Entropy Algorithm Research Articles

Research on the lateralization of brain functional complexity in mild cognitive impairment-Alzheimer’s disease progression based on multiscale lateralized brain entropy

ObjectiveDespite extensive recent interest in mild cognitive impairment (MCI) and Alzheimer’s disease (AD), few studies have examined the lateralization of their brain functions. This study describes the multiscale lateralized brain entropy (multi-LBE) algorithm and investigates the lateralization of brain functional complexity for MCI and AD. MethodsThe lateralized sample entropy (LSE) and lateralized cross-sample entropy (LCSE) are calculated over multiple time scales and used as lateralization indices of brain functional complexity to explore the progression of MCI-AD (from healthy control to early MCI, late MCI and AD). ResultsOur experimental results indicate that patients with AD have the weakest lateralization of functional complexity in most brain regions. The left hemisphere exhibits a trend to rightward laterality over an increasing number of time scales during the MCI-AD progression. Correlation analysis of LBEs demonstrates positive correlations among three patient groups, while negative correlations are found between healthy control group and each patient group. Furthermore, significance tests are performed on the whole brain regions of the four groups at multiple time scales, and the LBEs of several time scales are selected as features. ConclusionThe classification of the four groups using multi-LBEs achieves an accuracy of up to 97.46% by multiscale LBEs, indicating that the LBE is a possible indicator of different states during MCI-AD progression. SignificanceOur findings provide new insights into the lateralization of brain functional complexity and highlight the potential for using multi-LBEs as biomarkers for the MCI-AD.

Rotor equivalent wind speed prediction based on mechanism analysis and residual correction using Lidar measurements

Efficient power generation and reduced operational cost are crucial to make wind energy a successful market player. To achieve satisfactory performance in wind turbine technology, it is essential to accurately predict the rotor equivalent wind speed (REWS). Since traditional wind transducers are difficult to measure multiple-point wind speed, related researches on predicting REWS are lacking. In this paper, a hybrid REWS prediction framework is proposed, which combines mechanism analysis and data-driven technique, aided by Lidar measurements. The framework employs the mechanism modeling and time delay analysis to achieve preliminary REWS prediction, but the accuracy is restricted by the quantity of Lidar measurement points. To enhance the prediction accuracy, a residual prediction model based on the data-driven technique is created to correct the mechanism prediction. Specifically, a novel combined modeling approach based on empirical mode decomposition and sample entropy algorithms is presented. Through reconstructing the input data of the combined model into high, middle, and low frequency components and exploring the prediction laws of different frequency components obtained by typical machine learning models, the combined residual prediction model is established. Additionally, an enhanced whale optimization algorithm named WOAmM is presented to optimize the parameters of the combined model. The proposed method is validated through a four-beam Lidar measurement scenario simulated by BLADED software. The experimental results indicate that the combined model outperforms each single model and the mechanism prediction, and improves the REWS prediction accuracy by up to75.04%, 60.92%, 51.85%, and 57.52% in the four datasets, respectively. The proposed method could facilitate the utilization of Lidar in improving the performance of wind turbines.

System dynamics monitoring using PIC micro-controller-based PLSE

The permutation largest slope entropy (PLSE) algorithm has been shown to be effective to distinguish between regular and non-regular dynamics from time series analysis. However, as it is the case for many non-linear time series analysis algorithms, such a characterization is locally made and does not allow one to capture some micro-phenomena, such as intermittency, that may occur in the system behavior. This paper presents a PIC micro-controller based implementation of the PLSE for a real-time monitoring of system dynamics. The PLSE algorithm is optimized to fit the program and data memory of low-end processors using the XC8 compiler and the MPLAB X IDE. The resulting algorithm is implemented on the PIC16F18446 and deployed on the Explorer 8 development board. The effectiveness of the developed tool is validated by considering an electrical circuit of the Duffing oscillator that can generate both periodic and chaotic dynamics. By comparing the PLSE values with the phase portraits and previous results on the Duffing oscillator circuit, the developed tool efficiently allows one to monitor the behavior of dynamical systems.

High-Speed Maneuvering Target Inverse Synthetic Aperture Radar Imaging and Motion Parameter Estimation Based on Fast Spare Bayesian Learning and Minimum Entropy

High-speed maneuvering target inverse synthetic aperture radar (ISAR) imaging is always a hot topic in signal processing. High-speed maneuvering targets often have high-order maneuvering characteristics, such as translational and rotational characteristics, which destroy the signal structure of stationary targets and make basic imaging processing methods such as range-Doppler (RD) algorithm no longer suitable. In this paper, a high-resolution imaging method for high-speed maneuvering targets is proposed, which uses the fast sparse Bayesian learning (SBL) algorithm and the minimum entropy algorithm for ISAR high-resolution imaging and motion parameter estimation, respectively. Because SBL makes full use of the characteristics of the target and the environment, it can obtain an ISAR high-resolution image of the maneuvering target. However, the high computational complexity caused by matrix inversion and some matrix operations in SBL iteration limit the practical application of SBL in ISAR imaging. In view of the special structure of the matrix required to be inverted, we propose a fast SBL algorithm, which uses a new decomposition method to obtain the decomposition formula of the inverse matrix. Based on the decomposition factors, the multiplication operation involving the inverse matrix can be quickly calculated using fast Fourier transform (FFT), which greatly improves the computational efficiency. Image entropy represents the sharpness and focusing degree of an image, and so the minimum entropy algorithm can estimate the motion parameters of maneuvering targets more accurately. We combine the minimum entropy algorithm with the fast SBL algorithm to realize phase error correction and high-resolution imaging, which has better noise sensitivity and can obtain the best focusing degree image. Finally, simulation results prove the effectiveness of this algorithm.

Bioclimatic and Landscape Factors drive the Potential Distribution of Philaenus spumarius, Neophilaenus campestris and N. lineatus (Hemiptera, Aphrophoridae) in Southeastern Iberian Peninsula.

Philaenus spumarius and Neophilaenus campestris are the main vectors of the invasive bacteria Xylella fastidiosa and key threats to European plant health. Previous studies of the potential distribution of P. spumarius reveal that climatic factors are the main drivers of its distribution on the Mediterranean Basin scale. Other local studies reveal that the landscape could also have a role in the distribution of both species of P. spumarius and N. campestris. Our work is aimed at understanding the role and importance of bioclimatic and landscape environmental factors in the distributions of the vector and potential vector species P. spumarius, N. campestris, N. lineatus and L. coleoptrata on a regional scale across the Autonomous Community of Murcia (SE Spain), a region with relevant environmental gradients of thermality and crop intensity. We used sweeping nets for sampling 100 points during eight months in 2020. Using bioclimatic landscape composition and topographical variables, we carried out habitat suitability models for each species using the maximum entropy algorithm (MaxEnt). Distribution results for P. spumarius, N. campestris and N. lineatus indicate a gradient in habitat suitability, with the optimum in the coldest and wettest areas in landscapes with a high proportion of forest. All three species are absent from the southern third of the study region, the hottest, driest and most intensively cultivated area. These results are useful and should be considered in contingency plans against possible invasions of X. fastidiosa in Mediterranean regions.

Filling the data gaps: Transferring models from data-rich to data-poor deep-sea areas to support spatial management

Spatial management of the deep sea is challenging due to limited available data on the distribution of species and habitats to support decision making. In the well-studied North Atlantic, predictive models of species distribution and habitat suitability have been used to fill data gaps and support sustainable management. In the South Atlantic and other poorly studied regions, this is not possible due to a massive lack of data. In this study, we investigated whether models constructed in data-rich areas can be used to inform data-poor regions (with otherwise similar environmental conditions). We used a novel model transfer approach to identify to what extent a habitat suitability model for Desmophyllum pertusum reef, built in a data-rich basin (North Atlantic), could be transferred usefully to a data-poor basin (South Atlantic). The transferred model was built using the Maximum Entropy algorithm and constructed with 227 presence and 3064 pseudo-absence points, and 200 m resolution environmental grids. Performance in the transferred region was validated using an independent dataset of D. pertusum presences and absences, with assessments made using both threshold-dependent and -independent metrics. We found that a model for D. pertusum reef fitted to North Atlantic data transferred reasonably well to the South Atlantic basin, with an area under the curve of 0.70. Suitable habitat for D. pertusum reef was predicted on 20 of the assessed 27 features including seamounts. Nationally managed Marine Protected Areas provide significant protection for D. pertusum reef habitat in the region, affording full protection from bottom trawling to 14 of the 20 suitable features. In areas beyond national jurisdiction (ABNJ), we found four seamounts that provided suitable habitat for D. pertusum reef to be at least partially protected from bottom trawling, whilst two did not fall within fisheries closures. There are factors to consider when developing models for transfer including data resolution and predictor type. Nevertheless, the promising results of this application demonstrate that model transfer approaches stand to provide significant contributions to spatial planning processes through provision of new, best available data. This is particularly true for ABNJ and areas that have previously undergone little scientific exploration such as the global south.

The causality analysis of incipient fault in industrial processes using dynamic data stream transfer entropy

The propagation of the developing incipient fault embeds potential risks to the safety management of industrial processes. The transfer entropy (TE) based causality analysis method is an effective solution for early detection and timely intervention of fault propagation. However, the slow-varying incipient fault could not be analyzed timely since the conventional TE is restricted by the limited data processing capacity and fixed data selection mode. For real-time causality analysis of developing industrial fault, we proposed the dynamic data stream transfer entropy (DDSTE) algorithm and presented the DDSTE-based causality analysis method in this paper. Firstly, the conventional static data model is replaced by dynamic data stream model, which could be updated and expanded with continues import of new data and would not be restricted by the limited storage capacity. Secondly, concerning the varying timing feature of incipient fault, the adaptive data sampling window is designed to match with incipient fault evolution stages. Thirdly, the long-lasting fault sequence is coarse-grained to improve the calculation efficiency for on-line using. Compared to conventional methods, DDSTE-based causality analysis outperforms in rapid tracking of incipient fault propagation and accurate estimation of fault location. The data collected from a real coal gasification process is used to verify the reliability and superiority of the proposed method.

A Multithreaded Algorithm for the Computation of Sample Entropy

Many popular entropy definitions for signals, including approximate and sample entropy, are based on the idea of embedding the time series into an m-dimensional space, aiming to detect complex, deeper and more informative relationships among samples. However, for both approximate and sample entropy, the high computational cost is a severe limitation. Especially when large amounts of data are processed, or when parameter tuning is employed premising a large number of executions, the necessity of fast computation algorithms becomes urgent. In the past, our research team proposed fast algorithms for sample, approximate and bubble entropy. In the general case, the bucket-assisted algorithm was the one presenting the lowest execution times. In this paper, we exploit the opportunities given by the multithreading technology to further reduce the computation time. Without special requirements in hardware, since today even our cost-effective home computers support multithreading, the computation of entropy definitions can be significantly accelerated. The aim of this paper is threefold: (a) to extend the bucket-assisted algorithm for multithreaded processors, (b) to present updated execution times for the bucket-assisted algorithm since the achievements in hardware and compiler technology affect both execution times and gain, and (c) to provide a Python library which wraps fast C implementations capable of running in parallel on multithreaded processors.

SMSP Mainlobe Jamming Suppression with FDA-MIMO Radar Based on FastICA Algorithm

In the electronic warfare environment, the performance of ground-based radar target search is seriously degraded due to the existence of smeared spectrum (SMSP) jamming. SMSP jamming is generated by the self-defense jammer on the platform, playing an important role in electronic warfare, making traditional radars based on linear frequency modulation (LFM) waveforms face great challenges in searching for targets. To solve this problem, an SMSP mainlobe jamming suppression method based on a frequency diverse array (FDA) multiple-input multiple-output (MIMO) radar is proposed. The proposed method first uses the maximum entropy algorithm to estimate the target angle and eliminate the interference signals from the sidelobe. Then, the range-angle dependence of the FDA-MIMO radar signal is utilized, and the blind source separation (BSS) algorithm is used to separate the mainlobe interference signal and the target signal, avoiding the impact of mainlobe interference on target search. The simulation verifies that the target echo signal can be effectively separated, the similarity coefficient can reach more than 90% and the detection probability of the radar is significantly enhanced at a low signal-to-noise ratio.

Improved multivariate multiscale sample entropy and its application in multi-channel data.

Entropy, as a nonlinear feature in information science, has drawn much attention for time series analysis. Entropy features have been used to measure the complexity behavior of time series. However, traditional entropy methods mainly focus on one-dimensional time series originating from single-channel transducers and are incapable of handling the multidimensional time series from multi-channel transducers. Previously, the multivariate multiscale sample entropy (MMSE) algorithm was introduced for multi-channel data analysis. Although MMSE generalizes multiscale sample entropy and provides a new method for multidimensional data analysis, it lacks necessary theoretical support and has shortcomings, such as missing cross-channel correlation information and having biased estimation results. This paper proposes an improved multivariate multiscale sample entropy (IMMSE) algorithm to overcome these shortcomings. This paper highlights the existing shortcomings in MMSE under the generalized algorithm. The rationality of IMMSE is theoretically proven using probability theory. Simulations and real-world data analysis have shown that IMMSE is capable of effectively extracting cross-channel correlation information and demonstrating robustness in practical applications. Moreover, it provides theoretical support for generalizing single-channel entropy methods to multi-channel situations.

Augmented Complex Minimization of Error Entropy With Fiducial Points for Power System Frequency Estimation

Frequency estimation plays an important role in ensuring the stability of the power system. The augmented complex minimum error entropy (ACMEE) algorithm has achieved better performance in frequency estimation under impulsive noise environments. However, it has the problem of unknown error probability density function (PDF) in frequency tracking, the improved algorithms called the complex minimization of error entropy with fiducial points (CMEEF) and the augmented CMEEF (ACMEEF) are proposed in this paper. The ACMEEF algorithm based on widely linear modeling uses second-order statistical information to process the non-circular signal through the complex voltage signal. At the same time, it incorporates a location-sensitive cost into minimum error entropy (MEE) to automatically locate the peak of the error PDF at the origin, which can accurately estimate the grid frequency under the unbalanced system and interference of noise. The stability of the proposed algorithm and the computational complexity are analyzed. Finally, the enhanced frequency estimation performance of the proposed ACMEEF algorithm is verified through simulation results of different synthetic signals and real-world data.

0130 Reduced Entropy in EEG During Rapid Eye Movement Sleep in Men with Depression

Abstract Introduction Depression is an increasingly prevalent mental health condition. Patients with depression have disrupted rapid eye movement (REM) sleep as characterized by shortened REM latency, increased REM sleep duration, and increased REM density. However, it is unknown whether the dynamic patterns of EEG within REM episodes are altered in these patients. Here we investigated the complexity of EEG during REM sleep using the analysis of irregularity on multiple temporal time scales and compared the difference in such a nonlinear property of EEG between patients with depression and controls. Methods We analyzed the overnight EEG recordings (256 Hz) collected from the left central channel in 19 older men with depression and 19 age-matched otherwise healthy control men in the Osteoporotic Fractures in Men Study (MrOS) obtained from the National Sleep Research Resource (NSRR). To quantify the irregularity/complexity in EEG fluctuations during REM, a Multiscale Entropy (MSE) analysis was performed on each 30-second epoch to calculate the entropy at different time scales between ~0.004 and ~0.078 seconds (i.e., 1/256, 2/256, …, 20/256 seconds). Results As compared to control men, men with depression had significantly lower entropy values at multiple time scales between 0.023-0.031 seconds (time scale =6/256 second: 0.363□0.008 [SE] for depression, 0.408□0.009 for controls; time scale =7/256 second: 0.295□0.009 for depression, 0.342□0.008 for controls; time scale =8/256 second: 0.225□0.009 for depression, 0.269□0.008 for controls; all FDR-adjusted P-values< 0.001), indicating reduced temporal irregularity/complexity in EEG fluctuations. The differences were not statistically significant at smaller or larger time scales. Conclusion EEG complexity/irregularity within REM sleep were altered in patients with depression. Our results indicate the capability of MSE analysis in capturing important complexity features of EEG fluctuations, which might be missed using those entropy algorithms focused on EEG fluctuations at a single time scale. Support (if any) RF1AG059867, RF1AG064312. The National Heart, Lung, and Blood Institute provided funding for the ancillary MrOS Sleep Study, "Outcomes of Sleep Disorders in Older Men," under the following grant numbers: R01 HL071194, R01 HL070848, R01 HL070847, R01 HL070842, R01 HL070841, R01 HL070837, R01 HL070838, and R01 HL070839. The NSRR was supported by the National Heart, Lung, and Blood Institute (R24 HL114473, 75N92019R002).

Coalescing disparate data sources for the geospatial prediction of mosquito abundance, using Brazil as a motivating case study

One of the barriers to performing geospatial surveillance of mosquito occupancy or infestation anywhere in the world is the paucity of primary entomologic survey data geolocated at a residential property level and matched to important risk factor information (e.g., anthropogenic, environmental, and climate) that enables the spatial risk prediction of mosquito occupancy or infestation. Such data are invaluable pieces of information for academics, policy makers, and public health program managers operating in low-resource settings in Africa, Latin America, and Southeast Asia, where mosquitoes are typically endemic. The reality is that such data remain elusive in these low-resource settings and, where available, high-quality data that include both individual and spatial characteristics to inform the geospatial description and risk patterning of infestation remain rare. There are many online sources of open-source spatial data that are reliable and can be used to address such data paucity in this context. Therefore, the aims of this article are threefold: (1) to highlight where these reliable open-source data can be acquired and how they can be used as risk factors for making spatial predictions for mosquito occupancy in general; (2) to use Brazil as a case study to demonstrate how these datasets can be combined to predict the presence of arboviruses through the use of ecological niche modeling using the maximum entropy algorithm; and (3) to discuss the benefits of using bespoke applications beyond these open-source online data sources, demonstrating for how they can be the new “gold-standard” approach for gathering primary entomologic survey data. The scope of this article was mainly limited to a Brazilian context because it builds on an existing partnership with academics and stakeholders from environmental surveillance agencies in the states of Pernambuco and Paraiba. The analysis presented in this article was also limited to a specific mosquito species, i.e., Aedes aegypti, due to its endemic status in Brazil.

Counting independent sets in amenable groups

AbstractGiven a locally finite graph $\Gamma $ , an amenable subgroup G of graph automorphisms acting freely and almost transitively on its vertices, and a G-invariant activity function $\unicode{x3bb} $ , consider the free energy $f_G(\Gamma ,\unicode{x3bb} )$ of the hardcore model defined on the set of independent sets in $\Gamma $ weighted by $\unicode{x3bb} $ . Under the assumption that G is finitely generated and its word problem can be solved in exponential time, we define suitable ensembles of hardcore models and prove the following: if $\|\unicode{x3bb} \|_\infty < \unicode{x3bb} _c(\Delta )$ , there exists a randomized $\epsilon $ -additive approximation scheme for $f_G(\Gamma ,\unicode{x3bb} )$ that runs in time $\mathrm {poly}((1+\epsilon ^{-1})\lvert \Gamma /G \rvert )$ , where $\unicode{x3bb} _c(\Delta )$ denotes the critical activity on the $\Delta $ -regular tree. In addition, if G has a finite index linearly ordered subgroup such that its algebraic past can be decided in exponential time, we show that the algorithm can be chosen to be deterministic. However, we observe that if $\|\unicode{x3bb} \|_\infty> \unicode{x3bb} _c(\Delta )$ , there is no efficient approximation scheme, unless $\mathrm {NP} = \mathrm {RP}$ . This recovers the computational phase transition for the partition function of the hardcore model on finite graphs and provides an extension to the infinite setting. As an application in symbolic dynamics, we use these results to develop efficient approximation algorithms for the topological entropy of subshifts of finite type with enough safe symbols, we obtain a representation formula of pressure in terms of random trees of self-avoiding walks, and we provide new conditions for the uniqueness of the measure of maximal entropy based on the connective constant of a particular associated graph.

Robust multiple-scroll dynamics in memristive-based generator system

In-depth analysis of a novel multiple scroll memristive-based hyperchaotic system with no equilibrium is provided in this work. We identify a family of more complicated nmathrm{th}-order multiple scroll hidden attractors for a unique, enhanced 4-dimensional Sprott-A system. The system is particularly sensitive to initial conditions with coexistence and multistability of attractors when changing the associated parameters and the finite transient simulation time. The complexity (CO), spectral entropy (SE) algorithms, and 0-1 complexity characteristics was thoroughly discussed. On the other hand, the outcomes of the electronic simulation are validated by theoretical calculations and numerical simulations.

Multiscale Entropy Algorithms to Analyze Complexity and Variability of Trunk Accelerations Time Series in Subjects with Parkinson's Disease.

The aim of this study was to assess the ability of multiscale sample entropy (MSE), refined composite multiscale entropy (RCMSE), and complexity index (CI) to characterize gait complexity through trunk acceleration patterns in subjects with Parkinson's disease (swPD) and healthy subjects, regardless of age or gait speed. The trunk acceleration patterns of 51 swPD and 50 healthy subjects (HS) were acquired using a lumbar-mounted magneto-inertial measurement unit during their walking. MSE, RCMSE, and CI were calculated on 2000 data points, using scale factors (τ) 1-6. Differences between swPD and HS were calculated at each τ, and the area under the receiver operating characteristics, optimal cutoff points, post-test probabilities, and diagnostic odds ratios were calculated. MSE, RCMSE, and CIs showed to differentiate swPD from HS. MSE in the anteroposterior direction at τ4 and τ5, and MSE in the ML direction at τ4 showed to characterize the gait disorders of swPD with the best trade-off between positive and negative posttest probabilities and correlated with the motor disability, pelvic kinematics, and stance phase. Using a time series of 2000 data points, a scale factor of 4 or 5 in the MSE procedure can yield the best trade-off in terms of post-test probabilities when compared to other scale factors for detecting gait variability and complexity in swPD.

Evidence of Chaos in Electroencephalogram Signatures of Human Performance: A Systematic Review.

(1) Background: Chaos, a feature of nonlinear dynamical systems, is well suited for exploring biological time series, such as heart rates, respiratory records, and particularly electroencephalograms. The primary purpose of this article is to review recent studies using chaos theory and nonlinear dynamical methods to analyze human performance in different brain processes. (2) Methods: Several studies have examined chaos theory and related analytical tools for describing brain dynamics. The present study provides an in-depth analysis of the computational methods that have been proposed to uncover brain dynamics. (3) Results: The evidence from 55 articles suggests that cognitive function is more frequently assessed than other brain functions in studies using chaos theory. The most frequently used techniques for analyzing chaos include the correlation dimension and fractal analysis. Approximate, Kolmogorov and sample entropy account for the largest proportion of entropy algorithms in the reviewed studies. (4) Conclusions: This review provides insights into the notion of the brain as a chaotic system and the successful use of nonlinear methods in neuroscience studies. Additional studies of brain dynamics would aid in improving our understanding of human cognitive performance.

EEG-based real-time diagnostic system with developed dynamic 2TEMD and dynamic ApEn algorithms.

In real-time electroencephalography (EEG) analysis, the problem of observing dynamic changes and the problem of binary classification is a promising direction. EEG energy and complexity are important evaluation metrics in brain death determination in the field of EEG analysis. We developed two algorithms, dynamic turning tangent empirical mode decomposition to compute EEG energy and dynamic approximate entropy to compute EEG complexity for brain death determination. The developed algorithm is applied to analyze 50 EEG data of coma patients and 50 EEG data of brain death patients. The validity of the dynamic analysis is confirmed by the accuracy rate derived from the comparison with turning tangent empirical mode decomposition and approximate entropy algorithms. We evaluated the EEG data of three patients using the built diagnostic system. The experimental results visually showed that the EEG energy ratio was higher in a coma state than that in brain death, while the complexity was lower than that in brain death.

Ecological niche modelling and population genetic analysis of Indian temperate bamboo Drepanostachyum falcatum in the western Himalayas.

The present study was conducted to understand the key ecological and biological questions of conservation importance in Drepanostachyum falcatum which aimed to map potential distribution in the western Himalayas and decipher spatial genetic structure. Eco-distribution maps were generated through ecological niche modelling using the Maximum Entropy (MaxEnt) algorithm implemented with 228 geocoordinates of species presence and 12 bioclimatic variables. Concomitantly, 26 natural populations in the western Himalayas were genetically analysed using ten genomic sequence-tagged microsatellite (STMS) markers. Model-derived distribution was adequately supported with appropriate statistical measures, such as area under the 'receiver operating characteristics (ROC)' curve (AUC; 0.917 ± 0.034)", Kappa (K; 0.418), normalized mutual information (NMI; 0.673) and true skill statistic (TSS; 0.715). Further, Jackknife test and response curves showed that the precipitation (pre- and post-monsoon) and temperature (average throughout the year and pre-monsoon) maximize the probabilistic distribution of D. falcatum. We recorded a wide and abundant (4096.86 km2) distribution of D. falcatum in the western Himalayas with maximum occurrence at 1500 to 2500m asl. Furthermore, marker analysis exemplified high gene diversity with low genetic differentiation in D. falcatum. Relatively, the populations of Uttarakhand are more genetically diverse than Himachal Pradesh, whereas within the Uttarakhand, the Garhwal region captured a higher allelic diversity than Kumaon. Clustering and structure analysis indicated two major gene pools, where genetic admixing appeared to be controlled by long-distance gene flow, horizontal geographical distance, aspect, and precipitation. Both the species distribution map and population genetic structure derived herein may serve as valuable resources for conservation and management of Himalayan hill bamboos.

Risk Assessment for Water Disaster of Karst Tunnel Based on the Weighting of Reliability Measurement and Improved Extension Cloud Model

Risk assessment of water disaster in karst tunnels is a nonlinear, complex, and uncertain system problem. Based on the reliability measurement method and extension cloud theory, the reliability measurement weighting and improved extension cloud model are established for the risk assessment of water disaster in karst tunnels. Firstly, on the basis of fully considering the relevance of evaluation indicators, a dynamic weighting theory for reliability measurement of indicators based on Jousselme distance is proposed. Secondly, according to the two different entropy algorithms of the extension cloud model, an improved extension cloud model is proposed based on the entropy algorithm fusion of game theory. The comprehensive cloud correlation degree obtained by the improved extension cloud model is combined with the indicator reliability measure weight. Then, the dangerous state of the water disaster in karst tunnels is judged, and the visualization of the water disaster level judgment is realized. And the model is tested with sample data from six typical karst tunnels. Finally, the model is applied to the Yangpeng Karst Tunnel on the Beijing-Zhuhai expressway. The results show that the water disaster level of the tunnel is I, and the evaluation results are consistent with the actual situation. Compared with the matter element extension model and the extension cloud model, the calculation results are more accurate. The corresponding treatment measures have been taken, and the good effect of water disaster treatment has been achieved. The practical value of the model is further proved, and a new reference method is provided for the prediction and prevention of water disaster in karst tunnels.