Information Reconstruction Error Evaluation Method Based on Singular Entropy Method

Complexity versus regularity is an important component of appropriate joint position to retain balance but has not received much attention. The Singular value decomposition entropy (SvdEn) characterizes information content or regularity of a signal depending on the number of vectors attributed to the process. The current study aimed to investigate the effect of kinesiology tape compared to static strapping tape and no tape on ankle joint dynamics during the Y balance test. Forty-one participants (21 males; 20 females) aged between 18 and 34 years of age completed the Y-balance test with kinesiology tape, with strapping tape and without tape applied to the dominant leg. SvdEn was obtained from center of pressure values, as well as ankle and knee movement variability during the Y balance test. Center of pressure and knee joint dynamics did not change significantly between the two taped and no tape conditions during the YBT. Ankle joint SvdEn was significantly lower in the anterior-posterior (p<; .05) and superior-inferior (p<; .001) direction for both tape conditions compared to no tape. Greater regularity in the ankle joint dynamics indicates less vectors are required to describe the signal, which can be interpreted from a neurophysiological perspective as a decrease in feedforward and/or feedback input along the hierarchical sensorimotor processing pathway as an adjustment to taping and a possibly more reflex oriented response localised at the spinal cord level.

In nonlinear error growth dynamics, the initial error cannot be accurately determined, and the forecast error, which is also uncertain, can be considered to be a random variable. Entropy in information theory is a natural measure of the uncertainty of a random variable associated with a probability distribution. This paper effectively combines statistical information theory and nonlinear error growth dynamics, and introduces some fundamental concepts of entropy in information theory for nonlinear error growth dynamics. Entropy based on nonlinear error can be divided into time entropy and space entropy, which are used to estimate the predictabilities of the whole dynamical system and each of its variables. This is not only applicable for investigating the dependence between any two variables of a multivariable system, but also for measuring the influence of each variable on the predictability of the whole system. Taking the Lorenz system as an example, the entropy of nonlinear error is applied to estimate predictability. The time and space entropies are used to investigate the spatial distribution of predictability of the whole Lorenz system. The results show that when moving around two chaotic attractors or near the edge of system space, a Lorenz system with lower sensitivity to the initial field behaves with higher predictability and a longer predictability limit. The example analysis of predictability of the Lorenz system demonstrates that the predictability estimated by the entropy of nonlinear error is feasible and effective, especially for estimation of predictability of the whole system. This provides a theoretical foundation for further work in estimating real atmospheric multivariable joint predictability.

The characteristics of power electronic controlled sources are reflected at both ends of the AC line applied to the integration of long-distance wind farms into the MMC-HVDC converter station, and the fault characteristics of the system have undergone fundamental changes. For the doubly-fed wind power AC transmission line with a modular multilevel converter, the short-circuit current characteristics provided by the power supply at both ends of the line lead to the inadaptability of longitudinal differential protection. In view of the significant difference in the complexity of the short-circuit current component provided by the doubly-fed wind power and the converter at both ends of the AC transmission line, a line pilot protection idea based on the complexity of the current component is proposed. The complexity of the current component is characterized by singular entropy theory, and then the singular entropy algorithm and its scheme for pilot protection are constructed. A refined electromagnetic transient model of MMC-HVDC for doubly-fed wind farms is built in PSCAD for simulation verification. The simulation results show that the proposed method can quickly and reliably identify various types of internal and external faults, and solve the problem of incorrect action of traditional protection in this scenario. In addition, the scheme is not affected by fault type, location, or transition resistance.

Data Mining is the process to extract hidden predictive information from large databases. In Bioinformatics, data mining enables researchers to meet the challenge of mining large amount of biomolecular data to discover real knowledge. Major research efforts done in the area of bioinformatics involves sequence analysis, protein structure prediction and gene finding. Proteins are said to be prominent molecules in our cells. They involve virtually in all cell functions. The activities and functions of proteins can be determined by protein sequence motifs. These protein motifs are identified from the segments of protein sequences. All segments may not be important to produce good motif patterns. The generated sequence segments do not have classes or labels. Hence, unsupervised segment selection technique is adopted to select significant segments. Therefore Singular Value Decomposition (SVD) entropy method is adopted to select significant sequence segments. In this proposed work, weighted K-Means and Adaptive Fuzzy C-Means have been applied to the selected segments to generate granules, since large amount of segments cannot be grouped or clustered as such. Each granules generated by weighted K-Means algorithm are further clustered by using the K-Means algorithm and granules generated by Adaptive Fuzzy C-Means algorithm are clustered by using Weighted K-Means. The two proposed models are compared with K-Means granular computing model. The experimental results show that Adaptive Fuzzy C-Means with Weighted K-Means technique produces better results than K-Means and weighted K-Means granular computing methods.

Efficient methods for loading given classical data into quantum circuits are essential for various quantum algorithms. In this paper, we propose an algorithm called Approximate Amplitude Encoding that can effectively load all the components of a given real-valued data vector into the amplitude of quantum state, while the previous proposal can load only the absolute values of those components. The key of our algorithm is to variationally train a shallow parameterized quantum circuit, using the results of two types of measurement: the standard computational-basis measurement plus the measurement in the Hadamard-transformed basis, introduced in order to handle the sign of the data components. The variational algorithm changes the circuit parameters so as to minimize the sum of two costs corresponding to those two measurement basis, both of which are given by the efficiently computable maximum mean discrepancy. We also consider the problem of constructing the singular value decomposition entropy via the stock market data set to give a financial market indicator; a quantum algorithm (the variational singular value decomposition algorithm) is known to produce a solution faster than classical, which yet requires the sign-dependent amplitude encoding. We demonstrate, with an in-depth numerical analysis, that our algorithm realizes loading of time series of real stock prices on quantum state with small approximation error, and thereby it enables constructing an indicator of the financial market based on the stock prices.

Using Rényi parameter to improve the predictive power of singular value decomposition entropy on stock market

FEM-based scattered data modeling and visualization

Gappy POD, based on proper orthogonal decomposition (POD), is a method to repair missing data. A gappy POD-based interpolation method for the separation trajectory of the external store is proposed to address the challenge of low computational efficiency of the current numerical simulation based on computational fluid dynamics. Firstly, the numerical simulation method based on quasi-steady computational fluid dynamics was employed to calculate the separation trajectory of the external store in various drop conditions. Then, the data features of the separation trajectory, used as a known data set, were extracted using the gappy POD method for the reconstruction of the missing separation trajectory in the target drop condition. The effect of known sample size and data missing rate on reconstruction error was studied. The results show that the gappy POD method can quickly and accurately reconstruct the missing separation trajectory of the store in the target condition based on the known trajectory data set, even when only a small amount of data sample is known.

This paper deals with the results on the reconstruction accuracy of the irregularly sampled discrete-time signal (DTS) with unknown sampling locations. Reconstruction is performed by means of special reconstruction algorithms based on the DTS values correction. The first algorithm is drawn on applying of the non-recursive smoothing filter (NRSF). The second algorithm is based on the local least squares signal approximation. Its accuracy is validated in the numerical examples. The proposed algorithms were compared to the several interpolation methods, one's using digital lowpass filter and the fast Fourier transform (FFT), by the reconstruction error.

Flow guided interpolation – A GIS-based method to represent contaminant concentration distributions in groundwater

Abstract. This project produced a Python language implementation of locally interpolated regression (LIR) and neural network (NN) algorithms from empirical seawater property estimation routines (PyESPERv1.0.0). These routines estimate total alkalinity, dissolved inorganic carbon, total pH, nitrate, phosphate, silicate, and oxygen from geographic coordinates, depth, salinity, and 16 combinations of zero to four additional predictors (temperature and biogeochemical information) and were previously available only in the MATLAB programming language. Here, we document modifications to reduce discrepancies between the implementations, calculate the disagreements between the methods, and quantify Global Ocean Data Analysis Project (GLODAPv2.2022) reconstruction errors with PyESPER. While the PyESPER routine based on neural networks (PyESPER_NN) faithfully reproduces the corresponding MATLAB routine estimates of properties that do not require anthropogenic carbon change information, PyESPER_LIR and – to a lesser extent – PyESPER_NN estimates for total pH and dissolved inorganic carbon do not exactly reproduce the MATLAB routine estimates due to differences in interpolation and extrapolation methods between the programming languages. While the MATLAB and Python LIR-based estimates are not identical, we show that they are similarly skilled at reproducing the GLODAPv2.2022 data product and are thus comparable. This project increases the accessibility of ESPERv1.01.01 algorithms by providing users with code in the freely available Python language and enables future ESPER updates to be released in multiple coding languages.

The reconstruction error estimation of the Gaussian Markov process in the presence of jitter is investigated in this paper, taking into account mainly two samples in the analysis. Two different situations are considered. In the first situation, the position of the first sample does not have jitter, but it exists in the second sample. In the second condition, the two samples have the presence of jitter. The probability density functions of jitter are represented by the uniform and the Erlang distributions. The results are obtained by applying statistical averaging to the conditional mean rule with respect to the random variable of jitter. This rule defines the conditional variance function as reconstruction error function, which allows us to determine the reconstruction error of the Gaussian Markov process on the whole time domain.

This paper presents a novel approach to estimate the order of a parametric Linear Time-Invariant (LTI) system. To achieve this goal, we define a new objective function. This measure is denoted by reconstruction-error distortion. Tight probabilistic upper and lower bounds are obtained and a gap function for these bounds on the reconstruction-error distortion is derived. We propose to choose the order of the LTI system based on optimality the considered objective function in the form of reconstruction-error distortion. Information rate distortion function for this distortions is calculated. We show that the rate for reconstruction-error distortion is robust with respect to the probabilistic parameters in reconstruction error estimation. In addition, it is shown that the estimated order by reconstruction error distortion not only provides the maximum possible rate distortion, but also minimized the gap function.

Groundwater is one of the major sources of exploitation in mid-eastern China. Thus for protecting groundwater quality, data on spatial and temporal distribution is important. Geostatistics methods are one of the most advanced techniques for interpolation of groundwater quality. In this research, ordinary kriging was used for predicting spatial distribution of some groundwater characteristics including pH, salinity, total hardness, ammonia nitrogen, volatile phenol, CODMn, SO42-, Cl-, F-, nitrate nitrogen, and nitrite nitrogen. Sampling data were collected and statistical analyses from 45 wells even distributing in Huaihe river basin. After statistical analysis of data, for selecting suitable model for fitness on experimental variograme, a cross validation indicators and additional model parameters was used to select the best method for interpolation. Results showed that ordinary kriging methods are suit to spatial interpolation of groudwater quality. Finally, filled contour maps generating from their semivariograms are drawn and predict the change of groundwater quality in the basin.

The electromagnetic radiation (EMR) data collected along a road have a largely empty region overall, while they have a linear distribution locally. Moreover, the traditional spatial interpolation method is not suitable for the electromagnetic radiation space field (EMR-SF) construction collected along the road. In this paper, a layered radial basis function (LRBF) method is proposed to generate the EMR-SF, which interpolates from outside to inside in a layered strategy. First, the regular grid points are constructed based on RBF within the range of sampling data and then are layered based on Ripley’s K function. Second, on the basis of layering, the EMR of grid points is generated layer by layer using the LRBF method. Finally, EMR-SF is constructed by using the sampling data and grid points. The LRBF method is applied to EMR data from an area of Yunnan Normal University in Kunming, China. The results show that the LRBF accuracy is higher than that of the ordinary kriging (OK) and inverse-distance-weighted (IDW) interpolation methods. The LRBF interpolation accuracy can be improved through the strategy of regular grid point construction and layering, and the EMR-SF constructed by LRBF is more realistic than OK and IDW.