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Sequential recommender systems (SRS) have become the key technology in capturing user's dynamic interests and generating high-quality recommendations. Current state-of-the-art sequential recommender models are typically based on a…
Full-dimensional reactive potential energy surfaces (PESs) for the OCS$^+$ cation are constructed to describe S$^+$ loss in the electronic ground state and seven low-lying electronically excited states. High-level \textit{ab initio}…
Surface parameterizations are widely applied in computer graphics, medical imaging and transformation optics. In this paper, we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy for spherical…
Our first focus is the Capacitated Partition Vertex Cover (C-PVC) problem in hypergraphs. In C-PVC, we are given a hypergraph with capacities on its vertices and a partition of the hyperedge set into $\omega$ distinct groups. The objective…
The Principal Component Analysis (PCA) method and the Singular Value Decomposition (SVD) method are widely used for foreground subtraction in 21 cm intensity mapping experiments. We show their equivalence, and point out that the condition…
Polar codes with Reed-Solomon (RS) kernel have great potential in next-generation communication systems due to their high polarization rate. In this paper, we study the polarization characteristics of RS polar codes and propose two types of…
In this paper, we develop a new approach to the very short-term point forecasting of electricity prices in the continuous market. It is based on the Support Vector Regression with a kernel correction built on additional forecast of…
In contrast with Mercer kernel-based approaches as used e.g., in Kernel Principal Component Analysis (KPCA), it was previously shown that Singular Value Decomposition (SVD) inherently relates to asymmetric kernels and Asymmetric Kernel…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems.…
We propose a stochastic variant of the classical Polyak step-size (Polyak, 1987) commonly used in the subgradient method. Although computing the Polyak step-size requires knowledge of the optimal function values, this information is readily…
Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least…
Bilevel optimization has been widely used in many machine learning applications such as hyperparameter optimization and meta learning. Recently, many simple stochastic gradient descent(SGD) type algorithms(without using momentum and…
Proactive maintenance strategies, such as Predictive Maintenance (PdM), play an important role in the operation of Nuclear Power Plants (NPPs), particularly due to their capacity to reduce offline time by preventing unexpected shutdowns…
This paper reports a development in the proper symplectic decomposition (PSD) for model reduction of forced Hamiltonian systems. As an analogy to the proper orthogonal decomposition (POD), PSD is designed to build a symplectic subspace to…
Physics-Informed Neural Networks (PINNs) have shown continuous and increasing promise in approximating partial differential equations (PDEs), although they remain constrained by the curse of dimensionality. In this paper, we propose a…
Forecasting volcanic activity is critical for hazard assessment and risk mitigation. Volcanic Radiative Power (VPR), derived from thermal remote sensing data, serves as an essential indicator of volcanic activity. In this study, we employ…
Phase retrieval (PR) is an important component in modern computational imaging systems. Many algorithms have been developed over the past half-century. Recent advances in deep learning have introduced new possibilities for a robust and fast…
Feature extraction for tensor data serves as an important step in many tasks such as anomaly detection, process monitoring, image classification, and quality control. Although many methods have been proposed for tensor feature extraction,…
The Singular Value Decomposition (SVD) is one of the most important matrix factorizations, enjoying a wide variety of applications across numerous application domains. In statistics and data analysis, the common applications of SVD such as…