1,010 Results Found

Let $\mu$ be a self-similar measure with compact support K. The Hausdorff dimension of K is $\alpha$. The Cauchy transform of $\mu$ is denoted by $F\left(z\right)$. For $0<\beta <1,$ we define the function $F^{\left[\beta \right]},$ which compares with the fractional derivative...

This paper is devoted to the characterization of spectrum candidates with a new tree structure to be the spectra of a spectral self-similar measure ${\mu }_{N,D}$ generated by the finite integer digit set D and the compression ratio $N^{-1}$. The tree stru...

A long-standing conjecture of Lapidus asserts that under certain conditions a self-similar fractal set is not Minkowski measurable if and only if it is of lattice-type. For self-similar sets in $\mathbb{R}$, the Lapidus conjecture has been confirmed. However, i...

The Minkowski measurability of self-similar sets is closely linked to the lattice or non-lattice nature of the contraction ratios of the underlying iterated function system. A long-standing conjecture of Lapidus asserts that under certain conditions...

We conduct cluster analysis of a class of locally asymptotically self-similar stochastic processes with finite covariance structures, which includes Brownian motion, fractional Brownian motion, and multifractional Brownian motion as paradigmatic exam...

It is important for electronic commerce companies to understand the service quality of their systems, such as, the response time for users’ interactions, the service delay zone and the number of appropriate users accessing the systems concurrently. T...

In the paper the word-level n-grams based approach is proposed to find similarity between texts. The approach is a combination of two separate and independent techniques: self-organizing map (SOM) and text similarity measures. SOM’s uniqueness...

We propose a new measure (Γ) to quantify the degree of self-similarity of a shape using branch length similarity (BLS) entropy which is defined on a simple network consisting of a single node and its branches. To investigate the properties of t...

To solve the self-alignment problem of the Strapdown Inertial Navigation System (SINS), a novel adaptive filter based on Complementary Ensemble Empirical Mode Decomposition (CEEMD) is proposed. The Gravitational Apparent Motion (GAM) is used in the c...

The particle size distribution (PSD) of complex granular media is seen as a mathematical measure supported in the interval of grain sizes. A physical property characterizing granular products used in the Andreasen and Andersen model of 1930 is re-int...

Large-eddy simulation (LES) is performed to investigate self-similarity in a wind turbine wake flow. The turbine is represented using an actuator line model in a pseudo-spectral method-based solver. A new hybrid approach of smoothed pseudo-spectral m...

Complexity analysis of dynamic systems provides a better understanding of the internal behaviours that are associated with tension and efficiency, which in the socio-technical systems may lead to innovation. One of the popular approaches for the asse...

Self-nested trees present a systematic form of redundancy in their subtrees and thus achieve optimal compression rates by directed acrylic graph (DAG) compression. A method for quantifying the degree of self-similarity of plants through self-nested t...

This article contributes to clarifying the questions of whether and how fractal geometry, i.e., some of its main properties, are suitable to characterize architectural designs. This is done in reference to complexity-related aesthetic qualities in ar...

The present paper addresses the evolution of turbulence characteristics in wind turbine wakes immersed in a turbulent boundary layer. The study thereby focuses on finding physically consistent scaling laws for the wake width, the velocity deficit, an...

The intensity of tropical cyclones is highly dependent on air–sea enthalpy and momentum exchange. At extreme wind speeds, the values of the enthalpy, C_K, and momentum, C_D, exchange coefficients are characterized by high uncertainty. The present...

Water scarcity is a challenging global risk. Urban wastewater treatment technologies, which utilize processes based on single-stage ultrafiltration (UF) or nanofiltration (NF), have the potential to offer lean-and-green cost-effective solutions. Robu...

Effective shape representation of building footprints is essential for many geospatial analysis and applications, such as building retrieval, cartographic generalization, and urban morphology analysis. Constrained by scarce and coarse annotations of...

This is a brief survey of selected results obtained using the “transversality method” developed for studying parametrized families of fractal sets and measures. We mostly focus on the early development of the theory, restricting ourselves...

Lunar digital elevation models (DEMs) are a fundamental data source for lunar research and exploration. However, high-resolution DEM products for the Moon are only available in some local areas, which makes it difficult to meet the needs of scientifi...

Eye movement is one of the biological signals whose exploration may reveal substantial information, enabling greater understanding of the biology of the brain and its mechanisms. In this research, eye movement dynamics were studied in terms of chaoti...

Biomaterials are primarily insulators. For nearly a century, electromagnetic resonance and antenna–receiver properties have been measured and extensively theoretically modeled. The dielectric constituents of biomaterials—if arranged in di...

Self-similar growth and fractality are important properties found in many real-world networks, which could guide the modeling of network evolution and the anticipation of new links. However, in technology-convergence networks, such characteristics ha...

Autonomous underwater vehicles (AUVs) have obtained extensive application in the exploitation of marine resources. Terrain-aided navigation (TAN), as an accurate and reliable autonomous navigation method, is commonly used for AUV navigation. However,...

We study the spectrality of a class of self-affine measures with prime determinant. Spectral measures are connected with fractal geometry that shows some kind of geometrical self-similarity under magnification. To make the self-affine measure becomes...

Internet utilisation has steadily increased, predominantly due to the rapid recent development of information and communication networks and the widespread distribution of smartphones. As a result of this increase in Internet consumption, various typ...

In this paper, the fractal properties of stochastic processes and objects in different areas were specified and investigated. These included: measuring systems and sensors, navigation and motion controls, telecommunication systems and networks, and f...

Fractal dimension, a measure of self-similarity in a structure, is a powerful physical parameter for the characterization of structural property of many partially filled disordered materials. Biological tissues are fractal in nature and reports show...

Bacterial populations often form colonies and structures in biofilm. The paper aims to design suitable algorithms to simulate self-similar evolution in this context, specifically by employing a hybrid model that includes a cellular automaton for the...

In recent years, image denoising has seen a shift from traditional non-local self-similarity methods like BM3D to deep-learning based approaches that use learnable convolutions and attention mechanisms. While pixel-level attention is effective at cap...

During clathrin-mediated endocytosis in yeast cells, a small patch of flat membrane is deformed into a tubular shape. It is generally believed that the tubulation is powered by actin polymerization. However, studies based on quantitative measurement...

The interplanetary medium variability has been extensively studied by means of different approaches showing the existence of a wide variety of dynamical features, such as self-similarity, self-organization, turbulence and intermittency, and so on. Re...

The non-rigid multi-modal three-dimensional (3D) medical image registration is highly challenging due to the difficulty in the construction of similarity measure and the solution of non-rigid transformation parameters. A novel structural representati...

The interest in photoplethysmography (PPG) for sleep monitoring is increasing because PPG may allow assessing heart rate variability (HRV), which is particularly important in breathing disorders. Thus, we aimed to evaluate how PPG wearable systems me...

The knowledge of the air velocity distribution in the supply jets is essential when designing ventilation and air conditioning systems. In this study, we tested and analyzed the velocity distributions in the radial wall jets—these jets are comm...

The relatively high abundance of fractal properties of complex systems on Earth and in space is considered an argument in support of the general relativity of the geometric theory of gravity. The fractality may be called the fractal symmetry of physi...

The well-known power-law fractal element was determined to need several important revisions by the authors of this work. It is now possible to demonstrate that any scaling equation associated with a fractal element is actually K-fold degenerated and...

The study of fractals has a long history in mathematics and signal analysis, providing formal tools to describe self-similar structures and scale-invariant phenomena. In recent years, cognitive science has developed a set of powerful theoretical and...

“Odd” factor approximants of the special form suggested by Gluzman and Yukalov (J. Math. Chem. 2006, 39, 47) are amenable to optimization by power transformation and can be successfully applied to critical phenomena. The approach is based on the idea...

Over the Philippine Sea, the tropical cyclone (TC) Goni reaches category 5 on 29–31 October 2020. Multi-satellite observations, including CFOSAT SWIM/SCAT and Sentinel-1 SAR data, are jointly analyzed to assess the performances of a parametric...

In order to study the spread of an epidemic over a region as a function of time, we introduce an entropy ratio U describing the uniformity of infections over various states and their districts, and an entropy concentration coefficient $C=1-U.$ The latt...

In this paper, we propose an integrated action classification and regression learning framework for the fine-grained human action quality assessment of RGB videos. On the basis of 2D skeleton data obtained per frame of RGB video sequences, we present...

Wake analysis plays a significant role in wind-farm planning through the evaluation of losses and energy yield. Wind-tunnel tests for wake studies have high costs and are time-consuming. Therefore, computational fluid dynamics (CFD) emerges as an eff...

We investigate both theoretically and experimentally the properties of electromagnetic waves propagation and localization in periodic and quasi-periodic stub structures of Fibonacci type. Each block constituting the Fibonacci sequence (FS) is compose...

Axiomatically, symmetry is a fundamental property of mathematical functions defining similarity measures, where similarity measures are important tools in many areas of computer science, including machine learning and image processing. In this paper,...

The concept of dynamic symmetry in art and extensive measurements on Greek vases suggest that a vase and its parts can be inscribed into similar rectangles, with all rectangles having the same ratio of lengths of their side. Such an observation is of...

Motion blur degrades single-frame imaging when relative motion occurs during sensor exposure; yet, quantitative validation is difficult because ground-truth motion parameters are rarely available in real images. This paper presents an interpretable,...

The generator matrices of polar codes and Reed–Muller codes are submatrices of the Kronecker product of a lower-triangular binary square matrix. For polar codes, the submatrix is generated by selecting rows according to their Bhattacharyya parameter,...

Data availability should be guaranteed by a web service in order to satisfy customers. One of the main challenges of information security professionals is DDoS attack which affects the availability. By masquerading itself as a legitimate user, a DDoS...

This paper focuses on image compressive sensing (CS). As the intrinsic properties of natural images, nonlocal self-similarity and sparse representation have been widely used in various image processing tasks. Most existing image CS methods apply eith...