Multifractal Spectral Width Research Articles

Differentiation of task complexity in long-term memory retrieval using multifractal detrended fluctuation analysis of fNIRS recordings.

The retrieval of phonological, lexical, semantic, or syntactic language information from long-term memory plays an important role in language processing. However, it remains unclear whether variability analysis of brain signals obtained using functional near-infrared spectroscopy (fNIRS) is able to separate language-related task conditions. This study employed multifractal detrended fluctuation (MFDF) analysis focusing on the width of the multifractal spectrum to elucidate whether high complexity tasks increase the fractal dynamics of brain activation signals compared to low complexity tasks. Nine Japanese college students participated in a long-term memory retrieval experiment using low (n ± 1) and high (n ± 2) complexity tasks. Our results showed that high complexity tasks induced a significantly larger multifractal spectral width in the posterior medial temporal gyri bilaterally, due to higher cognitive demands. These findings suggest that in addition to conventional techniques based on mean amplitude analysis and general linear modelling of fNIRS data, the use of MFDF analysis offers a powerful alternative methodology to gain a deeper understanding of long-term memory retrieval in language memory processing.

Classification of two-phase flow patterns using multifractal analysis of pressure oscillations

The two-phase flow patterns (air–water) in horizontal square minichannel (3 × 3 mm) has been analysed. The multifractal analysis of pressure drop fluctuations was used for qualitative assessment of two-phase flow patterns. The results of the complexity analysis using the multifractal spectral width (Δh) are presented. The proposed method allows us to identify the following two-phase flow patterns: micro-bubbles flow, micro- and minibubbles flow, micro- and mini-bubbles with confined bubbles flow, slug flow, stratified flow. The obtained results confirm that this type of analysis can be considered as an alternative way of identification of two-phase flow patterns in the minichannel. The work also focuses on the discussion of the occurrence and identification of bubbles churns in slugs and churns.

Quantitative Evaluation of the Spatial Variation of Surface Soil Properties in a Typical Alluvial Plain of the Lower Yellow River Using Classical Statistics, Geostatistics and Single Fractal and Multifractal Methods

The spatial variability of soil properties has always been a significant research field in geoscience. The types of soil properties cover a wide range, but most studies have focused on the spatial variability of soil physicochemical properties over the past decades. Studies on soil hydraulic characteristics are limited, and most of them are limited to the farmland scale. However, the spatial variability of regional soil properties (soil texture and hydraulic properties) is valuable for the study of sedimentation processes and soil water transport. Therefore, here, the spatial variation of six soil properties (sand, silt, clay content, bulk density, saturated water content and saturated hydraulic conductivity) in the typical alluvial plain area of the lower Yellow River is quantitatively studied, by using classical statistics, geostatistics and single fractal and multifractal methods. This study mainly quantitatively analysed the spatial variability of different soil properties and compared four research methods. Although the coefficient of variation, nugget coefficient, single fractal dimension and multifractal spectral width can reflect spatial variability, diverse conclusions are drawn (on variability) if different methods are used, and the different soil properties show large disparities. These four methods show a different variation order of soil properties, but there are some common conclusions based on analysis and judgment. In general, the silt content in the study area is stable, mainly originating from loess transported by Yellow River erosion, which is also reflected in the Kriging interpolation maps under the geostatistical models. The variation in bulk density and saturated water content is weak, and the spatial variability of sand and clay content is moderate. In addition, the saturated hydraulic conductivity fluctuates violently. This may be related to the differences in local topography, human activity and the content of sand and clay, each of which significantly affects the saturated hydraulic conductivity. Classical statistics has a limitation because it fails to corelate with spatial location. Due to the small sample capacity and calculation error of lag distance, the accuracy of geostatistics and single fractal dimensions needs to be improved. Multifractal spectral analysis does not need to consider the normality of data and can quantitatively represent local characteristics; therefore, its results have high reliability.

Tagore and neuroscience: A non-linear multifractal study to encapsulate the evolution of Tagore songs over a century

The verses of Rabindranath Tagore have been sung by various artistes over generations spanning over almost 100 years. There are few songs which were popular in the early years and have been able to retain their popularity over the years while some others have faded away in the course of time. In this study we tried to find cues in the singing style of these songs, sung by different singers spanning over almost five generations, which have kept them alive for all these years. For this, we took 3 min clips of four Tagore songs which are being sung by atleast five generations of artistes over 100 years and analyzed the acoustic signals with the help of latest nonlinear technique Multifractal Detrended Fluctuation Analysis (MFDFA). Next EEG data was collected from 5 persons who listened to 30 sec clips of two Tagore songs sung over five generations of artistes in chronological order. The EEG response from the participants were analyzed with the help of the same MFDFA technique and the multifractal spectral width was considered as the parameter which can help in the identification of cognitive evolution of the Tagore songs. The multifractal spectral width is a manifestation of the inherent complexity of the signal and in future, may prove to be an important parameter to identify the singing style of a particular generation of singers and how this style varies over different generations. The EEG responses from the participants reflect how the perception and cognition of the same Tagore songs evolve over generations. The results and implications are discussed in detail.

PATTERN RECOGNITION OF MINE MICROSEISMIC AND BLASTING EVENTS BASED ON WAVE FRACTAL FEATURES

A microseismic (MS) monitoring system in a mine can monitor the MS signals generated by coal rock rupture and blasting waves and can distinguish the two types of waves more clearly to monitor and analyze the rupture and evolution process of coal rock. According to the nonlinearity characteristics of the waveform, the fractal characteristics of a mine’s MS and blasting waves are analyzed by simple fractal and multifractal theory, and the simple fractal dimension [Formula: see text] and multifractal parameters are obtained, respectively. Results show that the simple fractal dimension [Formula: see text] reflects the complexity and frequency structure of the wave. The simple fractal dimension [Formula: see text] of a blasting wave is larger than that of a mine MS wave, which indicates that the blasting wave is relatively complex with higher frequency, while the mine MS wave is relatively simple with lower frequency. However, the simple fractal dimension [Formula: see text] can only describe the wave integrity features, not the local features. The multifractal parameters can describe the local characteristics of the wave more finely, and the multifractal spectrum describes the probability information of the singularity exponent [Formula: see text]. The singularity exponential range and multifractal spectral width [Formula: see text] of the blasting wave are smaller than those of the mine MS wave, which indicates that the probability measure of distribution unevenness and the degree of partial parameter fluctuation of the blasting wave are more severe than those of the mine MS wave. Wave signal analysis based on simple fractal and multifractal methods can not only obtain the characteristics of the wave strength and spectral structure but also other important information, such as local singularity. Therefore, it is possible to more clearly and conspicuously identify mine MS and blasting waves, so that coal rock rupture can be monitored more accurately.

Multifractal Study of Three-Dimensional Pore Structure of Sand-Conglomerate Reservoir Based on CT Images

Sand-conglomerate reservoir has been scarcely studied, and there is no effective method available for quantitative characterization of pore structure of such a reservoir. In this paper, a multifractal study was made on the Triassic Karamay Formation sand-conglomerate reservoir in the Mahu rim region, the Junggar Basin, by using a variety of high-resolution analysis methods, such as Micro-CT, QEMSCAN, and MAPS, in order to quantitatively characterize the heterogeneity of pore size distribution, relative differentiation of large and small pores, and mineral composition. The results reveal that the multifractal parameters have more influence on permeability than on porosity. The smaller the Δα (the multifractal spectral width) and the larger the Δf (the difference in fractal dimension of the maximum and minimum probability subsets), the better the reservoir physical property. To some extent, the relationship between multifractal parameters and mineral composition provides an opportunity to reflect the diagen...

Universality and Domain Specificity of Emotion-A Quantitative Non Linear EEG Based Approach

Music has been present in human culture since time immemorial, some say music came even before speech. The effort to understand the wide variety of emotions evoked by music has started not long back. With the advent and rapid growth of various neurological bio-sensors we can now attempt to quantify various dimensions of emotional experience induced by music especially instrumental music – since it is free from any language barriers. In this study, we took eight (8) cross cultural instrumental clips originating mainly from Indian and Western music. A listening test comprising of 100 participants across the globe was conducted to associate each clip with its corresponding emotional valence. The participants were asked to mark each clip according to their perception of four basic emotions (joy/sorrow and anxiety/serenity) invoked by each instrumental clip. EEG study was then conducted on 10 participants to measure the response evoked by the same instrumental clips in the alpha and theta frequency regions. We took the help of latest non-linear multi-fractal analysis technique – MFDFA to estimate the change in multi-fractal spectral width (corresponding to alpha as well as theta waves) associated with each of the clips in frontal, temporal and occipital lobes. The response in the alpha domain reveals a hint in the direction of universality of music, while in theta domain we have culture specific response. Moreover, we tried to develop alpha as well as theta multi-fractal spectral width as a single parameter with which we can quantify the valence and arousal based effects corresponding to a particular musical clip. The results and implications are discussed in detail.

A study on Improvisation in a Musical performance using Multifractal Detrended Cross Correlation Analysis

Abstract MFDFA (the most rigorous technique to assess multifractality) was performed on four Hindustani music samples played on same ‘ raga ’ sung by the same performer. Each music sample was divided into six parts and ‘multifractal spectral width’ was determined for each part corresponding to the four samples. The results obtained reveal that different parts of all the four sound signals possess spectral width of widely varying values. This gives a cue of the so called ‘musical improvisation’ in all music samples, keeping in mind they belong to the bandish part of the same raga . Formal compositions in Hindustani raga are juxtaposed with the improvised portions, where an artist manoeuvers his/her own creativity to bring out a mood that is specific for that particular performance, which is known as ‘improvisation’. Further, this observation hints at the association of different emotions even in the same bandish of the same raga performed by the same artist, this interesting observation cannot be revealed unless rigorous non-linear technique explores the nature of musical structure. In the second part, we applied MFDXA technique to explore more in-depth about ‘improvisation’ and association with emotion. This technique is applied to find the degree of cross-correlation ( γ x ) between the different parts of the samples. Pronounced correlation has been observed in the middle parts of the all the four samples evident from higher values of γ x ​whereas the other parts show weak correlation. This gets further support from the values of spectral width from different parts of the sample — width of those parts is significantly different from other parts. This observation is extremely new both in respect of musical structure of so called improvisation and associated emotion. The importance of this study in application area of cognitive music therapy is immense.

Multifractal Detrended Fluctuation Analysis of alpha and theta EEG rhythms with musical stimuli

Electroencephalography (EEG) was performed on 10 participants using a simple acoustical stimuli i.e. a tanpura drone. The tanpura drone is free from any semantic content and is used with a hypothesis that it provides a specific resting environment for the listeners. The EEG data was extracted for all the frontal electrodes viz. F3, F4, F7, F8, Fp1, Fp2 and Fz. Empirical Mode Decomposition (EMD) was applied on the acquired raw EEG signal to make it free from blink as well as other muscular artifacts. Wavelet Transform (WT) technique was used to segregate alpha and theta waves from the denoised EEG signal. Non-linear analysis in the form of Multifractal Detrended Fluctuation Analysis (MFDFA) was carried out on the extracted alpha and theta time series data to study the variation of their complexity. It was found that in all the frontal electrodes alpha as well as theta complexity increases as is evident from the increase of multifractal spectral width. This study is entirely new and gives interesting data regarding neural activation of the alpha and theta brain rhythms while listening to simple acoustical stimuli. The importance of this study lies in the context of emotion quantification using multifractal spectral width as a parameter as well as in the field of cognitive music therapy. The results are discussed in detail.

Evaluation of breast cancer chemotherapy efficacy with multifractal spectrum analysis of magnetic resonance image

Multifractal spectrum analysis of dynamic contrast enhanced (DCE) breast MR images was used to establish a new quantitative analysis method for solid tumor blood perfusion and to explore its applicability in evaluating efficacy of breast cancer chemotherapy. Five randomly selected patients suffering from newly diagnosed malignant breast nodule lesions were enrolled in this study, and four of them were treated with neoadjuvant chemotherapy. Their DCE breast MR images were collected before and after treatment. Chemotherapeutic efficacy was analyzed using international response evaluation criteria for solid tumors (RECIST). Sandbox method for statistical number density was employed to measure and calculate multifractal spectra of DCE breast MR images with spatiotemporal characteristics. Multifractal spectral data of malignant lesions before and after chemotherapy were compared. Multifractal spectra of malignant lesions show an asymmetric bell-shape. Chemotherapy efficacy was assessed to be partial remission (PR) for three patients and their multifractal spectral width significantly increased after chemotherapy while to be stable disease (SD) for other patient and of her changed slightly. Multifractal spectral width correlates with blood-supply condition of tumor lesion before and after chemotherapy, providing a potential suitable characteristic parameter for evaluating chemotherapeutic efficacy quantitatively.

Multi-fractal Analysis for Pavement Roughness Evaluation

The paper employs multi-fractal theory to systematically research into appraising the road profile in order to overcome the shortages of the current used road roughness indices which cannot fine depict the characteristics of the road locally. The paper proves the road profile has the obvious multi-fractal characteristics. On this basis, multi-fractal spectrum and the parameters can be used in the research of the road profile. The results of road surface simulation results in each grades based on Fourier inverse transformation show there is no unique relation between multi-fractal spectral width and road roughness in different grades, while the vertical axis, intercept of the roads that have the same multi-fractal spectral width was different in Logarithmic distribution of measure and scale. Finally, the combination of multi-fractal spectral width and the IRI is proposed as supplement of current indices when necessary.