Kriging-based value function approximation for the strategic bidding problem of virtual power plant in the electricity market

Variable-order fractional wave equation: Analysis, numerical approximation, and fast algorithm

The theory and practice of computing the bus factor

Better approximation algorithms for clustered TSP and subgroup planning

Efficient data collection in Internet of Things enabled wireless sensor networks (WSNs) is essential for sustainability of the network. Nevertheless, the task is challenging as it is NP-hard in nature. In this paper, we address the issue by proposing a novel Steiner Tree–based Path Planning (STPP) scheme. The algorithm works in two phases, (1) A primal dual approximation algorithm is used to construct the Steiner tree, which is then used to ascertain the RPs. (2) Then, Christofide's algorithm is used to construct a tour using the previously obtained RPs. We model RP selection as a combinatorial optimization problem, obtain approximation bounds, and the computational complexity is also analyzed. We also analyze the practical constraints of centralized structure and describe the paths to extended distributed and dynamic forms. Extensive simulations over varying network sizes and communication ranges demonstrate that STPP achieves on average a 17% reduction in tour length, a 22% decrease in RP count, and a 19% improvement in network lifetime compared to state-of-the-art approaches.

Full-waveform inversion (FWI) adopts the dynamic and kinematic information contained in pre-stack seismic wavefields and fits actual observed seismic data using the wave equation. It can realize high-resolution quantitative imaging of physical property parameters of underground media, with a theoretical imaging accuracy reaching half of the seismic wavelength. Since Tarantola and Lailly established the core theoretical framework in the 1980s, FWI has gradually evolved from two-dimensional acoustic approximate algorithms to a three-dimensional elastic and viscoelastic multi-parameter inversion system, and its application scope has expanded from simple geological structures to complex stratigraphic regions. In recent years, the iteration and upgrading of high-performance computing hardware, the application of deep learning algorithms in geosciences, and the popularization of multi-component and wide-azimuth seismic acquisition equipment have jointly driven FWI into a brand-new development stage. This paper systematically sorts out the theoretical system and classical research methods of FWI, and summarizes the development context of core technologies including multi-scale inversion, objective function construction, initial model establishment and computational efficiency optimization. Meanwhile, it concludes the latest achievements of research hotspots such as elastic and viscoelastic multi-parameter inversion, deep learning integrated FWI, uncertainty quantification, 4D time-lapse monitoring and cross-scale imaging. Finally, combined with the industrial development trend, this paper prospects future research directions including deep integration of physics and artificial intelligence, large-scale high-efficiency inversion, multi-physical field coupled imaging, and standardization of result interpretability. It aims to provide a systematic literature review and research reference for researchers engaged in seismic inversion and oil and gas exploration.

Achieving quantum advantage remains a milestone in the noisy intermediate-scale quantum era. Without complexity proofs, scaling advantage-where quantum resource requirements grow more slowly than their classical counterparts-is the primary indicator. However, direct applications of quantum optimization algorithms to classically intractable problems have yet to demonstrate this advantage. Here we develop enhanced quantum solvers for the NP-complete one-in-three Boolean satisfiability problem. We propose a restricting space reduction algorithm that achieves optimal search-space dimensionality under mod-2 arithmetic, thereby reducing qubit requirements and time complexity. Numerical studies on instances with up to 70 variables demonstrate that our enhanced quantum approximate optimization algorithm- and quantum adiabatic algorithm-based solvers outperform state-of-the-art classical solvers; the quantum adiabatic algorithm-based solver serves as a lower-bound reference while retaining scaling advantage. Furthermore, experiments on a 13-qubit superconducting processor confirm the predicted improvements. Collectively, our results provide empirical evidence of quantum speedup for an NP-complete problem.

The aim of this paper is to construct stochastic processes allowing to obtain probabilistic representations of classical, weak or viscosity solutions of the forward Cauchy problem for several types of systems of nonlinear PDEs arising as viscous conservation and balance laws in various applications. The required stochastic processes are constructed as solutions of corresponding stochastic differential equations (SDEs) both forward and backward in time. Due to non-linearity of PDE systems under consideration additional relations must be added to the SDEs in order to obtain closed systems that can be studied independently. These relations are proved to generate probabilistic representations of the required solutions of the Cauchy problem for the original nonlinear PDE systems. Probabilistic representations are used to develop new numerical algorithms for approximation of classical and viscosity solutions to nonlinear PDEs.

To investigate the use of contrast-enhanced mammography (CEM) for preoperative prediction of lymphovascular invasion (LVI) status in invasive breast cancer. A total of 243 female patients diagnosed with invasive breast cancer (median age: 49 years; range: 27-77 years) who received preoperative CEM examination in our hospital between September 2018 and February 2024 were retrospectively collected and analyzed. The study population were chronologically divided into training and test datasets in an approximate ratio of 7:3. LVI status was determined using postoperative histopathologic examination. CEM features were analyzed on the low energy and the recombined images. To identify independent predictors for LVI status, univariable and multivariable logistic regression analyses were performed on CEM and clinicopathologic features. Logistic regression and six machine learning methods were used to construct prediction models in the training dataset, and their performance were evaluated with ROC curve in the test dataset. In training and test datasets, the rates of LVI-positive were 39% (67 of 172) and 34% (24 of 71), respectively. High Ki67 index, BI-RADS category 5, breast composition category c/d, axillary adenopathy, mild to marked background parenchymal enhancement level, and lesion with complete enhancement or enhancement extending on CEM images were significantly correlated with LVI-positive (all P < 0.05) and were incorporated to construct prediction models. The AUCs of seven prediction models were in the range of 0.713-0.850 in the test datasets, where the logistic regression model yielded an AUC of 0.835 (95%CI: 0.717-0.924), showing similar or higher AUC than the six machine learning models. CEM could be useful for preoperative noninvasive prediction of LVI status in invasive breast cancer. The prediction model integrating contrast-enhanced mammography features and Ki67 index may serve as a complementary tool to assist clinicians in preoperative prediction of lymphovascular invasion status in patients with invasive breast cancer.

Computer models are used to solve complex problems in many scientific applications, such as nuclear physics and climate research. Markov chain Monte Carlo-based Bayesian calibration of computer models although a popular approach, is computationally expensive. This work proposes a fast and scalable posterior approximation algorithm for Bayesian computer model calibration via Variational Inference. We provide the statistical guarantee of the proposed algorithm in the form of a posterior contraction theorem for the estimated physical process. To this end, we establish that the variational posterior concentrates in ϵ n neighbourhoods of the true physical process under regularity assumptions on the variational family. The main results are shown in the two widely used classes of Gaussian process priors, the Squared Exponential covariance class and the Matérn covariance class. Finally, we provide a simulation study to demonstrate the proposed method's computational efficiency and fidelity compared to the standard Markov chain Monte Carlo method.

Rule-based approximate equivalent consumption minimization strategy algorithm for through-the-road vehicles energy management strategy

Minimal sensor node selection (MSNS), an evolutionary algorithm for target coverage in clustered wireless sensor networks

Digital twin is emerging as a key technology to monitor the status of complex industry systems. Valuable insights, such as running statuses and anomalies, can be analyzed from the collected system status timely. Considering that the data updating from each system component (known as a physical object) to its digital twin is performed continuously, timely and accurate streaming analytics based on machine learning models is a key technology to analyze such data efficiently. In this paper, we focus on enabling low-delay yet highly-accurate streaming analytics for digital twin applications in mobile edge computing (MEC) networks. Specifically, we formulate a fundamental optimization problem of digital twin placements and model selections for streaming analytics, with the aim of minimizing both the analytic loss and the processing delay. To this end, we first consider the problem with a single query, for which, we propose an approximation algorithm with provable approximation ratio for a special case, and then devise an efficient algorithm for the original problem with a single query. We then study the online digital twin placement and model selection problem for streaming analytics with multiple queries under real scenarios, where resource demands of arrival queries and resource availability of MEC network are uncertain. We propose an online learning algorithm with a bounded regret to make admission policies. We finally evaluate the performance of the proposed algorithms by extensive simulations. Results show that the weighted sums of the total processing delay and the cumulative loss in the solution delivered by the proposed algorithms outperform their counterparts by 12.5% with a single query and 13.3% with multiple queries, respectively.

Purpose This paper aims to review the basic algorithm for 2D flow simulation around airfoils using the vortex particle method and to demonstrate that all time-consuming operations connected with the simulation of vorticity motion in the fluid domain, its generation on the airfoils in the flow, as well as some auxiliary operations, can be performed efficiently with quasilinear numerical complexity by using similar approaches. The suggested algorithms are based on the LBVH tree building and traversing. Specific features are discussed that enable an efficient implementation of the vortex particle method algorithm for CPUs and GPUs. Design/methodology/approach Vortex particle method is considered an efficient numerical method for flow simulation and fluid-structure interaction (FSI). An LBVH-tree-based (Linear Bounding Volumes Hierarchy) approach serves as a key tool for implementing approximate fast algorithms for all time-consuming operations in the main computational algorithm: from the N-body problem to the Boundary Integral Equation solution, neighbors search and penetration control. Findings Fast algorithms are proposed for all time-consuming operations in the computational algorithm of vortex particle method. Specific features are highlighted that are essential for efficient algorithm implementation on CPUs and GPUs. Research limitations/implications The algorithms are developed precisely for two-dimensional flow simulation by vortex particle method. However, some ideas can be easily (or non-trivially!) generalized to the three-dimensional case. Practical implications The paper provides practical guidelines to specialists in CFD who deal with vortex particle method. Originality/value The authors have generalized their experience in developing efficient fast algorithms in the framework of vortex particle method. The developed approaches are mainly based on some known ideas, but all existing methods have required significant modifications to adapt them to the considered problems and improve their performance and accuracy.

Motivated by batch-dependent processing constraints in semiconductor testing and other time-critical industrial applications, we consider a single-machine batch scheduling problem with a fixed maintenance activity, where jobs have equal processing time but different sizes. Each job can be split and processed in two consecutive batches if necessary. For the objective of minimising the makespan, we prove the NP-hardness of the problem and provide an approximation algorithm with a worst-case ratio of 3 2 , which is the best possible polynomial-time approximation algorithm under the assumption that P ≠ NP . For the objective of minimising the total completion time, we prove that the problem is NP-hard, and then present a pseudo-polynomial time dynamic programming algorithm and a 3 2 -approximation algorithm. Moreover, through computational experiments, we demonstrate that the approximation algorithm performs very well in practice, achieving an average relative error of only 0.36%.

Recurrent pituitary adenomas treated by endoscopic endonasal transsphenoidal surgery: The role of tumour extension and surgical feasibility

Stochastic approximation to contrastive learning.

Aromatic hydrocarbons such as benzene, toluene, and ethylbenzene are extensively used as solvents in coatings, resin, and artificial leather industries. Azeotropic mixtures involving these compounds are commonly encountered in chemical manufacturing, where accurate azeotropic temperature and composition are essential for designing and optimizing separation processes such as extractive and pressure-swing distillation. In this study, two quantitative structure-property relationship (QSPR) models were developed to predict the azeotropic temperature and composition of binary mixtures containing aromatic hydrocarbons using only molecular structural information. The models show excellent agreement with experimental data (R2 = 0.9454 and 0.9448, = 0.9400 and 0.9413). Internal validation via leave-one-out cross-validation yields = 0.9308 and 0.9364, while external validation using an independent test set yields = 0.8939 and 0.9364, indicating strong robustness and superior predictive performance compared to previously reported models. Molecular geometries were optimized using HyperChem 8.0, employing MM + and PM3 methods. Molecular descriptors were calculated using the Online Chemical Modeling Environment (OCHEM). Binary mixture descriptors were derived from pure-component descriptors via Kay's mixing rule. The genetic function approximation (GFA) algorithm was used to select the most relevant descriptors, and predictive models were constructed using multiple linear regression (MLR). Model robustness and predictive capacity were evaluated using leave-one-out cross-validation and an external test set, with applicability domains assessed via Williams plots. All computational procedures and modeling analyses were performed using OCHEM, SPSS, and HyperChem 8.0.

We propose a novel framework for statistical estimation on noisy datasets. Within this framework, we focus on the frequency moments ( F p ) problem and demonstrate that it is possible to approximate F p of the unknown ground-truth dataset using sublinear space in the data stream model and sublinear communication in the coordinator model, provided that the approximation ratio is parameterized by a data-dependent quantity, which we call the F p -mismatch-ambiguity. We also establish a set of lower bounds, which are tight in terms of the input size. Our results yield several interesting insights: -In the data stream model, the F p problem is inherently more difficult in the noisy setting than in the noiseless one. In particular, while F 2 can be approximated in logarithmic space in terms of the input size in the noiseless setting, any algorithm for F 2 in the noisy setting requires polynomial space. -In the coordinator model, in sharp contrast to the noiseless case, achieving polylogarithmic communication in the input size is generally impossible for F p under noise. However, when the F p mismatch ambiguity falls below a certain threshold, it becomes possible to achieve communication that is entirely independent of the input size.

We present a polynomial-time algorithm for minimum vertex cover achieving an approximation ratio strictly less than 2 for any finite undirected graph with at least one edge. The algorithm reduces the problem to a minimum weighted vertex cover on a degree-1 auxiliary graph using weights 1 / d v , solves it optimally via Cauchy–Schwarz-balanced selection, and projects the solution back to a valid cover. Correctness and the strict sub-2 ratio are rigorously proved. Runtime is O ( | V | + | E | ) , confirming practical scalability.