regularized methods
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Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2103
Author(s):  
Bingnan Jiang ◽  
Yuanheng Wang ◽  
Jen-Chih Yao

In this paper, we construct two multi-step inertial regularized methods for hierarchical inequality problems involving generalized Lipschitzian and hemicontinuous mappings in Hilbert spaces. Then we present two strong convergence theorems and some numerical experiments to show the effectiveness and feasibility of our new iterative methods.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Nguyen Hoang Luc ◽  
Devendra Kumar ◽  
Le Dinh Long ◽  
Ho Thi Kim Van

In this paper, we study a diffusion equation of the Kirchhoff type with a conformable fractional derivative. The global existence and uniqueness of mild solutions are established. Some regularity results for the mild solution are also derived. The main tools for analysis in this paper are the Banach fixed point theory and Sobolev embeddings. In addition, to investigate the regularity, we also further study the nonwell-posed and give the regularized methods to get the correct approximate solution. With reasonable and appropriate input conditions, we can prove that the error between the regularized solution and the search solution is towards zero when δ tends to zero.


2021 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Yiting Chen ◽  
◽  
Jia Li ◽  
Qingyun Yu

Author(s):  
Lixin Ren ◽  
Caixia Gao ◽  
Zhana Duren ◽  
Yong Wang

Abstract The DNA methyltransferases (DNMTs) (DNMT3A, DNMT3B and DNMT3L) are primarily responsible for the establishment of genomic locus-specific DNA methylation patterns, which play an important role in gene regulation and animal development. However, this important protein family’s binding mechanism, i.e. how and where the DNMTs bind to genome, is still missing in most tissues and cell lines. This motivates us to explore DNMTs and TF’s cooperation and develop a network regularized logistic regression model, GuidingNet, to predict DNMTs’ genome-wide binding by integrating gene expression, chromatin accessibility, sequence and protein–protein interaction data. GuidingNet accurately predicted methylation experimental data validated DNMTs’ binding, outperformed single data source based and sparsity regularized methods and performed well in within and across tissue prediction for several DNMTs in human and mouse. Importantly, GuidingNet can reveal transcription cofactors assisting DNMTs for methylation establishment. This provides biological understanding in the DNMTs’ binding specificity in different tissues and demonstrate the advantage of network regularization. In addition to DNMTs, GuidingNet achieves good performance for other chromatin regulators’ binding. GuidingNet is freely available at https://github.com/AMSSwanglab/GuidingNet.


Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1048
Author(s):  
Le Dinh Long ◽  
Yong Zhou ◽  
Tran Thanh Binh ◽  
Nguyen Can

We consider a time-fractional diffusion equation for an inverse problem to determine an unknown source term, whereby the input data is obtained at a certain time. In general, the inverse problems are ill-posed in the sense of Hadamard. Therefore, in this study, we propose a mollification regularization method to solve this problem. In the theoretical results, the error estimate between the exact and regularized solutions is given by a priori and a posteriori parameter choice rules. Besides, the proposed regularized methods have been verified by a numerical experiment.


2018 ◽  
Vol 8 (11) ◽  
pp. 2213 ◽  
Author(s):  
Krzysztof Przednowek ◽  
Zbigniew Barabasz ◽  
Maria Zadarko-Domaradzka ◽  
Karolina Przednowek ◽  
Edyta Nizioł-Babiarz ◽  
...  

This study presents mathematical models for predicting VO2max based on a 20 m shuttle run and anthropometric parameters. The research was conducted with data provided by 308 young healthy people (aged 20.6 ± 1.6). The research group includes 154 females (aged 20.3 ± 1.2) and 154 males (aged 20.8 ± 1.8). Twenty-four variables were used to build the models, including one dependent variable and 23 independent variables. The predictive methods of analysis include: the classical model of ordinary least squares (OLS) regression, regularized methods such as ridge regression and Lasso regression, artificial neural networks such as the multilayer perceptron (MLP) and radial basis function (RBF) network. All models were calculated in R software (version 3.5.0, R Foundation for Statistical Computing, Vienna, Austria). The study also involved variable selection methods (Lasso and stepwise regressions) to identify optimum predictors for the analysed study group. In order to compare and choose the best model, leave-one-out cross-validation (LOOCV) was used. The paper presents three types of models: for females, males and the whole group. An analysis has revealed that the models for females ( RMSE C V = 4.07 mL·kg−1·min−1) are characterised by a smaller degree of error as compared to male models ( RMSE C V = 5.30 mL·kg−1·min−1). The model accounting for sex generated an error level of RMSE C V = 4.78 mL·kg−1·min−1.


2018 ◽  
Author(s):  
Donald Ray Williams ◽  
Mijke Rhemtulla ◽  
Anna Wysocki ◽  
Philippe Rast

An important goal for psychological science is developing methods to characterize relationships between variables. The customary approach uses structural equation models to connect latent factors to a number of observed measurements. More recently, regularized partial correlation networks have been proposed as an alternative approach for characterizing relationships among variables through covariances in the precision matrix. While the graphical lasso (glasso) method has merged as the default network estimation method, it was optimized in fields outside of psychology with very different needs, such as high dimensional data where the number of variables (p) exceeds the number of observations (n). In this paper, we describe the glasso method in the context of the fields where it was developed, and then we demonstrate that the advantages of regularization diminish in settings where psychological networks are often fitted (p ≪ n). We first show that improved properties of the precision matrix, such as eigenvalue estimation, and predictive accuracy with cross-validation are not always appreciable. We then introduce non-regularized methods based on multiple regression, after which we characterize performance with extensive simulations. Our results demonstrate that the non-regularized methods consistently outperform glasso with respect to limiting false positives, and they provide more consistent performance across sparsity levels, sample composition (p=n), and partial correlation size. We end by reviewing recent findings in the statistics literature that suggest alternative methods often have superior than glasso, as well as suggesting areas for future research in psychology.


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