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Time series analysis predicts the future based on existing historical data and has a wide range of applications in finance, economics, meteorology, biology, engineering, and other fields. Although the combination of decomposition techniques and machine learning algorithms can effectively solve the problem of predicting nonstationary sequences, this kind of decomposition-integration-prediction strategy of the prediction method has serious defects. After the decomposition of the division of the training set and the test set, the information of the test set in the process of decomposition of the information leakage ultimately shows a high accuracy of the prediction of the illusionary. This paper proposes three improvement strategies for this type of “information leakage” problem: sliding window decomposition (SW-EMD), single training and multiple decomposition (STMP-EMD), and multiple training and multiple decomposition (MTMP-EMD). They are combined with a bidirectional multiscale temporal convolutional network (MSBTCN), bidirectional long- and short-term memory network (BiLSTM), and attention mechanism (DMAttention), which introduces a dependency matrix based on cosine similarity to be applied to water quality prediction. The experimental results show that the model achieves good performance in the prediction of three water quality indicators (pH, DO and KMnO 4 ), and the accuracies of the three models proposed in this paper are improved by 1.958% and 0.853% in terms of the RMSE and MAPE, respectively, compared with those of the mainstream LSTM models. The key contributions of this study include the following: (1) three methods are proposed to improve the class EMD decomposition, which can effectively solve the problem of “information leakage” that exists in the current models via class EMD decomposition; (2) the CEEMDAN-MSBTCN-BiLSTM-DMAttention model structure is innovated by combining improved class EMD decomposition methods; and (3) the three improved decomposition methods proposed in this paper can effectively solve the problem of “information leakage” and optimize the prediction model at the same time. This study provides an effective experimental method for water quality prediction and can effectively address the problem of “overfitting” models via class EMD decompositions during model training and testing.

Energy loss in shielding soft magnetic materials at low frequencies (1–100 Hz) can cause fluctuations in the material’s magnetic field, and the resulting magnetic noise can interfere with the measurement accuracy and basic precision physics of biomagnetic signals. This places higher demands on the credibility and accuracy of loss separation predictions. The current statistical loss theory (STL) method tends to ignore the high impact of the excitation dependence of quasi-static loss in the low-frequency band on the prediction accuracy. STL simultaneously fits and predicts multiple unknown quantities, causing its results to occasionally fall into the value boundary, and the credibility is low in the low-frequency band and with less data. This paper proposes a progressive loss decomposition (PLD) method. Through multi-step progressive predictions, the hysteresis loss simulation coefficients are first determined. The experimental data of the test ring verifies the credibility of PLD’s prediction of the two hysteresis coefficients, improving the inapplicability of the STL method. In addition, we use the proposed method to obtain the prediction results of the low-frequency characteristics of the loss of a variety of typical soft magnetic materials, providing a reference for analyzing the loss characteristics of materials.

This study proposes a strategy for decomposing the computational domain to solve differential equations using physics-informed neural networks (PINNs) and progressively saving the trained model in each subdomain. The proposed progressive domain decomposition (PDD) method segments the domain based on the dynamics of residual loss, thereby indicating the complexity of different sections within the entire domain. By analyzing residual loss pointwise and aggregating it over specific intervals, we identify critical regions requiring focused attention. This strategic segmentation allows for the application of tailored neural networks in identified subdomains, each characterized by varying levels of complexity. Additionally, the proposed method trains and saves the model progressively based on performance metrics, thereby conserving computational resources in sections where satisfactory results are achieved during the training process. The effectiveness of PDD is demonstrated through its application to complex PDEs, where it significantly enhances accuracy and conserves computational power by strategically simplifying the computational tasks into manageable segments.

Airborne bathymetric LiDAR (ABL) acquires waveform data with better accuracy and resolution and greater user control over data processing than discrete returns. The ABL waveform is a mixture of reflections from the water surface and bottom, water column backscattering, and noise, and it can be separated into individual components through waveform decomposition. Because the point density and positional accuracy of the point cloud are dependent on waveform decomposition, an effective decomposition technique is required to improve ABL measurement. In this study, a new progressive waveform decomposition technique based on Gaussian mixture models was proposed for universal applicability to various types of ABL waveforms and to maximize the observation of seafloor points. The proposed progressive Gaussian decomposition (PGD) estimates potential peaks that are not detected during the initial peak detection and progressively decomposes the waveform until the Gaussian mixture model sufficiently represents the individual waveforms. Its performance is improved by utilizing a termination criterion based on the time difference between the originally detected and estimated peaks of the approximated model. The PGD can be universally applied to various waveforms regardless of water depth or underwater environment. To evaluate the proposed approach, it was applied to the waveform data acquired from the Seahawk sensor developed in Korea. In validating the PGD through comparative evaluation with the conventional Gaussian decomposition method, the root mean square error was found to decrease by approximately 70%. In terms of point cloud extractability, the PGD extracted 14–18% more seafloor points than the Seahawk’s data processing software.

Alumina sol containing nano-meter sized Al 2 O 3 particles were synthesized using aluminum sec-butoxide and nitric acid as precursor and peptizing agent, respectively. Polyvinylpyrrolidone (PVP) was added to prevent particle growth and adjust sol viscosity. PVP/alumina hybrid fibers were drawn from the sol with a viscosity value in the range of 2,500–3,000 mPa.s. By guided through a temperature gradient tube furnace at a rate of 4 m/min, the wet PVP/alumina hybrid fibers were sufficiently dried. Sub-micro-sized pure alpha alumina fibers were obtained by sintering the dry hybrid fibers at 1,000 °C for 3 h. The organic matters were decomposed within a wide temperature range from 150 to 800 °C allowing the nano Al 2 O 3 particles to gradually get together and form solid alumina fibers with smooth surfaces.

BackgroundPrimary progressive aphasia (PPA) defines a group of neurodegenerative disorders characterised by language decline. Three PPA variants correlate with distinct underlying pathologies: semantic variant PPA (svPPA) with transactive response DNA-binding protein of 43 kD (TDP-43) proteinopathy, agrammatic variant PPA (agPPA) with tau deposition and logopenic variant PPA (lvPPA) with Alzheimer’s disease (AD). Our objectives were to differentiate PPA variants using clinical and neuroimaging features, assess progression and evaluate structural MRI and a novel 18-F fluorodeoxyglucose positron emission tomography (FDG-PET) image decomposition machine learning algorithm for neuropathology prediction.MethodsWe analysed 82 autopsied patients diagnosed with PPA from 1998 to 2022. Clinical histories, language characteristics, neuropsychological results and brain imaging were reviewed. A machine learning framework using a k-nearest neighbours classifier assessed FDG-PET scans from 45 patients compared with a large reference database.ResultsPPA variant distribution: 35 lvPPA (80% AD), 28 agPPA (89% tauopathy) and 18 svPPA (72% frontotemporal lobar degeneration-TAR DNA-binding protein (FTLD-TDP)). Apraxia of speech was associated with 4R-tauopathy in agPPA, while pure agrammatic PPA without apraxia was linked to 3R-tauopathy. Longitudinal data revealed language dysfunction remained the predominant deficit for patients with lvPPA, agPPA evolved to corticobasal or progressive supranuclear palsy syndrome (64%) and svPPA progressed to behavioural variant frontotemporal dementia (44%). agPPA-4R-tauopathy exhibited limited pre-supplementary motor area atrophy, lvPPA-AD displayed temporal atrophy extending to the superior temporal sulcus and svPPA-FTLD-TDP had severe temporal pole atrophy. The FDG-PET-based machine learning algorithm accurately predicted clinical diagnoses and underlying pathologies.ConclusionsDistinguishing 3R-taupathy and 4R-tauopathy in agPPA may rely on apraxia of speech presence. Additional linguistic and clinical features can aid neuropathology prediction. Our data-driven brain metabolism decomposition approach effectively predicts underlying neuropathology.

With the increased construction reservoirs, hydropower systems are becoming larger and more complex, which brings challenges of optimal operation of large-scale reservoirs to improve the power generation. To address this efficiently, we propose an aggregation-decomposition method based on cascade reservoir drawdown rule. Based on a two-stage method, we analyze the monotonicity of power generation increment of cascade reservoirs and propose the drawdown rule, which we used to guide the drawdown order of cascade reservoirs. On this basis, we propose an aggregation-decomposition coupling drawdown rule and progressive optimal algorithm (ADDR-POA) method of large-scale reservoirs. To confirm the viability of the proposed approach, we selected 29 series–parallel-mixed reservoirs in the upper Yangtze River Basin in China as the study subjects and optimized them with the goal of maximizing the total power generation. Results show that compared to conventional mathematical optimization method and heuristic algorithm, ADDR-POA can effectively express the compensation effect between reservoirs and has a good performance in improving the total power generation of the basin and reducing iteration times, which presents a novel approach for solving the problem of drawdown operation of large-scale reservoirs.

The concept of a stochastic variational inequality has recently been articulated in a new way that is able to cover, in particular, the optimality conditions for a multistage stochastic programming problem. One of the long-standing methods for solving such an optimization problem under convexity is the progressive hedging algorithm. That approach is demonstrated here to be applicable also to solving multistage stochastic variational inequality problems under monotonicity, thus increasing the range of applications for progressive hedging. Stochastic complementarity problems as a special case are explored numerically in a linear two-stage formulation.

JC polyomavirus (JCPyV) establishes a persistent, asymptomatic kidney infection in most of the population. However, JCPyV can reactivate in immunocompromised individuals and cause progressive multifocal leukoencephalopathy (PML), a fatal demyelinating disease with no approved treatment. Mutations in the hypervariable non-coding control region (NCCR) of the JCPyV genome have been linked to disease outcomes and neuropathogenesis, yet few metanalyses document these associations. Many online sequence entries, including those on NCBI databases, lack sufficient sample information, limiting large-scale analyses of NCCR sequences. Machine learning techniques, however, can augment available data for analysis. This study employs a previously compiled dataset of 989 JCPyV NCCR sequences from GenBank with associated patient PML status and viral tissue source to train multilayer perceptrons for predicting missing information within the dataset. The PML status and tissue source models were 100% and 87.8% accurate, respectively. Within the dataset, 348 samples had an unconfirmed PML status, where 259 were predicted as No PML and 89 as PML sequences. Of the 63 sequences with unconfirmed tissue sources, eight samples were predicted as urine, 13 as blood, and 42 as cerebrospinal fluid. These models can improve viral sequence identification and provide insights into viral mutations and pathogenesis.

We design inexact proximal augmented Lagrangian based decomposition methods for convex composite programming problems with dual block-angular structures. Our methods are particularly well suited for convex quadratic programming problems arising from stochastic programming models. The algorithmic framework is based on the application of the abstract inexact proximal ADMM framework developed in [Chen, Sun, Toh, Math. Prog. 161:237–270] to the dual of the target problem, as well as the application of the recently developed symmetric Gauss-Seidel decomposition theorem for solving a proximal multi-block convex composite quadratic programming problem. The key issues in our algorithmic design are firstly in designing appropriate proximal terms to decompose the computation of the dual variable blocks of the target problem to make the subproblems in each iteration easier to solve, and secondly to develop novel numerical schemes to solve the decomposed subproblems efficiently. Our inexact augmented Lagrangian based decomposition methods have guaranteed convergence. We present an application of the proposed algorithms to the doubly nonnegative relaxations of uncapacitated facility location problems, as well as to two-stage stochastic optimization problems. We conduct numerous numerical experiments to evaluate the performance of our method against state-of-the-art solvers such as Gurobi and MOSEK. Moreover, our proposed algorithms also compare favourably to the well-known progressive hedging algorithm of Rockafellar and Wets.