Fractal Index Research Articles

Using a Light Gradient-Boosting Machine–Shapley Additive Explanations Model to Evaluate the Correlation Between Urban Blue–Green Space Landscape Spatial Patterns and Carbon Sequestration

Global ecosystems are facing challenges posed by warming and excessive carbon emissions. Urban areas significantly contribute to carbon emissions, highlighting the urgent need to improve their ability to sequester carbon. While prior studies have primarily examined the carbon sequestration benefits of single green or blue spaces, the combined impact of urban blue–green spaces (UBGSs) on carbon sequestration remains underexplored. Meanwhile, the rise of machine learning provides new possibilities for assessing this nonlinear relationship. We conducted a study in the Yangzhou urban area, collecting Landsat remote sensing data and net primary productivity (NPP) data at five-year intervals from 2001 to 2021. We applied the LightGBM-SHAP model to systematically analyze the correlation between UBGSs and NPP, extracting key landscape metrics. The results indicated that landscape metrics had varying impacts on NPP. At the patch and type level, the Percentage of Landscape was significantly positively correlated with NPP in green space, while the contiguity index and fractal dimension index favored carbon sequestration under certain conditions. The contribution of blue space was lower, with some indicators exhibiting negative correlations. At the landscape level, the contagion index and aggregation index of UBGS had positive effects on NPP, while the division index and landscape shape index were negatively correlated with NPP. The results enhance the understanding of the relationship between UBGS and carbon sequestration, and provide a reference for urban planning.

Urban growth stage analysis with fractal dimension logistic curve modeling and head/tail breaks method

The fractal dimension logistic curve model offers a promising approach to understanding the dynamic patterns of urban development. By deriving formulas for growth rate and acceleration of fractal dimension, we can pinpoint the inflection points in urban growth and delineate distinct stages of development. Previous studies have focused on analyzing fractal dimension values over long time spans, which means determining inflection points within a sufficiently long time series and studying the growth patterns and stages within that fixed span of time. However, the applicability of this method to studying and predicting urban growth stages in different short-term periods remains uncertain and warrants further investigation. Furthermore, the commonly used calculation method for fractal dimension, the box-counting method, often yields results influenced by the time span or scale and may introduce errors in the results obtained through least squares regression. To address this issue, a new simplified fractal index value obtained through the head/tail breaks method was applied as a supplement to the box-counting method. This new method better captures the complexity of urban development and improves the effectiveness of dividing urban growth stages. To validate our approach, we conducted a case study using continuous short-span time series data from Changchun City. By applying the fractal dimension logistic curve model, we identified inflection points of past years and divide growth stages based on urban development background across different research periods, this achieves a new application of using the logistic model based on short-span time series to predict the growth stages of different periods in the past. Our findings aim to provide valuable insights and decision support for urban planning and development initiatives.

Monitoring Age-Related Changes in Gait Complexity in the Wild with a Smartphone Accelerometer System.

Stride-to-stride fluctuations during walking reflect age-related changes in gait adaptability and are estimated with nonlinear measures that confine data collection to controlled settings. Smartphones, with their embedded accelerometers, may provide accessible gait analysis throughout the day. This study investigated age-related differences in linear and nonlinear gait measures estimated from a smartphone accelerometer (SPAcc) in an unconstrained, free-living environment. Thirteen young adults (YA) and 11 older adults (OA) walked within a shopping mall with a SPAcc placed in their front right pants pocket. The inter-stride interval, calculated as the time difference between ipsilateral heel contacts, was used for dependent measures calculations. One-way repeated-measures analysis of variance revealed significant (p < 0.05) age-related differences (mean: YA, OA) for stride-time standard deviation (0.04 s, 0.05 s) and coefficient of variation (3.47%, 4.16%), sample entropy (SaEn) scale 1 (1.70, 1.86) and scale 3 (2.12, 1.80), and statistical persistence decay (31 strides, 23 strides). The fractal scaling index was not different between groups (0.93, 0.95), but exceeded those typically found in controlled settings, suggesting an upregulation in adaptive behaviour likely to accommodate the increased challenge of free-living walking. These findings support the SPAcc as a viable telehealth instrument for remote monitoring of gait dynamics, with implications for unsupervised fall-risk assessment.

Revealing the transformation of spatial structure of greater Cairo: Insights from satellite imagery and geospatial metrics

Greater Cairo (GC) is the seventh-largest metropolitan city globally. In recent decades, GC has witnessed massive urban expansion, which has yet to be empirically measured or characterized. This research seeks to explore the patterns of urban growth and changes in urban form in GC from 1973 to 2021 using remote sensing and geospatial metrics. Six Landsat images in 1973, 1984, 1992, 2003, 2013, and 2021 were used to explore urban growth in GC. Urban Land Density Function (ULDF), Landscape Expansion Index (LEI), and Fractal Dimension Index (FDI), were utilized to analyze various aspects of urban expansion. Additionally, the ratio of Land Consumption Rate (LCR) to Population Growth Rate (PGR) was calculated to assess the correlation between urban expansion and population changes. Our results reveal a substantial addition of 203 thousand hectares of urban areas over the last half-century. The ULDF highlights GC’s transformation from a condensed to a scattered urban landscape, particularly with the establishment of the New Administrative Capital in the vicinity. Edge expansion emerged as the principal type of urban growth throughout the research duration. The consistent increase in FDI from 1.44 in 1973 to 1.75 in 2021 signifies the fragmentation of the urban landscape. Moreover, the progressive rise in LCR from 0.023 in 1984 to 0.050 ​ha per person in 2021 suggests a steady expansion of low-density urban areas. Notably, the LCR-to-PGR ratio escalated from 0.878 in 1984 to 2.428 in 2021, indicating that urban expansion surpassed population growth. These results will help further understand the characteristics of GC’s urban expansion and may offer a scientific foundation for policymakers to reconsider the current horizontal expansion policy in GC.

Long-term skid resistance evolution and influence mechanism of asphalt pavement based on self-developed wear equipment

Skid resistance decay is the critical functional distress of asphalt pavement, directly restricting its safety and service life. In order to grasp the characteristics and mechanism of long-term skid resistance evolution, this study developed a laboratory wheel-accelerated wear equipment (WAWE) and its testing methodology for asphalt pavement and coarse aggregate. Five coarse aggregates and five gradations combinations were selected to investigate the evolution. The accuracy of the evolution model and the loading conversion relationship were analyzed based on the Research Institute of Highway (RIOH) Track. Finally, the pavement anti-skid texture tester (PATT) was used to investigate the evolution characteristics of coarse aggregate microtexture. Results showed that the Asymptotic evolution model could characterize the skid resistance under the influence of coarse aggregate and gradation. RIOH Track verified the model's accuracy and showed that a single WAWE wear was equivalent to 265 loading times on actual pavement. The long-term skid resistance could be improved by increasing the nominal maximum particle size and the gradation fractal dimension indexes D and Df. The microtexture roughness of the coarse aggregate decreased after wear, then stabilized and fluctuated, which showed "regeneration" characteristics. The study can guide asphalt mixture design and maintenance timing decisions based on long-term skid resistance.

A comprehensive logging evaluation method for identifying high-quality shale gas reservoirs based on multifractal spectra analysis

Conventional logging interpretation methods qualitatively identify shale reservoirs using shale attribute parameters and interpretation templates. However, improving the identification accuracy of complex shale reservoirs is challenging due to the numerous evaluation parameters and the complexity of model calculations. To quantitatively characterize high-quality shale reservoirs effectively, this study utilizes two wells in the Fuling shale gas field as examples and establishes a comprehensive evaluation method for identifying high-quality shale gas reservoirs utilizing multi-fractal spectral analysis of well logs. First, the conventional well logs are qualitatively analyzed and evaluated via multiple fractals and R/S analysis. Subsequently, a gray relational analysis is employed to combine the production well logging, which reflects dimensionless productivity contributions, with the fractal characteristics of conventional well logs to obtain the corrected weight multifractal spectrum width ∆α' and fractal dimension D’. Comprehensive fractal evaluation indices λ and γ are introduced, forming three categories of productivity evaluation standards for shale gas reservoirs characterized by fractals. Finally, a validation well is employed to demonstrate the effectiveness of the evaluation method. The results indicate that the identification of high-quality shale gas reservoirs based on the above comprehensive fractal evaluation method can reflect the productivity classification level of fractured well sections, simplify the calculation of formation evaluation parameters, and avoid the problem of poor correlation between predicted sweet spot zones and gas production. This approach has wide applicability and value for identifying high-quality reservoir areas in shale gas reservoirs and provides technical support for the effective large-scale development of shale reservoirs.

Monitoring urban growth and landscape fragmentation in Kaduna, Nigeria, using remote sensing approach

This study assessed urban growth in Kaduna using remote sensing indices, landscape metrics, and Landsat images (2003, 2013, and 2023). Land use/land cover was carried out using the decision tree algorithm, while the transition matrix was computed using ArcGIS 10.8. Landscape fragmentation was assessed using Fragstat 4.3. The results revealed that between 2003 and 2023, bare land, built-up areas, and water bodies increased by 596 km2, 121.04 km2, and 0.22 km2, respectively, while cultivated land and tree cover decreased by 525.54 km2 and 191.91 km2, respectively. For the rate of change, bare lands, built-up areas, and water bodies increased by 29.81 km2, 6.05 km2, and 0.01 km2 annually, respectively, while cultivated lands and water bodies decreased by 26.28 km2 and 9.60 km2, respectively. For the land-use transition, 112.71 km2 of the built-up areas remained persistent. Cultivated lands, tree cover, and water bodies transitioned to built-up areas, losing 85.43 km2, 13.91 km2, and 0.91 km2, respectively. Landscape fragmentation analysis revealed that the number of patches increased from 405 in 2003 to 614 in 2023. Patch density, largest patch index, total edge, edge density, area-weighted mean shape index, and fractal dimension index decreased between 2003 and 2013 but increased between 2013 and 2023, indicating urban sprawl. However, the area-weighted mean contiguity index consistently increased between 2003 and 2023. The study concluded that urbanization is the leading driver of landscape fragmentation. This study recommends that development should be controlled to reduce encroachment on agricultural lands and habitats, thereby reducing landscape fragmentation and land degradation.

Soil organic carbon sequestration can be promoted through the improvement of landscape configuration heterogeneity in typical agricultural regions of northeast China

Landscape heterogeneity is considered a promising option for building resilient and sustainable agroecosystems. Understanding the relationships between farmland soil organic carbon (SOC) and landscape heterogeneity can support soil carbon sequestration and better serve food security and climate change. However, the influence extent and optimal scale of farmland landscape heterogeneity (i.e. landscape composition and landscape configuration heterogeneity) on SOC remains unclear. In this study, we established the relationships between multi-scale landscape heterogeneity and SOC in a typical grain-production county of northeast China. Stepwise regression results showed that when the buffer radius was 2000 m, the interpretation of SOC by landscape heterogeneity was the largest. The effects of landscape composition and landscape configuration on SOC were further decomposed by Variance Partitioning Analysis, and we found that independent interpretation ability of landscape configuration (8%) exceeded landscape composition (7%). The result of soil mapping combined with landscape indexes also showed that landscape configuration contributed more to the increased accuracy. Moreover, we found that correlation between configuration indexes and SOC at the class level was less related than that at the landscape level, among which the two most important indexes were Mean Fractal Dimension Index (FRAC_MN) and Number of Patches (NP). FRAC_MN was even more important than natural factors, indicating the validity of landscape as an indicator of human activities should not be ignored when considering farmland SOC. Overall, the results of this study revealed that the negative effects of agricultural intensification on SOC can be buffered to a certain extent by increasing the complexity of patch shape and reducing the degree of landscape fragmentation at the landscape level, providing hope for the sustainable development in intensive agricultural areas. In addition, due to the scale effect of landscape heterogeneity on farmland SOC, we suggest that decision makers should consider the spatial scale in landscape allocation and planning. This study provides a scientific reference for realizing the balance between grain production and ecological function in intensive agricultural areas.

Spatially Explicit Analysis of Landscape Structures, Urban Growth, and Economic Dynamics in Metropolitan Regions

Assuming that settlement morphologies and landscape structures are the result of economic transformations, the present study illustrates a statistical framework investigating metropolitan growth due to the inherent changes in landscape configurations vis à vis socio-demographic functions. Focusing on the evolution of their spatial drivers over time, metropolitan development was studied by adopting land parcels (or ‘patches’, as they are referred to in the ecological literature) as the elementary analysis unit—with the individual surface area and a specific shape indicator as the dependent variables and background socioeconomic attributes as predictors of landscape change over time. We specifically ran a Multiscale Geographically Weighted Regression (MGWR) testing the spatial dependence of the size and shape of landscape parcels on a vast ensemble of socioeconomic factors in a dense region (metropolitan Athens, Greece) with natural landscapes exposed to increasing human pressure. To investigate the spatial direction and intensity of the settlement expansion and landscape change, local regressions using the parcel area and fractal index (perimeter-to-area ratio) as the dependent variables and the elevation, distance from selected economic nodes, transport infrastructures, and natural amenities as the predictors were run separately for 1990 and 2018, representative of, respectively, a mono-centric configuration and a moderately polycentric organization of economic spaces. In a strictly mono-centric setting (1990), the parcel size showed a linear dependence on the distance from business districts, elevation, and wealth. Changes in the relationship between the parcel size and spatial (economic and non-economic) drivers may suggest a latent process of settlement de-concentration, and a possible shift toward polycentric development (2018), as documented in earlier studies. By integrating socioeconomic and ecological dimensions of landscape analysis and land evaluation, the empirical results of this study outline the increased complexity of dispersed landscape structures within dense metropolitan regions and along urban–rural gradients in Europe.

Unveiling the threshold in forest patch shapes to soil retention ecosystem services

Soil erosion is a critical process that leads to landscape degradation, compromising soil fertility and ecosystem functions. Forest ecosystems, with their intricate characteristics, play a pivotal role in mitigating soil erosion and providing soil retention ecosystem services (SRES). This study explores the impact of forest patch thresholds and critical points on soil erosion rates, focusing on 401 catchments in Poland using generalised additive models to identify thresholds and critical points in forest patches.Landscape metrics were applied to measure landscape structure, including shape, fractal dimension, contiguity, related circumscribing circles, and perimeter-area ratio indexes. These metrics, along with slope, rainfall, organic carbon content, water content, and clay ratio variables, were considered dependent variables in the models. The developed models have demonstrated reliable performance in estimating soil erosion rates, with a significant deviation explained from 80.5 to 81.1 for coniferous forest patches, 79.1 to 80.1 for broad-leave forest patches, and 80.9 to 81.4 for mixed forest patches at p < 0.05.In broad-leaved forests, three thresholds are identified in the shape index, which influence soil erosion rates in a complex manner. For coniferous forests, thresholds in the perimeter area ratio, related circumscribing circles, and contiguity indexes exhibit nonlinear relationships with soil erosion rates. Mixed forests show two thresholds in the related circumscribing circle and one in the fractal dimension index, affecting soil erosion rates differently.This research contributes significantly to understanding the interplay between forest patch shapes and soil erosion rates, providing decision support for land use planning. The identified thresholds and critical points offer valuable tools to enhance sustainable landscape functionality, emphasizing the importance of considering forest landscape structure in preserving soil retention ecosystem services.

Scale effect of landscape characteristics on undergrowth vegetation variance with different ecological traits

Herbaceous understory vegetation plays a significant role in temperate forested ecosystems, with its diversity strongly dependent on both local and landscape conditions. However, the contribution of these factors across different spatial scales (e.g., scale effect) remains inadequately understood. The objective of this study was to determine the most important landscape and local characteristics influencing the species richness of the herb layer. We surveyed and sampled 53 sites in a mountainous forest within the Baihuashan National Nature Reserve of Beijing. Using generalized linear models, we investigated the simultaneous effect of local (e.g. tree density, average tree height, and cover of tree, shrub, and ground vegetation) and landscape (e.g. Area-weighted Mean Patch Size, Area-weighted Mean Euclidean Nearest Neighbor Distance, Area-weighted Mean Fractal Dimension Index, forest area, and shrubbery area) variables on the richness of species in the understory herb layer. Variation partitioning was used to examine the individual contribution of local and landscape variables. Our results identified 366 plant species from 95 families across 53 sampling sites. Significant differences in species richness were found among life forms, seed dispersal types, and habitat preferences (P < 0.001). Parsimonious models indicated that combining local and landscape factors at a 2 km scale explained the most variation in phanerophytes (R2 = 0.658). Locally, average tree height significantly influenced the species richness of biotic dispersal, phanerophytes, and geophytes. At the landscape level, variables such as the Area-weighted Mean Fractal Dimension Index and farmland area significantly impacted plant community traits across different scales. Understanding these effects is crucial for developing effective sustainable forest ecosystem management strategies and for establishing robust ecological conservation policies.

FDI: A MATLAB tool for computing the fractal dimension index of sources reconstructed from EEG data

BackgroundThe fractal dimension (FD) is a valuable tool for analysing the complexity of neural structures and functions in the human brain. To assess the spatiotemporal complexity of brain activations derived from electroencephalogram (EEG) signals, the fractal dimension index (FDI) was developed. This measure integrates two distinct complexity metrics: 1) integration FD, which calculates the FD of the spatiotemporal coordinates of all significantly active EEG sources (4DFD); and 2) differentiation FD, determined by the complexity of the temporal evolution of the spatial distribution of cortical activations (3DFD), estimated via the Higuchi FD [HFD(3DFD)]. The final FDI value is the product of these two measurements: 4DFD × HFD(3DFD). Although FDI has shown utility in various research on neurological and neurodegenerative disorders, existing literature lacks standardized implementation methods and accessible coding resources, limiting wider adoption within the field. MethodsWe introduce an open-source MATLAB software named FDI for measuring FDI values in EEG datasets. ResultsBy using CUDA for leveraging the GPU massive parallelism to optimize performance, our software facilitates efficient processing of large-scale EEG data while ensuring compatibility with pre-processed data from widely used tools such as Brainstorm and EEGLab. Additionally, we illustrate the applicability of FDI by demonstrating its usage in two neuroimaging studies. Access to the MATLAB source code and a precompiled executable for Windows system is provided freely. ConclusionsWith these resources, neuroscientists can readily apply FDI to investigate cortical activity complexity within their own studies.

Evaluation of forest loss data using fractal algorithms: case study Eastern Carpathians–Romania

Logging causes the fragmentation of areas with direct implications for hydrological processes, landslides, or habitats. The assessment of this fragmentation process plays an important role in the planning of future logging, reconstruction, and protection measures for the whole ecosystem. The methodology used includes imaging techniques applying two fractal indices: the Fractal Fragmentation Index (FFI) and the Fractal Fragmentation and Disorder Index (FFDI). The results showed the annual evolution and disposition of deforested areas. Only 3% of deforestation resulted in the fragmentation and splitting of forest plots. The remaining 97% resulted in the reduction of existing compact stands without fragmentation. The method has many advantages in quantifying the spatial evolution of forests, estimating the capture of carbon emissions and establishing sustainability of bird and animal habitats. The analysis took place in the Eastern Carpathians, in Romania, in the time period of 2001–2022.

Spatiotemporal Dynamics of Constructed Wetland Landscape Patterns during Rapid Urbanization in Chengdu, China

The degradation of urban ecology, particularly in metropolitan areas distinguished by dense populations and impervious surfaces, presents a worldwide challenge linked to swift urban expansion. Despite extensive documentation of urbanization’s impact on broad regions or specific urban ecosystems over defined time periods, there remains a scarcity of studies investigating the spatiotemporal dynamics of landscape pattern (LP) changes in specific ecosystems at small-to-medium scales within inland megacities as a response to urbanization. Therefore, this work focused on the Bailuwan Wetland Park (BWP) in Chengdu, an inland megacity in southwestern China. Employing satellite imagery data from selected years spanning the previous decade (2010–2021, encompassing 2010, 2012, 2015, 2018, and 2021), this investigation delved into the influences of urbanization on the LP over various time-frames and across different land use/land cover (LULC) types. Our study revealed that urbanization has a significant impact on the patch-/landscape-level characteristics, including the class area (CA), number of patches (NP), patch density (PD), percentage of landscape (PLAND), aggregation index (AI), contagion index (CONTAG), largest patch index (LPI), landscape shape index (LSI), fractal dimension index (FRAC_MN), Shannon’s diversity (SHDI), and evenness index (SHEI). Over the period from 2010 to 2021, NP and PD experienced notable increases, while landscape shape (LSI/FRAC_MN) exhibited greater complexity and fragmentation (PLAND) intensified. Further, landscape heterogeneity (AI/CONTAG) and diversity (SHDI/SHEI) decreased. Particularly significant was the conversion of 52 ha of agricultural land to vegetation, resulting in heightened complexity and fragmentation in vegetation patterns. Additionally, the CA of lakes and rivers decreased following the establishment of the park, while the CA and NP of bare land presented significant increases. These findings suggest that rapid urbanization significantly influences the spatial–temporal dynamics of wetland landscape patterns. Consequently, it is imperative for society to prioritize the restoration and protection of urban constructed wetlands.

Characterization of rutting damage based on two-dimensional image analysis of changes in mesoscopic aggregate properties of asphalt mixtures

Accurately predicting the rutting development law of asphalt pavement is of great significance for preventing and controlling pavement diseases. The aggregate skeleton of the asphalt mixture is the main load-bearing part and plays an important role in its anti-rutting performance. However, quantitative and mesoscopic evaluation indicators and standards for aggregate skeletons have not been established. This study aims to reveal the relationship between the mesostructured characteristics of asphalt mixtures and rutting damage. This paper uses two-dimensional image technology to analyze the dynamic change process of internal skeleton information of two graded asphalt mixtures under cyclic wheel load. According to the fractal theory, the fractal dimension and multifractal spectrum of the full-depth aggregate were calculated. The results indicate that the linear regression model between the mesoscopic skeleton information of asphalt mixture and the average rutting depth during the rutting test can be used to quantify the rutting performance. There is an obvious correlation between the fractal dimension of the section aggregate and the loading times, and there is a certain linear relationship between the multifractal spectrum indexes and the loading times. It indicates that the fractal theory index of aggregate can reflect the change of the macro performance of loading times.

Gait variability, fractal dynamics, and statistical regularity of treadmill and overground walking recorded with a smartphone

BackgroundThe nonlinear variability present during steady-state gait may provide a signature of health and showcase one’s walking adaptability. Although treadmills can capture vast amounts of walking data required for estimating variability within a small space, gait patterns may be misrepresented compared to an overground setting. Smartphones may provide a low-cost and user-friendly estimate of gait patterns among a variety of walking settings. However, no study has investigated differences in gait patterns derived from a smartphone between treadmill walking (TW) and overground walking (OW). Research questionThis study implemented a smartphone accelerometer to compare differences in temporal gait variability and gait dynamics between TW and OW. MethodsSixteen healthy adults (8F; 24.7 ± 3.8 years) visited the laboratory on three separate days and completed three 8-minute OW and three TW trials, at their preferred speed, during each visit. The inter-stride interval was calculated as the time difference between right heel contact events located within the vertical accelerometery signals recorded from a smartphone while placed in participants front right pant pocket during walking trials. The inter-stride interval series was used to calculate stride time standard deviation (SD) and coefficient of variation (COV), statistical persistence (fractal scaling index), and statistical regularity (sample entropy). Two-way analysis of variance compared walking condition and laboratory visits for each measure. ResultsCompared to TW, OW displayed significantly (p < 0.01) greater stride time SD (0.014 s, 0.020 s), COV (1.26 %, 1.82 %), fractal scaling index (0.70, 0.79) and sample entropy (1.43, 1.63). No differences were found between visits for all measures. SignificanceSmartphone-based assessment of gait provides the ability to distinguish between OW and TW conditions, similar to previously established methodologies. Furthermore, smartphones may be a low-cost and user-friendly tool to estimate gait patterns outside the laboratory to improve ecological validity, with implications for free-living monitoring of gait among various populations.

Evaluation of the optimal number of steps to obtain reliable running spatio-temporal parameters and their variability

BackgroundSpatio-temporal running parameters and their variability help to determine a runner's running style. However, determining whether a change is due to the measurement or to a specific condition such as an injury is a matter of debate, as no recommendation on the number of steps required to obtain reliable assessments exists. Research questionWhat is the optimal number of steps required to measure different spatio-temporal parameters and study their variability at different running speeds? MethodsTwenty-five runners performed three experimental sessions of three bouts of treadmill running at 8, 10 and 12 km/h separated by 24 h. We measured cadence, stride, step, contact and flight time. We calculated the duty factor and the leg stiffness index (Kleg). Mean spatio-temporal parameters and linear (coefficient of variation, standard deviation) and non-linear (Higuchi fractal index, α1 coefficient of detrended fluctuation analysis) analyses were computed for different numbers of steps. Relative reliability was determined using the intraclass coefficient correlation. The minimal number of steps which present a good reliability level was considered as the optimal number of steps for measurement. Absolute reliability was assessed by calculating minimal detectable change. ResultsTo assess the mean values of spatio-temporal running parameters, between 16 and 150 steps were required. We were unable to obtain an optimal number of steps for cadence, stride and step-time variabilities for all speeds. For the linear analyses, we deduced the optimal number of steps for Kleg and the contact time (around 350 steps). Non-linear analyses measurements required between 350 and 540 steps, depending on the parameter. SignificanceResearchers and clinicians should optimize experimental conditions (number of steps and running speed) depending on the parameter or the variability analysis targeted. Future studies must use absolute reliability metrics to report changes in response to a specific condition with no bias due to measurement error.

Dynamics of neuronal firing modulated by high-frequency electrical pulse stimulations at axons in rat hippocampus

Objective. The development of electrical pulse stimulations in brain, including deep brain stimulation, is promising for treating various brain diseases. However, the mechanisms of brain stimulations are not yet fully understood. Previous studies have shown that the commonly used high-frequency stimulation (HFS) can increase the firing of neurons and modulate the pattern of neuronal firing. Because the generation of neuronal firing in brain is a nonlinear process, investigating the characteristics of nonlinear dynamics induced by HFS could be helpful to reveal more mechanisms of brain stimulations. The aim of present study is to investigate the fractal properties in the neuronal firing generated by HFS. Approach. HFS pulse sequences with a constant frequency 100 Hz were applied in the afferent fiber tracts of rat hippocampal CA1 region. Unit spikes of both the pyramidal cells and the interneurons in the downstream area of stimulations were recorded. Two fractal indexes—the Fano factor and Hurst exponent were calculated to evaluate the changes of long-range temporal correlations (LRTCs), a typical characteristic of fractal process, in spike sequences of neuronal firing. Main results. Neuronal firing at both baseline and during HFS exhibited LRTCs over multiple time scales. In addition, the LRTCs significantly increased during HFS, which was confirmed by simulation data of both randomly shuffled sequences and surrogate sequences. Conclusion. The purely periodic stimulation of HFS pulses, a non-fractal process without LRTCs, can increase rather than decrease the LRTCs in neuronal firing. Significance. The finding provides new nonlinear mechanisms of brain stimulation and suggests that LRTCs could be a new biomarker to evaluate the nonlinear effects of HFS.

FRACTAL ANALYSIS OF BRANCHING OF HUMAN CEREBELLAR ARTERIES

Human cerebellum is supplied by three arteries: the superior surface is nourished by the superior cerebellar artery (SCA), while the inferior surface is supplied by the anterior inferior cerebellar artery (AICA) and the posterior inferior cerebellar artery (PICA). Traditionally, the branching pattern of the superfi cial vascular network is subjectively assessed, distinguishing between the trunk, lose or mixed types. Fractal analysis is an objective alternative method.The aim of this study is to investigate the fractal dimension of branching complexity of superfi cial arteries in the human cerebellum and to establish the relationship between the magnitude of the fractal index and the shape of the cerebellum.Material and Methods. A total of 100 cerebellum samples, including the brainstem, were examined. The width, length, and height of the cerebellum were measured. Parameters of cerebellar shape, namely relative width (rW), relative length (rL), and relative height (rH), were determined as the ratios of the square of one linear dimension to the product of the other two. For fractal analysis, 15 cerebellar samples of various shapes (9 from male and 6 from female individuals) were selected. Fractal analysis of digital images of the superior and inferior surfaces of the cerebellum was performed bilaterally using the box-counting method.Results. The range of fractal index values was determined, and intervals corresponding to the mixed (1.54-1.73), trunk (&lt;1.54) and loose (&gt;1.73) branching types were identifi ed. The superior surface predominantly exhibited trunk or mixed branching types, whereas the inferior surface was more characteristic of mixed or loose branching types. The greatest diversity of arterial branching patterns – from the trunk to lose type – is observed in the most numerous group – cerebella of proportional shape, regardless of which shape parameter is analyzed. The branching pattern of superfi cial cerebellar arteries tends towards a loose type in relatively narrow and relatively short cerebella, and conversely towards a trunk type in relatively wide and relatively long cerebella. Conversely, relative height has an opposite eff ect: the branching pattern of superfi cial cerebellar arteries tends towards a loose type as the relative height of the cerebellum increases. Thus, relatively low cerebella typically exhibit a trunk branching pattern (more noticeable on the superior surface), while in relatively high cerebella, the branching pattern tends towards loose (more noticeable on the inferior surface).

Multifractal characterization and recognition of animal behavior based on deep wavelet transform

The study conduct an in-depth exploration of the multifractal characteristics of dairy cows behavioral data, aiming to reveal their complexity and representation in behavioral patterns. By means of Multifractal Detrended Fluctuation Analysis (MFDFA) in conjunction with deep wavelet transform, we extract multifractal indices that precisely depict the differences and dynamic changes of cows behavior. Further, we delves into the potential correlations between these multifractal features and the physiological states of dairy cattle, particularly focusing on their potential applications in predicting different physiological conditions. And an assessment model is developed based on these fractal indices and utilize advanced machine learning techniques to evaluate their effectiveness and accuracy in predicting the physiological states of dairy cattle. This study not only unveils the multifractal properties of cattle behavior but also demonstrates how these features can be utilized to predict significant physiological states, providing new scientific bases and methods for dairy cattle health management.