Fractal Analysis Research Articles

The influence of an experimental physical training program on 100 m running speed indicators of educators of table tennis groups of a higher education institution. Dynamics and forecasting.

The problem of improving the process of physical education of students has been the subject of specialists' attention for many years. Analysis of literary sources shows that the level of physical fitness, mental and moral strength of the main mass of applicant’s education remains quite low. This requires finding new ways to improve physical, mental and moral condition of student youth. Purpose: experimental check the effect of specially designed classes included in the physical education program training of students of sports oriented groups in table tennis of the institution of higher education on the indicator of running speed for 100 m. Material: used in the experiment participation of 106 first-year students of different genders (53 – control group and 53 – experimental). The R/S method was proposed for processing experimental data. Informed consent to participate in this experiment was obtained from all participants. Results: at the end of the experiment (May), the results of the students of the experimental group qualitatively differed from the results of the students of the control group groups The results of the pedagogical experiment indicate the need for inclusion of the proposed classes in the educational program for physical education of students of groups with a sports orientation, in particular (sectional classes) table tennis. The experimental program included classes with running at the maximum pace at short distances from 15 to 30 m, at a distance of 60 and 100 m, running at maximum pace cross step in different directions. Relays with running were also used, moving in different ways, mobile games and sports team games. Organization education seekers was carried out by the frontal method and the method of circular training. When using circular training, accelerations for 100 m were used speed up to 65-70% of the maximum, which alternated with running for a distance of 50 m at a slow pace The training program also included classes with cross-country elements training and elements of basic aerobics, step aerobics, dance aerobics, which accounted for up to 25% of the time. The pedagogical experiment was conducted during the academic year with from October 2020 to June 2021. Conclusions: this experiment proved that that the inclusion of specially developed table tennis sections in the curriculum classes, made it possible to improve the indicators of education seekers in running a distance of 100 m. The method of exponential smoothing made it possible to predict the results on future. One of the advantages of the calculation method proposed in the article is that that fractal analysis allows to reveal stochastic (random) time series. In such, there is no long-term statistical dependence in the time series.

A New R35 and Fractal Joint Rock Typing Method Using MICP Analysis: A Case Study in Middle East Iraq

Reservoir characterization in carbonate formations plays a crucial role in understanding the complex pore structures and permeability properties. While absolute pore-throat radius (APTR) and R35 have been widely accepted in pore-scale rock typing, they fall short of providing detailed pore-throat distribution (PTD) information. To address this limitation and enhance PTD indication during rock classification, we introduce a novel approach—the R35 and fractal joint rock typing method—incorporating a new parameter, Dn (fractal dimension). This method is developed based on the analysis of mercury injection capillary pressure (MICP) data obtained from 20 carbonate samples in the Middle East, specifically Iraq. We delve into the discussion of APTR and R35 methods, employing both PTD and thin-section images to gain comprehensive insights into rock typing. Our approach incorporates a whole curve fractal-based model to determine the fractal dimension, Dn. The analysis reveals that Dn in each R35 rock type exhibits a decreasing trend with higher Hg intrusion peaks and wider pore-throat radius, providing valuable information on the distribution of pores within the rock samples. Furthermore, we extend our analysis to include the surface fractal dimension, Ds, obtained through two-dimensional (2D) fractal analysis on typical pores in binary thin-section images. The consistent decreasing trend of Dn aligns with the findings from Ds analysis, underscoring the effectiveness of parameter Dn in capturing the intricate pore structures within carbonate formations. Our results suggest that parameter Dn has the potential to serve as a standalone criterion in rock typing, eliminating the need for pretyping by R35 or APTR. The versatility of Dn as an indicator of pore distribution and complexity underscores its significance in advancing our understanding of carbonate reservoirs. As a recommendation, further exploration through additional fractal-based analyses is encouraged to solidify the role of parameter Dn in becoming a pivotal factor in the evolving field of rock typing.

Multifractal analysis of the perimeters of glaciers in the Svalbard Archipelago

The investigation of the evolution of glaciers largely relies on the characterisation of extensive quantities like their mass, area, and perimeter. In this work we use fractal and multifractal analysis to investigate the non-extensive structural properties of the perimeters of glaciers in the Svalbard Archipelago. We show that the perimeters of the glaciers exhibit a fractal structure with a fractal dimension Df≃1.25 , independently from the area of the glaciers. The investigation of the multifractal properties of the perimeters shows that small glaciers exhibit a more pronounced multifractal structure, as witnessed by the larger range of generalized dimensions Dq needed to characterise them. The range ΔD q of generalised dimensions required to characterise the multifractal perimeter of a glacier exhibits a power-law dependence with exponent −1.2 from the area, and represents a non-extensive parameter able to grab effectively the dependence of the multifractal structure of the perimeters on the size of glaciers. The comparison with similar results obtained in a previous study performed on glaciers in the Lombardy region of the Italian Alps confirms the robustness of the analysis performed, which does not appear to be affected by the morphology of the substrate or by climate conditions.

Fractal analysis of dimensionless permeability and Kozeny–Carman constant of spherical granular porous media with randomly distributed tree-like branching networks

The seepage of porous media has garnered significant interest due to its ubiquitous presence in nature, but most of the research is based on the model of a single dendritic branching network. In this study, we derive a fractal model of the dimensionless permeability and the Kozeny–Carman (KC) constant of porous media consisting of spherical particles and randomly distributed tree-like branching networks based on fractal theory. In addition, three different types of corrugated pipes are considered. Then, the relationships between the KC constant, dimensionless permeability, and other structural parameters were discussed in detail. It is worth noting that the KC constant of the porous media composed of three types of pipes decreases sharply first and then increases with the increase in the internal diameter ratio, while the dimensionless permeability has the opposite trend and conforms to the physical law. In addition, empirical constants are not included in the analytical formulas of the present model, and the physical mechanism of fluid flow in spherical granular porous media with randomly distributed tree-like branching networks is clearly revealed.

Fractal Analysis of Time Domain Dielectric Response to Reduce Complexity of Insulation Condition Diagnosis Methodology

Fractal Analysis of Time Domain Dielectric Response to Reduce Complexity of Insulation Condition Diagnosis Methodology

Microscopic Characterization and Fractal Analysis of Pore Systems for Unconventional Reservoirs

The complex pore structure of unconventional oil and gas reservoirs is one of the reasons for the difficulties in resource evaluation and development. Therefore, it is crucial to comprehensively characterize the pore structure, understand reservoir heterogeneity from multiple perspectives, and gain an in-depth understanding of fluid migration and accumulation mechanisms. This review outlines the methods and basic principles for characterizing microporous systems in unconventional reservoirs, summarizes the fractal analysis corresponding to the different methods, sorts out the relationship between the fractals and reservoir macroscopic physical properties (porosity, permeability, etc.) with the reservoir microscopic pore structures (pore structure parameters, pore connectivity, etc.). The research focuses on cutting-edge applications of characterization techniques, such as improved characterization accuracy, calibration of PSD ranges, and identification of different hydrogen compositions in pore systems for dynamic assessment of unconventional reservoirs. Fractal dimension analysis can effectively identify the quality level of the reservoir; complex pore-throat structures reduce permeability and destroy free fluid storage space, and the saturation of removable fluids is negatively correlated with Df. As for the mineral composition, the fractal dimension is positively correlated with quartz, negatively correlated with feldspar, and weakly correlated with clay mineral content. In future qualitative characterization studies, the application and combination of contrast agents, molecular dynamics simulations, artificial intelligence techniques, and 4D imaging techniques can effectively improve the spatial resolution of the images and explore the adsorption/desorption of gases within the pores, and also help to reduce the computational cost of these processes; these could also attempt to link reservoir characterization to research on supercritical carbon dioxide-enhanced integrated shale gas recovery, carbon geological sequestration, and advanced underground hydrogen storage.

Static and impact performance of engineered cementitious composites with hybrid graphite nano platelets modified PVA and shape memory alloy fibres

Polyvinyl alcohol (PVA) fibre has been widely adopted to produce engineered cementitious composites (ECC), the overall performance of which is highly dependent on the fibre surface characteristics. The traditional approach to improve PVA fibre bridging ability is to tailor the surrounding matrix properties. However, this common practice need to do a lot of laborious experimental works, and thus it has limited efficiency and practicality. Therefore, special surface treatments on PVA fibres are required to create synergistic interactions between fibre and surrounding matrix to retain excellent tensile ductility and better mechanical performance. This paper proposes a novel treatment method for PVA fibres using nano graphite platelets to modify the PVA fibre surface and improve the mechanical properties of PVA fibre reinforced ECC. To evaluate the effectiveness of such treatment, a systematic experimental study was performed. Firstly, static contact angle measurements, scanning electron microscopy and atomic force microscopy were employed to monitor the wettability and physical changes on the fibre surface. Then, the static and dynamic mechanical properties as well as microstructural characteristics of ECC with hybrid modified PVA fibres (2 vol%) and shape memory alloy (SMA) fibres (0.25 vol%, 0.50 vol% and 1 vol%) were examined. The results indicate that the graphite nanoplatelets treated PVA fibres (GPVA) exhibit high hydrophobicity and surface roughness providing steady-state crack propagation, which is a necessary condition to ensure multiple cracking and improving the higher fibre bridging complementary energy. This is evidenced by significantly densified the transition zone between the graphite treated PVA fibres and the matrix, and improved the flexural tensile strength and the toughness. The calculated surface roughness of 28.86 μm and lots of peaks and valleys on the 3D topographical micrographs of the cracking faces confirmed that 1 SMA-2 GPVA specimen efficiently participated in transferring stress through the composite, leading to a greater vertical impact reaction force. Finally, the structure-property relation for flexural versus fracture behaviour and the effectiveness of SMA fibres on the crack-healing feature of the composites were studied by using digitized fractal analysis and through the heat treatment. The disseminated fracture energy (Ws/Gf) value reached 130 and the crack sizes the crack size decreased by 34 %, which were much better than that of the reference composites. The nano treatment of PVA fibres in ECC provides an innovative and sustainable solution for engineering structures with requirement of high tensile ductility and high impact resistance, e.g., military infrastructure and industrial floors.

Banana fruit bruise detection using fractal dimension based image processing

The study used the fractal dimension (FD), browning incidence, and grayscale values using machine vision to describe the bruise magnitude and quality of mechanically damaged ‘Fard’ bananas bruised from 20, 40, 60 cm drop heights by 66, 98, and 110 g ball weights conditioned at different storage temperatures (5, 13, 22 °C) after 48 h. Conventional analyses like bruise area (BA), bruise volume (BV), and bruise susceptibility (BS) were also conducted. A correlation was performed to determine the relationship between image processing and conventional assessment of bruise damage in bananas. Weight, firmness, color, sugar content, and acidity were investigated. The results demonstrated that bananas bruised from the highest force and stored at 5 and 22 °C reported the lowest FD with values of 1.7162 and 1.7403, respectively. Increasing the level of damage reduced the fractal dimension and grayscale values and increased browning incidence and bruise susceptibility values after 48 h of storage. The total color change values showed a strong Pearson's correlation coefficient (r≥-0.81) with image analysis fractal dimension and grayscale values. The findings also indicated that higher bruising and temperature can induce weight loss, firmness reduction, lightness, and yellowness increment, and sugar and acidity changes. Overall, the fractal image analysis conducted in this study was highly effective in describing the bruising magnitude of bananas under different conditions.

Exploring the physicochemical traits, antifungal capabilities, and 3D spatial complexity of hydroxyapatite with Ag+[sbnd]Mg2+ substitution in the biocomposite thin films

The silver/magnesium doped hydroxyapatite (AgMgHAp, Ca10−x-yAgxMgy(PO4)6(OH)2, xAg=0.05 and yMg=0.02) nanocomposites coatings were deposited on Si substrate using the dip coating technique. The resulting coatings were characterized by scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), Fourier transform infrared (FTIR-ATR) spectroscopy, atomic force microscopy (AFM) and X-ray photoelectron spectroscopy (XPS). The EDS analysis highlighted the presence of the constitutive elements of the silver/magnesium doped hydroxyapatite (AgMgHAp) nanocomposites coatings. The surface microtexture of the AgMgHAp was assessed by atomic force microscopy (AFM) technique. The AFM data suggested the obtaining of a uniform deposited layer comprised of equally distributed nanoconglomerates. FT-IR studies highlighted the presence of vibrational modes associated with the phosphate and hydroxyl groups. No bands associated with silver or magnesium were observed. The XPS analysis highlighted the presence of the constituent elements of hydroxyapatite (Ca 2p, P 2 s, O 1 s), as well as dopants (Ag 3d, Mg 1 s and Mg 2p). The antifungal evaluation of AgMgHAp coatings was carried out using the Candida albicans ATCC 10231 fungal strain. The results of the antifungal assay revealed that the AgMgHAp coatings exhibited a strong inhibitory antifungal activity. Furthermore, the data highlighted that the AgMgHAp inhibited the development of biofilm on their surface. The results revealed that the antifungal activity of the coating varied based on the duration of incubation. On the other hand, the data also showed that AgMgHAp nanocomposites coatings inhibited the fungal cell adhesion and development from the early stages of the incubation. In addition to morphological analysis, we additionally take advantage of AFM images to investigate and explore the domain of fractal and multifractal analysis applied to the films under evaluation. Our studies indicates that nanocomposite coatings made from AgMgHAp demonstrate strong antifungal properties. Our studies indicates that nanocomposite coatings made from AgMgHAp demonstrate strong antifungal properties. These results suggest the potential of AgMgHAp nanocomposite coatings as a promising solution for developing innovative antifungal devices in biomedical applications.

Fractal Analysis of Cement-Based Composite Microstructure and Its Application in Evaluation of Macroscopic Performance of Cement-Based Composites: A Review

Cement-based composites’, as the most widely used building material, macroscopic performance significantly influences the safety of engineering structures. Meanwhile, the macroscopic properties of cement-based composites are tightly related to their microscopic structure. The complexity of cement-based composites’ microscopic structure is challenging to describe geometrically, so fractal theory is extensively applied to quantify the microscopic structure of cement-based composites. However, existing studies have not clearly defined the quantification methods for various microscopic structures in CCs, nor have they provided a comprehensive evaluation of the correlation between the fractal dimensions of different microscopic structures and macroscopic performance. So, this study categorizes the commonly used testing methods in fractal theory into three categories: particle distribution (laser granulometry, etc.), pore structure (mercury intrusion porosity, etc.), and fracture (computed tomography, etc.). It systematically establishes a detailed process for the application of testing methods, the processing of test results, model building, and fractal dimension calculation. The applicability of different fractal dimension calculation models and the range of the same fractal dimension established by different models are compared and discussed, and the advantages and disadvantages of different models are analyzed. Finally, the research delves into an in-depth analysis of the relationship between the fractal dimension of cement-based composites’ microscopic structure and its macroscopic properties, such as compressive strength, corrosion resistance, impermeability, and high-temperature resistance. The principle that affects the positive and negative correlation between fractal dimension and macroscopic performance is discussed and revealed in this study. The comprehensive review in this paper provides scholars with methods and models for quantitative research on the microscopic structural parameters of cement-based composites and offers a pathway for the non-destructive assessment of the macroscopic performance of cement-based composites.

A Fractal Dimensional Analysis of Vernacular House Façades in Indonesia: Rumah Gadang and Uma

Vernacular house façades have distinct visual characteristics as a reflection of the factors that influence vernacular architecture, one of which is how the locals perceive and interpret aesthetics. This study attempts to quantitatively examine the aesthetic qualities of the façades of two vernacular houses, namely Rumah Gadang from West Sumatra, western Indonesia, and Uma from Sumba Island, eastern Indonesia. Both have very different geographical conditions, cultural, and historical backgrounds. The fractal dimension analysis is used by breaking down the façade into 5 layers of architectural attribute; silhouette, main tripartite, structure, façade components, and material texture. Using the box-counting method, it is known which layer is the biggest contributor to the visual complexity of the façades. Based on the calculations, it is concluded that there are differences in the degree and proportion of visual complexity in the case of the two houses. The façade of Rumah Gadang has higher visual complexity than Uma. Material texture is the most dominant contributor to visual complexity of both houses. In Rumah Gadang, the façade components greatly contribute to visual complexity, while in Uma the silhouette has a big influence. This finding can be attributed to the way the homeowners place importance on the façade and the house in its respective social system, or even the development of civilization behind the two houses. It is also found that subjective-qualitative visual observation and philosophical approach do not always correspond with the result of mathematical calculation.

A fractal modification of the tropical algebra for noise removal and optimal control

This paper proposes a fractal modification of tropical algebra for noise removal and optimal control. Fractal addition, fractal multiplication, and fractal dot product are defined and explained in a fractal space. A fractal tropical polynomials function can model a coastline at any scale, providing a new tool for fractal analysis of any irregular curve. An example is given to solve an optimal control subject to a fractal tropical polynomials function. This paper provides a new window for tropical algebra, combining fractal geometry and algebra.

Radiologic evaluation of associated symptoms and fractal analysis of unilateral dens invaginatus cases.

The aim of this study is to determine the age-based prevalence of dens invaginatus cases and to learn the radiologic findings. In addition, fractal analysis of the periapical regions of unilateral dens invaginatus cases and contralateral teeth was performed to determine the effect of possible microleakage on fractal dimension. A total of 136 patients (170 teeth) identified in panoramic radiographs taken for diagnostic purposes between January 2018 and December 2023 at our Department of Oral and Maxillofacial Radiology were included in the study. Data were analysed using IBM SPSS V23. The Chi-square test was used for comparing categorical variables between groups. The relationship between the FD values calculated around the apexes of the teeth with unilateral dens invaginatus and the contralateral teeth was analyzed by paired t test. A significance level of p < 0.050 was adopted. The mean age of the cases was calculated as 28.1 (8-63) years. 66 (48.5%) of the cases were female, and 70 (51.1%) were male. The lateral incisor was the most affected tooth among these cases. Bilateral cases were observed in 34 patients. Type 2 was detected in 93 patients, Type 1 in 35 patients, and Type 3 dens invagination in 8 patients. Dens invaginatus cases were observed in 134 maxillary and 2 mandibular teeth. Periapical lesions were seen in 22 of these cases. Dens invaginatus cases are a congenital anomaly encountered at any age. Early diagnosis is crucial to prevent the loss of pulp vitality due to these invaginations. It should be noted that these invaginations can affect both jaws. However, due to the prevalence of occurrence in the maxillary anterior teeth and asymptomatic nonvitality, particular attention should be paid to evaluating this region.

Acoustic signals associated with the multifractal breakage patterns of brittle and crispy foods

Food breakage is an important issue in industry and is coupled to acoustic signals. The aim of this work was to analyse the breakage phenomenon with time in commercial crispy and brittle foods, using acoustic techniques and mechanical-textural features using Digital Image Analysis (DIA) and fractal analysis. Breakage patterns were coupled to the acoustic signals of six brittle foods by capturing the audio during breaking and then, applying DIA to audio signals and breakage patterns, which depicted multifractal spectra. Results showed that samples with less irregular acoustic patterns presented higher spectrum amplitudes and low generalised fractal dimension (GFD) (1.245 ± 0.045) and lacunarity (Ʌ) (0.269 ± 0.209) while materials presenting the largest irregularity had shorter spectrum amplitudes and depicted high GFD (1.656 ± 0.177) and Ʌ(0.745 ± 0.007). For global analysis of the transverse and longitudinal rupture pattern, four breakage zones were defined. In all cases, multifractal breakage patterns were associated to multifractal acoustic signals.

Comprehensive Wheat Straw Processing with Deep Eutectic Solvent to Deliver Reducing Sugar

Pretreatment is one of the bottlenecks in the cost and energy-efficient biomass valorization. Deep eutectic solvents are potential candidates for being used to address these challenges. In this work, the deep eutectic solvent composed of choline chloride, and acetic acid was studied for its use in wheat straw fractionation. The pretreated biomass was assessed concerning the lignin and glucan content. Under optimized time and temperature conditions, defined using Doehlert matrix chemometric tool, of 3 h 47 min and 139.6 °C, the processed wheat straw contained as much as 42.5 ± 0.42 wt.% and 38.59 ± 1.26 wt.% of glucan and lignin contents, respectively. The need for biomass washing after the pretreatment with deep eutectic solvents and before the enzymatic hydrolysis step was also evaluated. The obtained enzymatic hydrolysis results, i.e., glucan to glucose yield of 27.13 ± 0.25 vs. 25.73 ± 0.08 for washed or unwashed biomass correspondingly, are equally good substrates. Fractal kinetic analysis of the data showed similar values of k and h for both glucose and xylose reactions between washed and unwashed biomass. This confirmed that biomass washing is an unnecessary step, which in turn opens room for biomass processing intensification.

Recovery of synaptic loss and depressive-like behavior induced by GATA1 through blocking of the neuroinflammatory response.

GATA1, a member of the GATA transcription factor family, is a critical factor in hematopoietic system development. In a previous study, we demonstrated the increased expression of GATA1 in the dorsolateral prefrontal cortex (dlPFC) of patients suffering from depression and described its role as a transcriptional repressor of synapse-related genes. In this study, we investigated how GATA1 globally altered gene expression using multi-omics approaches. Through the combined analyses of ChIPseq, mRNAseq, and small RNAseq, we profiled genes that are potentially affected by GATA1 in cultured cortical neurons, and Gene Ontology (GO) analysis revealed that GATA1 might be associated with immune-related functions. We hypothesized that GATA1 induces immune activation, which has detrimental effects including synapse loss and depressive-like behavior. To test this hypothesis, we first performed a microglial morphometric analysis of a brain having overexpression of GATA1 because microglia are the resident immune cells of the central nervous system. Fractal analysis showed that the ramification and process length of microglia decreased in brains having GATA1 overexpression compared to the control, suggesting that GATA1 overexpression increases the activation of microglia. Through flow cytometry and immunohistochemical analysis, we found that activated microglia showed pro-inflammatory phenotypes characterized by the expression of CD86 and CD68. Finally, we demonstrated that the effects of GATA1 overexpression including synapse loss and depressive-like behavior could be blocked by inhibiting microglial activation using minocycline. These results will elucidate the regulatory mechanisms of GATA1 that affect pathophysiological conditions such as depression and provide a potential target for the treatment of depression.

Cortex and White Matter of the Cerebral Hemispheres: Anatomical Correlations and Age-Related Changes Measured with Fractal Analysis

Aim. The aim of the present study was to determine the fractal dimension (FD) values of the cortex and white matter of the cerebral hemispheres using fractal analysis of two-dimensional magnetic resonance images, explore the anatomical correlations of the cortex and white matter FD, and study age-associated changes in the cortex and white matter. Methods. Two-dimensional brain magnetic resonance images of 100 apparently healthy individuals of both genders (44 males and 56 females) aged 18-86 years were studied. Five sections of each participant’s brain were selected (4 coronal and 1 axial). After image segmentation, the FD values and sectional areas of the cortex and white matter were determined. Fractal analysis was conducted using a two-dimensional variant of the box-counting method. Results. The FD values of the cortex and white matter varied across the five brain sections analyzed. Specifically, the cortex exhibited a decrease in the FD, whereas the white matter showed an increase in the FD in the coronal sections along the rostro-caudal direction. The FD values obtained from different sections displayed weak to moderate correlations. Additionally, no significant differences were observed in the FD values of the cortex and white matter between males and females. However, the sectional area values of the cortex and white matter were slightly higher in males as compared to females. Furthermore, a negative correlation was identified between the FD values of the cortex and white matter of the cerebral hemispheres, while sectional areas did not exhibit significant correlations. The cortex FD positively correlated with the gyrification index, whereas the white matter FD showed a negative correlation with this parameter. Additionally, both the FD and sectional area values of the cortex displayed strong and moderate negative correlations with age, respectively. In contrast, the FD and sectional area values of the white matter demonstrated weak negative correlations with age. Males showed stronger correlations of the studied parameters with age across the majority of the analyzed sections compared to females, although these differences were not statistically significant. Conclusions. In this study, a negative correlation was found between the cortex and white matter FD values, influenced by anatomical factors such as the degree of gyrification. While the cortex FD values significantly decreased with age, age-related changes in the white matter FD values were relatively weak.

Fractal Analysis of Trabecular Alveolar Bone with Intrabony and Furcation Defects Using Periapical Dental Radiographs

Objective: Fractal analysis (FA) is a non-invasive method that quantitatively measures complex patterned geometric structures present throughout the image. Trabecular morphology of the alveolar bone and the changes occurring in the trabeculae in case of periodontitis can be detected with this method. To examine the periodontal defects in human skull bones using the FA, to compare them with healthy alveolar bone regions. Methods: Furcation and intrabony defects were artificially created in the mandible alveolar bones (n:24). Periapical X-ray images of alveolar bone regions containing teeth with defects were taken using the parallel technique. Fractal analysis was performed by box-counting method using Image J software on images from areas containing healthy and defective trabecular bone. Results: No statistically significant difference was found between the fractal values of healthy tissue and bifurcation defetcs and between the healthy tissue and intrabony defects (p&gt;0.05). Conclusion: Many factors may have affected the outcomes; patient selection, imaging methods, sample size, Region of interest (ROI) selection-location and size, individual and anatomical variations. These variables need to be standardized as much as possible and the limitations of the method need to be improved.

A novel approach to assessing the anaerobic bio-accessibility of straw using fractal dimension

Traditional methods for evaluating the bioconversion capacity of organic solid waste are known for time-consuming property and often exhibit low prediction accuracy. However, leveraging fractal dimensions offers a more precise characterization of the complexity, irregularity, and spatial structure of organic solid waste. In this study, a novel and efficient method for evaluating the bio-accessibility of straw's anaerobic transformation, based on fractal dimensions, was introduced. To comprehensively compare the structural differences, this research encompasses the measurement of nine different varieties of straw under ten distinct pretreatment conditions. The regression sum of squares for these correlations consistently exceeds 0.83, highlighting the robustness of our findings. The results unequivocally demonstrate the close relationship between the fractal dimension and the structural characteristics of straw. This relationship underscores the utility of fractal dimension analysis as a reliable tool for evaluating the anaerobic bio-accessibility of organic solid waste.

Automatic Classification of Cancerous Masses in Digital Mammograms Using Curvelet Analysis and Hybrid Genetic Algorithm-Artificial Neural Network Model

Background: Mammography is the most fundamental and widely used method for detecting breast abnormalities. Distinguishing malignant from benign lesions requires extracting relevant information, which can be challenging and time-consuming for radiologists. Computer-aided diagnosis (CAD) techniques can serve as complementary diagnostic tools, assisting radiologists in the early detection and analysis of abnormalities in mammograms. Objectives: This study aimed to propose a CAD system for extracting significant features of abnormalities in breast mammograms using Curvelet transform and fractal analysis, and classifying breast tumors as malignant or benign based on the calculated features. Patients and Methods: In this study, an efficient feature extraction method was applied, utilizing Curvelet transform and fractal analysis, on a dataset comprising 113 abnormal images from the Mammographic Image Analysis Society (MIAS) database, which included 62 benign and 51 malignant cases. The method yielded 575 features, but due to potential irrelevance or redundancy, a multi-objective optimization (MOO) approach based on a genetic algorithm (GA) for an artificial neural network (ANN), named GA-MOO-ANN, was proposed to obtain and focus on an optimal and effective feature set. As a result of this approach, a set of 17 efficient features was extracted. The proposed algorithm was implemented in MATLAB 2014a, and the performance metrics were calculated using 6-fold cross-validation. Results: The experimental results demonstrated exceptional performance, with an accuracy (Acc) of 98.2%, specificity (Sp) of 100%, sensitivity (Se) of 96.8%, positive predictive value (PPV) of 100%, negative predictive value (NPV) of 96.2%, and an impressive area under the curve (AUC) of 0.98, providing comparable results to other recent methods. Conclusion: The current findings suggest that the proposed method could be a valuable tool for breast cancer diagnosis, potentially reducing the number of unnecessary breast biopsies. This method may lead to more efficient patient evaluation and earlier detection of breast tumors.