Ridge Trace Research Articles

Ridge estimation for uncertain autoregressive moving average model with imprecise observations

An uncertain time series is a sequence of imprecisely observed values arranged in chronological order, whose main purpose is to predict future values based on previously observed values. It is significant to select an appropriate parameter estimation method in uncertain time series analysis. Firstly, the paper transforms a one-order uncertain autoregressive moving average model into an uncertain autoregressive model by the iterative method. Secondly, the ridge method is used to estimate the unknown parameters in the uncertain autoregressive moving average model, in which the shrinkage parameter is determined by ridge trace analysis. Thirdly, the forecast value and confidence interval are acquired by the residual analysis of the fitted model. Finally, two examples are provided to verify the validity and feasibility of the method. The result shows that the ridge method can effectually cut down the affection of outliers and improve the prediction accuracy compared with the least square estimation.

RETRACTED: Elasticity of substitution between clean energy and non-clean energy: Evidence from the Chinese electricity industry

At present, China is in a stage of high-quality economic development. Rising demand for electricity has created a lot of CO2 emissions, which has put great pressure on the low-carbon development of China's power industry. Therefore, China attaches great importance to the potential of various clean power generation to replace thermal power generation. Given this, the study examines the potential for substitution of non-clean energy generation (thermal power generation) and clean energy generation (hydropower, nuclear power generation, and other energy generation) from 1993 to 2022 by using the translog production function and provides a scenario analysis of energy substitution for power generation. Firstly, the k-fold cross-validation method is used for ridge regression estimation in this paper, which avoids the subjective bias caused by the ridge trace diagram method used in most of the previous literatures. Secondly, compared with the previous research on the substitution elasticity of the power sector, this paper subdivides the types of clean power energy when estimating the substitution elasticity, which can better analyze the substitution relationship between thermal power and various clean power. Finally, the estimated substitution elasticity of thermal power and various clean energy sources is greater than 1, which indicates that clean energy generation can effectively replace non-clean energy generation. This provides an effective substitution elasticity parameter for the power sector to study low-carbon development. The scenario analysis show China's power sector can increase the proportion of clean power generation to reduce the carbon emission intensity while ensure power supply, which can help the Chinese government adjust the implementation of policies to promote the early peak of carbon emissions and keep carbon emission at a low level in the power sector.

A Method for Solving Ill-Conditioned Nonlinear Least Squares Problems and Its Application in Image Distortion Correction Using Self-Calibration

In this study, the ill-conditioning of the iterative method for nonlinear models is discussed. Due to the effectiveness of ridge estimation for ill-conditioned problems and the lack of a combination of the H-K formula with the iterative method, the improvement of the LM algorithm is studied in this paper. Considering the LM algorithm for ill-conditioned nonlinear least squares, an improved LM algorithm based on the H-K formula is proposed for image distortion correction using self-calibration. Three finite difference methods are used to approximate the Jacobian matrix, and the H-K formula is used to calculate the damping factor in each iteration. The Brown model, quadratic polynomial model and Fourier model are applied to the self-calibration, and the improved LM algorithm is used to solve the model parameters. In the simulation experiment of space resection of a single image, we evaluate the performance of the LM algorithm based on the gain ratio (LMh) and the improved LM algorithm based on the H-K formula (LMHK), and the accuracy of different models and algorithms is compared. A ridge trace analysis is carried out on the damping factor to illustrate the effects of the improved algorithm in handling ill-conditioning. In the second experiment, the improved algorithm is applied to measure the diameter of a coin using a single camera. The experimental results show that the improved LM algorithm can reach the same or higher accuracy as the LMh algorithm, and it can weaken the ill-conditioning to a certain extent and enhance the stability of the solution. Meanwhile, the applicability of the improved LM algorithm in self-calibration is verified.

Study of the fingerprints of a Spanish sample for the determination of the hand and finger

The individuality and permanence of fingerprints make of them a very useful feature in the identification of individuals. There are now automated computer programmes that allow a quick comparison between a fingermark and a database. However, in order to assess the strength of evidence in fingerprint identification, complementary information on the frequencies of the different morphological features of the dermopapillary ridges is required. This idea is used in this work as a starting point to evaluate the frequencies of the parameters used in the determination of the hand and finger in a large sample of 2600 fingerprints taken from 134 male and 127 female Spanish population. Based on these fingerprints, the frequencies of different categories of the following parameters were obtained: type of pattern, slope of the apex ridge, subtype of two-delta pattern, ridge tracing, major angle, major ridge count, bisector, rotation of the central ridge, assimilation to loops and slant. Moreover, the results have shown that these characters are useful for the determination of the hand in whorls (two-delta pattern) and loops (one-delta pattern), but not for the determination of the finger. The most useful and classificatory parameter when determining the hand of origin of a two-delta fingerprint is the slope of the apex ridge, and for the one-delta pattern, knowing the location of the delta allows the correct estimation of the hand of a fingerprint in more than 93% of the cases. The data presented in this paper are novel and can be used by latent print examiners to improve the statistical basis of their decisions in reaching conclusions.

Multidimensional Attribution and Governance Optimization Path of State Audit to Promote Rural Revitalization in the Information Age

Abstract With the in-depth implementation of the rural revitalization strategy, it is of great significance to study the supervision and governance mechanism of national audit in the implementation of the rural revitalization strategy. As the main components with smaller contribution rates will be discarded when evaluating and analyzing the influencing factors of rural revitalization, it may affect the analytical judgment of the actual problem. Therefore, based on stepwise regression, this paper adopts ridge regression to correct multicollinearity, with the help of the ridge trace diagram to judge the correlation between independent variables intuitively and quickly, and through the ridge calculation as much as possible to retain the independent variables that have a greater impact on rural revitalization. The principal component-ridge regression model is proposed because it takes into account the advantages and disadvantages of various regression methods. To solve the problem of unstable regression coefficients caused by multiple covariances, to analyze the important influencing factors of state auditing on rural revitalization according to the regression coefficients, and to establish the governance optimization path of state auditing to promote rural revitalization. According to the regression results, the government audit variable has a significance level of 1%. The comprehensive governance function of government audit has a regression coefficient of -0.038 that shows significant and negative results at a 1% confidence level. The performance scores of rural sustainability as well as financial dimensions are in the range of 0.8 to 1, which is a good level.

An investigation on the application of Ridge regression model in the optimization of virtual practice teaching innovation path of Civics and Politics courses in colleges and universities

Abstract Civic and political affairs course is a key course for colleges and universities to implement the fundamental task of cultivating people with moral character, and the rapid development of network technology and the information age has had a direct impact on the Civic and political affairs course in colleges and universities. This paper puts forward the optimization path of virtual practice teaching for Civic and Political Science courses in colleges and universities from three aspects: establishing a virtual simulation practice teaching website for Civic and Political Science courses in colleges and universities, constructing a virtual simulation practice teaching information resource base for Civic and Political Science courses and optimizing the content system of virtual simulation practice teaching for Civic and Political Science courses. In order to verify the effect of virtual practice teaching, this paper proposes a new determination method as well as a Ridge regression model for the selection of Ridge parameter K in the Ridge trace method by analyzing the existence of Ridge parameter K and the excellence of Ridge estimation. The Ridge regression model was used to examine the impact of virtual teaching on college Civics and Politics classes and found that the standardized regression coefficient beta for the virtual teaching environment is 0.113, showing significant performance. For the virtual practice teaching of Civic and Political Science classes in colleges and universities, the better the virtual teaching environment is, the better the classroom learning effect.

Evaluation and Improvement of the Method for Selecting the Ridge Parameter in System Differential Response Curves

The selection of an appropriate ridge parameter plays a crucial role in ridge estimation. A smaller ridge parameter leads to larger residuals, while a larger ridge parameter reduces the unbiasedness of the estimation. This paper proposes a constrained L-curve method to accurately select the optimal ridge parameter. Additionally, the constrained L-curve method, traditional L-curve method, and ridge trace method are individually coupled with the system differential response curve to update the streamflow in the Jianyang Basin using the SWAT model. Multiple evaluation criteria are employed to analyze the efficacy of the three methods for correction. The results demonstrate that the constrained L-curve method accurately identifies the optimal ridge parameter in the actual model. Furthermore, the coupling of the constrained L-curve method with the system differential response curve exhibits markedly superior accuracy of simulated streamflow compared to the traditional L-curve and ridge trace methods, with the mean Nash–Sutcliffe efficiency (NSE) improving from 0.71 to 0.88 after correction. The constrained L-curve method, which incorporates the physical interpretation of the estimated parameters, effectively identifies the optimal ridge parameter in practical scenarios. As a result, it demonstrates superior usability and applicability when compared to the traditional L-curve method.

Research on the role of psychological education in college Civic Education under the background of Internet

Abstract Psychological education in colleges and universities can inject new vitality into Civic Education. In this paper, the ridge estimation of regression parameters is based on the linear regression model, the canonical form of ridge regression is constructed, and the selection method of ridge parameters is proposed by combining the ridge trace plot and the Mcdorard-Garaneau method. The prediction accuracy of the ridge regression is optimized by using the idea of partial least squares for the shortcomings of the general ridge regression. After completing the improvement of ridge regression, the quantitative evaluation indexes of psychological education and Civic Education in colleges and universities were established, and the influence of psychological education on Civic Education was studied through regression analysis. The correlation coefficient R of faculty and hardware construction of psychological education on the content richness of Civic Education reached 0.725, and the standardized regression coefficient T of the former was −0.357, while the latter was −4.257, and the former was more significant than the latter. Meanwhile, the regression coefficients of organizational management and institutional setting, faculty construction and work organization and effectiveness on the level of college students’ psychological education were 0.54, 0.26 and 0.24, respectively, with significant joint effects. This study realizes the quantitative analysis of psychological education influencing Civic Education, which helps to promote the integration and development of psychological education and Civic Education.

On the choice of the ridge parameter: a generalized maximum Tsallis entropy approach

In multiple Regression Model the absence of multicollinearity is essential. The presence of multicollinearity is often caused by including too many (highly correlated) regressors and in this case, the estimates tend to be less precise. For this reason, varies methods have been introduced to solve these problems caused by the existence of multicollinearity. In this paper, a new method to estimate the ridge parameter, based on the ridge trace and an analytical method borrowed from Generalized Maximum Tsallis Entropy, is presented and we call that the Ridge GMET2 estimator. The performance of the new estimator is illustrated through a Monte Carlo simulation study. We compared the Ridge GMET2, Ridge GME and OLS estimators. Mean square error of Ridge GMET2 estimates, is less than corresponding for Ridge-GME and OLS estimates. In some case also, the value of the Ridge-GME and Ridge-GMET2 estimators are nearer, since Tsallis entropy does not depend on the logarithm unlike, the Shannon entropy, so that it is a substantial point that we prefer the Ridge-GMET2 estimator.

Efficient Generalized Ridge Regression

Abstract The original ridge estimator of the unknown p×1 vector of β-coefficients in a linear model used a single scalar, k, to determine a point on a shrinkage path of finite length that extends from the Ordinary Least Squares estimator, ^β 0, to the shrinkage terminus (usually ^β ≡ 0). Generalized ridge estimators use two or more parameters to determine not only the shape of their shrinkage path but also a specific point on that path. The efficient generalized ridge regression path proposed here is a continuous two-piece linear function that (1) starts at ^β 0, the Best Linear Unbiased Estimator, (2) has its interior knot at the ^ β-estimator with Maximum Likelihood of achieving overall minimum MSE risk under normal distribution-theory, and (3) ends at the shrinkage terminus. This new path is efficient in the senses that it is the shortest path and, at least when p > 2, essentially the only known shrinkage path that always contains the ^ β-vector that is most likely to be optimally biased. Functions in R-packages freely distributed via CRAN perform the calculations and produce the graphics used here to illustrate shrinkage concepts by interpreting ridge Trace diagnostic plots. These new concepts and visual tools provide invaluable data-analytic insights and improved self-confidence to applied researchers and data scientists fitting linear models when p, the number of non-constant X-predictor variables in the model, is strictly less than the number of observations available.

Current Smoking is a Risk Factor for the Irregular Surface and Calcification of Carotid Plaque in Men.

ObjectiveTo explore whether current smoking could influence plaque characteristics and determine its correlation to the irregular surface and calcification of carotid plaque.MethodsThree hundred and seventeen patients with severe carotid atherosclerosis stenosis (SCAS) detected by color duplex flow imaging (CDFI) and confirmed by CT angiography (CTA) were recruited. The results of laboratory parameters were collected by using electronic database of the hospital. Computerized tomography (CT) scanning and high-resolution ultrasonography were performed for assessment of plaque morphology, respectively.ResultsAll enrolled smokers and non-smokers had no significant difference among all characteristics not related to smoking. CT scanning could efficiently identify the difference among enrolled smokers and non-smokers not only for the characteristics related to smoking but also the onsets of carotid plaque. Surface morphology was also efficiently detected by ultrasonography. Further ridge trace analysis showed that ultrasonography is efficient for diagnosis of calcified plaque compared with gold standard for plaque diagnosis. Further correlation analysis showed that ultrasonography parameters could offer reliable evidence for plaque scores, which was associated with age index. Ultrasonography parameters could efficiently differentiate plaque morphologies among enrolled smokers and never-smokers.ConclusionCurrent smoking was positively associated with plaque calcification onsets, and smoking cessation could efficiently attenuate such injury. High-frequency ultrasound can clearly distinguish the details of calcification with promising clinical significance for current smoking patients.

Ridge Estimation for Uncertain Autoregressive Model with Imprecise Observations

The objective of time series analysis is to study the relationship between the data over time and to predict future values. Traditionally, statisticians assume that the observation data are precise, and we can get some exact values. However, in many cases, the imprecise observation data are available. We assume that these data are uncertain variables in the sense of uncertainty theory. In this paper, the ridge method is used to compute the unknown parameters in the uncertain autoregressive model. First, the ridge estimation of the parameters is given. The shrinkage parameter in the ridge estimation is obtained by ridge trace analysis. Based on the fitted autoregressive model, the forecast value and confidence interval of the future data are derived. Then two numerical examples are presented to verify the feasibility of this approach. Finally, the effectiveness of our model in reducing the influence of the outliers is shown by the comparative analysis.

Application of the ridge regression in the back analysis of a virgin stress field

When the least square approach is used to solve regression coefficients during the back analysis of a virgin stress field, the multicollinearity among independent variables may cause negative, too large, or non-significant regression coefficients, which can lead to an unreasonable virgin stress field. To make the virgin stress field obtained by a back analysis more reasonable, it is proposed that the ridge regression can be used to solve regression coefficients if multicollinearity exists. In the ridge regression, a small constant term was added to all diagonal elements of the correlation matrix to eliminate multicollinearity. Then this constant term was determined by ridge traces, the residual sum of squares, variance inflation factors, and statistical significance tests. To show the feasibility of determining a virgin stress field by the ridge regression, it was applied to the Heai tunnel located in Huili County, Sichuan Province, China. Results show that the ridge regression can avoid negative, too large, or non-significant regression coefficients effectively, and the virgin stress field obtained by the ridge regression is more reasonable and reliable than that obtained by the least square approach.

Model of Colour Value and Substance Concentration Based on Ridge Regression

Based on the data of colour value and substance concentration, the quantitative relationship between colour reading and substance concentration in digital photos is studied in this paper. Correlation coefficient, variance inflation factor (VIF) and condition indices are used to analyse the collinearity of variables, and the regression model of colour value and material concentration of digital photos is established by ridge regression method. The ridge trace shows that the least square regression coefficient is very unstable at high collinearity. As the bias parameter increases from 0 to 0.0477, the ridge regression coefficient becomes stabilized and the model’s coefficient of determination does not decrease significantly. The maximum VIF (k) is 3.5161 (less than 10), which indicates that the coefficients of the model constructed by the ridge regression method is more robust, and the prediction effect of the model is better than that estimated by the least square method.

In silico evaluation of inhibitory potential of novel triazole derivatives against therapeutic target myristoyl-CoA: protein N-myristoyltransferase (NMT) of Candida albicans

This paper explores the confluence of genetic algorithm-multiple linear regression (GA-MLR) based quantitative structure–activity relationship (QSAR) modeling and molecular docking simulation studies relevant to the novel and effective triazole derivatives as NMT inhibitors in an attempt to develop superior antifungal activity coupled with less susceptibility to develop resistance. Initially, thirteen penta-variant models were generated through hybrid GA-MLR based QSAR approach. Eventually, a general pooled model was derived through the collective consideration of all the descriptors incorporated in the stated thirteen models. The model was found to be predictive model as per traditional internal and external validation parameters (R2 = 0.829, Q2 = 0.759, $${R}_{\mathrm{adj}}^{2}\hspace{0.17em}$$ = 0.796, $${R}_{\mathrm{Pred}}^{2}$$ = 0.613) along with Y-randomization test and recently proposed various $$r_{m}^{2}$$ metrics. The proposed model is in agreement with Golbraikh and Tropsha recommendations supplemented by non-existence of multicollinearity via ridge trace, VIF trace and tolerance data analysis. The modeled descriptors signify the role of atomic van der Waals volume, nitrogen-containing fragment, number of hydrogen atoms and hydrogen bonding in modulating antifungal activity. Further, the molecular docking simulation studies reinforce the role of hydrogen bonding interactions in modulating the activity; as reflected by QSAR analysis; docking poses have revealed that four triazole derivatives were profusely bonded through hydrophobic, electrostatic and hydrogen bond interactions and stabilize into the active site of target protein NMT. Asn392 and His227 are key amino acid residues liable for generation of hydrogen bond interactions whereas Leu350 and Tyr354 amino acid residues were accountable for steric interactions. Based on the studies the two molecules are hypothesized and proposed with optimized biological function.

Single-digit fingerprint analysis for hand determination: A study of twinned loops.

In fingerprint analysis, the determination of hand (right or left) is one of the keys to resolving questions regarding the identity of the donor of the print. It is rare to encounter a complete set of 10-digit fingerprints from the scene of a crime. Although vital and imperative, except for a few studies on whorl patterns, the use of single-digit prints and patterns to ascertain the hand of the donor is scarcely reported in the literature. This research describes a novel approach whereby an analysis of twinned loops was carried out to identify the various parameters that may be helpful in ascertaining the hand of the donor. Bilateral rolled fingerprints from 180 healthy consenting adults belonging to a heterogeneous population of central India were collected. Out of the total of 1800 prints taken, 100 twinned loops (50 on the right hand and 50 on the left hand) were analysed. The following six parameters were considered: the slope of the flow of the apex ridges, the distance between the left delta and the ascending core, the distance between the right delta and the ascending core, mid-core position, the position of the loop and ridge tracing. On applying the chi-square test, the results were found to be statistically significant. Therefore, these parameters were found suitable for the determination of the hand from a single twinned-loop print.

Coastline Extraction from SAR Images Using Robust Ridge Tracing

Although ridge tracing has the advantages of continuity and high positioning accuracy compared with other edge-based methods, it is difficult to use ridge tracing to extract coastlines from Synthetic Aperture Radar (SAR) images because of the speckle noise that occurs in SAR images. This paper presents a new coastline extraction method for SAR images based on a more robust ridge tracing method. First, according to the statistical properties of the pixel intensities in the land and sea regions in a SAR image, an edge magnitude map that characterizes the boundary between them is produced by the ratio of the variance to the mean such that the magnitude at the land-sea boundary is much higher than that at other locations. Second, the pixel with the maximum magnitude in the map is adopted as the starting point for tracing, and strip windows, which reduce tracing failures, are adopted to obtain different average magnitudes corresponding to the eight neighborhood pixels around the starting point. Then, the neighborhood pixel with the maximum magnitude is adopted as the next tracing point. The above procedure is repeated to determine the direction of the next point. This process achieves part of the tracing operation. The complete coastline is then extracted by performing the other part of the tracing operation. The experimental results show that the proposed method is more robust than traditional methods, and we demonstrate its effectiveness with RADARSAT-2 and Sentinel-1A data.

Distribution of landslides along the Andean active orogenic front (Argentinean Precordillera 31–33° S)

As one of the main environmental effects of earthquakes, the distribution of landslides could reflect regional neotectonic activity. To that end, we carried out an inventory of landslides along the Precordillera range (31°-33°S) comprising the most seismically active region of Argentina. Main Quaternary deformation is concentrated in this Western central part of the country associated with active faults linked to intense shallow seismic activity (<35 km depth). During the last 150 years, the region has suffered at least six major earthquakes with a magnitude greater than Ms ≥ 7.0. The main focus of this research is to analyse the distribution of landslides along this Andean active orogenic front and characterize the response of collapses. We analysed morphological parameters of these landslides. According to our results, collapses match with traces of active Quaternary faults in this region. Landslides are clustered however, being more densely splayed in the centre of the study area and decreasing gradually towards the North and the South. We propose that the Juan Fernandez Ridge trace promotes a higher rate of deformation in this area, matching with higher historical seismicity and distribution of landslides.

Workload Frequency Scaling Law - Derivation and Verification

This article presents equations that relate to workload utilization scaling at a per-DVFS subsystem level. A relation between frequency, utilization, and scale factor (which itself varies with frequency) is established. The verification of these equations turns out to be tricky, since inherent to workload, the utilization also varies seemingly in an unspecified manner at the granularity of governance samples. Thus, a novel approach called histogram ridge trace is applied. Quantifying the scaling impact is critical when treating DVFS as a building block. Typical application includes DVFS governors and or other layers that influence utilization, power, and performance of the system. The scope here though, is limited to demonstrating well-quantified and verified scaling equations.

Spatial Upscaling of Sparse Soil Moisture Observations Based on Ridge Regression

Available ground-based observation networks for the validation of soil moisture remote sensing products are commonly sparse; thus, ground truth determinations are difficult at the validated remote sensing pixel scale. Based on the consistency of temporal trends between ground truth and in situ measurements, it is feasible to estimate ground truth by building a linear relationship between temporal sparse ground observations and truth samples. Herein, auxiliary remote sensing data with a moderate spatial resolution can be transformed into truth samples depending on the stronger representation of remote sensing data to spatial heterogeneity in the validated pixel relative to limited sites. When solving weighting coefficients for the relationship model, the underlying correlations among the in situ measurements cause the multicollinearity problem, leading to failed predictions. An upscaling algorithm called ridge regression (RR) addresses this by introducing a regularization parameter. With sparse sites, the RR method is tested in two cases employing six and nine sites, and compared with the ordinary least squares and the arithmetic mean. The upscaling results of the RR method show higher prediction accuracies compared to the other two methods. When the RR method is used, the six-site case has the same estimation accuracy as the nine-site case due to maintaining the diversity of in situ measurements through the analysis of the ridge trace and variance inflation factor (VIF). Thus, the ridge trace and VIF analysis is considered as the optimal selection method for the existing observation networks if the RR method will be used in future validation work. With a different number of sites, the RR method always displays the best estimation accuracy and is not sensitive to the number of sites, which indicates that the RR method can potentially upscale sparse sites. However, if the sites are too few, e.g., one to four, it is difficult to perform the upscaling method.