Fractal Signature Research Articles

On the scaling of river network biogeochemical function

AbstractRiver networks play a fundamental biogeochemical role in the Earth system by transporting and processing materials from terrestrial to ocean ecosystems. The cumulative biogeochemical function of a watershed of area can broadly be referred to as the total processing rate of material performed by its river network. An important recent research, conducted through network simulations, has revealed that the biogeochemical function of rivers can scale superlinearly with the area under certain scenarios. This finding has significant implications for the role of river networks in regional and global biogeochemical cycles. Here, we demonstrate how such scaling can be derived analytically by combining the power law distribution of drainage area, the universal fractal signature of river networks and the scaling of channel hydraulic geometry, utilising the theory of finite‐size scaling. The results enable the discrimination between linear and superlinear behaviours, as well as the calculation of the exact exponent based on parameters that define how the biogeochemical function and the river width change with river drainage area. Furthermore, we investigate the difference between the scaling of the biogeochemical function with the area of the watershed and with the area of a region drained by multiple river networks, emphasising the implications for upscaling efforts.

Fractal signatures of non-Kerr spacetimes in the shadow of light-ring bifurcations

Fractal signatures of non-Kerr spacetimes in the shadow of light-ring bifurcations

Subchondral bone in knee osteoarthritis: bystander or treatment target?

The subchondral bone is an important structural component of the knee joint relevant for osteoarthritis (OA) incidence and progression once disease is established. Experimental studies have demonstrated that subchondral bone changes are not simply the result of altered biomechanics, i.e., pathologic loading. In fact, subchondral bone alterations have an impact on joint homeostasis leading to articular cartilage loss already early in the disease process. This narrative review aims to summarize the available and emerging imaging techniques used to evaluate knee OA-related subchondral bone changes and their potential role in clinical trials of disease-modifying OA drugs (DMOADs). Radiographic fractal signature analysis has been used to quantify OA-associated changes in subchondral texture and integrity. Cross-sectional modalities such as cone-beam computed tomography (CT), contrast-enhanced cone beam CT, and micro-CT can also provide high-resolution imaging of the subchondral trabecular morphometry. Magnetic resonance imaging (MRI) has been the most commonly used advanced imaging modality to evaluate OA-related subchondral bone changes such as bone marrow lesions and altered trabecular bone texture. Dual-energy X-ray absorptiometry can provide insight into OA-related changes in periarticular subchondral bone mineral density. Positron emission tomography, using physiological biomarkers of subchondral bone regeneration, has provided additional insight into OA pathogenesis. Finally, artificial intelligence algorithms have been developed to automate some of the above subchondral bone measurements. This paper will particularly focus on semiquantitative methods for assessing bone marrow lesions and their utility in identifying subjects at risk of symptomatic and structural OA progression, and evaluating treatment responses in DMOAD clinical trials.

Is housing price distribution across cities, scale invariant? Fractal distribution of settlements' house prices as signature of self-organized complexity

Locations and sizes of settlements within regions often exhibit a self-organized central place pattern, where larger settlements are encircled by smaller ones, with the former more set apart. This hierarchical spatial pattern is displayed by the fractal signature of the power law typical of the rank-size distribution of settlements. Is a similar pattern also revealed in the housing prices across settlements? An empirical analysis on the almost 8000 Italian municipalities, whose residential population varies between 33 and ∼3 million, shows that, for 15 out of 20 regions, the upper tails rank-house price distribution of settlements is plausibly following a power law. This result discloses a universality in the function behaviour: a scale invariance. The average scaling parameters have been estimated via Maximum Likelihood Estimator and Kolmogorov–Smirnov statistics, and the goodness-of-fit assessed via bootstrapping. Ordinary Least Squares regressions have also been used for comparative purposes. In average, Maximum Likelihood Estimator found a scaling parameter of 4.4. Namely, doubling the rank of the settlement (in terms of housing price), its housing price decreases by 15 %: between the settlement with the highest average house prices (ranked 1), and the settlement with the second highest average house prices (ranked 2), there is a 15 % difference in the average house prices. Idem between the ranked 5 and 10, 10 and 20 … it does not matter; it is a universal behavioural pattern whose scale invariance suggests a self-organized complexity in the phenomena behind it.

Sea State Characterization Using Experimental Synthetic Aperture Radar Raw Data in Two-Dimensions and the Modified Fractal Signature Method

This paper presents a novel method for the characterization of the sea state using a set of raw experimental Synthetic Aperture Radar (SAR) data in two dimensions, i.e., in the “fast time” and “slow time” directions (as explained in the text) and the so-called “Modified Fractal Signature” (MFS) method. That is, experimental SAR radar signatures in the above two dimensions (i.e., “raw data” in the time domain) were provided to our research group by the Norwegian Institute of Defence (FFI Institute), Norway, which we processed and analyzed using the MFS method in a novel way, as presented in detail in this paper. The numerical results obtained here show an easy categorization of the sea surface as “calm sea” or “turbulent sea”, thus establishing a very promising technique for the characterization of sea state in real time, as described in detail in the text.

Fractal signature as a rotational modulation and stellar noise classifier based on the active kepler stars

In this study, we report on the analysis of 701 stars in a solar vicinity defined in three categories namely subsolar, solar, and supersolar with rotation periods between 1 and 70 days, based on rotational modulation signatures inferred from time series from the Kepler mission’s Public Archives. In our analysis, we performed an initial selection based on the rotation period and position in the period–H diagram, where H denotes the Hurst exponent extracted from fractal analysis. To refine our analysis, we applied a fractal approach known as the R/S method, taking into account the fluctuations of the features associated with photometric modulation at different time intervals and the fractality traces that are present in the time series of our sample. In this sense, we computed the so-called Hurst exponent for the referred stars and found that it can provide a strong discriminant of rotational modulation and background noise behavior, going beyond what can be achieved with solely the rotation period itself. Furthermore, our results emphasize that the rotation period of stars is scaled by the exponent H which increases following the increase in the rotation period. Finally, our approach suggests that the referred exponent may be a powerful rotational modulation and noise classifier.

Multi-class skin lesion classification using prism- and segmentation-based fractal signatures

Today, due to technological advances, specialists can count on a wide range of computer-aided diagnostic applications. However, there are still significant challenges to overcome. That is the case when it comes to automating the classification of skin lesions. Amorphous pigmentation, fuzzy edges, unbalanced databases, unrepresentative minority classes, images of different sizes, and resolutions. Reproducibility of the models are examples that we face to develop computer-assisted diagnostic models. In this work, we tackle the problem of amorphous pigmentation lesions and fuzzy edges by proposing two new fractal signatures, which we call a fractal signature based on statistical prisms (SSPF) and a statistical fractal signature (SSTF). The methodologies presented in this work for the multi-class classification of skin lesions were evaluated using the International Skin Imaging Collaboration (ISIC) database from 2019 containing 25,331 images divided into eight highly unbalanced classes. The database was randomly divided into 80%–20% for the training and test datasets images, respectively. In that manner, could be assured the reproducibility of the models. The performance metrics reported for both the training and testing part are accuracy, sensitivity, specificity, and precision. In our methodology, each study case was repeated 30 times to avoid bias, according to the central limit theorem, and the mean ±1 standard deviation was reported. The results showed that it is imperative to have balanced databases and that the marked imbalance affects minority classes. All works must report the training performance and the test datasets to ensure the reproducibility of the models. We obtained that SSTF (the signature that combines the statistical prism-based fractal signature SSPF and SSF) can increase the classifier’s performance instead of the use of each fractal signature by itself. The methodology proposed using the SSTF with the LDA classifier is robust and reproducible for the simultaneous classification of 4 classes; we achieved 87% accuracy, 63% sensitivity, 89% specificity, and 65% precision. In the case of the simultaneous 7-class classification, the results were 88% accuracy, 41% sensitivity, 92% specificity, and 46% precision.

Local Directional Fractal Signature Method for Surface Texture Analysis

Local Directional Fractal Signature Method for Surface Texture Analysis

Diversity-Robust Acoustic Feature Signatures Based on Multiscale Fractal Dimension for Similarity Search of Environmental Sounds

This paper proposes new acoustic feature signatures based on the multiscale fractal dimension (MFD), which are robust against the diversity of environmental sounds, for the content-based similarity search. The diversity of sound sources and acoustic compositions is a typical feature of environmental sounds. Several acoustic features have been proposed for environmental sounds. Among them is the widely-used Mel-Frequency Cepstral Coefficients (MFCCs), which describes frequency-domain features. However, in addition to these features in the frequency domain, environmental sounds have other important features in the time domain with various time scales. In our previous paper, we proposed enhanced multiscale fractal dimension signature (EMFD) for environmental sounds. This paper extends EMFD by using the kernel density estimation method, which results in better performance of the similarity search tasks. Furthermore, it newly proposes another acoustic feature signature based on MFD, namely very-long-range multiscale fractal dimension signature (MFD-VL). The MFD-VL signature describes several features of the time-varying envelope for long periods of time. The MFD-VL signature has stability and robustness against background noise and small fluctuations in the parameters of sound sources, which are produced in field recordings. We discuss the effectiveness of these signatures in the similarity sound search by comparing with acoustic features proposed in the DCASE 2018 challenges. Due to the unique descriptiveness of our proposed signatures, we confirmed the signatures are effective when they are used with other acoustic features.

Математические основы фрактально-скейлингового метода в статистической радиофизике и приложениях

The system of basic mathematical concepts and constructions underlying the modern global fractal-scaling method developed by the author is presented. An overview of the main results on the creation of new information technologies based on textures, fractals (multifractals), fractional operators, scaling effects and nonlinear dynamics methods obtained by the author and his students for more than 40 years (from 1979 to the present) at the V.A. Kotelnikov Institute of Radioengineering and Electronics of RAS. It is shown that, for the first time in the world, new dimensional and topological (and not energy!) Features or invariants were proposed and then effectively applied for problems in radio physics and radio electronics, which are combined under the generalized concept of "sample topology" ~ "fractal signature". The author discovered, proposed and substantiated a new type and new method of modern radar, namely, fractal-scaling or scale-invariant radar. It should be noted that fractal radars are, in fact, a necessary intermediate stage on the path of transition to cognitive radar and quantum radar.

Trabecular subchondral bone analysis of the distal radius at ultra-high field (7t) MRI: comparison with 3T MRI and radiography

Purpose: Bone fractal signature analysis (FSA) is a tool assessing structural changes that may relate to clinical outcomes and function. Bone structural changes play a role in onset and progression of several musculoskeletal diseases, and FSA has been applied to different anatomic body regions. However, its applicability in a routine clinical environment has not been extensively explored. Our aim was to evaluate and compare bone texture analysis of the distal radius in patients and controls using radiography, 3 Tesla (T) and 7T magnetic resonance imaging (MRI).

Numerical analysis of rough hydrodynamic bearings for various deterministic micro-asperity features

The hydrodynamic analysis of isotropic and anisotropic Gaussian surfaces has been studied well. However, the analysis reported earlier cannot simply apply to non-Gaussian and self-affine fractal rough surfaces, which demands a thorough investigation to study the effect of non-Gaussian nature of surfaces having different deterministic asperity features. This work demonstrates the effect of non-Gaussian and fractal nature of rough surfaces on hydrodynamic bearing characteristics. The modified Reynolds equation is used in this work with consideration of cavitation. The variation of asperity pressure, hydrodynamic load, and friction force with lambda ratio (the ratio of nominal film thickness to composite roughness) for various types of non-Gaussian and fractal rough surfaces is presented and discussed in detail. It is found that skewness, kurtosis, and fractal signature significantly affect the bearing load capacity and bearing friction force. No significant effect of types micro features is observed on asperity pressure. Asperity pressure is found to decrease with an increase in lambda ratio. More negative skewness results in a decrease in asperity pressure.

Bone Structure Analysis of the Radius Using Ultrahigh Field (7T) MRI: Relevance of Technical Parameters and Comparison with 3T MRI and Radiography.

Bone fractal signature analysis (FSA—also termed bone texture analysis) is a tool that assesses structural changes that may relate to clinical outcomes and functions. Our aim was to compare bone texture analysis of the distal radius in patients and volunteers using radiography and 3T and 7T magnetic resonance imaging (MRI)—a patient group (n = 25) and a volunteer group (n = 25) were included. Participants in the patient group had a history of chronic wrist pain with suspected or confirmed osteoarthritis and/or ligament instability. All participants had 3T and 7T MRI including T1-weighted turbo spin echo (TSE) sequences. The 7T MRI examination included an additional high-resolution (HR) T1 TSE sequence. Radiographs of the wrist were acquired for the patient group. When comparing patients and volunteers (unadjusted for gender and age), we found a statistically significant difference of horizontal and vertical fractal dimensions (FDs) using 7T T1 TSE-HR images in low-resolution mode (horizontal: p = 0.04, vertical: p = 0.01). When comparing radiography to the different MRI sequences, we found a statistically significant difference for low- and high-resolution horizontal FDs between radiography and 3T T1 TSE and 7T T1 TSE-HR. Vertical FDs were significantly different only between radiographs and 3T T1 TSE in the high-resolution mode; FSA measures obtained from 3T and 7T MRI are highly dependent on the sequence and reconstruction resolution used, and thus are not easily comparable between MRI systems and applied sequences.

Classification of Dermoscopy Skin Lesion Color-Images Using Fractal-Deep Learning Features

The detection of skin diseases is becoming one of the priority tasks worldwide due to the increasing amount of skin cancer. Computer-aided diagnosis is a helpful tool to help dermatologists in the detection of these kinds of illnesses. This work proposes a computer-aided diagnosis based on 1D fractal signatures of texture-based features combining with deep-learning features using transferred learning based in Densenet-201. This proposal works with three 1D fractal signatures built per color-image. The energy, variance, and entropy of the fractal signatures are used combined with 100 features extracted from Densenet-201 to construct the features vector. Because commonly, the classes in the dataset of skin lesion images are imbalanced, we use the technique of ensemble of classifiers: K-nearest neighbors and two types of support vector machines. The computer-aided diagnosis output was determined based on the linear plurality vote. In this work, we obtained an average accuracy of 97.35%, an average precision of 91.61%, an average sensitivity of 66.45%, and an average specificity of 97.85% in the eight classes’ classification in the International Skin Imaging Collaboration (ISIC) archive-2019.

Fractal signatures of the COVID-19 spread.

Recent quantitative approaches for studying several aspects of urban life and infrastructure have shown that scale properties allow the understanding of many features of urban infrastructure and of human activity in cities. In this paper, we show that COVID-19 virus contamination follows a similar pattern in different regions of the world. The superlinear power-law behavior for the number of contamination cases as a function of the city population, with exponent β of the order of 1.15 is always obtained. Due to the strong indication that scaling is a determinant feature of covid-19 spread, we propose an epidemiological model that embodies a fractal structure, allowing a more detailed description of the observed data about the virus spread in different countries and regions. The hypothesis that fractal structures can be formed in cities as well as in larger networks is tested, indicating that indeed self-similarity may be found in networks connecting several cities.

Building Systems for Object Recognition by Multichannel Sensing Systems Based on Neural Networks and Fractal Signatures

An approach to building a multichannel pattern-recognition system by sensing systems is proposed. A list of problems solved by the sensing systems in the construction of object-recognition systems is specified. The problem of image preprocessing is formulated in the form of an ill-posed problem. The value of the fractal dimension D (the fractal signature) of images of contours of objects is used to create an additional characteristic. The methods for solving the problems of building modern object-recognition systems are evaluated.

Fractal signature of coronaviruses related to severe acute respiratory syndrome

PurposeThe aim of this work was to investigate the genome of SARS-CoV, MERS-CoV, and SARS-CoV-2 by the paradigm of chaos theory and fractal geometry. Coronavirus is the agent that causes the severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS) and emergent infections such as the present pandemic of COVID-19. Understanding its genome pattern is important for developing new and faster ways of testing for identifying the genome of the virus and also for better understanding of its origin and evolution.MethodsFor that, it was calculated the alpha coefficient by detrended fluctuation analysis (DFA) for the sequences of these genomes converted to binary numbers in order to determine if it is a chaotic or a random series of data. Also, it applied the random walking for obtaining a fractal map of the whole genome and calculated the fractal dimension (FD) by box-counting of this map by two different software.ResultsWith this, it was found that the alpha coefficient of the first SARS viruses was > 0.5, indicating that the series is chaotic or fractal, and has a persistent long-range memory or self-similarity along its sequence. This is not the case for MERS virus, which showed to have a completely random sequence (α < 0.5). For the fractal dimension, SARS viruses presented a FD around 1.5, and for MERS the fractal dimension decreases (FD < 1.5).ConclusionThe images generated by random walking of the entire RNA genome are by itself a fractal signature of the virus, which may be applied for studying its origin and for faster diagnostic of COVID-19.

Comparison of radiography, 3T and 7T magnetic resonance imaging for analysis of distal radius trabecular bone in patients with established or suspected wrist osteoarthritis using fractal signature analysis

Purpose: The fractal dimension (FD) or signature of cancellous bone takes into account its composite nature, which is determined principally by trabecular number, spacing, and cross-connectivity. In the knee, fractal signature analysis (FSA) has been reported to predict structural outcomes such as radiographic osteoarthritis (OA) progression and total joint replacement. In patients with rheumatoid arthritis, lower FSA scores along the vertical trabeculae of the distal radius were reported to correlate with bone loss in those with increasing radiographic severity.

High-Reynolds-number fractal signature of nascent turbulence during transition

Transition from laminar to turbulent flow occurring over a smooth surface is a particularly important route to chaos in fluid dynamics. It often occurs via sporadic inception of spatially localized patches (spots) of turbulence that grow and merge downstream to become the fully turbulent boundary layer. A long-standing question has been whether these incipient spots already contain properties of high-Reynolds-number, developed turbulence. In this study, the question is posed for geometric scaling properties of the interface separating turbulence within the spots from the outer flow. For high-Reynolds-number turbulence, such interfaces are known to display fractal scaling laws with a dimension [Formula: see text], where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogorov scaling of velocity fluctuations. The data used in this study are from a direct numerical simulation, and the spot boundaries (interfaces) are determined by using an unsupervised machine-learning method that can identify such interfaces without setting arbitrary thresholds. Wide separation between small and large scales during transition is provided by the large range of spot volumes, enabling accurate measurements of the volume-area fractal scaling exponent. Measurements show a dimension of [Formula: see text] over almost 5 decades of spot volume, i.e., trends fully consistent with high-Reynolds-number turbulence. Additional observations pertaining to the dependence on height above the surface are also presented. Results provide evidence that turbulent spots exhibit high-Reynolds-number fractal-scaling properties already during early transitional and nonisotropic stages of the flow evolution.

Fractals in radar and radio physics: 40 years of research experience

A review of the main scientific results on creation of new information technologies on the basis of textures, fractals, fractional operators and non-linear dynamic methods which were obtained by the author has been presented in this work. The researchers are conducted in the framework of scientific direction &laquo;Fractal radio physics and fractal radio electronics: designing of fractal radio systems&raquo; which is being developed by the author starting from 1979 and up to the present. It is shown that new dimensional and topological (not energy!) signs or invariants that are combined under the generalized concept of &laquo;Sampling topology&raquo; ~ &laquo;Fractal signature&raquo; were proposed for the first time and then applied. Texture and fractal-scaling (topological) methods for detecting superweak signals and fields in intense noise and interferences are proposed. A new type and a new method of modern radiolocation, namely, fractal-scaling or scale-invariant radiolocation was proposed, discovered, and developed. This entails fundamental changes in the structure of theoretical radiolocation, as well as in its mathematical apparatus. The fractal radiolocation postulates were developed: (1) intelligent signal/image processing based on the theory of fractional measures and scaling effects for calculating the field of fractal dimensions D, (2) the sample of the received signal in noise belongs to the class of stable non-Gaussian probability distributions of the D signal, and (3) the topology maximum with the minimal energy of the input random signal (i.e., the maximal &laquo;escape&raquo; from the energy of the received signal). These postulates open new possibilities for ensuring stable operation at a small signal/(noise + interference) ratio or an increase in the radar range. These studies are priorities in the world and serve as a basis for the further development and substantiation of the practical application of fractal-scaling and texture methods in modern radiophysics, radio-electronic systems, and nanotechnology, as well as in the creation of fundamentally new and more accurate fractal-texture (topological) methods for detecting and measuring the parameters of radio signals in the space&ndash;time radar channel for electromagnetic wave propagation with scattering.