrusion Detection System’s (IDS) capabilities. The Hurst parameter, which quantifies the self-similarity in a dataset, is instrumental in detecting anomalies. Our in-depth analysis of the CICIDS2017 dataset sheds light on contemporary attack patterns and network traffic behaviors. The CNN-LSTM architecture was substantially altered by adding multiple convolutional layers with progressively increasing filters, batch normalization for stable training, and dropout layers for regularization. Principal Component Analysis (PCA) was applied for dimensionality reduction, thereby optimizing the dataset. Test results demonstrate the superior performance of the model incorporating the Hurst parameter, achieving 95.21% accuracy and 82.59% recall, significantly surpassing the standard model. The inclusion of the Hurst parameter marks a substantial advancement in identifying emerging threats, while architectural improvements to the CNN-LSTM model led to more robust and accurate intrusion detection in industrial control settings.

The edge-Wiener index, an invariant index representing the summation of the distances between every pair of edges in the graph, has monumental influence on the study of chemistry and materials science. In this paper, drawing inspiration from Gromov's idea, we use the finite pattern method proposed by Wang et al. [Average geodesic distance of Sierpinski gasket and Sierpinski networks, Fractals 25(5) (2017) 1750044] to figure out the exact formula of edge-Wiener index of the Sierpinski fractal networks. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical approach for studying the changes in pressure and temperature variables in flames. This conception extends beyond the traditional second-order Laplacian diffusion model by considering the p-Laplacian operator and a bi-stable reaction term, thereby providing a more generalized framework for flame diffusion analysis. Given the structure of our equations, we provide the boundedness and uniqueness of the solutions in a weak sense from both analytical and numerical approaches. We further reformulate the governing equations in the context of traveling wave solutions, applying singular geometric perturbation theory to derive the analytical expressions of these profiles. This theoretical development is complemented by numerical assessments, which not only validate our theoretical predictions, but also optimize the traveling wave speed to minimize the error between numerical and analytical solutions. Additionally, we explore self-similar structured solutions. The paper then concludes with a perspective on future research, with emphasis being placed on the need for experimental validation in laboratory settings. Such empirical studies could test the robustness of our model and allow for refinement based on actual measurements, thereby broadening the applicability and accuracy of our findings in practical scenarios. [ABSTRACT FROM AUTHOR]

We propose some crystalline materials showing a strong correspondence with a construction by Ball and Murat for elastostatic problems. Such a construction, translated into a space-time setting, is producing a plenty of turbulence self similar solutions. [ABSTRACT FROM AUTHOR]