Journal of Computational Mathematics and Data Science最新文献

In this research. we study anomaly detection in univariate time series and optimize according to a business objective using a novel active learning approach. The motivation is to detect anomalies while monitoring systems within an IT infrastructure, known as intrusion detection, specifically for hotel organizations. The proposed detector is based on moving averages in combination with a prediction interval, where parameters are optimized via an active learning component. By using prediction intervals, the results are easily interpretable for domain experts due to the white-box nature of the detector. Annotations originating from domain experts serve as input to acquire oracle parameters, which are obtained via Bayesian optimization using Gaussian process. The detector is tested on the Numenta Anomaly Benchmark (NAB) and is compared to commonly used black-box models.

In this article, we proposed a new three-parameter model with a bathtub failure rate. The main properties of the new model are derived, such as quantile function, moments, the moment of residual life, stress strength reliability parameter, order statistics, extreme value distribution, Shannon entropy, and Renyi entropy. Maximum likelihood estimation (MLE) is considered for the parameter estimation, and the information matrix is obtained. Simulation studies were used to assess the performances of the estimators by discussing their bias, mean square error, confidence interval, and coverage probability. In addition, we discussed the quantile regression model based on the proposed model; we examined the performance of their MLEs by simulation studies via the randomized quantile residuals. Two real data sets are used to illustrate the importance of the new model in practice.

The purpose of this study is to establish an iterative algorithm for approximating a solution of SEGFPP and prove strong convergence of the sequence generated by the proposed scheme to a solution of the problem in Banach spaces. In addition, we apply our result to find a solution of SEMPP and provide a numerical example to support our result. Our result generalize and extend many results in the literature.

We propose a methodology for sampling from time-integrated stochastic bridges, i.e., random variables defined as ${\int }_{t_1}^{t_2}f\left(Y\left(t\right)\right)dt$ conditional on $Y\left(t_1\right)=a$ and $Y\left(t_2\right)=b$, with $a,b\in R$. The techniques developed in Grzelak et al. (2019) – the Stochastic Collocation Monte Carlo sampler – and in Liu et al. (2020) – the Seven-League scheme – are applied for this purpose. Notably, the time-integrated bridge distribution is approximated using a polynomial chaos expansion constructed over an appropriate set of stochastic collocation points. In addition, artificial neural networks are employed to learn the collocation points. The result is a robust, data-driven procedure for Monte Carlo sampling from time-integrated conditional processes, which guarantees high accuracy and generates thousands of samples in milliseconds. Applications are also presented, with a focus on finance.

Treecode algorithms efficiently approximate N-body interactions in $O\left(N\right)$ or $O\left(N\text{log}N\right)$. In order to treat general 3D kernels, recent developments employ polynomial interpolation to approximate the kernels. The polynomials are a tensor product of 1-dimensional polynomials. Here, we develop an $O\left(N\text{log}N\right)$ tricubic interpolation based treecode method for 3D kernels. The tricubic interpolation is inherently three-dimensional and as such does not employ a tensor product. The form allows for easy evaluation of the derivatives of the kernel, required in dynamical simulations, which is not the case for the tensor product approach. We develop both a particle-cluster and cluster-particle variants and present results for the Coulomb, screened Coulomb and the real space Ewald kernels. We also present results of an MD simulation of a Lennard-Jones liquid using the tricubic treecode.

Decoding higher-order structure on sequential data is an indispensable task in data science. It requires models to have the capability to characterize interdependencies among hidden events that have generated observable data. However, to be able to decode arbitrary structures, such models would need to cope with the intractability arising from computing context-sensitive relations, likely compromising the quality of answers. To address this important issue, the current paper introduces the arbitrary order hidden Markov model ($\alpha$-HMM), an extension of the HMM that permits decoding of the optimal higher-order structure with an assurance of computational tractability. The advantage of the $\alpha$-HMM is made possible by an identified principle on how random variables influence each other in a stochastic process. In particular, it is shown that decoding the optimal structure with an $\alpha$-HMM can be computed in $O\left(n^3\right)$-time for any stochastic process of $n$ random variables. As an application, it is demonstrated the decoding algorithm inspires a simple yet effective algorithm for RNA secondary structure prediction.

Dominant-feature identification decomposes spatial data into several additive components to make different features apparent on each component. It recognizes their dominant features credibly and assesses feature attributes. This paper describes the pipeline to apply this method to regular and irregular lattice data as well as geostatistical data. These implementations are all openly available and templates for each case are provided in an associated git repository. As geostatistical data is typically large, we propose several efficient approximations suitable for such data. Emphasizing the use of these approximations in the context of dominant-feature identification, we apply them to data from a climate model describing the monthly mean diurnal range for the period between the years 2081 and 2100.

In the current investigation, it is explored the unsteady MHD free convective Casson fluid movement over a boundless straight up inclined absorbent plate with heat source and/or heat absorption. The established equations are subsequently solved thoroughly by utilize of perturbation method. The velocity, temperature as well as concentration profiles are shown in graphical profiles. The consequences on the stream region for disparate foremost parameter had been investigated. Furthermore the skin friction factor, Nusselt number in addition to Sherwood numbers are found by the disparate foremost parameters as well as revealed in the tabular formats. The velocity reduces by an escalating into the chemical reaction constraint in addition to improved by an enhancement into heat resources parameters. The temperatures fields reduce by an enhancement into the Prandtl number, whereas it enlarges with an augment in temperature absorption parameter. The concentration field is enhances with an escalating into the chemical reaction constraint, while this retards by an enhancing into Schmidt number.

The Singular Value Decomposition (SVD) is one of the most used factorizations when it comes to Data Science applications. In particular, given the big size of the processed matrices, in most of the cases, a truncated SVD algorithm is employed. In the following manuscript, we review some of the state-of-the-art approaches considered for the selection of the number of components (i.e., singular values) to retain to apply the truncated SVD. Moreover, three new approaches based on the Kullback–Leibler divergence and on unsupervised anomaly detection algorithms, are introduced. The revised methods are then compared on some standard benchmarks in the image processing context.

In view of the dominant properties of hybrid nanofluid such as high thermal and electrical conductivity in addition to enhanced heat transfer rate, efforts had been strengthened by many researchers to upgrade the thermal behavior of the base fluid through different approaches. In this study, viscous dissipation and thermal radiation effects on unsteady incompressible squeezing flow conveying $CuO-A{l}_2{O}_3/$water hybrid nanoparticles between two aligned surfaces with variable viscosity is examined. The fluid model is transformed to ordinary differential equations by incorporating appropriate similarity transformation. The numerical simulation is carried out in MATLAB software package via shooting procedure coupled with $4th$ order Runge–Kutta integration scheme. The limiting case is found to be in accord relative to the preceding reports. The outcomes of the scrutiny are unveiled in tables and graphs. It was revealed that the velocity and temperature augment with increasing viscosity variation and squeezing fluid parameters. Meanwhile, increasing viscous dissipation and thermal radiation parameters decrease the temperature distribution with no significant change in the fluid velocity.