The transverse relaxation time (T_(2)) cut-off value plays a crucial role in nuclear magnetic resonance for identifying movable and immovable boundaries, evaluating permeability, and determining fluid saturation in pe...The transverse relaxation time (T_(2)) cut-off value plays a crucial role in nuclear magnetic resonance for identifying movable and immovable boundaries, evaluating permeability, and determining fluid saturation in petrophysical characterization of petroleum reservoirs. This study focuses on the systematic analysis of T_(2) spectra and T_(2) cut-off values in low-permeability reservoir rocks. Analysis of 36 low-permeability cores revealed a wide distribution of T_(2) cut-off values, ranging from 7 to 50 ms. Additionally, the T_(2) spectra exhibited multimodal characteristics, predominantly displaying unimodal and bimodal morphologies, with a few trimodal morphologies, which are inherently influenced by different pore types. Fractal characteristics of pore structure in fully water-saturated cores were captured through the T_(2) spectra, which were calculated using generalized fractal and multifractal theories. To augment the limited dataset of 36 cores, the synthetic minority oversampling technique was employed. Models for evaluating the T_(2) cut-off value were separately developed based on the classified T_(2) spectra, considering the number of peaks, and utilizing generalized fractal dimensions at the weight <0 and the singular intensity range. The underlying mechanism is that the singular intensity and generalized fractal dimensions at the weight <0 can detect the T_(2) spectral shift. However, the T_(2) spectral shift has negligible effects on multifractal spectrum function difference and generalized fractal dimensions at the weight >0. The primary objective of this work is to gain insights into the relationship between the kurtosis of the T_(2) spectrum and pore types, as well as to predict the T_(2) cut-off value of low-permeability rocks using machine learning and data augmentation techniques.展开更多
Traditional microstructure scale parameters have difficulty describing the structure and distribution of a roughmaterial’s surface morphology comprehensively and quantitatively. This study constructs hydrophilic and ...Traditional microstructure scale parameters have difficulty describing the structure and distribution of a roughmaterial’s surface morphology comprehensively and quantitatively. This study constructs hydrophilic and underwateroleophobic surfaces based on polyvinylidene fluoride (PVDF) using a chemical modification method, and the fractaldimension and multifractal spectrum are used to quantitatively characterize the microscopic morphology. A new contactangle prediction model for underwater oleophobic surfaces is established. The results show that the fractal dimension ofthe PVDF surface first increases and then decreases with the reaction time. The uniformity characterized by the multifractalspectrum was generally consistent with scanning electron microscope observations. The contact angle of water droplets onthe PVDF surface is negatively correlated with the fractal dimension, and oil droplets in water are positively correlated.When the fractal dimension is 2.0975, the new contact angle prediction model has higher prediction accuracy. Themaximum and minimum relative deviations of the contact angle between the theoretical and measured data are 18.20%and 0.72%, respectively. For water ring transportation, the larger the fractal dimension and spectral width of the materialsurface, the smaller the absolute value of the spectral difference, the stronger the hydrophilic and oleophobic properties, andthe better the water ring transportation stability.展开更多
We performed a multifractal analysis using wavelet transform to detect the changes in the fractality of the USD/JPY and EUR/JPY exchange rates, and predicted their extreme values using extreme value theory. After the ...We performed a multifractal analysis using wavelet transform to detect the changes in the fractality of the USD/JPY and EUR/JPY exchange rates, and predicted their extreme values using extreme value theory. After the 1997 Asian financial crisis, the USD/JPY and EUR/JPY became multifractal, then the USD/JPY became monofractal and stable, and yen depreciation was observed. However, the EUR/JPY became multifractal and unstable, and a strong yen depreciation was observed. The coherence between the USD/JPY and EUR/JPY was strong between 1995 and 2000. After the 2007-2008 financial crisis, the USD/JPY became monofractal and stable, and yen appreciation was observed. However, the EUR/JPY became multifractal and unstable, and strong yen appreciation was observed. Various diagnostic plots for assessing the accuracy of the GP model fitted to USD/JPY and EUR/JPY are shown, and all the diagnostic plots support the fitted GP model. The shape parameters of USD/JPY and EUR/JPY were close to zero, therefore the USD/JPY and EUR/JPY did not have finite upper limits. We predicted the maximum return level for the return periods of 10, 20, 50, 100, 350, and 500 years and their respective 95% confidence intervals (CI). As a result, the 10-year and 100-year return levels for USD/JPY were estimated to be 149.6 and 164.8, with 95% CI [143.2, 156.0] and [149.4, 180.1], respectively.展开更多
Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar patter...Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation.展开更多
Spatially superimposed multiple processes such as multiplicative cascade processes often generate multifractal measures possessing so-called self-similarity or self-affinity that can be described by power- law type of...Spatially superimposed multiple processes such as multiplicative cascade processes often generate multifractal measures possessing so-called self-similarity or self-affinity that can be described by power- law type of functions within certain scale ranges The multifractalities can be estimated by applying multifractal modeling to the measures reflecting the characteristics of the physical processes such as the element concentration values analyzed in rock and soil samples and caused by the underlying mineralization processes and the other geological processes. The local and regional geological processes may result in geochemical patterns with distinct multifractalities as wall as variable scaling ranges. Separation of these multifractal measures on the basis of both the distinct multifractalities and the scaling ranges will be significant for both theoretical studies of multifractal modeling and its applications. Multifractal scaling breaks have been observed from various multifractal patterns. This paper introduces a technique for separating multifractal measures on the basis of scaling breaks. It has been demonstrated that the method is effective for decomposing geochemical and geophysical anomalies required for mineral exploration. A dataset containing the element concentration values of potassium and phosphorus in soil samples was employed for demonstrating the application of the method for studying the fertilizer and yield optimization in展开更多
The Cantor’s dust theory is applied to investigate the scaling properties of the spatial distribution of natural fractures obtained from detailed scanline surveys of 27 field sites in the Appalachian Plateau of weste...The Cantor’s dust theory is applied to investigate the scaling properties of the spatial distribution of natural fractures obtained from detailed scanline surveys of 27 field sites in the Appalachian Plateau of western New York, USA. The results obtained in this study indicate: 1) fracture spacing is characterized by fractal and multifractal properties. On small scales analyses yield an average fractal dimension of 0.15, which suggests a very high degree of clustering. In contrast, on large scales, fractures tend to be more regular and evenly distributed with an average fracture dimension of 0.52; 2) fractal dimension varies with different sets in different orientations, which can be attributed to interactions between pre-existing fractures and younger ones, as well as variations of the intensity of the stresses under which the fractures were formed; 3) a time sequence of fracture set formation can be proposed based on fractal and multifractal analyses, which consists of (from old to young): N-S, NW,展开更多
Based on the experiments of nitrogen gas adsorption(N_2 GA) and nuclear magnetic resonance(NMR),the multifractal characteristics of pore structures in shale and tight s andstone from the Chang 7 member of Trias sic Ya...Based on the experiments of nitrogen gas adsorption(N_2 GA) and nuclear magnetic resonance(NMR),the multifractal characteristics of pore structures in shale and tight s andstone from the Chang 7 member of Trias sic Yanchang Formation in Ordos Basin,NW China,are investigated.The multifractal spectra obtained from N2 GA and NMR are analyzed with pore throat structure parameters.The results show that the pore size distributions obtained from N2 GA and NMR are different,and the obtained multifractal characteristics vary from each other.The specific surface and total pore volume obtained by N2 GA experiment have correlations with multifractal characteristics.For the core samples with the similar specific surface,the value of the deviation of multifractal spectra Rd increases with the increase in the proportion of large pores.When the proportion of macropores is small,the Rd value will increase with the increase in specific surface.The multifractal characteristics of pore structures are influenced by specific surface area,average pore size and adsorption volume measured from N2 GA experiment.The multifractal characteristic parameters of tight sandstone measured from NMR spectra are larger than those of shale,which may be caused by the differences in pore size distribution and porosity of shale and tight sandstone.展开更多
Massive seamounts have been surveyed and documented in the last decades.However,the morphologies of seamounts are usually described in qualitative manners,yet few quantitative detections have been carried out.Here,bas...Massive seamounts have been surveyed and documented in the last decades.However,the morphologies of seamounts are usually described in qualitative manners,yet few quantitative detections have been carried out.Here,based on the high-re solution multi-beam bathymetric data,we report a recentlysurveyed guy ot on the Caroline Ridge in the West Pacific,and the large-scale volcanic structures and smallscale erosive-depositional landforms in the guyot area have been identified.The multifractal features of the guyot are characterized for the first time by applying multifractal detrended fluctuation analysis on the surveyed bathymetric data.The results indicate that the multifractal spectrum parameters of the seafloor have strong spatial dependency on the fluctuations of local landforms.Both small-and large-scale components contribute to the degree of asymmetry of the multifractal spectrum(B),while the fluctuations of B are mostly attributed to the changes in small-scale roughness.The maximum singularity strength(α0)correlates well with the roughness of large-scale landforms and likely reflects the large-scale topographic irregularity.Comparing to traditional roughness parameters or monofractal exponents,multifractal spectra are able to depict not only the multiscale characteristics of submarine landforms,but also the spatial variations of scaling behaviors.Although more comparative works are required for various seamounts,we hope this study,as a case of quantifying geomorphological characters and multiscale behaviors of seamounts,can encourage further studies on seamounts concerning geomorphological processes,ocean bottom circulations,and seamount ecosystems.展开更多
A recently developed method, on the bases of “multifractal spectrum” filters for mineral exploration, is introduced in this paper. The “multifractal spectrum” filters, a group of irregularly shaped filters that ar...A recently developed method, on the bases of “multifractal spectrum” filters for mineral exploration, is introduced in this paper. The “multifractal spectrum” filters, a group of irregularly shaped filters that are constructed on each processed datum, can be used to separate various types of geochemical and geophysical anomalies. The basic model, with an emphasis on the GIS based implementation and the application to the geochemical and geophysical data processing for mineral exploration in southern Nova Scotia, Canada, indicates its advantage in the separation of multiple anomalies from the background.展开更多
Characterizing soil particle-size distribution is a key measure towards soil property.The purpose of this study was to evaluate the multifractal characteristics of soil particle-size distribution among different land-...Characterizing soil particle-size distribution is a key measure towards soil property.The purpose of this study was to evaluate the multifractal characteristics of soil particle-size distribution among different land-use from a purple soil catchment and to generalize the spatial variation trend of multifractal parameters across the catchment.A total of 84 soil samples were collected from four kinds of land use patterns(dry land,orchard,paddy,and forest)in an agricultural catchment in the Three Gorges Reservoir Region,China.The multifractal analysis method was applied to quantitatively characterize the soil particle size distribution.Six soil particle size distribution(PSD)multifractal parameters(D(0),D(1),D(2),(35)a(q),(35)f[a(q)],α(0))were computed.Additionally,a geostatistical analysis was employed to reveal the spatial differentiation and map the spatial distribution of these parameters.Evident multifractal characteristics were found.The trend of generalized dimension spectrum of four land use patterns was basically consistent with the range of 0.8 to 2.0.However,orchard showed the largest monotonic decline,while the forest demonstrated the smallest decrease.D(0)of the four land use patterns were ranked as:dry land<orchard<forest<paddy,the order of D(1)was:dry land<paddy<orchard<forest,D(2)presented a rand-size relationship as dry land<forest<paddy<orchard.Furthermore,all land-use patterns presented asΔf[α(q)]<0.The rand-size relationship ofα(0)was same as D(0).The best-fitting model for D(0),D(1),D(2)andΔf[α(q)]was spherical model,forΔα(q)was gaussian model,and forα(0)was exponential model with structure variance ratio was 1.03%,49.83%,0.84%,1.48%,22.20%and 10.60%,respectively.The results showed that soil particles of each land use pattern were distributed unevenly.The multifractal parameters under different land use have significant differences,except forΔα(q).Differences in the composition of soil particles lead to differences in the multifractal properties even though they belong to the same soil texture.Farming behavior may refine particles and enhance the heterogeneity of soil particle distribution.Our results provide an effective reference for quantifying the impact of human activities on soil system in the Three Gorges Reservoir region.展开更多
Investigating the biological function of proteins is a key aspect of protein studies.Bioinformatic methods become important for studying the biological function of proteins.In this paper,we first give the chaos game r...Investigating the biological function of proteins is a key aspect of protein studies.Bioinformatic methods become important for studying the biological function of proteins.In this paper,we first give the chaos game representation (CGR) of randomly-linked functional protein sequences,then propose the use of the recurrent iterated function systems (RIFS) in fractal theory to simulate the measure based on their chaos game representations.This method helps to extract some features of functional protein sequences,and furthermore the biological functions of these proteins.Then multifractal analysis of the measures based on the CGRs of randomly-linked functional protein sequences are performed.We find that the CGRs have clear fractal patterns.The numerical results show that the RIFS can simulate the measure based on the CGR very well.The relative standard error and the estimated probability matrix in the RIFS do not depend on the order to link the functional protein sequences.The estimated probability matrices in the RIFS with different biological functions are evidently different.Hence the estimated probability matrices in the RIFS can be used to characterise the difference among linked functional protein sequences with different biological functions.From the values of the D q curves,one sees that these functional protein sequences are not completely random.The D q of all linked functional proteins studied are multifractal-like and sufficiently smooth for the C q (analogous to specific heat) curves to be meaningful.Furthermore,the D q curves of the measure μ based on their CGRs for different orders to link the functional protein sequences are almost identical if q ≥ 0.Finally,the C q curves of all linked functional proteins resemble a classical phase transition at a critical point.展开更多
As the scale and complexity have been increased in software systems, developers place more emphases on software engineering and system designs. Software architecture is evolved with update of softwares, and it plays a...As the scale and complexity have been increased in software systems, developers place more emphases on software engineering and system designs. Software architecture is evolved with update of softwares, and it plays a fundamental role in determining quality of software systems. Multifractal characteristics of software networks can reflect software quality. In this paper, we construct a software network from the dependencies between object classes, and gain a deep understanding of software through network analysis. To be specific, multifractal analysis of the software network is performed based on a modified box-covering algorithm that yields fewer boxes. We verify that software with different functions and dependencies is multifractal. Further, different versions of the software are compared to discover the evolution of the software architecture. The results show that the singularity of class dependencies decreases as the software is updated. This trend leads to a more specific division of functions between software modules. One of the visible advantages of our work is that it allows the characterization of software structures at the code level. The methodology and results of this paper provide new insights into the evaluation and design of large-scale software systems.展开更多
AIM: To characterize the human retinal vessel arborisation in normal and amblyopic eyes using multifractal geometry and lacunarity parameters.·METHODS: Multifractal analysis using a box counting algorithm was car...AIM: To characterize the human retinal vessel arborisation in normal and amblyopic eyes using multifractal geometry and lacunarity parameters.·METHODS: Multifractal analysis using a box counting algorithm was carried out for a set of 12 segmented and skeletonized human retinal images, corresponding to both normal(6 images) and amblyopia states of the retina(6 images).·RESULTS: It was found that the microvascular geometry of the human retina network represents geometrical multifractals, characterized through subsets of regions having different scaling properties that are not evident in the fractal analysis. Multifractal analysis of the amblyopia images(segmented and skeletonized versions)show a higher average of the generalized dimensions(D q) for q =0, 1, 2 indicating a higher degree of the treedimensional complexity associated with the human retinal microvasculature network whereas images of healthy subjects show a lower value of generalized dimensions indicating normal complexity of biostructure.On the other hand, the lacunarity analysis of the amblyopia images(segmented and skeletonized versions)show a lower average of the lacunarity parameter Λ than the corresponding values for normal images(segmented and skeletonized versions).·CONCLUSION: The multifractal and lacunarity analysis may be used as a non-invasive predictive complementary tool to distinguish amblyopic subjects from healthy subjects and hence this technique could be used for an early diagnosis of patients with amblyopia.展开更多
In this paper, authors study the properties of multifractal Hausdorff and packing measures for a class of self-affine sets and use them to study the multifractal properties of general Sierpinski carpet E, and they get...In this paper, authors study the properties of multifractal Hausdorff and packing measures for a class of self-affine sets and use them to study the multifractal properties of general Sierpinski carpet E, and they get that the multifractal Hausdorff and packing measure are mutual singular, when they are restricted on some subsets of E.展开更多
By using part of CTD data collected at 2°S, 155° E during the fall cruise of TOGA project in 1992, themultifractal characters of temperature finestructures are investigated. The absolute temperature gradient...By using part of CTD data collected at 2°S, 155° E during the fall cruise of TOGA project in 1992, themultifractal characters of temperature finestructures are investigated. The absolute temperature gradients are supposedto be multifractal and their moments are computed by conventional box-counting method. It is found that these moments have power dependence on the box size. This power dependence has two different scaling regimes, called Sregime and I-regime resistively, with different scaling exponents. This is consistent with the combined effects of internal waves and boxing. Accordingly, the generalized fractal dimensions (Renyi dimension) of temperature gradientsare derived. A nonlinear curve of the scaling exponents suggest a possible multifractal approach of the temperatureshear. In fact, both regimes can be approximated by Besicovitch- Cantor model, respectively, by suitably chosenmoduel parameters. A phenomenological model is developed on the basis of this two-regime mechanism. The model iscompared with field data and good agreement is achieved.展开更多
The open set condition is the weakest condition hitherto in multifractal de- composition on the recursive sets. This paper deals with certain recursive fractals which have no relevence to the separation condition and ...The open set condition is the weakest condition hitherto in multifractal de- composition on the recursive sets. This paper deals with certain recursive fractals which have no relevence to the separation condition and gives their multifractal decomposition.展开更多
Soil physical properties(SPP)are considered to be important indices that reflect soil structure,hydrological conditions and soil quality.It is of substantial interest to study the spatial distribution of SPP owing to ...Soil physical properties(SPP)are considered to be important indices that reflect soil structure,hydrological conditions and soil quality.It is of substantial interest to study the spatial distribution of SPP owing to the high spatial variability caused by land consolidation under various land restoration modes in excavated farmland in the loess hilly area of China.In our study,three land restoration modes were selected including natural restoration land(NR),alfalfa land(AL)and maize land(ML).Soil texture composition,including the contents of clay,silt and sand,field capacity(FC),saturated conductivity(Ks)and bulk density(BD)were determined using a multifractal analysis.SPP were found to possess variable characteristics,although land consolidation destroyed the soil structure and decreased the spatial autocorrelation.Furthermore,SPP varied with land restoration and could be illustrated by the multifractal parameters of D1,ΔD,ΔαandΔf in different modes of land restoration.Owing to multiple compaction from large machinery in the surface soil,soil particles were fine-grained and increased the spatial variability in soil texture composition under all the land restoration modes.Plough numbers and vegetative root characteristics had the most significant impacts on the improvement in SPP,which resulted in the best spatial distribution characteristics of SPP found in ML compared with those in AL and NR.In addition,compared with ML,Δαvalues of NR and AL were 4.9-and 3.0-fold that of FC,respectively,andΔαvalues of NR and AL were 2.3-and 1.5-fold higher than those of Ks,respectively.These results indicate that SPP can be rapidly improved by increasing plough numbers and planting vegetation types after land consolidation.Thus,we conclude that ML is an optimal land restoration mode that results in favorable conditions to rapidly improve SPP.展开更多
Let x∈(0,1)be a real number with continued fraction expansion[a_(1)(x),a_(2)(x),a_(3)(x),⋯].This paper is concerned with the multifractal spectrum of the convergence exponent of{a_(n)(x)}_(n≥1) defined by τ(x):=in...Let x∈(0,1)be a real number with continued fraction expansion[a_(1)(x),a_(2)(x),a_(3)(x),⋯].This paper is concerned with the multifractal spectrum of the convergence exponent of{a_(n)(x)}_(n≥1) defined by τ(x):=inf{s≥0:∑n≥1an^(-s)(x)<∞}.展开更多
AIM:To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina.METHODS:Fifty volunteers were enrolled in th...AIM:To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina.METHODS:Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca,Romania,between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images,corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms,applying the standard boxcounting method. Statistical analyses were performed using the Graph Pad In Stat software.RESULTS:The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions(D_q)for q=0,1,2,the width of the multifractal spectrum(Δα=α_(max)-α_(min))and the spectrum arms' heights difference(│Δf│)of the normal images were expressed as mean±standard deviation(SD):for segmented versions,D_0=1.7014±0.0057; D_1=1.6507±0.0058; D_2=1.5772±0.0059; Δα=0.92441±0.0085; │Δf│= 0.1453±0.0051; for skeletonised versions,D_0=1.6303±0.0051; D_1=1.6012±0.0059; D_2=1.5531± 0.0058; Δα=0.65032±0.0162; │Δf│= 0.0238±0.0161. The average of generalized dimensions(D_q)for q=0,1,2,the width of the multifractal spectrum(Δα)and the spectrum arms' heights difference(│Δf│)of the segmented versions was slightly greater than the skeletonised versions.CONCLUSION:The multifractal analysis of fundus photographs may be used as a quantitative parameter for the evaluation of the complex three-dimensional structure of the retinal microvasculature as a potential marker for early detection of topological changes associated with retinal diseases.展开更多
We introduce a novel approach to multifractal data in order to achieve transcended modeling and forecasting performances by extracting time series out of local Hurst exponent calculations at a specified scale.First,th...We introduce a novel approach to multifractal data in order to achieve transcended modeling and forecasting performances by extracting time series out of local Hurst exponent calculations at a specified scale.First,the long range and co-movement dependencies of the time series are scrutinized on time-frequency space using multiple wavelet coherence analysis.Then,the multifractal behaviors of the series are verified by multifractal de-trended fluctuation analysis and its local Hurst exponents are calculated.Additionally,root mean squares of residuals at the specified scale are procured from an intermediate step during local Hurst exponent calculations.These internally calculated series have been used to estimate the process with vector autoregressive fractionally integrated moving average(VARFIMA)model and forecasted accordingly.In our study,the daily prices of gold,silver and platinum are used for assessment.The results have shown that all metals do behave in phase movement on long term periods and possess multifractal features.Furthermore,the intermediate time series obtained during local Hurst exponent calculations still appertain the co-movement as well as multifractal characteristics of the raw data and may be successfully re-scaled,modeled and forecasted by using VARFIMA model.Conclusively,VARFIMA model have notably surpassed its univariate counterpart(ARFIMA)in all efficacious trials while re-emphasizing the importance of comovement procurement in modeling.Our study’s novelty lies in using a multifractal de-trended fluctuation analysis,along with multiple wavelet coherence analysis,for forecasting purposes to an extent not seen before.The results will be of particular significance to finance researchers and practitioners.展开更多
基金supported by National Natural Science Foundation of China(Nos.42002171,42172159)China Postdoctoral Science Foundation(Nos.2020TQ0299,2020M682520)Postdoctoral Innovation Science Foundation of Hubei Province of China.
文摘The transverse relaxation time (T_(2)) cut-off value plays a crucial role in nuclear magnetic resonance for identifying movable and immovable boundaries, evaluating permeability, and determining fluid saturation in petrophysical characterization of petroleum reservoirs. This study focuses on the systematic analysis of T_(2) spectra and T_(2) cut-off values in low-permeability reservoir rocks. Analysis of 36 low-permeability cores revealed a wide distribution of T_(2) cut-off values, ranging from 7 to 50 ms. Additionally, the T_(2) spectra exhibited multimodal characteristics, predominantly displaying unimodal and bimodal morphologies, with a few trimodal morphologies, which are inherently influenced by different pore types. Fractal characteristics of pore structure in fully water-saturated cores were captured through the T_(2) spectra, which were calculated using generalized fractal and multifractal theories. To augment the limited dataset of 36 cores, the synthetic minority oversampling technique was employed. Models for evaluating the T_(2) cut-off value were separately developed based on the classified T_(2) spectra, considering the number of peaks, and utilizing generalized fractal dimensions at the weight <0 and the singular intensity range. The underlying mechanism is that the singular intensity and generalized fractal dimensions at the weight <0 can detect the T_(2) spectral shift. However, the T_(2) spectral shift has negligible effects on multifractal spectrum function difference and generalized fractal dimensions at the weight >0. The primary objective of this work is to gain insights into the relationship between the kurtosis of the T_(2) spectrum and pore types, as well as to predict the T_(2) cut-off value of low-permeability rocks using machine learning and data augmentation techniques.
基金the Natural Science Basic Research Program of Shaanxi(Program No.2023-JC-YB-351)the Scientific Research Program Funded by the Shaanxi Provincial Education Department(Program No.20JS118)the Xi’an Shiyou University Graduate Innovation and Practice Ability Training Plan(YCS21212097,YCS21212092).
文摘Traditional microstructure scale parameters have difficulty describing the structure and distribution of a roughmaterial’s surface morphology comprehensively and quantitatively. This study constructs hydrophilic and underwateroleophobic surfaces based on polyvinylidene fluoride (PVDF) using a chemical modification method, and the fractaldimension and multifractal spectrum are used to quantitatively characterize the microscopic morphology. A new contactangle prediction model for underwater oleophobic surfaces is established. The results show that the fractal dimension ofthe PVDF surface first increases and then decreases with the reaction time. The uniformity characterized by the multifractalspectrum was generally consistent with scanning electron microscope observations. The contact angle of water droplets onthe PVDF surface is negatively correlated with the fractal dimension, and oil droplets in water are positively correlated.When the fractal dimension is 2.0975, the new contact angle prediction model has higher prediction accuracy. Themaximum and minimum relative deviations of the contact angle between the theoretical and measured data are 18.20%and 0.72%, respectively. For water ring transportation, the larger the fractal dimension and spectral width of the materialsurface, the smaller the absolute value of the spectral difference, the stronger the hydrophilic and oleophobic properties, andthe better the water ring transportation stability.
文摘We performed a multifractal analysis using wavelet transform to detect the changes in the fractality of the USD/JPY and EUR/JPY exchange rates, and predicted their extreme values using extreme value theory. After the 1997 Asian financial crisis, the USD/JPY and EUR/JPY became multifractal, then the USD/JPY became monofractal and stable, and yen depreciation was observed. However, the EUR/JPY became multifractal and unstable, and a strong yen depreciation was observed. The coherence between the USD/JPY and EUR/JPY was strong between 1995 and 2000. After the 2007-2008 financial crisis, the USD/JPY became monofractal and stable, and yen appreciation was observed. However, the EUR/JPY became multifractal and unstable, and strong yen appreciation was observed. Various diagnostic plots for assessing the accuracy of the GP model fitted to USD/JPY and EUR/JPY are shown, and all the diagnostic plots support the fitted GP model. The shape parameters of USD/JPY and EUR/JPY were close to zero, therefore the USD/JPY and EUR/JPY did not have finite upper limits. We predicted the maximum return level for the return periods of 10, 20, 50, 100, 350, and 500 years and their respective 95% confidence intervals (CI). As a result, the 10-year and 100-year return levels for USD/JPY were estimated to be 149.6 and 164.8, with 95% CI [143.2, 156.0] and [149.4, 180.1], respectively.
文摘Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation.
文摘Spatially superimposed multiple processes such as multiplicative cascade processes often generate multifractal measures possessing so-called self-similarity or self-affinity that can be described by power- law type of functions within certain scale ranges The multifractalities can be estimated by applying multifractal modeling to the measures reflecting the characteristics of the physical processes such as the element concentration values analyzed in rock and soil samples and caused by the underlying mineralization processes and the other geological processes. The local and regional geological processes may result in geochemical patterns with distinct multifractalities as wall as variable scaling ranges. Separation of these multifractal measures on the basis of both the distinct multifractalities and the scaling ranges will be significant for both theoretical studies of multifractal modeling and its applications. Multifractal scaling breaks have been observed from various multifractal patterns. This paper introduces a technique for separating multifractal measures on the basis of scaling breaks. It has been demonstrated that the method is effective for decomposing geochemical and geophysical anomalies required for mineral exploration. A dataset containing the element concentration values of potassium and phosphorus in soil samples was employed for demonstrating the application of the method for studying the fertilizer and yield optimization in
文摘The Cantor’s dust theory is applied to investigate the scaling properties of the spatial distribution of natural fractures obtained from detailed scanline surveys of 27 field sites in the Appalachian Plateau of western New York, USA. The results obtained in this study indicate: 1) fracture spacing is characterized by fractal and multifractal properties. On small scales analyses yield an average fractal dimension of 0.15, which suggests a very high degree of clustering. In contrast, on large scales, fractures tend to be more regular and evenly distributed with an average fracture dimension of 0.52; 2) fractal dimension varies with different sets in different orientations, which can be attributed to interactions between pre-existing fractures and younger ones, as well as variations of the intensity of the stresses under which the fractures were formed; 3) a time sequence of fracture set formation can be proposed based on fractal and multifractal analyses, which consists of (from old to young): N-S, NW,
基金supported by the National Natural Science Foundation of China(No.51874320)Scientific Research Foundation of China University of Petroleum,Beijing(No.2462017BJB11)。
文摘Based on the experiments of nitrogen gas adsorption(N_2 GA) and nuclear magnetic resonance(NMR),the multifractal characteristics of pore structures in shale and tight s andstone from the Chang 7 member of Trias sic Yanchang Formation in Ordos Basin,NW China,are investigated.The multifractal spectra obtained from N2 GA and NMR are analyzed with pore throat structure parameters.The results show that the pore size distributions obtained from N2 GA and NMR are different,and the obtained multifractal characteristics vary from each other.The specific surface and total pore volume obtained by N2 GA experiment have correlations with multifractal characteristics.For the core samples with the similar specific surface,the value of the deviation of multifractal spectra Rd increases with the increase in the proportion of large pores.When the proportion of macropores is small,the Rd value will increase with the increase in specific surface.The multifractal characteristics of pore structures are influenced by specific surface area,average pore size and adsorption volume measured from N2 GA experiment.The multifractal characteristic parameters of tight sandstone measured from NMR spectra are larger than those of shale,which may be caused by the differences in pore size distribution and porosity of shale and tight sandstone.
基金the Senior User Project of R/V Kexue(No.KEXUE2018G11)the Science and Technology Basic Resources Investigation Program ofChina(No.2017FY100801)the Open Fund of the Key Laboratoryof Marine Geology and Environment,Chinese Academy of Sciences(No.MGE2018KG02)。
文摘Massive seamounts have been surveyed and documented in the last decades.However,the morphologies of seamounts are usually described in qualitative manners,yet few quantitative detections have been carried out.Here,based on the high-re solution multi-beam bathymetric data,we report a recentlysurveyed guy ot on the Caroline Ridge in the West Pacific,and the large-scale volcanic structures and smallscale erosive-depositional landforms in the guyot area have been identified.The multifractal features of the guyot are characterized for the first time by applying multifractal detrended fluctuation analysis on the surveyed bathymetric data.The results indicate that the multifractal spectrum parameters of the seafloor have strong spatial dependency on the fluctuations of local landforms.Both small-and large-scale components contribute to the degree of asymmetry of the multifractal spectrum(B),while the fluctuations of B are mostly attributed to the changes in small-scale roughness.The maximum singularity strength(α0)correlates well with the roughness of large-scale landforms and likely reflects the large-scale topographic irregularity.Comparing to traditional roughness parameters or monofractal exponents,multifractal spectra are able to depict not only the multiscale characteristics of submarine landforms,but also the spatial variations of scaling behaviors.Although more comparative works are required for various seamounts,we hope this study,as a case of quantifying geomorphological characters and multiscale behaviors of seamounts,can encourage further studies on seamounts concerning geomorphological processes,ocean bottom circulations,and seamount ecosystems.
文摘A recently developed method, on the bases of “multifractal spectrum” filters for mineral exploration, is introduced in this paper. The “multifractal spectrum” filters, a group of irregularly shaped filters that are constructed on each processed datum, can be used to separate various types of geochemical and geophysical anomalies. The basic model, with an emphasis on the GIS based implementation and the application to the geochemical and geophysical data processing for mineral exploration in southern Nova Scotia, Canada, indicates its advantage in the separation of multiple anomalies from the background.
基金funded by the National Key R&D Program of China(2017YFD0800505)Chongqing Key R&D Project of Technology Innovation and Application(NO.cstc2018jscxmszd X0055)。
文摘Characterizing soil particle-size distribution is a key measure towards soil property.The purpose of this study was to evaluate the multifractal characteristics of soil particle-size distribution among different land-use from a purple soil catchment and to generalize the spatial variation trend of multifractal parameters across the catchment.A total of 84 soil samples were collected from four kinds of land use patterns(dry land,orchard,paddy,and forest)in an agricultural catchment in the Three Gorges Reservoir Region,China.The multifractal analysis method was applied to quantitatively characterize the soil particle size distribution.Six soil particle size distribution(PSD)multifractal parameters(D(0),D(1),D(2),(35)a(q),(35)f[a(q)],α(0))were computed.Additionally,a geostatistical analysis was employed to reveal the spatial differentiation and map the spatial distribution of these parameters.Evident multifractal characteristics were found.The trend of generalized dimension spectrum of four land use patterns was basically consistent with the range of 0.8 to 2.0.However,orchard showed the largest monotonic decline,while the forest demonstrated the smallest decrease.D(0)of the four land use patterns were ranked as:dry land<orchard<forest<paddy,the order of D(1)was:dry land<paddy<orchard<forest,D(2)presented a rand-size relationship as dry land<forest<paddy<orchard.Furthermore,all land-use patterns presented asΔf[α(q)]<0.The rand-size relationship ofα(0)was same as D(0).The best-fitting model for D(0),D(1),D(2)andΔf[α(q)]was spherical model,forΔα(q)was gaussian model,and forα(0)was exponential model with structure variance ratio was 1.03%,49.83%,0.84%,1.48%,22.20%and 10.60%,respectively.The results showed that soil particles of each land use pattern were distributed unevenly.The multifractal parameters under different land use have significant differences,except forΔα(q).Differences in the composition of soil particles lead to differences in the multifractal properties even though they belong to the same soil texture.Farming behavior may refine particles and enhance the heterogeneity of soil particle distribution.Our results provide an effective reference for quantifying the impact of human activities on soil system in the Three Gorges Reservoir region.
基金Project partially supported by the National Natural Science Foundation of China (Grant No.30570426)the Chinese Program for New Century Excellent Talents in University (Grant No.NCET-08-06867)+1 种基金Fok Ying Tung Education Foundation (Grant No.101004)Australian Research Council (Grant No.DP0559807)
文摘Investigating the biological function of proteins is a key aspect of protein studies.Bioinformatic methods become important for studying the biological function of proteins.In this paper,we first give the chaos game representation (CGR) of randomly-linked functional protein sequences,then propose the use of the recurrent iterated function systems (RIFS) in fractal theory to simulate the measure based on their chaos game representations.This method helps to extract some features of functional protein sequences,and furthermore the biological functions of these proteins.Then multifractal analysis of the measures based on the CGRs of randomly-linked functional protein sequences are performed.We find that the CGRs have clear fractal patterns.The numerical results show that the RIFS can simulate the measure based on the CGR very well.The relative standard error and the estimated probability matrix in the RIFS do not depend on the order to link the functional protein sequences.The estimated probability matrices in the RIFS with different biological functions are evidently different.Hence the estimated probability matrices in the RIFS can be used to characterise the difference among linked functional protein sequences with different biological functions.From the values of the D q curves,one sees that these functional protein sequences are not completely random.The D q of all linked functional proteins studied are multifractal-like and sufficiently smooth for the C q (analogous to specific heat) curves to be meaningful.Furthermore,the D q curves of the measure μ based on their CGRs for different orders to link the functional protein sequences are almost identical if q ≥ 0.Finally,the C q curves of all linked functional proteins resemble a classical phase transition at a critical point.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61877067 and 61572435)。
文摘As the scale and complexity have been increased in software systems, developers place more emphases on software engineering and system designs. Software architecture is evolved with update of softwares, and it plays a fundamental role in determining quality of software systems. Multifractal characteristics of software networks can reflect software quality. In this paper, we construct a software network from the dependencies between object classes, and gain a deep understanding of software through network analysis. To be specific, multifractal analysis of the software network is performed based on a modified box-covering algorithm that yields fewer boxes. We verify that software with different functions and dependencies is multifractal. Further, different versions of the software are compared to discover the evolution of the software architecture. The results show that the singularity of class dependencies decreases as the software is updated. This trend leads to a more specific division of functions between software modules. One of the visible advantages of our work is that it allows the characterization of software structures at the code level. The methodology and results of this paper provide new insights into the evaluation and design of large-scale software systems.
文摘AIM: To characterize the human retinal vessel arborisation in normal and amblyopic eyes using multifractal geometry and lacunarity parameters.·METHODS: Multifractal analysis using a box counting algorithm was carried out for a set of 12 segmented and skeletonized human retinal images, corresponding to both normal(6 images) and amblyopia states of the retina(6 images).·RESULTS: It was found that the microvascular geometry of the human retina network represents geometrical multifractals, characterized through subsets of regions having different scaling properties that are not evident in the fractal analysis. Multifractal analysis of the amblyopia images(segmented and skeletonized versions)show a higher average of the generalized dimensions(D q) for q =0, 1, 2 indicating a higher degree of the treedimensional complexity associated with the human retinal microvasculature network whereas images of healthy subjects show a lower value of generalized dimensions indicating normal complexity of biostructure.On the other hand, the lacunarity analysis of the amblyopia images(segmented and skeletonized versions)show a lower average of the lacunarity parameter Λ than the corresponding values for normal images(segmented and skeletonized versions).·CONCLUSION: The multifractal and lacunarity analysis may be used as a non-invasive predictive complementary tool to distinguish amblyopic subjects from healthy subjects and hence this technique could be used for an early diagnosis of patients with amblyopia.
基金the National Natural Sciences Foundation of China Special Funds of State Education Committee for Doctorate Scientific Resear
文摘In this paper, authors study the properties of multifractal Hausdorff and packing measures for a class of self-affine sets and use them to study the multifractal properties of general Sierpinski carpet E, and they get that the multifractal Hausdorff and packing measure are mutual singular, when they are restricted on some subsets of E.
文摘By using part of CTD data collected at 2°S, 155° E during the fall cruise of TOGA project in 1992, themultifractal characters of temperature finestructures are investigated. The absolute temperature gradients are supposedto be multifractal and their moments are computed by conventional box-counting method. It is found that these moments have power dependence on the box size. This power dependence has two different scaling regimes, called Sregime and I-regime resistively, with different scaling exponents. This is consistent with the combined effects of internal waves and boxing. Accordingly, the generalized fractal dimensions (Renyi dimension) of temperature gradientsare derived. A nonlinear curve of the scaling exponents suggest a possible multifractal approach of the temperatureshear. In fact, both regimes can be approximated by Besicovitch- Cantor model, respectively, by suitably chosenmoduel parameters. A phenomenological model is developed on the basis of this two-regime mechanism. The model iscompared with field data and good agreement is achieved.
文摘The open set condition is the weakest condition hitherto in multifractal de- composition on the recursive sets. This paper deals with certain recursive fractals which have no relevence to the separation condition and gives their multifractal decomposition.
基金The study was funded by the National Key Research and Development Program of China(2017YFD0800502)the National Natural Science Foundation of China(41671510).
文摘Soil physical properties(SPP)are considered to be important indices that reflect soil structure,hydrological conditions and soil quality.It is of substantial interest to study the spatial distribution of SPP owing to the high spatial variability caused by land consolidation under various land restoration modes in excavated farmland in the loess hilly area of China.In our study,three land restoration modes were selected including natural restoration land(NR),alfalfa land(AL)and maize land(ML).Soil texture composition,including the contents of clay,silt and sand,field capacity(FC),saturated conductivity(Ks)and bulk density(BD)were determined using a multifractal analysis.SPP were found to possess variable characteristics,although land consolidation destroyed the soil structure and decreased the spatial autocorrelation.Furthermore,SPP varied with land restoration and could be illustrated by the multifractal parameters of D1,ΔD,ΔαandΔf in different modes of land restoration.Owing to multiple compaction from large machinery in the surface soil,soil particles were fine-grained and increased the spatial variability in soil texture composition under all the land restoration modes.Plough numbers and vegetative root characteristics had the most significant impacts on the improvement in SPP,which resulted in the best spatial distribution characteristics of SPP found in ML compared with those in AL and NR.In addition,compared with ML,Δαvalues of NR and AL were 4.9-and 3.0-fold that of FC,respectively,andΔαvalues of NR and AL were 2.3-and 1.5-fold higher than those of Ks,respectively.These results indicate that SPP can be rapidly improved by increasing plough numbers and planting vegetation types after land consolidation.Thus,we conclude that ML is an optimal land restoration mode that results in favorable conditions to rapidly improve SPP.
基金This research was supported by National Natural Science Foundation of China(11771153,11801591,11971195,12171107)Guangdong Natural Science Foundation(2018B0303110005)+1 种基金Guangdong Basic and Applied Basic Research Foundation(2021A1515010056)Kunkun Song would like to thank China Scholarship Council(CSC)for financial support(201806270091).
文摘Let x∈(0,1)be a real number with continued fraction expansion[a_(1)(x),a_(2)(x),a_(3)(x),⋯].This paper is concerned with the multifractal spectrum of the convergence exponent of{a_(n)(x)}_(n≥1) defined by τ(x):=inf{s≥0:∑n≥1an^(-s)(x)<∞}.
基金the Program"Partnerships in priority domains"with the support of the National Education Ministry,the Executive Agency for Higher Education,Research,Development and Innovation Funding (UEFISCDI),Romania (Project code:PN-II-PT-PCCA-2013-4-1232)
文摘AIM:To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina.METHODS:Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca,Romania,between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images,corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms,applying the standard boxcounting method. Statistical analyses were performed using the Graph Pad In Stat software.RESULTS:The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions(D_q)for q=0,1,2,the width of the multifractal spectrum(Δα=α_(max)-α_(min))and the spectrum arms' heights difference(│Δf│)of the normal images were expressed as mean±standard deviation(SD):for segmented versions,D_0=1.7014±0.0057; D_1=1.6507±0.0058; D_2=1.5772±0.0059; Δα=0.92441±0.0085; │Δf│= 0.1453±0.0051; for skeletonised versions,D_0=1.6303±0.0051; D_1=1.6012±0.0059; D_2=1.5531± 0.0058; Δα=0.65032±0.0162; │Δf│= 0.0238±0.0161. The average of generalized dimensions(D_q)for q=0,1,2,the width of the multifractal spectrum(Δα)and the spectrum arms' heights difference(│Δf│)of the segmented versions was slightly greater than the skeletonised versions.CONCLUSION:The multifractal analysis of fundus photographs may be used as a quantitative parameter for the evaluation of the complex three-dimensional structure of the retinal microvasculature as a potential marker for early detection of topological changes associated with retinal diseases.
文摘We introduce a novel approach to multifractal data in order to achieve transcended modeling and forecasting performances by extracting time series out of local Hurst exponent calculations at a specified scale.First,the long range and co-movement dependencies of the time series are scrutinized on time-frequency space using multiple wavelet coherence analysis.Then,the multifractal behaviors of the series are verified by multifractal de-trended fluctuation analysis and its local Hurst exponents are calculated.Additionally,root mean squares of residuals at the specified scale are procured from an intermediate step during local Hurst exponent calculations.These internally calculated series have been used to estimate the process with vector autoregressive fractionally integrated moving average(VARFIMA)model and forecasted accordingly.In our study,the daily prices of gold,silver and platinum are used for assessment.The results have shown that all metals do behave in phase movement on long term periods and possess multifractal features.Furthermore,the intermediate time series obtained during local Hurst exponent calculations still appertain the co-movement as well as multifractal characteristics of the raw data and may be successfully re-scaled,modeled and forecasted by using VARFIMA model.Conclusively,VARFIMA model have notably surpassed its univariate counterpart(ARFIMA)in all efficacious trials while re-emphasizing the importance of comovement procurement in modeling.Our study’s novelty lies in using a multifractal de-trended fluctuation analysis,along with multiple wavelet coherence analysis,for forecasting purposes to an extent not seen before.The results will be of particular significance to finance researchers and practitioners.
