Probability Density Values Research Articles

Synthetic oversampling with Mahalanobis distance and local information for highly imbalanced class-overlapped data

Minority oversampling is currently one of the most popular and effective methods for handling imbalanced data. However, oversampling that relies on the observations of the minority class to generate new samples is not applicable in the scenario of imbalanced data with extremely scarce minority samples, because the strongly underrepresented minority class does not contain enough information to support the oversampling process. Since some recent studies have exhibited the effectiveness of using majority information to bootstrap oversampling, the neglect of class overlap in the sampling process would increase the overlapping degree and complicate the decision boundary. To this end, this paper proposes a Mahalanobis distance and Local information based OverSampling (MLOS) for highly imbalanced class-overlapped data. MLOS first employs the majority density to guide the sample synthesis, with Mahalanobis distance to extract the majority probability contour. Then for each minority seed sample, to avoid the generation of overlapping samples, MLOS constrain the synthetic process by finding the auxiliary sample (in its 5 nearest neighbors) with similar probability density value to the seed. Finally, MLOS uses a pair-wise data cleaning process to improve the visibility of the decision boundary according to the probability density of synthetic samples. Comparative experiments conducted on 16 highly imbalanced class-overlapped datasets, using 17 different methods, demonstrates the superiority of our proposed method in terms of three popular evaluation metrics AUC, G-mean and Recall for imbalance classification. The source code of MLOS is available at https://github.com/ytyancp/MLOS.

Robust adaptive analysis of dynamic responses of wave energy converters

PurposeThe purpose of this paper is to exploit a new and robust method to forecast the long-term extreme dynamic responses for wave energy converters (WECs).Design/methodology/approachA new adaptive binned kernel density estimation (KDE) methodology is first proposed in this paper.FindingsBy examining the calculation results the authors has found that in the tail region the proposed new adaptive binned KDE distribution curve becomes very smooth and fits quite well with the histogram of the measured ocean wave dataset at the National Data Buoy Center (NDBC) station 46,059. Carefully studying the calculation results also reveals that the 50-year extreme power-take-off heaving force value forecasted based on the environmental contour derived using the new method is 3572600N, which is much larger than the value 2709100N forecasted via the Rosenblatt-inverse second-order reliability method (ISORM) contour method.Research limitations/implicationsThe proposed method overcomes the disadvantages of all the existing nonparametric and parametric methods for predicting the tail region probability density values of the sea state parameters.Originality/valueIt is concluded that the proposed new adaptive binned KDE method is robust and can forecast well the 50-year extreme dynamic responses for WECs.

Development of Sports Tourism Resources Based on Spatial Analysis Perspective

Abstract This paper examines the reality of sports tourism resources by effectively integrating the universal symbiosis and spatial hierarchy of sports tourism resources. Spatial analysis is utilized to view each element of the near-neighboring related element environment to find the spatial distribution probability density value of the random distribution within the sports tourism resources. The overall data distribution can be inferred from the limited samples, and calculations are performed to recognize localized density changes in the distribution of point-like samples. The highest mean value of sports resources density is 0.827, the highest comprehensive value of tourism resources evaluation is 0.82 points, and the maximum value of tourism competitiveness is 0.389. The spatial analysis perspective greatly improves the sports tourism industry’s comprehensive strength and the economy’s sustainable development is realized.

Stationary response analysis for a linear system under non-Gaussian random excitation by the equivalent non-Gaussian excitation method and the Hermite moment model

An approximate analytical method is developed to obtain the stationary response probability density and mean upcrossing rate for a linear system subjected to non-Gaussian random excitation. The random excitation is a stationary stochastic process prescribed by an arbitrary first-order probability density and a class of power spectral density with a bandwidth parameter, and is described by an Itô stochastic differential equation. In the proposed method, the equivalent non-Gaussian excitation method is first utilized to derive a closed set of moment equations for the system response. The exact solutions of response moments up to the fourth order are calculated from the moment equations. Next, using the response moments, the Hermite moment model is built for the stationary displacement response, and its probability density function is obtained through the model. Finally, the mean upcrossing rate of the displacement is determined from the response probability distribution by making two approximations that the displacement and velocity of the system are independent and the velocity is Gaussian. The proposed method can be used for any excitation probability density and bandwidth parameter value as long as the skewness and kurtosis of the response are within the applicable range of the Hermite moment model. In illustrative examples, the proposed method is applied to linear systems under random excitations with two-types of non-Gaussian probability densities. The effectiveness of the method is demonstrated by comparing the analytical results with the pertinent Monte Carlo simulation results while widely varying the bandwidth ratio between the excitation spectral density and the frequency response function of the system. Moreover, the effect of excitation non-Gaussianity on the mean upcrossing rate is discussed. It is shown that for small bandwidth ratio, the crossing rate differs considerably depending on the excitation probability density. The difference due to the excitation distribution decreases monotonically as the bandwidth ratio increases, and the crossing rate becomes almost the same as that in the case of Gaussian excitation when the bandwidth ratio is large.

DDOFM: Dynamic malicious domain detection method based on feature mining

The domain name system is an essential part of the network, and target hosts are often attacked by malicious domain names to steal resources. Some traditional detection methods have low accuracy, poor generalization ability, and high resource overhead on model construction to deal with complex and variable malicious domain names. A three-level dynamic malicious domain detection method (DDOFM) is proposed in this paper. DDOFM only needs to combine a few high-order statistical features of benign domains with some DNS features, without flagging malicious samples and involving them in training. Firstly, the boundary recognition of passive DNS (PDNS) features extracted from DNS traffic is carried out to conduct an early- warning for some domains. Second, the Hidden Markov Model (HMM) forward algorithm and normal distribution probability density function are used to calculate the formation probabilities of the warned domains and their probability density values. Then the probabilities of every character in the warned domain name and the standard deviation between these probabilities are counted. Further, the probability density values and the standard deviations of these warned domain names are compared with their respective thresholds to identify the attribution of the warned domain names. Finally, if the domain name is not warned, the Jensen–Shannon divergence (JS divergence) between it and the previous domain name will be calculated. Then the local iterative threshold finding algorithm (LLTFA) proposed in this paper will be combined to determine its attribution and identify whether the host is connected to the command and control (C&C) server. Experiments show that the detection indexes of this method exceed 99% for multiple types of malicious domain names. The C&C servers can also be identified by DDOFM faster than similar methods.

Adaptive filter entropy monitoring method for scalar magnetic detection using optically pumped magnetometers

In this paper, an adaptive filtering minimum entropy detector (AF-MED) method is proposed, which is an improvement on the minimum entropy detector (MED) method. The improvement can be divided into two parts. Firstly, in view of the low detection rate of the MED method in the case of low signal-to-noise ratio (SNR), an adaptive filtering technology is added, which can accurately and dynamically determine the frequency range of the magnetic field according to the moving speed of the magnetic target, and effectively restrain the influence of environmental noise on the magnetic field. Compared with the MED method, the detection rate is increased by 48%. Secondly, using the kernel density estimation method to calculate the probability density value, the advantage is that there is no need to make any predictions or assumptions about the target, which makes the method more convenient to achieve. Furthermore, in this study, numerous simulations and experiments were performed, and the cell averaging constant false alarm rate detector was used to calculate the detection rate. The average value of detection rates of AF-MED, MED and the orthogonal basis function (OBF) are about 69%, 21% and 43% respectively when SNR is low (SNR from −25 dB to −50 dB). The results demonstrated the superiority of the proposed method over the MED and the OBF.

Novel Distance Measures on Hesitant Fuzzy Sets Based on Equal-Probability Transformation and Their Application in Decision Making on Intersection Traffic Control

The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets (HFSs). The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements (HFEs) in a special way. Firstly, a probability density function is assigned for any given HFE. Thereafter, equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function. The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs, the higher the credibility of the mentioned membership degrees is, then, the bigger the probability density values for them are. According to this transformation technique, a set of novel distance measures on HFSs is provided. Finally, an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures. The example also shows that this study is a good complement to operation theories on HFSs.

Scattering of a twisted electron wavepacket by a finite laser pulse

The behavior of a twisted electron colliding with a linearly polarized laser pulse is investigated within relativistic quantum mechanics. In order to better fit the real experimental conditions, we introduce a Gaussian spatial profile for the initial electron state as well as an envelope function for the laser pulse, so the both interacting objects have a finite size along the laser propagation direction. For this setup we analyze the dynamics of various observable quantities regarding the electron state: the probability density, angular momentum, and mean values of the spatial coordinates. It is shown that the motion of a twisted wavepacket can be accurately described by averaging over classical trajectories with various directions of the transverse momentum component. On the other hand, full quantum simulations demonstrate that the ring structure of the wavepacket in the transverse plane can be significantly distorted leading to large uncertainties in the total angular momentum of the electron. This effect remains after the interaction once the laser pulse has a nonzero electric-field area.

Reliability analysis of underground tunnel by a novel adaptive Kriging based metamodeling approach

An adaptive Kriging based metamodeling approach for tunnel reliability analysis strategy is proposed with due consideration to accuracy and efficiency. Based on a preliminary design of experiments (DOE), an initial Kriging model is constructed. Subsequently, a reduced space is built from the Monte Carlo Simulation (MCS) points located near the limit state surface. The MCS points closer to the existing training points are removed from the reduced space to avoid clustering. Finally, the MCS point having the highest joint probability density value is selected from the reduced space. The inclusion of such a point in the DOE is expected to improve the prediction accuracy of a maximum number of neighbouring points. The selection of new training points and updating the Kriging model iteratively is continued until no point is left in the reduced space. The estimated failure probability is considered final if its coefficient of variation is less than a predefined threshold; otherwise a new set of MCS samples are considered for further iterations. The effectiveness of the proposed algorithm is demonstrated by three tunnel reliability analysis problems and noted to be quite efficient and superior over the AK-MCS method in most of the cases.

An improved entorpy-based representation for mixed uncertainty about intervals and points data

In engineering design problems, intervals refer to any kind of lack of information. This paper presents an improved entorpy-based methodology for a probabilistic representation of a stochastic quantity for which only sparse point data and/or interval data may be available. The combined entropy function is used to measure the uncertainty in data, which is evaluated from the non-parametric probability density function for sparse point data and the cumulative distribution function for interval data, Wherein the entire non-parametric distribution can be discretized at a finite number of points and the probability density values at these points can be inferred using the principle of maximum-entropy, thus avoiding the assumption of any particular distribution. The proposed improved Entorpy-based methodology is then employed in the attempt of interval uncertainty propagation, with the results compared with previous studies. Examples are provided to demonstrate the effectiveness of present method. The study reveals great potentials of the probabilistic method for the treatment of the uncertainty in presence of the sparse point data and/or interval data.

Estimation of dynamic systems using a method of characteristics filter

This paper deals with the technical formulation and implementation details of an algorithm that provides an estimate of the probability density function of the state of a nonlinear dynamical system from discrete time measurements. In contrast to other state estimation methods that propagate the conditional moments, the proposed filter is shown to propagate and update the full probability density function of the state. Characteristic solutions to the Liouville equation are used to propagate the exact probability density values along the flow of the dynamical system. The reconstruction of the state probability density function is then posed as a convex programming problem. An adaptive regression-tree based region-decomposition approach is used to efficiently compute expectation integrals involved in implementing the Bayes rule associated with posterior density function. Numerical examples capturing the non-Gaussian nature of the uncertainty in the duffing oscillator problem and the two body problem are used to demonstrate the efficacy of the proposed methods.

Spin relevant invariants and the general solution of the Dirac equation for the Coulomb fields

The Dirac equation with the Coulomb potential is studied. A new spin relevant invariant is introduced, which does not commute with the Dirac and Johnson–Lippmann integrals of motion. The solutions of the Dirac equation compatible with each of the above three invariants are found and shown to be different. The explicit expressions for the Dirac bispinors are found for each of the three spin related invariants. The generalized invariant is constructed and corresponding to it general solution of the Dirac equation with the Coulomb potential is obtained. The general solution contains free parameters, whose particular values reduce it to any of the three particular solution. It is shown that the distributions of the electron probability density and expectation values of the electron spin direction in the hydrogen-like energy spectrum depend essentially on the spin relevant invariant. This demonstrates physical difference of the states corresponding to different invariants, which can be experimentally manifested.

Improvement of Automatic Measurement Evaluation System for Subway Structures by Adjacent Excavation.

This study evaluated the structural stability of subway structures based on adjacent excavations by comparing automatically measured and numerically analyzed data. The reliability of the automated measurement methodology was evaluated by first applying probability statistical analysis to the measured results and then comparing these results with the numerically analyzed results. An improvement in the calculation method evaluation system, including the method of processing and analysis of the automatically measured data of subway structures through the average value of probability density, was proposed. As a result of the field measurement and numerical analysis, the measured results of tunnel displacement and track deformation exhibited some differences. However, it was determined that the construction stage and location where the maximum values of the tunnel displacement and track deformation occurred had similarities.

Estimation of sea clutter parameter based on the multi-feature-point model validation method

Research on sea clutter modeling is meaningful for the sea clutter jamming rejection in radar detection. The previous methods cannot fit the characteristics such as the peak value and amplitude width of the sea clutter amplitude distribution curves. Thus, an estimation method of sea clutter based on the multi-feature-point model validation is proposed. First, the amplitude distribution characteristics and temporal correlation of sea clutter are analyzed, and the spherically invariant random process is used to simulate the K-distribution sea clutter model. Then, six feature points are constructed, (i.e., the maximum probability density, the amplitude value of maximum probability density, the 3 dB amplitude width, the amplitude widths corresponding to 1/3, and 2/3 of the maximum probability density, and the amplitude critical value corresponding to probability density lower than 0.01). Based on the multigroup feature points of the amplitude distribution curves, the radial basis function (RBF) neural network is trained to derive the relationship between the multiple features and the shape parameter and predict the shape parameter of the measured data. Finally, the simulation results show that the proposed method can fit the characteristics of the actual sea clutter amplitude distribution more accurately than the previous estimation methods.

Fat Tail in the Phytoplankton Movement Patterns and Swimming Behavior: New Insights into the Prey-Predator Interactions

Phytoplankton movement patterns and swimming behavior are important and basic topics in aquatic biology. Heavy tail distribution exists in diverse taxa and shows theoretical advantages in environments. The fat tails in the movement patterns and swimming behavior of phytoplankton in response to the food supply were studied. The log-normal distribution was used for fitting the probability density values of the movement data of Oxyrrhis marina. Results showed that obvious fat tails exist in the movement patterns of O. marina without and with positive stimulations of food supply. The algal cells tended to show a more chaotic and disorderly movement, with shorter and neat steps after adding the food source. At the same time, the randomness of turning rate, path curvature and swimming speed increased in O. marina cells with food supply. Generally, the responses of phytoplankton movement were stronger when supplied with direct prey cells rather than the cell-free filtrate. The scale-free random movements are considered to benefit the adaption of the entire phytoplankton population to varied environmental conditions. Inferentially, the movement pattern of O. marina should also have the characteristics of long-range dependence, local self-similarity and a system of fractional order.

Probability granular distance-based fuzzy rough set model

Fuzzy rough set theory is sensitive to noisy samples as the fuzzy approximations are proposed based on sensitive statistics, i.e. minimum and maximum. Here, we develop a robust fuzzy rough set model called probability granular distance-based fuzzy rough sets (PGDFRS), in which the similarity between samples is substituted by that between granules to reduce the impact of noise on the statistical minimum and maximum. The robust principle is to take the probability density values of samples as weights for computing probability distances between granules. By using PGDFRS, a feature selection algorithm is created. This algorithm limits feature selection to two-dimensional space and avoids the difficulty of parameter setting in high-dimensional space. The experimental results indicate that the designed feature selection algorithm is effective and robust. Additionally, it confirms that the proposed PGDFRS model is more robust than some existing fuzzy rough set models.

Spiral spectrum of the phase singularity beam in the source plane and atmospheric turbulence

The phase singularity beam has a unique wavefront phase structure—a screw dislocation (optical vortex) or edge dislocation—which is closely related to the orbital angular momentum (OAM). Screw dislocation refers to the phase change of integer multiples of 2π around a point, while edge dislocation refers to the existing π phase shift along a curve in the wavefront phase distribution. In this study, we derived the OAM detection probability expression and mode probability density expression of the phase singularity beam propagating through atmospheric turbulence. These expressions were used to examine the spiral spectrum and the OAM mode probability density of the phase singularity beam. It was determined that the phase singularity beam carrying a noncanonical optical vortex or an edge dislocation has more than one OAM state, whereas the phase singularity beam carrying a canonical optical vortex has only one OAM state. In atmospheric turbulence transmission, atmospheric disturbances will cause crosstalk between OAM states. The larger is the detection probability of the OAM state at the source plane, the closer is the maximum value of the OAM mode probability density throughout the transmission process to the beam center. The conclusions obtained have important applications in optical communications.

Colorist: An r package for colouring wildlife distributions in space–time

Abstract Maps are essential tools for communicating information about wildlife distributions in space and time. As observational datasets grow and enable description of distributions at broader spatiotemporal extents and finer spatiotemporal resolutions, new opportunities arise for visualizing when and where animals occur. Here we present a package for the r statistical computing environment, colorist, that facilitates visualization of animal distributions in space and time using raster inputs. In addition to enabling display of sequential change in distributions through the use of small multiples, colorist provides functions for extracting several features of interest from a sequence of distributions and for visualizing those features within an HCL (hue–chroma–luminance) colour space. Resulting maps allow for ‘fair’ visual comparison of occurrence, abundance or probability density values across space and time and can be used to address questions about where, when and how consistently a species or individual is likely to be found. Functions can also be harnessed to visualize distributions of multiple species or individuals within a single time period when research questions are focused on understanding the degree to which species or individuals partition space. By colouring temporal features of distributions, while simultaneously controlling their perceptual weight, we expand the set of tools available for exploring wildlife movements through space–time and for communicating research results. We expect colorist functions will prove useful for visualizing other types of multivariate data that we have yet to consider.

Coherent states in magnetized anisotropic 2D Dirac materials

In this work, we construct coherent states for electrons in anisotropic 2D Dirac materials immersed in a uniform magnetic field orthogonal to the sample. In order to describe the bidimensional effects on electron dynamics in a semiclassical approach, we adopt the symmetric gauge vector potential to describe the magnetic field. By solving a Dirac-like equation with an anisotropic Fermi velocity, we define two sets of generalized ladder operators that are generators of either the Heisenberg–Weyl or su(1,1) algebra and construct coherent states as eigenstates of the generalized annihilation operators with complex eigenvalues. In order to illustrate the anisotropy effects on these states, we obtain their probability density and mean energy value. Depending upon the anisotropy, expressed by the ratio between the Fermi velocities along the x- and y -axes, the shape of the probability density is modified on the xy-plane with respect to the isotropic case and according to the classical dynamics.

Numerical solution of Fokker-Planck equation for single domain particles

The Fokker-Planck equation proposed by Brown to describe the evolution of the probability distribution density of the orientation of the magnetic moment of a single-domain particle is usually solved by expanding the unknown function in a series of spherical harmonics. In this paper, we use a different method to solve the Fokker-Planck equation, namely, the finite element method. We describe the procedure for constructing a triangular grid on the surface of a sphere and give formulas for calculating the coefficients of the equations for the probability density values at the grid nodes. As an example, the results of calculating the dynamic magnetic hysteresis for particles with cubic anisotropy are demonstrated.