Functional Decomposition Research Articles

A partitioned functional-decomposition scheme for modelling wave-ship-sloshing interaction

A novel partitioned function decomposition method is proposed and validated for accurately and effectively solving the interaction between waves and ships with sloshing effect. This scheme employs a hybrid functional-decomposition method that utilizes both potential and viscous flows to accurately and efficiently solve the wave-ship interaction in the external domain, while employing the original viscous method for simulating sloshing in the internal domain. To further enhance computational efficiency, a single-phase Level-set method is employed. Firstly, the issue of non-conservation in the level-set model is addressed through the application of a mass correction method. Additionally, based on the principle of mass conservation, modifications are made to the boundary conditions for free surface motion. As a result, an improved single-phase Level-set method is developed, which combines jump condition correction and mass correction. Through simulations involving linear and nonlinear free surfaces, impulsive pressures, overall forces on the tank, as well as comparisons with experimental data, it is observed that the proposed Level-set method effectively solves the sloshing in the internal domain, a problem for which the traditional single-phase Level-set method often fails to tackle with. Subsequently, by adopting a multi-block grid technique to mark tank and non-tank grid blocks and integrating the improved single-phase Level-set method with the SWENSE model, a partitioned function decomposition method is established to handle ship motions with sloshing effect in waves. It is found that simultaneously solving the internal and external flow problems using traditional implicit and explicit motion-solving methods poses certain challenges. Therefore, an implicit-inner-iteration solution method is proposed. By combining the proposed motion-solving method with the partitioned function decomposition model, satisfactory results are achieved for the wave-ship-sloshing interaction.

A Preliminary Study on The Causes of the "Triple-peak" La Niña During 2020-2022

The 2020-2022 triple-peak La Niña is the first consecutive three-year La Niña event in this century. In order to investigate the similarities and differences between this event and the other observed bimodal and triple events, this study uses synthetic and regression analysis, empirical orthogonal function decomposition, and mixed layer heat budget diagnosis to compare other events with this one in terms of location of anomalous negative sea surface temperature (SST), anomalous wind direction, and mixed layer heat budget. In the previous bimodal events, the centers of SST negative anomalies were both in the (5°S-5°N, 180°-120°W) region; there were anomalous northerly and westerly winds east of 140°W, and the negat precipitation anomalies were distributed along north of the equator. In contrast, the peak position of the second negative SST anomaly in this event is more eastward and southward; the anomalous easterlies continue from 120°E to the eastern boundary of the basin, and there is an anomalous southerlies in the eastern part of the basin. To further investigate the role of the anomalous easterlies and southerlies, this study calculates the mixed layer heat budget in key region. Corresponding to the latitudinal (longitudinal) wind anomalies, the latitudinal (longitudinal) temperature advection dominates the robust difference between the bimodal event and this triple-peak event. The anomalous easterlies and southerlies in the equatorial Pacific are favorable to the appearance of the third La Niña year in this event. This study is important in understanding the dynamics of triple-peak La Niña events, and will facilitate the forecast of such event.

ENSO‐Modulated Variability in Winter Shelf Circulation of the Northern South China Sea

AbstractWe combined long‐term observational data from 1999 to 2021 with numerical simulations to study the seasonal changes in the currents along the continental shelf in the Northern South China Sea (NSCS) during winter and how these changes relate to the El Niño‐Southern Oscillation (ENSO). Our results indicate that during El Niño events, the eastward movement of the warm pool in the tropical Pacific Ocean not only leads to colder sea surface temperatures and a stronger Kuroshio current intrusion but also significantly affects the formation of a high‐pressure system in the subtropics over the NSCS. In El Niño years, an anomalous anticyclonic wind stress curl in the South China Sea weakens the northeast winter monsoon, which in turn weakens the cyclonic shelf circulation. The first principal component from the multivariate empirical orthogonal function decomposition, which accounts for 49.02% of the total variance, shows a significant correlation of 0.64 with the Niño 3.4 index, indicating the circulation's sensitivity to tropical climate changes. Our analysis of the winter shelf circulation, based on the along‐isobath depth‐integrated vorticity equation, reveals that the exchange of water across the isobaths over the shelf is mainly controlled by the nonlinear advection of relative vorticity, with wind stress curl and bottom stress curl playing a less significant role in regulating the structure of these exchanges. The combined effect of baroclinic forces and topography likely governs the dynamics over the slope.

The Interplay of Foreign Direct Investment in Unravelling the Nexus of Technological Innovation and Economic Dynamics: An Integrated Study Using Vector Error Correction Model

Most lower-middle income countries prioritise innovation, with foreign direct investment (FDI) as a key funding source for sustainable development. This article studies the interplay between FDI, technological innovation (measured by patent-granted residents), gross domestic product (GDP), research and development (R&D) expenditure (RDE) and inflation of the Indian economy from 2002–2003 to 2022–2023. It uses a vector error correction model, Johansen cointegration tests, Granger causality tests, the impulse response function and variance decomposition. The study finds two cointegration relationships between the variables. GDP and RDE have a significant positive effect on technological innovation in the long term. Neither FDI nor inflation shows such an impact. FDI policies should therefore consider factors such as a conducive regulatory framework, tax breaks and grants for R&D to enhance their impact on innovation. JEL Codes: O31, O32, F21, F23, E01, O47

A River Water Quality Prediction Method Based on Dual Signal Decomposition and Deep Learning

Traditional single prediction models struggle to address the complexity and nonlinear changes in water quality forecasting. To address this challenge, this study proposed a coupled prediction model (RF-TVSV-SCL). The model includes Random Forest (RF) feature selection, dual signal decomposition (Time-Varying Filtered Empirical Mode Decomposition, TVF-EMD, and Sparrow Search Algorithm-Optimized Variational Mode Decomposition, SSA-VMD), and a deep learning predictive model (Sparrow Search Algorithm-Convolutional Neural Network-Long Short-Term Memory, SSA-CNN-LSTM). Firstly, the RF method was used for feature selection to extract important features relevant to water quality prediction. Then, TVF-EMD was employed for preliminary decomposition of the water quality data, followed by a secondary decomposition of complex Intrinsic Mode Function (IMF) components using SSA-VMD. Finally, the SSA-CNN-LSTM model was utilized to predict the processed data. This model was evaluated for predicting total phosphorus (TP), total nitrogen (TN), ammonia nitrogen (NH3-N), dissolved oxygen (DO), permanganate index (CODMn), conductivity (EC), and turbidity (TB), across 1, 3, 5, and 7-d forecast periods. The model performed exceptionally well in short-term predictions, particularly within the 1–3 d range. For 1-, 3-, 5-, and 7-d forecasts, R2 ranged from 0.93–0.96, 0.79–0.87, 0.63–0.72, and 0.56–0.64, respectively, significantly outperforming other comparison models. The RF-TVSV-SCL model demonstrates excellent predictive capability and generalization ability, providing robust technical support for water quality forecasting and pollution prevention.

Stream of variation modeling and monitoring for heterogeneous profiles in multi-stage manufacturing processes

ABTRACT Advanced manufacturing systems typically involve multiple operating stages, where in-process data are observed in the form of profiles that contain rich information for process monitoring. Emerging methodologies have been developed for multi-stage profile monitoring. However, the cases where different stages’ profiles are heterogeneous and variations propagate over stages have not been addressed so far. To this end, this article proposes a heterogeneous profiles-based stream of variation (HP-SoV) framework for multi-stage manufacturing process monitoring. It uses functional decomposition to extract features of heterogeneous profiles from different stages, where the decomposition coefficients are regarded as latent states that propagate along consecutive stages to capture the variation propagation. HP-SoV includes many existing models as its special cases, and enjoys an efficient inference algorithm via maximum likelihood estimation. Based on the one-step-ahead forecast errors of HP-SoV, a group monitoring scheme is further developed for online monitoring. Extensive numerical studies explore the modeling robustness and monitoring effectiveness of HP-SoV under different settings. A case study demonstrates the applicability of HP-SoV in multi-stage process monitoring for heterogeneous profiles.

Determinants of Household and Professional Forecasters’ Inflation Expectations in India

ABSTRACTThis study analyses and compares the determinants of inflation expectations among households and professional forecasters in India. To this end, we utilize quarterly survey data from the Reserve Bank of India (RBI), specifically the Inflation Expectations Survey of Households (IESH) and the Professional Forecasters’ Survey (SPF). The analysis employs a non‐recursive structural vector autoregressive (SVAR) model to explore the relationships between variables. The impulse response function and variance decomposition analysis shed light on the response of inflation expectations to macroeconomic shocks. Our findings indicate that apart from conventional macroeconomic factors like realized inflation and monetary policy, exogenous factors such as oil prices significantly shape inflation expectations. Comparing IESH and SPF, we found out that household expectations are more sensitive to shocks related to food prices, reflecting the influence of food expenses on household decision‐making. Conversely, professional forecasters’ expectations are more influenced by core inflation. Finally, we observed that inflation expectations adjust more quickly than realized inflation in response to macroeconomic shocks, suggesting a leading role. This study is novel with the contribution to the existing literature as it provides a comparative analysis of determinants of inflation expectations between households and professional forecasters in India, while also considering inflation targeting as a significant factor.

On the structure of species-function participation in multilayer ecological networks

Understanding how biotic interactions shape ecosystems and impact their functioning, resilience and biodiversity has been a sustained research priority in ecology. Yet, traditional assessments of ecological complexity typically focus on species-species interactions that mediate a particular function (e.g., pollination), overlooking both the synergistic effect that multiple functions might develop as well as the resulting species-function participation patterns that emerge in ecosystems that harbor multiple ecological functions. Here we propose a mathematical framework that integrates various types of biotic interactions observed between different species. Its application to recently collected data of an islet ecosystem—reporting 1537 interactions between 691 plants, animals and fungi across six different functions (pollination, herbivory, seed dispersal, decomposition, nutrient uptake, and fungal pathogenicity)—unveils a non-random, nested structure in the way plant species participate across different functions. The framework further allows us to identify a ranking of species and functions, where woody shrubs and fungal decomposition emerge as keystone actors whose removal have a larger-than-random effect on secondary extinctions. The dual insight—from species and functional perspectives—offered by the framework opens the door to a richer quantification of ecosystem complexity and to better calibrate the influence of multifunctionality on ecosystem functioning and biodiversity.

Concurrent Inter‐Model Spread of Boreal Winter Westerly Jet Meridional Positions Between the Northern and Southern Hemispheres in CMIP6 Models

ABSTRACTThis study investigates the inter‐model spread of climatological extratropical westerly jets in boreal winter, using the historical simulation of 52 Coupled Model Intercomparison Project phase 6 (CMIP6) models from 1851 to 2014. The results show that there is a substantial spread in the latitude of the upper‐tropospheric westerly jet across models, characterised by large inter‐model standard deviations to both the poleward and equatorward sides of the jet axis, although the multi‐model ensemble mean (MME) performs well in simulating meridional position of westerly jets. Furthermore, we detect the consistency of inter‐model jet position spread between the Northern and Southern Hemispheres, based on the inter‐model empirical orthogonal function (EOF) decomposition and correlation of regional‐averaged zonal winds. Specifically, the models that simulate the westerly jets poleward/equatorward relative to the MME position in one hemisphere also tend to simulate the jets poleward/equatorward in the other hemisphere. Accordingly, we define a global jet spread index to depict the concurrence of jet shift in the two hemispheres. The results of inter‐model regression analyses based on this index indicate that the models positioning the jets poleward than the MME tend to simulate a wider Hadley Cell, a poleward‐shifted Ferrel Cell in the Southern Hemisphere, enhanced precipitation in the subtropics and suppressed precipitation in the tropics, and warmer sea surface temperatures in the subtropics and mid‐latitudes. The present results suggest that improving the simulation of jet positions in climate models requires a comprehensive consideration of thermal states in the tropics and subtropics/mid latitudes.

About Air Quality Assessment using Time Series Analysis Techniques on Air Particles Data

This study investigates the dynamics of air pollution caused by particulate matter (PM10 and PM2.5) in Omsk, Russia. Data collected from the Sensor.Community network between 2021 and 2023 were analyzed using time series analysis methods. The findings reveal a subtle weekly seasonality in the data, potentially attributed to fluctuations in industrial activity and traffic patterns throughout the week. Additionally, a concerning trend of deteriorating air quality was identified, characterized by increasing annual average concentrations of PM10 and PM2.5. The study employed various time series analysis techniques, including Empirical Cumulative Distribution Function (ECDF), Seasonal and Trend decomposition using Loess (STL), and autocorrelation function (ACF) analysis. These methods allowed for the visualization and examination of data distribution, trend identification, and seasonality detection. Furthermore, the Mann-Kendall test confirmed a statistically significant trend of increasing pollution levels over the three-year period. To enhance the accuracy of spatial analysis, data interpolation was performed using kriging with a Gaussian model. This method, compared to simple interpolation, provides a more precise assessment of the spatial distribution of pollutants. The study also implemented Long Short-Term Memory (LSTM) for forecasting hourly pollution values. LSTM exhibited promising results, demonstrating its potential for developing early warning systems, particularly when combined with meteorological data such as wind forecasts. The results highlight the need for effective measures to mitigate air pollution in Omsk and emphasize the importance of utilizing data from diverse sources, including official air quality monitoring stations, to ensure accuracy and reliability in air quality assessments.

Maneuvering Trajectory Synthetic Aperture Radar Processing Based on the Decomposition of Transfer Functions in the Frequency Domain Using Average Blurred Edge Width Assessment

With the rapid development of synthetic aperture radar (SAR), delivery platforms are gradually becoming diversified and miniaturized. The SAR flight process is susceptible to external influences, resulting in unsatisfactory imaging results, so it is necessary to optimize imaging processing in combination with the SAR imaging quality assessment (IQA) index. Based on the principle of SAR imaging, this paper analyzes the impact of defocusing on imaging results caused by mismatched filters and draws on the assessment algorithm of motion blur, proposing a SAR IQA index based on average blurred edge width (ABEW) in the salient area. In addition, the idea of decomposing the transfer function in the frequency domain and fitting the matched filter with a polynomial is also proposed. The estimation of the flight trajectory is changed to a correction of the matched filter, avoiding the precise estimation of Doppler parameters and complex calculations during the time–frequency conversion process. The effectiveness of ABEW was verified by using SAR images of real scenes, and the results were highly consistent with the actual image quality. The imaging processing was tested using the echo signals generated by the errors introduced during the flight process, and more satisfactory imaging results were obtained by using ABEW with the filter for correction. The imaging process was tested using the echo signal generated by introducing errors during the flight, and the filter was corrected using ABEW as an index, obtaining a comparatively ideal imaging result.

LinApart: Optimizing the univariate partial fraction decomposition

We present LinApart, a routine designed for efficiently performing the univariate partial fraction decomposition of large symbolic expressions. Our method is based on an explicit closed formula for the decomposition of rational functions with fully factorized denominators. We provide an implementation in the Wolfram Mathematica language, which can lead to very significant performance gains over the built-in Apart command. Furthermore, a C language library implementing the core functionality and suitable for interfacing with other software is also provided. Both codes are made available at https://github.com/fekeshazy/LinApart.

Hierarchical Equations of Motion for Quantum Chemical Dynamics: Recent Methodology Developments and Applications.

ConspectusQuantum effects are critical to understanding many chemical dynamical processes in condensed phases, where interactions between molecules and their environment are usually strong and non-Markovian. In this Account, we review recent progress from our group in development and application of the hierarchical equations of motion (HEOM) method, highlighting its ability to address some challenging problems in quantum chemical dynamics.In the HEOM method, the bath degrees of freedom are represented using effective modes from exponential decomposition of the bath correlation function. Complex spectral densities and low temperature simulations often require a larger number of modes, making the simulations very expensive. Recent advances, such as the barycentric spectral decomposition (BSD) technique, can significantly reduce the number of effective modes, allowing to handle complex spectral densities and enabling simulations at very low temperatures, including near-zero temperature dynamics.Another key improvement in the computational efficiency is the use of tensor network methods like matrix product states and hierarchical tensor networks. These techniques allow for efficient HEOM propagation with thousands of effective modes, crucial for simulating large molecular systems interacting with multiple baths. This combination enables simulations of excitation energy transfer (EET) in systems like the Fenna-Matthews-Olson (FMO) complex and even larger systems with experimentally determined spectral densities.The versatility of the HEOM method is demonstrated through applications to a wide range of chemical dynamics problems. Simulations of EET and related ultrafast spectroscopy are first briefly covered. Applications of the HEOM to quantum tunneling effects in proton transfer reactions are then presented. Early works have studied the non-Kramers dependence of the rate constant as a function of bath friction due to deep tunneling and revealed vibrationally nonadiabatic dynamics within the so-called nontraditional view of proton transfer reactions. A recent work on the large kinetic isotope effects in soybean lipoxygenase also indicated that many quantum correction approximations to classical transition-state theory may fall short in describing deep tunneling effects.Charge transport and separation dynamics in organic semiconductors are another area where the HEOM method has been instrumental. We first demonstrate that the HEOM provides a unified description of both band-like and thermally assisted charge carrier transport in organic materials. The effect of non-nearest neighbor transitions is then investigated by combining generalized master equations with exact memory kernels. The HEOM method also enables simulation of charge separation in organic photovoltaics (OPVs) and reveals how factors such as external electric fields, entropy, and charge delocalization influence the charge separation barrier and dynamics.Moreover, HEOM has been applied to investigate hydrogen atom scattering on the Au(111) surface and vibrational energy relaxation at molecule-metal interfaces. These studies provide deeper insights into how electron-hole pair excitations and temporary charge transfer states influence the nuclear motion, offering a new framework for simulating nonadiabatic dynamics on metal surfaces.In summary, the HEOM method has developed into a robust tool for simulating quantum effects in condensed phases. Future developments in algorithm efficiency and computational power will likely expand its applicability to even more complex systems.

Intractability results for integration in tensor product spaces

We prove lower bounds on the worst-case error of numerical integration in tensor product spaces. The information complexity is the minimal number N of function evaluations that is necessary such that the N-th minimal error is less than a factor ε times the initial error, i.e., the error for N=0, where ε belongs to (0,1). We are interested to which extent the information complexity depends on the number d of variables of the integrands. If the information complexity grows exponentially fast in d, then the integration problem is said to suffer from the curse of dimensionality.Under the assumption of the existence of a worst-case function for the uni-variate problem, we present two methods for providing lower bounds on the information complexity. The first method is based on a suitable decomposition of the worst-case function and can be seen as a generalization of the method of decomposable reproducing kernels. The second method, although only applicable for positive quadrature rules, does not require a suitable decomposition of the worst-case function. Rather, it is based on a spline approximation of the worst-case function and can be used for analytic functions. Several applications of both methods are presented.

Responses of surface ozone under the tropical cyclone circulations: Case studies from Fujian Province, China

The circulation of tropical cyclones (TCs) exerts a multifaceted influence on the spatial and temporal distribution of surface pollutants. This study investigates the response of surface ozone (O3) concentration to the TCs in Fujian Province from June to December 2022 by analyzing the contributions of atmospheric pollutants, meteorological conditions, and dynamical transports. Empirical orthogonal function (EOF) decomposition methods are used to analyze the spatio-temporal distribution patterns of affected O3, and a Gradient Boosting Regression Trees (GBRT) machine learning model is employed to estimate surface O3 concentration, quantifying the influence of each factor. The results indicate an anomaly increase in O3 concentration during this period, with photochemistry-related meteorological conditions being the primary influencer, accounting for 66.9% of O3 variations, elucidating the interpretability of the GBRT model for attributing changes in O3 concentration. Low relative humidity and high temperature conditions have been identified as pivotal factors influencing the rise in O3 concentrations. The presence of TC undermines this predominant influence, amplifying the role of transport factors and other atmospheric pollutants. In the case studies of TC (Muifa and Nanmadol, 2022), the slow or stagnant TCs triggered persistent downdrafts in its periphery and brought favorable meteorological conditions such as clear sky and warm temperature for photochemistry. TCs also enhances the impact of horizontal and vertical dynamic transport on O3 concentrations. This work provides vital insights into the complex interplay between TCs and surface O3 concentrations, highlighting the need for targeted environmental and air quality management strategies in regions frequently impacted by TCs.

Penalized Functional Decomposition for Detecting Bursts in Water Distribution Systems

Penalized Functional Decomposition for Detecting Bursts in Water Distribution Systems

Impact of Digital Economy Development on Financialization of Firms: Empirical Evidence from PVAR Model

In this paper, we select several indicators to measure the level of the digital economy in cities, the index of digital inclusive finance in cities and the degree of financialization of enterprises, we apply variables mentioned above to analyze the complex relationship between multiple variables based on the PVAR model, we firstly suppose a unique order and use impulse response function(IRF) and variance decomposition measures to predict the impact of the relationship between variables, so as to provide a reference for policy making and risk prevention. and use impulse response and variance decomposition methods to predict the future direction of the relationship between variables, so as to provide certain reference significance for policy making and risk prevention.

Analysis of the Combined Impact of Socio-Economic Factors on House Price Volatility in the Housing Market

As an important variable in China’s economic system, real estate price is a key point closely linked to the country’s economy and people’s livelihood. It is of great practical significance to study the impact of socio-economic factors in the housing market on China’s house prices and its transmission mechanism, so as to put forward corresponding policy recommendations for stabilizing house prices and preventing real estate market and financial risks. Taking China’s time series data from 2014 to 2023 as a sample, this paper empirically investigates the law of the relationship between socio-economic factors in the housing market and house price fluctuations by constructing a structural vector autoregressive model, and employs impulse response function and variance decomposition to analyze the relationship between the two dynamically. The study shows that the 15-period variance decomposition effect of itself and residents’ disposable income are the main influencing factors of house price fluctuation, and the degree of explanation of its fluctuation is 55.5% and 23.2% respectively. In a market economy, real estate prices fluctuate up and down around their value due to the law of value. Therefore, real estate prices cannot rise indefinitely, and the final result should be stabilized within a reasonable level.

Reinforcement Learning with Value Function Decomposition for Hierarchical Multi-Agent Consensus Control

A hierarchical consensus control algorithm based on value function decomposition is proposed for hierarchical multi-agent systems. To implement the consensus control algorithm, the reward function of the multi-agent systems can be decomposed, and two value functions can be obtained by analyzing the communication content and the corresponding control objective of each layer in the hierarchical multi-agent systems. Therefore, for each agent in the systems, a dual-critic network and a single-actor network structure are applied to realize the objective of each layer. In addition, the target network is introduced to prevent overfitting in the critic network and improve the stability of the online learning process. During the updating of network parameters, a soft updating mechanism and experience replay buffer are introduced to slow down the update rate of the network and improve the utilization rate of training data. The convergence and stability of the consensus control algorithm with the soft updating mechanism are analyzed theoretically. Finally, the correctness of the theoretical analysis and the effectiveness of the algorithm were verified by two experiments.

Determinants of the Developed Country Index and Indonesian Macroeconomic on the IDX Growth 30 and IDX Value 30

This study analyzes the determinants of the Developed Country Index (Hang Seng Index, Dow Jones Index) and Indonesian macroeconomic variables (10-Year Government Bond Yield, Foreign Ownership in Government Bonds, and the BI-7 Day Reverse Repo Rate, BI7DRR) on the movement of the IDX Growth 30 Index (IDXG30) and IDX Value 30 Index (IDXV30) from 2018–2022. Monthly time series data is used with a saturated sampling technique, processed via Eviews 12 using VECM analysis. The study conducts Stationarity, Optimal Lag, VAR Stability, and Cointegration Tests, along with Impulse Response Function (IRF) and Forecast Error Variance Decomposition (FEVD) analyses Results show that the Hang Seng Index and Foreign Ownership in Government Bonds negatively affect IDXG30 and IDXV30, while BI7DRR positively influences both. The Dow Jones Index positively affects IDXG30 but negatively impacts IDXV30. Meanwhile, the 10-Year Government Bond Yield negatively affects IDXG30 and positively influences IDXV30. Additionally, the performance of IDXG30 and IDXV30 themselves and BI7DRR significantly contribute to both indices' movements.