Development, Application and Utility of a Machine Learning Approach for Melanoma and Non-Melanoma Lesion Classification Using Counting Box Fractal Dimension.

The diagnosis and identification of melanoma are not always accurate, even for experienced dermatologists. Histopathology continues to be the gold standard, assessing specific parameters such as the Breslow index. However, it remains invasive and may lack effectiveness. Therefore, leveraging mathematical modeling and informatics has been a pursuit of diagnostic methods favoring early detection. Fractality, a mathematical parameter quantifying complexity and irregularity, has proven useful in melanoma diagnosis. Nonetheless, no studies have implemented this metric to feed artificial intelligence algorithms for the automatic classification of dermatological lesions, including melanoma. Hence, this study aimed to determine the combined utility of fractal dimension and unsupervised low-computational-requirements machine learning models in classifying melanoma and non-melanoma lesions. We analyzed 39,270 dermatological lesions obtained from the International Skin Imaging Collaboration. Box-counting fractal dimensions were calculated for these lesions. Fractal values were used to implement classification methods by unsupervised machine learning based on principal component analysis and iterated K-means (100 iterations). A clear separation was observed, using only fractal dimension values, between benign or malignant lesions (sensibility 72.4% and specificity 50.1%) and melanoma or non-melanoma lesions (sensibility 72.8% and specificity 50%) and subsequently, the classification quality based on the machine learning model was ≈80% for both benign and malignant or melanoma and non-melanoma lesions. However, the grouping of metastatic melanoma versus non-metastatic melanoma was less effective, probably due to the small sample size included in MM lesions. Nevertheless, we could suggest a decision algorithm based on fractal dimension for dermatological lesion discrimination. On the other hand, it was also determined that the fractal dimension is sufficient to generate unsupervised artificial intelligence models that allow for a more efficient classification of dermatological lesions.

Use of fractals in determining the malignancy degree of lung nodules.

Introduction: A Computer-Assisted Detection (CAD) System for classification into malignant-benign classes using CT images is proposed. Methods: Two methods that use the fractal dimension (FD) as a measure of the lung nodule contour irregularities (Box counting and Power spectrum) were implemented. The LIDC-IDRI database was used for this study. Of these, 100 slices belonging to 100 patients were analyzed with both methods. Results: The performance between both methods was similar with an accuracy higher than 90%. Little overlap was obtained between FD ranges for the different malignancy grades with both methods, being slightly better in Power spectrum. Box counting had one more false positive than Power spectrum. Discussion: Both methods are able to establish a boundary between the high and low malignancy degree. To further validate these results and enhance the performance of the CAD system, additional studies will be necessary.

A comprehensive study from the micro- to the nanometric scale: Evaluation of chilling injury in tomato fruit (Solanum lycopersicum).

Tomato fruit is susceptible to chilling injury (CI) during its postharvest handling at low temperature. The symptoms caused by this physiological disorder have been commonly evaluated by visual inspection at a macro-observation scale on fruit surface; however, the structure at deeper scales is also affected by CI. This work aimed to propose a descriptive model of the CI development in tomato tissue under the micro-scale, micro-nano-scale and nano-scale approaches using fractal analysis. For that, quality and fractal parameters were determined. In this sense, light microscopy, Environmental Scanning Electron Microscopy (ESEM) and Atomic Force Microscopy (AFM) were applied to analyse micro-, micro-nano- and nano-scales, respectively. Results showed that the morphology of tomato tissue at the micro-scale level was properly described by the multifractal behaviour. Also, generalised fractal dimension (Dq=0) and texture fractal dimension (FD) of CI-damaged pericarp and cuticle were higher (1.659, 1.601 and 1.746, respectively) in comparison to non-chilled samples (1.606, 1.578 and 1.644, respectively); however, FD was unsuitable to detect morphological changes at the nano-scale. On the other hand, lacunarity represented an appropriate fractal parameter to detect CI symptoms at the nano-scale due to differences observed between damaged and regular ripe tissue (0.044 and 0.025, respectively). The proposed multi-scale approach could improve the understanding of CI as a complex disorder to the development of novel techniques to avoid this postharvest issue at different observation scales.

Fractal analysis is a useful tool for evaluating prostate tissue remodeling caused by ethanol consumption and androgen therapy.

Alcohol has been widely consumed for centuries and is linked to the aggravation of diseases. Several studies have shown that excessive consumption of ethanol results in morphophysiological changes in the male reproductive system. One of the effects of ethanol is the decrease in testosterone concentration and hormonal therapies are an alternative to minimize the changes resulting from chronic alcoholism. Qualitative studies were commonly carried out to evaluate the male histopathological alterations resulting from ethanol consumption, being necessary quantitative and non-subjective techniques. This study analyzes the importance of fractal analysis as a useful tool to identify and quantify tissue remodeling in rats submitted to ethanol consumption and hormone therapy with testosterone. Prostate of animals submitted to chronic ethanol consumption showed tissue disorganization, which was confirmed by an increasing of fractal dimension. Regarding the prostatic stroma, collagen fractal dimension and quantification revealed lower values in animals that were only submitted to androgen therapy. Thus, we can conclude that the fractal analysis was a useful tool to quantify tissue changes caused by ethanol consumption and androgen therapy.

Supervised Machine-Learning Methodology for Industrial Robot Positional Health Using Artificial Neural Networks, Discrete Wavelet Transform, and Nonlinear Indicators.

Robotic systems are a fundamental part of modern industrial development. In this regard, they are required for long periods, in repetitive processes that must comply with strict tolerance ranges. Hence, the positional accuracy of the robots is critical, since degradation of this can represent a considerable loss of resources. In recent years, prognosis and health management (PHM) methodologies, based on machine and deep learning, have been applied to robots, in order to diagnose and detect faults and identify the degradation of robot positional accuracy, using external measurement systems, such as lasers and cameras; however, their implementation is complex in industrial environments. In this respect, this paper proposes a method based on discrete wavelet transform, nonlinear indices, principal component analysis, and artificial neural networks, in order to detect a positional deviation in robot joints, by analyzing the currents of the actuators. The results show that the proposed methodology allows classification of the robot positional degradation with an accuracy of 100%, using its current signals. The early detection of robot positional degradation, allows the implementation of PHM strategies on time, and prevents losses in manufacturing processes.

Evaluation of entropy and fractal dimension as biomarkers for tumor growth and treatment response using cellular automata.

Cell-based models provide a helpful approach for simulating complex systems that exhibit adaptive, resilient qualities, such as cancer. Their focus on individual cell interactions makes them a particularly appropriate strategy to study cancer therapies' effects, which are often designed to disrupt single-cell dynamics. In this work, we propose them as viable methods for studying the time evolution of cancer imaging biomarkers (IBM). We propose a cellular automata model for tumor growth and three different therapies: chemotherapy, radiotherapy, and immunotherapy, following well-established modeling procedures documented in the literature. The model generates a sequence of tumor images, from which a time series of two biomarkers: entropy and fractal dimension, is obtained. Our model shows that the fractal dimension increased faster at the onset of cancer cell dissemination. At the same time, entropy was more responsive to changes induced in the tumor by the different therapy modalities. These observations suggest that the prognostic value of the proposed biomarkers could vary considerably with time. Thus, it is essential to assess their use at different stages of cancer and for different imaging modalities. Another observation derived from the results was that both biomarkers varied slowly when the applied therapy attacked cancer cells scattered along the automatons' area, leaving multiple independent clusters of cells at the end of the treatment. Thus, patterns of change of simulated biomarkers time series could reflect on essential qualities of the spatial action of a given cancer intervention.

Fractal analysis is a useful tool for evaluating prostate tissue remodeling caused by ethanol consumption and androgen therapy

Abstract Alcohol has been widely consumed for centuries and is linked to the aggravation of diseases. Several studies have shown that excessive consumption of ethanol results in morphophysiological changes in the male reproductive system. One of the effects of ethanol is the decrease in testosterone concentration and hormonal therapies are an alternative to minimize the changes resulting from chronic alcoholism. Qualitative studies were commonly carried out to evaluate the male histopathological alterations resulting from ethanol consumption, being necessary quantitative and non-subjective techniques. This study analyzes the importance of fractal analysis as a useful tool to identify and quantify tissue remodeling in rats submitted to ethanol consumption and hormone therapy with testosterone. Prostate of animals submitted to chronic ethanol consumption showed tissue disorganization, which was confirmed by an increasing of fractal dimension. Regarding the prostatic stroma, collagen fractal dimension and quantification revealed lower values in animals that were only submitted to androgen therapy. Thus, we can conclude that the fractal analysis was a useful tool to quantify tissue changes caused by ethanol consumption and androgen therapy.

Soil Pore Network Complexity Changes Induced by Wetting and Drying Cycles-A Study Using X-ray Microtomography and 3D Multifractal Analyses.

Soils are dynamic and complex systems in their natural state, which are subjected to profound changes due to management. Additionally, agricultural soils are continuously exposed to wetting and drying (W-D) cycles, which can cause modifications in the complexity of their pores. Thus, we explore how successive W-D cycles can affect the pore network of an Oxisol under contrasting managements (conventional tillage-CT, minimum tillage-MT, no tillage-NT, and secondary forest-F). The complexity of the soil pore architecture was evaluated using a 3D multifractal approach combined with lacunarity, Shannon's entropy, and pore geometric parameters. Our results showed that the multifractal approach effectively identified and quantified the changes produced in the soil pore architecture by the W-D cycles. The lacunarity curves revealed important aspects of the modifications generated by these cycles. Samples under F, NT, and MT suffered the most significant changes. Pore connectivity and tortuosity were largely affected by the cycles in F and NT. Our findings demonstrated that the 3D geometric parameters and normalized Shannon's entropy are complementary types of analysis. According to the adopted management, they allowed us to separate the soil into two groups according to their similarities (F and NT; CT and MT).

Morphological and Fractal Properties of Brain Tumors.

Tumor interface dynamics is a complex process determined by cell proliferation and invasion to neighboring tissues. Parameters extracted from the tumor interface fluctuations allow for the characterization of the particular growth model, which could be relevant for an appropriate diagnosis and the correspondent therapeutic strategy. Previous work, based on scaling analysis of the tumor interface, demonstrated that gliomas strictly behave as it is proposed by the Family-Vicsek ansatz, which corresponds to a proliferative-invasive growth model, while for meningiomas and acoustic schwannomas, a proliferative growth model is more suitable. In the present work, other morphological and dynamical descriptors are used as a complementary view, such as surface regularity, one-dimensional fluctuations represented as ordered series and bi-dimensional fluctuations of the tumor interface. These fluctuations were analyzed by Detrended Fluctuation Analysis to determine generalized fractal dimensions. Results indicate that tumor interface fractal dimension, local roughness exponent and surface regularity are parameters that discriminate between gliomas and meningiomas/schwannomas.

A spatial randomness test based on the box-counting dimension.

Statistical modelling of a spatial point pattern often begins by testing the hypothesis of spatial randomness. Classical tests are based on quadrat counts and distance-based methods. Alternatively, we propose a new statistical test of spatial randomness based on the fractal dimension, calculated through the box-counting method providing an inferential perspective contrary to the more often descriptive use of this method. We also develop a graphical test based on the log-log plot to calculate the box-counting dimension. We evaluate the performance of our methodology by conducting a simulation study and analysing a COVID-19 dataset. The results reinforce the good performance of the method that arises as an alternative to the more classical distances-based strategies.

Fractal evaluation in retinographies of individuals with different grades of diabetic retinopathy / Avaliação fractal de retinografias de indivíduos com diferentes graus de retinopatia diabética

ABSTRACT Purpose To evaluate the retinal blood vascular network of the retinographies of patients with different grades of diabetic retinopathy. Methods Ninety Retinographies (MESSIDOR database) were used, with different grades of diabetic retinopathy divided into 4 groups: no retinopathy (n=23), grade one (n=20), grade two (n=20) and grade three (n=27) diabetic retinopathy. The grades of diabetic retinopathy were classified according to the number of microaneurysms, number of hemorrhages and the presence of neovascularization. The images were skeletonized and quantified by fractal methods: dimension of box-counting (Dbc) and information (Dinf). Results The means of Dbc values of groups were around 1.25, without statistically significant difference in the dimension values between groups for whole retina. There was also no statistical difference in Dinf values between groups, whose means ranged between 1.294 ± 0.013 (group of grade 1) and 1.3 ± 0.017 (group of grade 3). The retinographies were divided into regions of equal areas. The fractal values of some retinal regions showed statistical differences, but these differences were not enough to show the sensitivity of fractal methods in identifying diabetic retinopathy. Conclusion The fractal methods were not able to identify the different grades of diabetic retinopathy in retinographies.

RESUMO Objetivo Avaliar a rede vascular sanguínea da retina a partir de retinografias de pacientes com diferentes graus de retinopatia diabética. Métodos Foram utilizadas 90 retinografias (banco de dados MESSIDOR), com diferentes graus de retinopatia diabética divididas em quatro grupos: sem retinopatia (n=23), retinopatia diabética de grau um (n=20), grau dois (n=20) e grau três (n=27). Os graus de retinopatia foram classificados conforme o número de microaneurismas, número de hemorragias e presença de neovascularização. As imagens foram esqueletizadas e quantificadas pelos métodos fractais: dimensão da contagem de caixas e informação. Resultados As médias dos valores das dimensões de contagem de caixas para todos os grupos foram próximas a 1,25, sem diferença estatisticamente significativa nos valores das dimensões entre os grupos para retina inteira. Também não houve diferença estatística nos valores da dimensão de informação entre os grupos, cujas médias variaram entre 1,294 ± 0,013 (grupo do grau 1) e 1,3 ± 0,017 (grupo do grau 3). As imagens retinianas foram divididas em regiões de áreas iguais. Os valores fractais de algumas regiões retinais mostraram diferenças estatísticas, mas estas não foram suficientes para mostrar a sensibilidade dos métodos fractais na identificação da retinopatia diabética. Conclusão Os métodos fractais não foram capazes de identificar os diferentes graus de retinopatia diabética em retinografias.

Fractal dimension analysis as an easy computational approach to improve breast cancer histopathological diagnosis.

Histopathology is a well-established standard diagnosis employed for the majority of malignancies, including breast cancer. Nevertheless, despite training and standardization, it is considered operator-dependent and errors are still a concern. Fractal dimension analysis is a computational image processing technique that allows assessing the degree of complexity in patterns. We aimed here at providing a robust and easily attainable method for introducing computer-assisted techniques to histopathology laboratories. Slides from two databases were used: A) Breast Cancer Histopathological; and B) Grand Challenge on Breast Cancer Histology. Set A contained 2480 images from 24 patients with benign alterations, and 5429 images from 58 patients with breast cancer. Set B comprised 100 images of each type: normal tissue, benign alterations, in situ carcinoma, and invasive carcinoma. All images were analyzed with the FracLac algorithm in the ImageJ computational environment to yield the box count fractal dimension (Db) results. Images on set A on 40x magnification were statistically different (p = 0.0003), whereas images on 400x did not present differences in their means. On set B, the mean Db values presented promissing statistical differences when comparing. Normal and/or benign images to in situ and/or invasive carcinoma (all p < 0.0001). Interestingly, there was no difference when comparing normal tissue to benign alterations. These data corroborate with previous work in which fractal analysis allowed differentiating malignancies. Computer-aided diagnosis algorithms may beneficiate from using Db data; specific Db cut-off values may yield ~ 99% specificity in diagnosing breast cancer. Furthermore, the fact that it allows assessing tissue complexity, this tool may be used to understand the progression of the histological alterations in cancer.

A Novel Method for a COVID-19 Classification of Countries Based on an Intelligent Fuzzy Fractal Approach.

We outline in this article a hybrid intelligent fuzzy fractal approach for classification of countries based on a mixture of fractal theoretical concepts and fuzzy logic mathematical constructs. The mathematical definition of the fractal dimension provides a way to estimate the complexity of the non-linear dynamic behavior exhibited by the time series of the countries. Fuzzy logic offers a way to represent and handle the inherent uncertainty of the classification problem. The hybrid intelligent approach is composed of a fuzzy system formed by a set of fuzzy rules that uses the fractal dimensions of the data as inputs and produce as a final output the classification of countries. The hybrid approach calculations are based on the COVID-19 data of confirmed and death cases. The main contribution is the proposed hybrid approach composed of the fractal dimension definition and fuzzy logic concepts for achieving an accurate classification of countries based on the complexity of the COVID-19 time series data. Publicly available datasets of 11 countries have been the basis to construct the fuzzy system and 15 different countries were considered in the validation of the proposed classification approach. Simulation results show that a classification accuracy over 93% can be achieved, which can be considered good for this complex problem.

Evaluation of Decision-Making Chains and their Fractal Dimensions.

A decision-making process is a part of the decision-making theory, reasonably placing a major research interest on the question how the process is conducted and what affects the process itself in general. Naturally it is perceived as a sequence of steps, where things are moving forward little-by-little towards to the settled goal. An analysis could be done before (planning), during the process (control + adaption) or afterwards (analysis and evaluation). Also, we can just study someone's decision process first, mainly trying to avoid making "their" mistakes. Anyway, making decisions or just observing and studying them is a part of life. Either one assumes evaluation of the current situation and of the expected outcomes, assigning to each decision some "quality" according to the fixed set of criteria (like probabilistic), or the flexible ones (different heuristics). Thus, from the mathematical and the philosophic points of view we will face three principle questions applicable to any particular decision-making theory: (1) How many criteria do we need? (2) How well they are defined/described? (3) Are there any relations between them, or we can consider them to be independent ones? Besides, any admissible theory also will consider some kind of underground efficiency questions (at least not to over-complicate and postpone a decision-making process), possibility to track and secure the major and intermediate goals and et cetera. It is clear that theoretical research and even the hated ad-hoc hypothesis use some reasonable assumptions about criteria selection and their quantity: pure or context oriented, but we want to consider the presented problem without restrictions of any specific theory, domain or context; using just common sense and analogies between exact and human sciences detected in twentieth century an later. Therefore, we created a hypothesis on how many evaluation criteria do we really need to operate inside an abstract decision domain-regardless the nature of criteria and their relations with real-world processes. Actually, it was not a big surprise that it resulted to be related with concepts of fractals, chaos and the notion of the fractal dimension. Their clear presence was discovered in many social and biological sciences recently, so an investigation was continued not only in terms of finding "deep" arguments to prove our postulates: recent results in math and physics also showed that most dynamic processes could be described differently considering an analysis of the current situation, short-term and long-term runs. Hence, the nature and the quantity of the involved criteria may vary (they could be implicitly time-dependent) and we need to study this kind of relation also.

Fractal and Polarization Properties of Light Scattering Using Microcrystalline Pharmaceutical Aggregates.

Fractal and polarization analysis of diffusively scattered light is applied to determine the complex relationship between fractal dimension of structural morphology and concentration of chemically active ingredients in two pharmaceutical mixture systems including a series of binary mixtures of acetaminophen in lactose and three multicomponent blends with a proprietary active ingredient. A robust approach is proposed to identify and filter out multiple- and single-scattering components of scattering indicatrix. The fractal dimension extracted from scattering field reveals complex structural details of the sample, showing strong dependence on low-dose drug concentration in the blend. Low-angle diffraction shows optical "halo" patterns near the angle of specular reflection caused by light refraction in microcrystalline aggregates. Angular measurements of diffuse reflection demonstrate noticeable dependence of Brewster's angle on drug concentration. It is shown that the acetaminophen microcrystals produce scattered light depolarization due to their optical birefringence. The light scattering measurement protocol developed for diffusively scattered light by microcrystalline pharmaceutical compositions provides a novel approach for the pattern recognition, analysis and classification of materials with a low concentration of active chemical ingredients.

Fractal features of soil texture and physical attributes in indian dark earth under different uses in Western Amazon / Características fractais da textura e atributos físicos do solo em áreas com terra preta de índio sob diferentes usos na Amazônia Ocidental

Studying particle size distribution is important to understand soil structure and formation processes. This research aimed to assess the fractal dimension of soil texture in Indian Dark Earth (IDE) areas in southern Amazonas state under different land uses, as follows: two areas in the municipality of Apuí, one growing cocoa and the other coffee; a grassland area in the municipality of Manicoré; and a forest area in the municipality of Novo Aripuanã. A sampling grid containing 88 collection points (intersecting points on the grid) was established in each area, measuring 80 x 42 m for the cocoa and coffee-growing sites, and 80 x 56 m and 60 x 42 m for the grassland and forest areas, respectively. Soil samples were collected in soil core and as clumps at a depth of 0.0-0.20m to determine the structural physical properties and texture of the soil. The following physical attributes were assessed: texture (PSD), bulk density (BD), macroporosity (Macro), microporosity (Micro), total porosity (TP) and aggregate stability (GMD and WMD). The fractal dimension (D) of the soil texture was determined, followed by analysis of variance and comparison of the means using Tukey's test (p≤0.05). Pearson's correlation was applied to assess the correlation between variables. There was a significant difference between the IDEs studied, with a higher D value in the cocoa-growing area in relation to the other sites. Additionally, the larger the clay fraction, the higher the D value. Fractal dimension (D) showed a positive correlation with sand, clay, BD, Macro, GMD and WMD, and a negative correlation with silt, micro, TP. Based on the D values obtained, the ADE cultivated with cocoa showed superior quality in relation to the other areas studied.KEYWORDS: Fractal dimension. Soil physics. Soil use. INTRODUCTION Applications of fractal geometry in soil science have shown that soil exhibits fractal characteristics, being a porous medium having different particle compositions, with irregular shape and self-similar structure (TYLER; WHEATCRAFT, 1989; KRAVCHENKO; ZHANG, 1998). Fractal geometry, proposed and established by Mandelbrot (1982), is a method for describing systems with non-characteristic scales and self-similarity. In recent years, this theory has been used to quantitatively describe the particle size distribution of soil, attracting the interest of pedologists worldwide (DENG et al., 2017). Particle size distribution is one of the most important physical characteristics of soil because of its significant influence on water flow and soil erosion (XU; LI; LI, 2013). In this respect, broad and precise knowledge of particle size distribution is vital to understanding soil structures and formation, since it is closely related to soil erosion, organic matter content and moisture content (DU et al., 2017). Deng et al. (2017) studied the fractal features of soil particle size distribution and found an association between fractal dimensions and the physical and chemical properties of the soil analyzed, indicating that the lower the fractal dimension, the worse the soil physical and chemical properties. Recently, the fractal method was applied to estimate soil structure and proved to be an efficient tool in analyzing soil Received: 01/04/2019 Accepted: 30/01/2020

Estudar a distribuição do tamanho das partículas é importante para entender a estrutura do solo e os processos de formação. Esta pesquisa teve como objetivo avaliar a dimensão fractal da textura do solo em áreas de Terra Preta de Índio (TPI) no sul do Estado do Amazonas sob diferentes usos da terra: duas áreas no município de Apuí, uma com cultivo de cacau e outra de café; uma área de pastagem no município de Manicoré; e uma área florestal no município de Novo Aripuanã. Uma malha de amostragem contendo 88 pontos de coleta (pontos de interseção na grade) foi estabelecida em cada área, medindo 80 x 42 m para as áreas de cacau e café, e 80 x 56 m e 60 x 42 m para as áreas de pastagem e floresta, respectivamente. Amostras de solo foram coletadas em torrões a uma profundidade de 0,0-0,20 m para determinar as propriedades físicas estruturais e a textura do solo. Os seguintes atributos físicos foram avaliados: textura, densidade do solo (DS), macroporosidade (Macro), microporosidade (Micro), porosidade total (PT) e estabilidade de agregados (DMG e DMP). Determinou-se a dimensão fractal da textura do solo (D), seguida da análise de variância e comparação das médias pelo teste de Tukey (p≤0,05). A correlação de Pearson foi aplicada para avaliar a correlação entre as variáveis. Houve uma diferença significativa entre as TPIs estudadas, com um maior valor D na área de cultivo de cacau em relação aos outros locais. Além disso, quanto maior a fração argila, maior o valor de D. A dimensão fractal (D) apresentou correlação positiva com areia, argila, DS, Macro, DMG e DMP, e correlação negativa com silte, micro, PT. Com base nos valores de D obtidos, as TPIs cultivadas com cacau apresentaram qualidade superior em relação às demais áreas estudadas.PALAVRAS-CHAVES: Dimensão Fractal. Física do solo. Uso do solo. REFERENCES ALVARENGA, R. C.; FERNANDES, B.; SILVA, T. C. A.; RESENDE, M. Estabilidade de agregados de um Latossolo Roxo sob diferentes métodos de preparo do solo e de manejo da palha do milho. Revista Brasileira de Ciência do Solo, Viçosa, v. 10, n. 2, p. 273-277, 1986.

Morphometric evaluation of Japanese quail embryos and their extraembryonic vascular networks exposed to low-frequency magnetic field with two different intensities.

Animals developed or in an embryonic stage, are constantly subjected to magnetic pollution generated by electrical and electronic devices. Several researches have used the bird embryo as an experimental model to evaluate the action of magnetic field (MF) and electromagnetic field (EMF). This study proposed to perform a morphometric evaluation in the embryos and in the blood vascular network of the yolk sac membranes (YSM) of Japanese quail (Coturnix japonica) exposed to the 60 Hz MF with two different intensities (0.16 and 0.65 mT). A total of 30 eggs were used, 10 eggs were used for each assay. Each assay formed a group (control group, group submitted to the MF of 0.16 mT and 0.65 mT). The images of the skeletonized vascular network of YSM were evaluated by two methods of fractal dimension: box-counting dimension (Dbc) and information dimension (Dinf). The embryos were evaluated by body mass, percentage cephalic length and body area. The fractal dimensions revealed no difference among groups. There were no significant differences in relation to embryonic body mass among groups. However, the embryos exposed to 0.65 mT MF presented a smaller embryonic body development (body area and percentage cephalic length). In conclusion, 0.16 mT and 0.65 mT magnetic fields were not able to generate significant effects on vasculogenesis and angiogenesis. However, the embryos exposed to 6 h of magnetic field with 0.65 mT intensity and 60 Hz frequency showed a decrease in embryonic body development.

Forecasting of COVID-19 time series for countries in the world based on a hybrid approach combining the fractal dimension and fuzzy logic.

We describe in this paper a hybrid intelligent approach for forecasting COVID-19 time series combining fractal theory and fuzzy logic. The mathematical concept of the fractal dimension is used to measure the complexity of the dynamics in the time series of the countries in the world. Fuzzy Logic is used to represent the uncertainty in the process of making a forecast. The hybrid approach consists on a fuzzy model formed by a set of fuzzy rules that use as input values the linear and nonlinear fractal dimensions of the time series and as outputs the forecast for the countries based on the COVID-19 time series of confirmed cases and deaths. The main contribution is the proposed hybrid approach combining the fractal dimension and fuzzy logic for enabling an efficient and accurate forecasting of COVID-19 time series. Publicly available data sets of 10 countries in the world have been used to build the fuzzy model with time series in a fixed period. After that, other periods of time were used to verify the effectiveness of the proposed approach for the forecasted values of the 10 countries. Forecasting windows of 10 and 30 days ahead were used to test the proposed approach. Forecasting average accuracy is 98%, which can be considered good considering the complexity of the COVID problem. The proposed approach can help people in charge of decision making to fight the pandemic can use the information of a short window to decide immediate actions and also the longer window (like 30 days) can be beneficial in long term decisions.

A novel methodology for automated differential diagnosis of mild cognitive impairment and the Alzheimer's disease using EEG signals.

BACKGROUND: EEG signals obtained from Mild Cognitive Impairment (MCI) and the Alzheimer's disease (AD) patients are visually indistinguishable. NEW METHOD: A new methodology is presented for differential diagnosis of MCI and the AD through adroit integration of a new signal processing technique, the integrated multiple signal classification and empirical wavelet transform (MUSIC-EWT), different nonlinear features such as fractality dimension (FD) from the chaos theory, and a classification algorithm, the enhanced probabilistic neural network model of Ahmadlou and Adeli using the EEG signals. RESULTS: Three different FD measures are investigated: Box dimension (BD), Higuchi's FD (HFD), and Katz's FD (KFD) along with another measure of the self-similarities of the signals known as the Hurst exponent (HE). The accuracy of the proposed method was verified using the monitored EEG signals from 37 MCI and 37 AD patients. COMPARISON WITH EXISTING METHODS: The proposed method is compared with other methodologies presented in the literature recently. CONCLUSIONS: It was demonstrated that the proposed method, MUSIC-EWT algorithm combined with nonlinear features BD and HE, and the EPNN classifier can be employed for differential diagnosis of MCI and AD patients with an accuracy of 90.3%.

Fractal dimension in liver histological findings of Wistar rats experimentally intoxicated with venom of Crotalus durissus terrificus

Background: Accidents caused by venom of Crotalus durissus snakes, popularly known in Brazil as rattlesnake, aresecond in relation to the occurrence and first place in deaths in humans and animals, mainly due to the great neurotoxic,myotoxic, coagulant, nephrotoxic and hepatotoxic potential of their venom. The effects observed are due to the action ofthe main poison fractions and among them we can mention crotoxin (representing 50% of the total poison), crotamine,gyroxine and conxulxin. The present study aimed to analyze the liver of experimentally poisoned Wistar rats with venomof Crotalus durissus terrificus by means of histological and fractal analysis. The hypothesis is that the venom of Crotalusdurissus terrificus is can induce hepatic damage at the dose recommended in this study, that its alterations can be quantifiedby the fractal dimension and that the antiofidic serum botropic crotalic be able to minimize the hepatic lesions inducedby the venom.Materials, Methods & Results: Ninety rats were distributed into different groups and treated with: control group (GC, n= 30) 0.9% sodium chloride solution; venom group (GV, n = 30) crotalic venom at the dose of 1 mg/kg; (GVS, n = 30)crotalic venom at the dose of 1 mg/Kg and antiofidic serum 6 h after the application of the venom at the dose recommendedby the manufacturer. Liver samples were collected at 2 h (M1), 8 h (M2) and 24 h (M3) after venom administration andsubmitted to histological analysis and fractal dimension (DF) using the ImageJ® software and box-counting method. Procedures for collecting, processing and analyzing samples were standardized. For statistical analyzes, after the normalitywas verified by the Shapiro-Wilk test and homogeneity by the Bartlett test, the data were submitted to analysis of variance(ANOVA) with Duncan test contrast with a significance level of 5%. No significant lesions were observed in GC, howevernecrosis...(AU)