The current overview of the devices of temporary anchorage placed on the palatal bone: CBCT study.

Temporary anchorage devices (TADs) are frequently applied to different anatomic areas with different protocols to increase skeletal effects and anchorage in orthodontic treatment planning. It has been reported in many literatures that primary stability for orthodontic TADs is significant for long-term survival rate. For this reason, different areas of the palatal region, which has many indications, have been widely used in the studies. In this evaluation where bone quality and thickness are important, density, bone thickness, and fractal dimension (FD) on cone beam computed tomography (CBCT) will provide more predictable clinical results. The aim of this study was to evaluate bone thickness, density, and FD in the palatal region of the first, and second premolars, and first molars. There was a remarkable difference (p < 0.05) between the parameters of FD, thickness and density of bone in the identified areas in the palatal region. In terms of thickness and FD, the 1st premolar region had significantly higher values than the other regions (p < 0.05). In terms of density, the values in the right 1st molar and right 1st premolar regions were significantly higher (p < 0.05). The 1st premolar region is an ideal site for placement of palatal TADs. CBCT-assisted preliminary evaluation of FD value, bone density, and thickness may increase clinical success when selecting the location of TADs to be applied to the palatal bone.

Classifying breast cancer and fibroadenoma tissue biopsies from paraffined stain-free slides by fractal biomarkers in Fourier Ptychographic Microscopy.

Breast cancer is one of the most spread and monitored pathologies in high-income countries. After breast biopsy, histological tissue is stored in paraffin, sectioned and mounted. Conventional inspection of tissue slides under benchtop light microscopes involves paraffin removal and staining, typically with H&E. Then, expert pathologists are called to judge the stained slides. However, paraffin removal and staining are operator-dependent, time and resources consuming processes that can generate ambiguities due to non-uniform staining. Here we propose a novel method that can work directly on paraffined stain-free slides. We use Fourier Ptychography as a quantitative phase-contrast microscopy method, which allows accessing a very wide field of view (i.e., mm2) in one single image while guaranteeing high lateral resolution (i.e., 0.5 µm). This imaging method is multi-scale, since it enables looking at the big picture, i.e. the complex tissue structure and connections, with the possibility to zoom-in up to the single-cell level. To handle this informative image content, we introduce elements of fractal geometry as multi-scale analysis method. We show the effectiveness of fractal features in describing and classifying fibroadenoma and breast cancer tissue slides from ten patients with very high accuracy. We reach 94.0 ± 4.2% test accuracy in classifying single images. Above all, we show that combining the decisions of the single images, each patient's slide can be classified with no error. Besides, fractal geometry returns a guide map to help pathologist to judge the different tissue portions based on the likelihood these can be associated to a breast cancer or fibroadenoma biomarker. The proposed automatic method could significantly simplify the steps of tissue analysis and make it independent from the sample preparation, the skills of the lab operator and the pathologist.

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

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

A CONSTRAINED CONSTRUCTIVE OPTIMIZATION MODEL OF BRANCHING ARTERIOLAR NETWORKS IN RAT SKELETAL MUSCLE.

Blood flow regulation within the microvasculature reflects a complex interaction of regulatory mechanisms and varies spatially and temporally according to conditions such as metabolism, growth, injury, and disease. Understanding the role of microvascular flow distributions across conditions is of interest to investigators spanning multiple disciplines; however, data collection within networks can be labour-intensive and challenging due to limited resolution. To overcome these experimental challenges, computational network models which can accurately simulate vascular behavior are highly beneficial. Constrained Constructive Optimization (CCO) is a commonly used algorithm for vascular simulation, particularly well known for its adaptability towards vascular modelling across tissues. The present work demonstrates an implementation of CCO aimed to simulate a branching arteriolar microvasculature in healthy skeletal muscle, validated against literature including comprehensive rat gluteus maximus vasculature datasets, and reviews a list of user-specified adjustable model parameters to understand how their variability affects the simulated networks. Network geometric properties, including mean element diameters, lengths, and numbers of bifurcations per order, Horton's Law ratios, and fractal dimension, demonstrate good validation once model parameters are adjusted to experimental data. This model successfully demonstrates hemodynamic properties such as Murray's Law and the network Fahraeus effect. Application of centrifugal and Strahler ordering schemes results in divergent descriptions of identical simulated networks. This work introduces a novel CCO-based model focused on generating branching skeletal muscle microvascular arteriolar networks based on adjustable model parameters, thus making it a valuable tool for investigations into skeletal muscle microvascular structure and tissue perfusion.

Effect of different buried depth on the disintegration characteristic of red-bed soft rock and the evolution model of disintegration breakage under cyclic drying-wetting.

The disintegration of red-bed soft rock exhibits a strong correlation with various geological disasters. However, the investigation into the evolutionary mechanisms underlying disintegration breakage has not yet received extensive exploration. In order to comprehensively examine the disintegration characteristics of red-bed soft rock, the slake durability tests were conducted to red-bed soft rocks of varying burial depths. Subsequently, an investigation was carried out to examine the disintegration characteristics and the evolution of disintegration parameters, including the coefficient of uniformity (Cu), coefficient of curvature (Cc), disintegration rate (DRE), disintegration ratio (Dr), and fractal dimension (D), throughout the disintegration process. Finally, employing the energy dissipation theory, an energy dissipation model was developed to predicate the disintegration process of samples at various burial depths. The findings demonstrate a decrease in the abundance of large particles and a concurrent increase in the abundance of small particles as the number of drying-wetting cycles increases. Furthermore, as the number of drying-wetting cycles increases, a significant alteration is observed in the content of particles larger than 10 mm, whereas the content of particles smaller than 10 mm undergoes only minor changes. The disintegration parameters, including the curvature coefficient, non-uniformity coefficient, disintegration rate, and fractal dimension, exhibit a positive correlation with the number of drying-wetting cycles. Conversely, the disintegration index demonstrates a decreasing trend with the increasing number of cycles. Nevertheless, as the burial depth increases, a notable trend emerges in the disintegration process, characterized by a gradual increase in the content of large particles alongside a progressive decrease in the content of small particles. Concurrently, the curvature coefficient, non-uniformity coefficient, disintegration rate, and fractal dimension exhibit a gradual decline, while the durability index experiences a gradual increase. In addition, based on the principle of energy dissipation, it is revealed that the surface energy increment of red-bed soft rock increases with the increase of the number of drying-wetting cycles, but decreases with the increase of burial depth. Ultimately, by leveraging the outcomes of energy dissipation analyses, a theoretical model is constructed to elucidate the correlation between surface energy and both the number of drying-wetting cycles and burial depth. This model serves as a theoretical reference for predicting the disintegration behavior of samples, offering valuable insights for future research endeavors.

Time-dependent complexity characterisation of activity patterns in patients with Chronic Fatigue Syndrome.

BACKGROUND: Chronic Fatigue Syndrome patients suffer from symptoms that cannot be explained by a single underlying biological cause. It is sometimes claimed that these symptoms are a manifestation of a disrupted autonomic nervous system. Prior works studying this claim from the complex adaptive systems perspective, have observed a lower average complexity of physical activity patterns in chronic fatigue syndrome patients compared to healthy controls. To further study the robustness of such methods, we investigate the within-patient changes in complexity of activity over time. Furthermore, we explore how these changes might be related to changes in patient functioning. METHODS: We propose an extension of the allometric aggregation method, which characterises the complexity of a physiological signal by quantifying the evolution of its fractal dimension. We use it to investigate the temporal variations in within-patient complexity. To this end, physical activity patterns of 7 patients diagnosed with chronic fatigue syndrome were recorded over a period of 3 weeks. These recordings are accompanied by physicians' judgements in terms of the patients' weekly functioning. RESULTS: We report significant within-patient variations in complexity over time. The obtained metrics are shown to depend on the range of timescales for which these are evaluated. We were unable to establish a consistent link between complexity and functioning on a week-by-week basis for the majority of the patients. CONCLUSIONS: The considerable within-patient variations of the fractal dimension across scales and time force us to question the utility of previous studies that characterise long-term activity signals using a single static complexity metric. The complexity of a Chronic Fatigue Syndrome patient's physical activity signal does not suffice to characterise their high-level functioning over time and has limited potential as an objective monitoring metric by itself.

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

BACKGROUND: The 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 QUESTION: This study implemented a smartphone accelerometer to compare differences in temporal gait variability and gait dynamics between TW and OW. METHODS: Sixteen 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. RESULTS: Compared 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. SIGNIFICANCE: Smartphone-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.

Enhancing Concrete Mechanical Properties through Basalt Fibers and Calcium Sulfate Whiskers: Optimizing Compressive Strength, Elasticity, and Pore Structure.

To study the effects of basalt fibers (BFs), calcium sulfate whiskers (CSWs), and modified calcium sulfate whiskers (MCSWs) on the compressive strength and dynamic modulus of elasticity of concrete, this paper utilizes Mercury Intrusion Porosimetry (MIP) to measure the microstructure of concrete and calculate the fractal dimension of pore surface area. The results indicate that both CSWs and BFs can increase the compressive strength of concrete. CSWs can enhance the dynamic modulus of elasticity of concrete, while the effect of BFs on the dynamic modulus of elasticity is not significant. The improvement in compressive strength and dynamic modulus of elasticity provided by MCSWs is significantly greater than that provided by CSWs. Both CSWs and BFs can effectively improve the pore structure of concrete and have a significant impact on the surface fractal dimension. CSWs inhibit the formation of ink-bottle pores, while BFs increase the number of ink-bottle pores. Due to the ink-bottle pore effect, the fractal dimension of the capillary pore surface is generally greater than three, lacking fractal characteristics. The compressive strength and dynamic modulus of elasticity of concrete have a good correlation with the fractal dimensions of large pores and transition pores.

Multifractal characteristics of soil particle size distribution of abandoned homestead reclamation under different forest management modes.

In this study, fast-growing poplar reclaimed from abandoned homestead in Xixian New District, Xi'an City, Shaanxi Province, was used as the research object to explore the multi-fractal characteristics of soil particle size distribution under different management modes of abandoned land (control), irrigation, fertilizer irrigation and mixed fertilizer irrigation. The results showed that the mean values of soil clay, silt and sand in abandoned land were 14.58%, 81.21% and 4.22% respectively, 14.08%, 79.92% and 5.99% under irrigation, 15.17%, 81.19% and 3.64% under fertilizer irrigation, and 16.75%, 80.20% and 3.05% in mixed fertilizer treatment. From 40 cm, with increasing soil depth, soil clay particles increase under irrigation, fertilizer irrigation, and mixed fertilizer irrigation modes. The single fractal dimension of soil particle size distribution (D) in each treatment ranges from 2.721 to 2.808. At 60-100 cm, D shows fertilizer irrigation > mixed fertilizer irrigation > irrigation > abandoned land, indicating that fertilization and irrigation can increase the fine-grained matter of deep soil particles and reduce soil roughness. Compared with abandoned land, under irrigation, fertilizer irrigation and mixed fertilizer modes the capacity dimension (D0), entropy dimension (D1), correlation dimension(D2), shape characteristics of the multifractal spectrum (Δf) and overall inhomogeneity of the soil particle size distribution (D0-D10) indicate an uneven distribution of soil particle size; fractal structure characteristics of soil (D-10-D0) indicate a simplified soil structure, and degree of dispersion of soil particle size distribution (D1/D0) indicates that soil particle size is distributed in dense areas. Pearson correlation analysis showed that D was significantly correlated with clay, sand, D0-D10, soil organic matter (SOM) and soil available phosphorus (SAP) (P < 0.05). Stepwise regression analysis showed that clay was the main controlling factor of D and D0-D10 changes. The research results can provide some potential indicators for the quality evaluation of abandoned homestead reclamation.

BP neural network-based analysis of the applicability of NMF in side-step cutting.

Background: Although the spatio-temporal structure of muscle activation in cutting have been studied extensively, including time-varying motor primitives and time-invariant motor modules under various conditions, the factorisation methods suitable for cutting are unclear, and the extent to which each factorisation method loses information about movement during dimensionality reduction is uncertain. Research question: To clarify the extent to which NMF, PCA and ICA retain information about movement when downscaling, and to explore the factorisation method suitable for cutting. Methods: The kinematic data during cutting was captured with a Vicon motion capture system, from which the kinematic features of the pelvic centre of mass were calculated. NMF, PCA and ICA were used to obtain muscle synergies based on sEMG of the cutting at different angles, respectively. A back propagation neural network was constructed using temporal component of synergy as input and the kinematics data of pelvic as output. Calculation of the Hurst index using fractal analysis based on the temporal component of muscle synergy. Results: The quality of sEMG reconstruction is significantly higher with ICA (P < 0.01) than with NMF and PCA for the cutting. The NMF reconstruction has a high degree of preservation of movement, whereas the ICA loses movement information about the most of the swing phase, and the PCA loses information related to the change of direction. Hurst index less than 0.5 for all three angles of cutting. Significance: NMF is suitable for extracting muscle synergies in all directions of cutting. Information related to movement may be lost when using PCA and ICA to extract the synergy of cutting. The high individual variability of muscle synergy in cutting may be responsible for the loss of movement information in muscle synergy.

Evaluation of the Correlation Between the Structural Parameters of Trabecular Bone in CBCT and the Primary Stability of Dental Implants.

PURPOSE: To investigate the relationship between the structural parameters of trabecular bone obtained from CBCT imaging and the primary stability of dental implants. MATERIALS AND METHODS: Sixty patients underwent implant placement followed by primary stability evaluation via measurement of the insertion torque (IT) and the implant stability quotient (ISQ). Gray values (GV) and the fractal dimension (FD) were also measured using pretreatment CBCT images. RESULTS: FD values showed a positive and significant relationship with ISQ and IT values (P = .017 and P = .004, respectively). Additionally, there was a positive and significant correlation between GV and IT (P = .004) as well as between GV and ISQ (P = .010). FD and GV showed a considerable difference between the maxillary and mandibular jaws and were higher in the mandible. Only FD was significantly different between men and women and was higher in men. In the two age groups (older and younger than 45 years), only GV was considerably higher in people older than 45 (P < .05). CONCLUSIONS: Both fractal dimension and gray values obtained from CBCT are efficient methods for predicting the primary stability of the implant due to their relationship with ISQ and IT values.

Investigation on acoustic emission characteristics of fault stick-slip under different lateral pressures.

To explore the effect of different stress environments on fault-slip rockbursts. Bidirectional shear friction experiments with different lateral pressures were conducted on precracked syenogranites buried at 800 m. The macroscopic statistical parameters (cumulative number of AE events, magnitude and b value) and local characteristic parameters (amplitude and dominant frequency) of acoustic emission during the stick-slip process under different lateral pressures were investigated. In addition, based on fractal theory, the nonlinear characteristics of AE spectrum were analyzed. On this basis, the microscopic mechanism of fault stick-slip was discussed. The results show that the lateral pressure influences the friction strength of the fault and stick-slip motion characteristics. With increasing lateral pressure, the proportion of transgranular shear fractures increases, which leads to an increase of cumulative number of AE events and magnitude. The periodic decrease in the b value is more significant at high lateral pressure. There is a good correlation between a high-magnitude AE event and a stress drop. The AE frequency with phased response characteristics can be used to effectively identify the evolution of fault stick-slip instability at the laboratory scale. A sharp increase in the amplitude of the dominant frequency can be regarded as one of the precursory features of fault stick-slip instability. The AE frequency spectra have multifractal characteristics, that differ among the different stages. The maximum multifractal dimension and spectral width can reflect the difference in energy released during fault stick-slip motion.

Bone Trabecular Pattern Analysis in Odontogenic Cysts Using Cone Beam Computed Tomography: A Clinical Retrospective Study.

Introduction The cysts of the maxillofacial region account for one of the most common pathologies of the head and neck region after the mucosal pathologies. Radiography provides an essential clue in early diagnosis and triaging, but it continues further as it is used to evaluate the post-treatment outcome. However, manual analysis is prone to errors. In this scenario, fractal analysis (FA) in radiographs uses mathematical methods to analyse the changes in grey scales in a given radiographic image. FA in odontogenic cysts is used to characterise their complexity, uncover hidden patterns, monitor treatment response, and potentially provide prognostic information. This paper aimed to assess the fractal characteristics of the radicular cyst (RC), dentigerous cyst (DC), and odontogenic keratocyst (OKC) using cone beam computed tomography (CBCT). The objective was to calculate fractal dimension (FD) values expressed in each of these cysts, which could prove to be a radiological adjunct in diagnosing the above cysts. Materials and methods As this is a retrospective study, the archives of CBCT images from June 2021 to December 2023 were obtained from patients diagnosed and confirmed with a histopathological diagnosis with RC, DC, and OKC. The FA was performed using Image J Software (Ver 1.51, National Institute of Health Bethesda, Fiji). The cortical and cancellous bones were segmented using thresholding techniques and converted to binary images. The mean FD of the three planes was then compared to establish the distinctive fractal characteristic for the specific odontogenic cysts. A one-way ANOVA was performed using the Statistical Product and Service Solutions (SPSS) (version 23.0; IBM SPSS Statistics for Windows, Armonk, NY) to determine the difference between FD values of RC, DC, and OKC with a significance level less than 0.05. Results The FD values of DC, RC, and OKC were 1.33 ± 0.17, 1.08 ± 0.16, and 1.65 ± 0.12, respectively. The results indicated that OKC had higher FD values than DC and RC, which means that OKC had lesser bone destruction compared to DC and RC. Inferential statistics showed that the one-way ANOVA was used to compare the means of the three groups of FD data. When calculated for the three groups, the F-statistic value was at 7.29, which yielded a P value of 0.03, making it statistically significant for a 95% confidence interval (p<0.05). Conclusion Our CBCT study on bone trabecular pattern analysis using FD and FA in odontogenic cysts reveals distinct alterations in bone parameters among different cyst types. The probability of higher FD values in OKC is because of lesser cortical bone destruction in OKC compared to the other cyst types. These findings have potential implications for diagnosing, treating, and prognosticating odontogenic cysts.

Development of a Powder Analysis Procedure Based on Imaging Techniques for Examining Aggregation and Segregation Phenomena.

In this manuscript, a method that utilizes classical image techniques to assess particle aggregation and segregation, with the primary goal of validating particle size distribution determined by conventional methods, is presented. This approach can represent a supplementary tool in quality control systems for powder production processes in industries such as manufacturing and pharmaceuticals. The methodology involves the acquisition of high-resolution images, followed by their fractal and textural analysis. Fractal analysis plays a crucial role by quantitatively measuring the complexity and self-similarity of particle structures. This approach allows for the numerical evaluation of aggregation and segregation phenomena, providing valuable insights into the underlying mechanisms at play. Textural analysis contributes to the characterization of patterns and spatial correlations observed in particle images. The examination of textural features offers an additional understanding of particle arrangement and organization. Consequently, it aids in validating the accuracy of particle size distribution measurements. To this end, by incorporating fractal and structural analysis, a methodology that enhances the reliability and accuracy of particle size distribution validation is obtained. It enables the identification of irregularities, anomalies, and subtle variations in particle arrangements that might not be detected by traditional measurement techniques alone.

Restoring the Fluctuation-Dissipation Theorem in Kardar-Parisi-Zhang Universality Class through a New Emergent Fractal Dimension.

The Kardar-Parisi-Zhang (KPZ) equation describes a wide range of growth-like phenomena, with applications in physics, chemistry and biology. There are three central questions in the study of KPZ growth: the determination of height probability distributions; the search for ever more precise universal growth exponents; and the apparent absence of a fluctuation-dissipation theorem (FDT) for spatial dimension d>1. Notably, these questions were answered exactly only for 1+1 dimensions. In this work, we propose a new FDT valid for the KPZ problem in d+1 dimensions. This is achieved by rearranging terms and identifying a new correlated noise which we argue to be characterized by a fractal dimension dn. We present relations between the KPZ exponents and two emergent fractal dimensions, namely df, of the rough interface, and dn. Also, we simulate KPZ growth to obtain values for transient versions of the roughness exponent α, the surface fractal dimension df and, through our relations, the noise fractal dimension dn. Our results indicate that KPZ may have at least two fractal dimensions and that, within this proposal, an FDT is restored. Finally, we provide new insights into the old question about the upper critical dimension of the KPZ universality class.

Combining detrended cross-correlation analysis with Riemannian geometry-based classification for improved brain-computer interface performance.

Riemannian geometry-based classification (RGBC) gained popularity in the field of brain-computer interfaces (BCIs) lately, due to its ability to deal with non-stationarities arising in electroencephalography (EEG) data. Domain adaptation, however, is most often performed on sample covariance matrices (SCMs) obtained from EEG data, and thus might not fully account for components affecting covariance estimation itself, such as regional trends. Detrended cross-correlation analysis (DCCA) can be utilized to estimate the covariance structure of such signals, yet it is computationally expensive in its original form. A recently proposed online implementation of DCCA, however, allows for its fast computation and thus makes it possible to employ DCCA in real-time applications. In this study we propose to replace the SCM with the DCCA matrix as input to RGBC and assess its effect on offline and online BCI performance. First we evaluated the proposed decoding pipeline offline on previously recorded EEG data from 18 individuals performing left and right hand motor imagery (MI), and benchmarked it against vanilla RGBC and popular MI-detection approaches. Subsequently, we recruited eight participants (with previous BCI experience) who operated an MI-based BCI (MI-BCI) online using the DCCA-enhanced Riemannian decoder. Finally, we tested the proposed method on a public, multi-class MI-BCI dataset. During offline evaluations the DCCA-based decoder consistently and significantly outperformed the other approaches. Online evaluation confirmed that the DCCA matrix could be computed in real-time even for 22-channel EEG, as well as subjects could control the MI-BCI with high command delivery (normalized Cohen's κ: 0.7409 ± 0.1515) and sample-wise MI detection (normalized Cohen's κ: 0.5200 ± 0.1610). Post-hoc analysis indicated characteristic connectivity patterns under both MI conditions, with stronger connectivity in the hemisphere contralateral to the MI task. Additionally, fractal scaling exponent of neural activity was found increased in the contralateral compared to the ipsilateral motor cortices (C4 and C3 for left and right MI, respectively) in both classes. Combining DCCA with Riemannian geometry-based decoding yields a robust and effective decoder, that not only improves upon the SCM-based approach but can also provide relevant information on the neurophysiological processes behind MI.

Effects of train vibration load on the structure and hydraulic properties of soils.

Investigating the impact of train-induced vibration loads on soil hydraulic properties, this study conducted experiments using a self-designed indoor soil seepage platform that incorporates vibration loads. The experiments were complemented with scanning electron microscopy to analyze the influence of train-induced vibration loads on soil hydraulic conductivity and its evolutionary characteristics under different vibration frequencies. The experimental results indicated that as the vibration frequency increases from no vibration (0 Hz) to 20 Hz, the time required for the soil volumetric moisture content to reach its peak and stabilize decreases rapidly. However, after the vibration frequency exceeds 20 Hz, the rate at which the time required for the volumetric moisture content to reach its peak and stabilize decreases slows down. Furthermore, the soil pore water pressure increases with the increase in vibration frequency. At a vibration frequency of 80 Hz, the peak value of pore water pressure increases by 105% compared to the non-vibration state, suggesting that higher vibration frequencies promote the development and acceleration of soil pore moisture migration. Additionally, as the vibration frequency increases, the soil hydraulic conductivity initially experiences a rapid increase, with a growth rate ranging from 40.1 to 47.4%. However, after the frequency exceeds 20 Hz, this growth rate significantly decreases, settling to only 18.6% to 7.8%. When the soil was subjected to a vibration load, the scanning electron microscopy test revealed alterations in its pore structure. Micropores and small pores transformed into macropores and mesopores. Additionally, the microstructural parameters indicated that vibration load decreased the complexity of soil pores, thereby speeding up the hydraulic conduction process. This, in turn, affected the hydraulic properties of the soil and established a relationship between pore structure complexity and soil hydraulic properties.

Analysis and comparative study of a deterministic mathematical model of SARS-COV-2 with fractal-fractional operators: a case study.

In this paper, we investigate a fractal-fractional-order mathematical model with the influence of hospitalized patients and the impact of vaccination with fractal-fractional operators. The respective derivatives are considered in the Caputo, Caputo Fabrizio, and Atangana-Baleanu senses of fractional order α and fractal dimension τ . For the proposed problem, some results regarding basic reproduction number and stability are given. Using the next-generation matrix approach, we have investigated the global and local stability of several types of equilibrium points. We provide a detailed analysis of the existence and uniqueness of the solution. Moreover, we fit the model with the real data of Pakistan from June 01, 2020, till March 24, 2021. Then, we use the fractal-fractional derivative to find a numerical solution for the model. MATLAB software is used for numerical illustration. Graphical presentations corresponding to different parameteric values are given as well.

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.Mainresults. 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.

Mitotic chromosomes are self-entangled and disentangle through a topoisomerase-II-dependent two-stage exit from mitosis.

The topological state of chromosomes determines their mechanical properties, dynamics, and function. Recent work indicated that interphase chromosomes are largely free of entanglements. Here, we use Hi-C, polymer simulations, and multi-contact 3C and find that, by contrast, mitotic chromosomes are self-entangled. We explore how a mitotic self-entangled state is converted into an unentangled interphase state during mitotic exit. Most mitotic entanglements are removed during anaphase/telophase, with remaining ones removed during early G1, in a topoisomerase-II-dependent process. Polymer models suggest a two-stage disentanglement pathway: first, decondensation of mitotic chromosomes with remaining condensin loops produces entropic forces that bias topoisomerase II activity toward decatenation. At the second stage, the loops are released, and the formation of new entanglements is prevented by lower topoisomerase II activity, allowing the establishment of unentangled and territorial G1 chromosomes. When mitotic entanglements are not removed in experiments and models, a normal interphase state cannot be acquired.