Problem In Many Fields Of Science Research Articles

A Bayesian Collocation Integral Method for Parameter Estimation in Ordinary Differential Equations

Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on basis functions or Gaussian processes to approximate the ODE solution and its derivatives. Due to the sensitivity of the ODE solution to its derivatives, these methods can be hindered by estimation error, especially when only sparse time-course observations are available. We present a Bayesian collocation framework that operates on the integrated form of the ODEs and also avoids the expensive use of numerical solvers. Our methodology has the capability to handle general nonlinear ODE systems. We demonstrate the accuracy of the proposed method through simulation studies, where the estimated parameters and recovered system trajectories are compared with other recent methods. A real data example is also provided. Supplementary materials for this article are available online.

Analytical and numerical simulation of the conformable new extended (2 + 1) dimensional Kadomtsev–Petviashvili equation

Partial differential equations are used to model problems in many scientific fields. To solve these equations, analytical and numerical techniques are created. This study considers the conformable version of the expanded Kadomtsev–Petviashvili equation in -dimensions for the first time. New exact and approximative solutions to the equation that do not exist in the literature are obtained using the analytical techniques of the -expansion and modified Kudryashov methods, as well as the numerical technique residual power series method. To better understand the dynamic nature of these findings, we have given 3D, contour, and 2D plots of some of the solutions. The development of numerous new exact solutions has demonstrated the reliability and effectiveness of the methods. We also provide an approximation table of values for the approximate solutions of the given equation using different values for various parameters.

Reproducible learning for accelerated failure time models via deep knockoffs

Selecting truly relevant variables contributing to the response is a fundamental problem in many scientific fields. One of major challenges in variable selection is to effectively control the false discovery rate (FDR). Most existing variable selection procedures in survival analysis neglect the FDR control. In this article, we fill such a gap and propose a new and flexible variable selection method with guaranteed FDR control for accelerated failure time models. The proposed method combines the strengths of deep knockoffs and the weighted M-estimation procedure and enjoys the FDR control for arbitrarily high dimension with finite samples. More importantly, our method does not require prior knowledge about the joint distribution of covariates. Extensive simulation studies confirm the generality, effectiveness, and power of the proposed method. Finally, the proposed method is used to analyze a primary biliary cirrhosis data to demonstrate its practical utility.

Deep Learning Solution of the Eigenvalue Problem for Differential Operators

Solving the eigenvalue problem for differential operators is a common problem in many scientific fields. Classical numerical methods rely on intricate domain discretization and yield nonanalytic or nonsmooth approximations. We introduce a novel neural network-based solver for the eigenvalue problem of differential self-adjoint operators, where the eigenpairs are learned in an unsupervised end-to-end fashion. We propose several training procedures for solving increasingly challenging tasks toward the general eigenvalue problem. The proposed solver is capable of finding the M smallest eigenpairs for a general differential operator. We demonstrate the method on the Laplacian operator, which is of particular interest in image processing, computer vision, and shape analysis among many other applications. In addition, we solve the Legendre differential equation. Our proposed method simultaneously solves several eigenpairs and can be easily used on free-form domains. We exemplify it on L-shape and circular cut domains. A significant contribution of this work is an analysis of the numerical error of this method. In particular an upper bound for the (unknown) solution error is given in terms of the (measured) truncation error of the partial differential equation and the network structure.

False Discovery Rate Control via Data Splitting

Selecting relevant features associated with a given response variable is an important problem in many scientific fields. Quantifying quality and uncertainty of a selection result via false discovery rate (FDR) control has been of recent interest. This article introduces a data-splitting method (referred to as “DS”) to asymptotically control the FDR while maintaining a high power. For each feature, DS constructs a test statistic by estimating two independent regression coefficients via data splitting. FDR control is achieved by taking advantage of the statistic’s property that, for any null feature, its sampling distribution is symmetric about zero; whereas for a relevant feature, its sampling distribution has a positive mean. Furthermore, a Multiple Data Splitting (MDS) method is proposed to stabilize the selection result and boost the power. Surprisingly, with the FDR under control, MDS not only helps overcome the power loss caused by data splitting, but also results in a lower variance of the false discovery proportion (FDP) compared with all other methods in consideration. Extensive simulation studies and a real-data application show that the proposed methods are robust to the unknown distribution of features, easy to implement and computationally efficient, and are often the most powerful ones among competitors especially when the signals are weak and correlations or partial correlations among features are high. Supplementary materials for this article are available online.

A variational non-linear constrained model for the inversion of FDEM data* *Dedicated to Lothar Reichel on the occasion of his 70th birthday.

Reconstructing the structure of the soil using non-invasive techniques is a very relevant problem in many scientific fields, like geophysics and archaeology. This can be done, for instance, with the aid of frequency domain electromagnetic (FDEM) induction devices. Inverting FDEM data is a very challenging inverse problem, as the problem is extremely ill-posed, i.e. sensible to the presence of noise in the measured data, and non-linear. Regularization methods substitute the original ill-posed problem with a well-posed one whose solution is an accurate approximation of the desired one. In this paper we develop a regularization method to invert FDEM data. We propose to determine the electrical conductivity of the ground by solving a variational problem. The minimized functional is made up by the sum of two term: the data fitting term ensures that the recovered solution fits the measured data, while the regularization term enforces sparsity on the Laplacian of the solution. The trade-off between the two terms is determined by the regularization parameter. This is achieved by minimizing an ℓ 2 − ℓ q functional with 0 < q ⩽ 2. Since the functional we wish to minimize is non-convex, we show that the variational problem admits a solution. Moreover, we prove that, if the regularization parameter is tuned accordingly to the amount of noise present in the data, this model induces a regularization method. Some selected numerical examples on synthetic and real data show the good performances of our proposal.

A Comparative Study of Several EOF Based Imputation Methods for Long Gap Missing Values in a Single-Site Temporal Time Dependent (SSTTD) Air Quality (PM10) Dataset

Missing values are often a major problem in many scientific fields of environmental research, leading to prediction inaccuracy and biased analysis results. This study compares the performance of existing Empirical Orthogonal Functions (EOF) based imputation methods. The EOF mean centred approach (EOF-mean) with several proposed EOF based methods, which include the EOF-median, EOF-trimmean and the newly applied Regularised Expectation-Maximisation Principal Component Analysis based method, namely R-EMPCA in estimating missing values for long gap sequence of missing values problem that exists in a Single Site Temporal Time-Dependent (SSTTD) multivariate structure air quality (PM10) data set. The study was conducted using real PM10 data set from the Klang air quality monitoring station. Performance assessment and evaluation of the methods were conducted via a simulation plan which was carried out according to four percentages (5, 10, 20 and 30) of missing values with respect to several long gap sequences (12, 24, 168 and 720) of missing points (hours). Based on several performance indicators such as RMSE, MAE, R-Square and AI, the results have shown that R-EMPCA outperformed the other methods. The results also conclude that the proposed EOF-median and EOF-trimmean have better performance than the existing EOF-mean based method in which EOF-trimmean is the best among the three. The methodology and findings of this study contribute as a solution to the problem of missing values with long gap sequences for the SSTTD data set.

Machine Learning in Rheumatic Diseases.

With advances in information technology, the demand for using data science to enhance healthcare and disease management is rapidly increasing. Among these technologies, machine learning (ML) has become ubiquitous and indispensable for solving complex problems in many scientific fields, including medical science. ML allows the development of guidelines and framing of the evaluation system for complex diseases based on massive data. In the analysis of rheumatic diseases, which are chronic and remarkably heterogeneous, ML can be anticipated to be extremely helpful in deciphering and revealing the inherent interrelationships in disease development and progression, which can further enhance the overall understanding of the disease, optimize patients' stratification, calibrate therapeutic strategies, and predict prognosis and outcomes. In this review, the basics of ML, its potential clinical applications in rheumatology, together with its strengths and limitations are summarized.

Application of a novel hybrid method for spatiotemporal data imputation: A case study of the Minqin County groundwater level

The techniques for data analyses have been widely developed in past years, however, missing data still represent a ubiquitous problem in many scientific fields. In particular, dealing with missing spatiotemporal data presents an enormous challenge. Nonetheless, in recent years, a considerable amount of research has focused on spatiotemporal problems, making spatiotemporal missing data imputation methods increasingly indispensable. In this paper, a novel spatiotemporal hybrid method is proposed to verify and imputed spatiotemporal missing values. This new method, termed SOM-FLSSVM, flexibly combines three advanced techniques: self-organizing feature map (SOM) clustering, the fruit fly optimization algorithm (FOA) and the least squares support vector machine (LSSVM). We employ a cross-validation (CV) procedure and FOA swarm intelligence optimization strategy that can search available parameters and determine the optimal imputation model. The spatiotemporal underground water data for Minqin County, China, were selected to test the reliability and imputation ability of SOM-FLSSVM. We carried out a validation experiment and compared three well-studied models with SOM-FLSSVM using a different missing data ratio from 0.1 to 0.8 in the same data set. The results demonstrate that the new hybrid method performs well in terms of both robustness and accuracy for spatiotemporal missing data.

Community Detection Using Differential Evolution Algorithm with Multiple Objective Function

In this paper, we conducted an experiment on differential evolution algorithm with multiple objective functions for community detection. The community detection in social networks is an important problem in many scientific fields. Differential algorithms use modularity as a fitness function in general. In this work, we have used different objective function such as conductance, normalized cut, Average degree and two well known datasets such as Zachary Karate Club and American College Football Network. We evaluated DECD on several artificial and real-world social and biological networks using multiple objective functions. After result analysis shows that DECD with multiple objective functions has very competitive performance compared with other community detection algorithms.

Nonparametric Detection of Signals by Information Theoretic Criteria: Performance Analysis and an Improved Estimator

Determining the number of sources from observed data is a fundamental problem in many scientific fields. In this paper we consider the nonparametric setting, and focus on the detection performance of two popular estimators based on information theoretic criteria, the Akaike information criterion (AIC) and minimum description length (MDL). We present three contributions on this subject. First, we derive a new expression for the detection performance of the MDL estimator, which exhibits a much closer fit to simulations in comparison to previous formulas. Second, we present a random matrix theory viewpoint of the performance of the AIC estimator, including approximate analytical formulas for its overestimation probability. Finally, we show that a small increase in the penalty term of AIC leads to an estimator with a very good detection performance and a negligible overestimation probability.

Determining the number of components in a factor model from limited noisy data

Determining the number of components in a linear mixture model is a fundamental problem in many scientific fields, including chemometrics and signal processing. In this paper we present a new method to automatically determine the number of components from a limited number of (possibly) high dimensional noisy samples. The proposed method, based on the eigenvalues of the sample covariance matrix, combines a matrix perturbation approach for the interaction of signal and noise eigenvalues, with recent results from random matrix theory regarding the behavior of noise eigenvalues. We present the theoretical derivation of the algorithm and an analysis of its consistency and limit of detection. Results on simulated data show that under a wide range of conditions our method compares favorably with other common algorithms.

Real-time accurate circle fitting with occlusions

Accurate location of circles inside images is a common problem in many scientific fields. Traditional algorithms, based on fitting a parameterized model, cannot accurately determine the circle in presence of partial occlusions. A novel problem formulation, based on maximum likelihood, allows estimating circles in real-time with sub-pixel accuracy also when occlusions are present.

Single imputation method of missing values in environmental pollution data sets

Missing data represent a general problem in many scientific fields above all in environmental research. Several methods have been proposed in literature for handling missing data and the choice of an appropriate method depends, among others, on the missing data pattern and on the missing-data mechanism. One approach to the problem is to impute them to yield a complete data set. The goal of this paper is to propose a new single imputation method and to compare its performance to other single and multiple imputation methods known in literature. Considering a data set of PM 10 concentration measured every 2 h by eight monitoring stations distributed over the metropolitan area of Palermo, Sicily, during 2003, simulated incomplete data have been generated, and the performance of the imputation methods have been compared on the correlation coefficient ( ρ ) , the index of agreement ( d), the root mean square deviation (RMSD) and the mean absolute deviation (MAD). All the performance indicators agree to evaluate the proposed method as the best among the ones compared, independently on the gap length and on the number of stations with missing data.

Fitting optimal piecewise linear functions using genetic algorithms

Constructing a model for data in R/sup 2/ is a common problem in many scientific fields, including pattern recognition, computer vision, and applied mathematics. Often little is known about the process which generated the data or its statistical properties. For example, in fitting a piecewise linear model, the number of pieces, as well as the knot locations, may be unknown. Hence, the method used to build the statistical model should have few assumptions, yet, still provide a model that is optimal in some sense. Such methods can be designed through the use of genetic algorithms. We examine the use of genetic algorithms to fit piecewise linear functions to data in R/sup 2/. The number of pieces, the location of the knots, and the underlying distribution of the data are assumed to be unknown. We discuss existing methods which attempt to solve this problem and introduce a new method which employs genetic algorithms to optimize the number and location of the pieces. Experimental results are presented which demonstrate the performance of our method and compare it to the performance of several existing methods, We conclude that our method represents a valuable tool for fitting both robust and nonrobust piecewise linear functions.

STATISTICAL EVALUATION OF ELECTRICAL SOUNDlNG METHODS. PART I: EXPERIMENT DESIGN

Traditional experiment design techniques, widely applied to both linear and nonlinear problems in many scientific fields, is applicable to the design of exploration geophysical surveys. The design technique is formulated using the mathematics of the generalized inverse and its construction via eigenvalue decomposition. The design technique is demonstrated by the designing of electromagnetic sounding surveys for a horizontal loop source. The experiment is designed whereby it is determined (1) which one of the electromagnetic field quantities, vertical and horizontal magnetic field amplitudes or phases, and polarization ellipse quantities, tilt angle, and ellipticity, and (2) which set of transmitter and receiver separations and transmitter frequencies, best resolve the conductivities and thicknesses of a given layered earth model. Model resolution is sensitive to the data error. As an example, for different assumed data errors, a model is best resolved in one instance by the phase of the two components of the magnetic field, while in another instance it is best resolved by tilt angle and ellipticity measurements. The best designs are obtained using field measurements made at several transmitter frequencies and at two or more transmitter and receiver separations. The functional relationship between the earth model parameters and the magnetic field quantities is nonlinear. The effect of this nonlinearity on the statistics applied in the method of experiment design has been reported in the literature and is reexamined here. Based on Beale's measure of nonlinearity, the models studied here exhibit adequate linearity to permit use of the linear statistics for experiment design. A study of the eigenvectors and information density matrix provide insight to model parameter correlations and measurement correlations which can be exploited for improving the design of an experiment.