Classical Decomposition Method Research Articles

Time Series Decomposition of Land Surface Temperature for Long-Term Trend Forecasting and Impact on Nesting Sea Turtle Habitats in the Arabian Gulf

Abstract Improving land surface temperature (LST) modeling is vital for mitigating climate change effects on various ecosystems and marine habitats such as important sea turtle habitats. Over the past decade, extreme temperatures have likely significantly affected nesting sea turtle habitats in the Arabian Gulf, with predominantly female hatchlings creating an imbalance in the sex ratio. Such shifts have profound implications for these habitats’ long-term survival and conservation management. This study leverages statistical machine learning models to measure ongoing temporal variations in LST. We break down the LST time series into trend, seasonal, and noise components using classical decomposition methods like X11, Seasonal Extraction in autogressive integrated moving average (ARIMA) Time Series (SEATS), and the seasonal and trend decomposition using local regression (Loess) (STL) approach. The long-term trends in LST data are driven by climate change rather than seasonal fluctuations. We employed neural network autoregression (NNAR), bagged error, trend, and seasonal (BaggedETS), exponential smoothing models, and the STL method to project future LST values. We also explored advanced forecasting models like dynamic harmonic regression; trigonometric seasonality, Box–Cox transformation, autoregressive moving average (ARMA) errors, and trend and seasonal components (TBATS); and seasonal autoregressive integrated moving average (SARIMA) for comparative performance analysis. Extended warm periods were identified for Abu Ali Island between 2017 and 2018 through several decomposition methods, likely linked to the 2015/16 El Niño event. We also conducted a marine heatwave (MHW) analysis from 2010 to 2020, establishing a pronounced impact of the 2015/16 El Niño on the Arabian Gulf. In nesting beach environments with high LST, marine heatwaves could have a significant impact on sea turtle populations without human intervention such as artificially cooling the nest temperature. The SARIMA model showed higher forecasting precision for in situ weather data, while the NNAR model demonstrated superior performance with remotely sensed data.

An explicit nonlinear model for large spatial deflections of symmetric slender beams

Flexible slender beams are commonly used in compliant mechanisms and continuum robots. However, the modeling of these beams can be complicated due to the geometric nonlinearity becoming significant at large elastic deflections. This paper presents an explicit nonlinear model for large spatial deflections of a slender beam with uniform, symmetrical sections subjected to general end-loading. The elongation, bending, torsion, and shear deformations of the beams are modeled based on Timoshenko’s assumptions and Cosserat rod theory. Subsequently, the nonlinear governing differential equations for the beam are derived from the quaternion representation of the rotation matrix. The explicit load–displacement relations of the beam are obtained using the improved Adomian decomposition method. This method is superior to the classical Adomian decomposition method in terms of convergence rate and domain. The convergence and superiority of the method are also rigorously demonstrated. Simulations are provided to verify the one-, two-, and three-dimensional deflections of beams. Real-world experiments have also been performed to validate our method’s effectiveness with two different beam configurations. The results indicate that the proposed method accurately estimates large spatial deflections of flexible beams.

A novel tensor-based modal decomposition method for reduced order modeling and optimal sparse sensor placement

Data-driven modal decomposition methods have become fundamental algorithms in constructing reduced order models (ROMs), which serve as a critical tool in the digital twin modeling of large complex systems. Classical modal decomposition methods are particularly adept at handling matrix-form input data that contains columnized snapshots without retaining spatial structure and neighborhood information. Focusing on addressing this problem, this paper proposed a Tensor-Based Modal Decomposition (TBMD) method to deal with the high-order tensor-form input data. TBMD method is effective in finding the potential low-order manifolds of a given high-order dynamical system with low energy loss within fewer decomposited modes. Moreover, TBMD is extended to be used in the field of optimal sensor placement via the development of a tensor-based QR factorization method and a tensor-based compressive sensing algorithm. The tensor-based QR factorization method is able to consider the spatial structure and neighborhood information of the basis matrices data in tensor form. This is the first time that a compressive sensing model has been discussed and solved for the frontal slice-wise product of a tensor and a vector. Subsequently, comprehensive case studies are conducted based on the cylinder wake dataset, airfoil vortex dataset, sea surface temperature dataset, eigenfaces dataset and turbulent channel flow dataset. The experiment results show that TBMD can accurately capture lower-order manifolds, and the tensor-based QR factorization is effective in optimizing sensor placement with fewer sensors while maintaining high reconstruction accuracy. The proposed methods in this paper is promising to be utilized in the construction of large-scale complex system digital twins, in which TBMD can serve as a fundamental algorithm in constructing ROM.

Multilevel domain decomposition-based architectures for physics-informed neural networks

Physics-informed neural networks (PINNs) are a powerful approach for solving problems involving differential equations, yet they often struggle to solve problems with high frequency and/or multi-scale solutions. Finite basis physics-informed neural networks (FBPINNs) improve the performance of PINNs in this regime by combining them with an overlapping domain decomposition approach. In this work, FBPINNs are extended by adding multiple levels of domain decompositions to their solution ansatz, inspired by classical multilevel Schwarz domain decomposition methods (DDMs). Analogous to typical tests for classical DDMs, we assess how the accuracy of PINNs, FBPINNs and multilevel FBPINNs scale with respect to computational effort and solution complexity by carrying out strong and weak scaling tests. Our numerical results show that the proposed multilevel FBPINNs consistently and significantly outperform PINNs across a range of problems with high frequency and multi-scale solutions. Furthermore, as expected in classical DDMs, we show that multilevel FBPINNs improve the accuracy of FBPINNs when using large numbers of subdomains by aiding global communication between subdomains.

Scorpion envenomation in Brazil and its relationship with the social determinants of health: A population-based ecological study

This study comprehensively analyzed cases of scorpion envenomation in Brazil, exploring the temporal trends and geographic patterns of such incidents between January 1, 2012, and December 31, 2022. Simultaneously, we assessed the correlation between scorpion envenomation and social determinants of health and social vulnerability. We conducted a population-based ecological study, gathering information on the number of scorpion envenomation cases in Brazil, as well as socioeconomic data and social vulnerability indicators across the 5,570 Brazilian municipalities. The season-trend model, based on the classical additive decomposition method, informed estimations of scorpion envenomation variations over time. The spatial correlation of scorpion envenomation with socioeconomic and vulnerability indicators was assessed using the Bivariate Moran's I. A total of 1,343,224 cases of scorpion envenomation were recorded in Brazil from Jan 2012 to Dec 2022. A single increasing time trend was observed for the entire country for this period (APC 8.94, P < 0.001). The seasonal analysis was significant for Brazil as a whole and all regions (p < 0.001), with peaks evident between October and November. The spatial distribution of cases was heterogeneous, with spatial clusters concentrated in the high-risk Southeast and Northeast regions. There was a high incidence of scorpion envenomation in municipalities facing social vulnerability, and, paradoxically, in those with better sanitation and waste collection. Our study revealed a heterogeneous geographical distribution of scorpion accidents in Brazil. Municipalities with higher social vulnerability exhibited a high incidence of scorpion envenomation.

METODE TRIPLE EXPONENTIAL SMOOTHING HOLT-WINTER’S MULTIPLICATIVE DAN DEKOMPOSISI KLASIK MULTIPLIKATIF UNTUK PERAMALAN RATA-RATA KENAIKAN KONSENTRASI KARBON DIOKSIDA (CO2) GLOBAL

Global warming occurs due the high concentration of Greenhouse Gases (GHG) in the atmosphere, which is called the greenhouse effect. The highest greenhouse gas that causes global warming that is being piled up in the atmosphere due human activity is carbon dioxide. Data on the average increase in global carbon dioxide (C02) concentrations are assumed contain elements of trend and seasonality. Holt-Winter's Multiplicative Triple Exponential Smoothing Method and Multiplicative Classical Decomposition the best choices in predicting data that contains trend and seasonality elements. Forecasting data on the global average increase CO2 has the objective of predicting data for the next 12 periods. The data used is data on the global average increase for the period January 2013 to December 2022. The prediction error measure used is MAPE (Mean Absolute Percentage Error). The results of the analysis on the Triple Exponential Smoothing Holt-Winter's Multiplicative method obtained a MAPE value of 0.09395%, indicating very good prediction category, while the results of the analysis of the Multiplicative Classical Decomposition method had a MAPE value of 0.07021%, which means that it has very good category in do forecasting. Based on the MAPE value obtained, the best method is the Multiplicative Classical Decomposition method.

Domain Decomposition with Neural Network Interface Approximations for time-harmonic Maxwell’s equations with different wave numbers

In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface conditions between the subdomains. The advantage is that the interface condition can be updated without recomputing the Maxwell system at each step. The main part consists of a detailed description of the construction of the neural network for domain decomposition and the training process. To substantiate this proof of concept, we investigate a few subdomains in some numerical experiments with low frequencies. Therein the new approach is compared to a classical domain decomposition method. Moreover, we highlight current challenges of training and testing with different wave numbers and we provide information on the behaviour of the neural-network, such as convergence of the loss function, and different activation functions.

Drag Decomposition Using Partial-Pressure Fields: Ventus-3 and NASA Common Research Model

The development of partial-pressure field (PPF) theory (Schmitz, S “Drag Decomposition Using Partial-Pressure Fields in the Compressible Navier–Stokes Equations,” AIAA Journal, Vol. 57, No. 5, 2019, pp. 2030–2038) and the application of the concept to conditions relevant to commercial transport aircraft, operating in both the subsonic and transonic regimes (Hart, P. L., and Schmitz, S., “Drag Decomposition using Partial-Pressure Fields: ONERA M6 Wing,” AIAA Journal, Vol. 60, No. 5, 2022 pp. 2941–2951), have shown promise as complements to classical far-field methods. In the present work, a further comprehensive analysis of drag decomposition methods is applied to wing and aircraft configurations. First, the Ventus-3 sailplane wing case demonstrates the ability of PPFs to successfully deconstruct drag on industry-relevant cases including transition modeling and winglets. A quantitative comparison to classical aerodynamic theory and far-field methods supports PPF theory and provides additional insight to viscous–inviscid interaction by means of a viscous interactional aerodynamics term in PPF theory. Second, the NASA Common Research Model is simulated in transonic flow to showcase drag decomposition of full aircraft configurations where PPF applications are used to provide further insight into wave drag sources acting on the aircraft in comparison to classical far-field decomposition methods.

Decomposing the Intraurban Malnutrition Gap Between Poor and Non-poor Children in Colombia : Decomposing the Intraurban Malnutrition Gap Between Poor and Non-poor Children in Colombia.

In Colombia, although it can be said that, on average children living in urban areas have better quality of life than their rural peers, it is also true that within cities, there are high levels of socioeconomic inequality. Our objective is to identify the contribution of the factors that explain the gap in stunting and excess weight between poor and non-poor children under 5years of age in urban areas of Colombia. We use data from the 2015 National Nutritional Status Survey, and two nonlinear decomposition techniques based on the classical decomposition method developed by Blinder-Oaxaca. With a sample of 6877 observations, the results show that the intraurban gap of stunting between poor and non-poor children in urban areas is 4.8 percentage points. Its main determinants are the mother's educational level (46.5%), affiliation to the health system by the mother (19.4%), and assisted delivery in a medical institution (16.6%). For excess weight, the gap is - 2.1 percentage points, and its main determinants are the mother's educational level (39.2%) and birth attended by a physician (21.8%). This study suggests the coexistence of a double burden of malnutrition (DBM) in children under 5years of age living in urban areas of Colombia. Stunting is associated with low-income levels while excess weight is associated with higher income levels. The identification of the main determinants of DBM and its relative importance, constitutes a contribution for public policy makers aimed at reducing socioeconomic gaps.

Multivariate Analysis of Rotifer Community and Environmental Factors Using the Decomposed Components Extracted from a Time Series

Zooplankton abundance patterns exhibit apparent seasonality depending on seasonal variations in water temperature. To analyze the abundance patterns of zooplankton communities, it is necessary to consider the environmental factors that are essential for zooplankton community succession. However, this approach is challenging due to the seasonal variability of environmental factors. In this study, all rotifer species inhabiting a water body were classified into three groups based on their abundance and frequency of occurrence, and decomposition method was used to classify them into groups that exhibit seasonal vs. non-seasonal variability. Multivariate analysis was performed on the seasonal, trend, and random components derived from the classical decomposition method of zooplankton abundance and related environmental factors. This approach provided more precise results and higher explanatory power for the correlations between rotifer communities and environmental factors, which cannot be clarified with a simple abundance-based approach. Using this approach, we analyzed the seasonality-based patterns of the abundance of rotifer species by dividing the environmental factors into those associated with seasonal and non-seasonal variabilities. Overall, the results demonstrated that the explanatory power of redundancy analysis was higher when using the three time series components than when using undecomposed abundance data.

Dating death

The estimation of the postmortem interval (PMI), particularly the late time since death, is a crucial issue when dealing with human remains. Its establishment is an important task for forensic scientists since it has important legal implications such as identifying a victim or prosecuting an offender. However, dating death is a very complex and challenging task due to the amount of intrinsic and extrinsic factors, that may influence the rate and nature of body decomposition. Many methods have been used to estimate PMI, from classical decomposition methods to entomological and botanical methods or more recently physics and biochemical methods.&#x0D; This paper reviews current forensic dating methods, focusing especially on forensic anthropological techniques. Nevertheless, the existing literature is insufficient, denoting a lack of effective methods to achieve an accurate and reliable PMI estimation and further investigation is required. A holistic approach, where every element must be considered, is the key to achieving a reliable estimation of PMI. Interdisciplinarity is thus mandatory, allied with the capacity of forensic anthropologists to denote all the details.

Computationally semi-numerical technique for solving system of intuitionistic fuzzy differential equations with engineering applications

Some complex problems in science and engineering are modeled using fuzzy differential equations. Many fuzzy differential equations cannot be solved by using exact techniques because of the complexity of the problems mentioned. We utilize analytical techniques to solve a system of fuzzy differential equations because they are simple to use and frequently result in closed-form solutions. The Generalized Modified Adomian Decomposition Method is developed in this article to compute the analytical solution to the linear system of intuitionistic triangular fuzzy initial value problems. The starting values in this case are thought of as intuitionistic triangular fuzzy numbers. Engineering examples, such as the Brine Tanks Problem, are used to demonstrate the proposed approach and show how the series solution converges to the exact solution in closed form or in series. The corresponding graphs at different levels of uncertainty show the example’s numerical outcomes. The graphical representations further demonstrate the effectiveness and accuracy of the proposed method in comparison to Taylor’s approaches and the classical Decomposition method.

Sea Clutter Suppression and Target Detection Algorithm of Marine Radar Image Sequence Based on Spatio-Temporal Domain Joint Filtering.

In marine radar target detection, sea clutter will cause a large number of missed alarms and false alarms, which will affect the accuracy of target detection. In order to suppress sea clutter effectively, a sea clutter suppression and target detection algorithm of marine radar image sequence based on spatio-temporal domain joint filtering is proposed in this paper. The proposed method is to add a sea clutter suppression link before detecting the target. Firstly, the marine radar image sequence is transformed into three-dimensional frequency wavenumber domain by three-dimensional fast Fourier transform (3D-FFT), and then the three-dimensional image spectrum is obtained. According to the fact that the sea clutter spectrum obtained from the image spectrum satisfies the dispersion relation of linear wave theory in the three-dimensional frequency wavenumber domain, a sea clutter model is established. Then, through the established sea clutter model, a spatio-temporal domain joint sea clutter suppressor is designed to filter the image spectrum. After that, the filtered image spectrum is transformed by three-dimensional inverse fast Fourier transform (3D-IFFT) to obtain the image sequence in which sea clutter is suppressed. Finally, target detection is carried out for sea clutter suppressed image sequence. The method is validated by using the real data of X-band marine radar. Compared with the classical Empirical mode decomposition (EMD) method, the improvement of signal-to-noise ratio (SNR) is more obvious, and SNR can be increased by 15.3 db at most. In addition, compared with target detection on original images directly, the proposed method has excellent detection rate and can increase detection rates by at least 8%.

Analytical and numerical solution of the longitudinal porous fin with multiple power‐law‐dependent thermal properties and magnetic effects

AbstractThe present study is concentrated on the application of electric and magnetic fields on the longitudinal porous fin with power‐law‐dependent heat transfer coefficient, surface emissivity, and heat generation. The porosity parameter controls the amount of empty spaces or voids in the porous fin and its practical value lies in the range . In industrial application, the heat transfer coefficient is governed by a power law and its specific value defines a certain heat transfer process. The heat generation and surface emissivity of the longitudinal porous fin are assumed to be varied according to the power law and the whole fin is under the influence of an external electric field. The resulting nonlinear equation is solved by the classical Adimian decomposition method (ADM) and the obtained solutions are verified further by the finite difference method (FDM). It has been found that both ADM and FDM are in good agreement for lower values of thermophysical parameters. The effects of power index of heat generation, surface emissivity, and heat transfer coefficient parameter on the temperature distribution, heat flux, and efficiency are analyzed at different values of the porosity parameter comprehensively.

TÜRKİYE'DE EKONOMİK BÜYÜME İLE ÇEVRE KİRLİLİĞİ ARASINDAKİ İLİŞKİ

This study examines the relationship between economic growth and environmental pollution in Turkey. The research uses annual time series data from 1970 to 2017. Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root tests were used to test the stationarity of the series. In this the Autoregressive Distributed Lag (ARDL) model is used as an estimation technique. Furthermore, the classical additive decomposition method was used to forecast the pollution. The results indicate that economic growth has a positive significant effect on environmental pollution in the short-run and positive but insignificant effect in the long-run. When the long-run and short-run elasticities were compared it is found that the long-run elasticity is greater than the short-run elasticity which challenges the validity of the Environmental Kuznets Curve (EKC) hypothesis and provides evidence against its existence in Turkey. The paper suggests that robust and effective environmental policies should be strictly implemented and closely monitored to reduce the environmental pollution and to ensure the preservation of resources for future generations.

Robust Bayesian matrix decomposition with mixture of Gaussian noise

Matrix decomposition is a popular and fundamental approach in machine learning. The classical matrix decomposition methods with Frobenius norm loss is only optimal for Gaussian noise and thus suffer from the sensitivity to outliers and non-Gaussian noise. To address these limitations, the proposed methods can be divided into two categories. One type of approach is to replace the Frobenius norm loss with robust loss functions. The other type of approach is to impose the Bayesian priors to reduce the risk of overfitting. This paper combines these two approaches. Specifically, we model the noise by a mixture of Gaussian distribution, enabling the model to approximate a wide range of noise distributions. Meanwhile, we put a Laplace prior on the basis matrix to enforce the sparsity and a Dirichlet prior on the coefficient matrix to improve the interpretability. Extensive experiments in synthetic data and real-world data demonstrate that this method outperforms several competing ones. Ablation studies show that this method benefits from both the Bayesian priors and the Mixture of Gaussian noise loss, which confirms the necessity of combining the two schemes.

Ranking influential nodes in complex networks based on local and global structures

Identifying influential nodes in complex networks is an open and challenging issue. Many measures have been proposed to evaluate the influence of nodes and improve the accuracy of measuring influential nodes. In this paper, a new method is proposed to identify and rank the influential nodes in complex networks. The proposed method determines the influence of a node based on its local location and global location. It considers both the local and global structure of the network. Traditional degree centrality is improved and combined with the notion of the local clustering coefficient to measure the local influence of nodes, and the classical k-shell decomposition method is improved to measure the global influence of nodes. To evaluate the performance of the proposed method, the susceptible-infected-recovered (SIR) model is utilized to examine the spreading capability of nodes. A number of experiments are conducted on 11 real-world networks to compare the proposed method with other methods. The experimental results show that the proposed method can identify the influential nodes more accurately than other methods.

New decomposition method for the solutions of linear Schrödinger equation

The Schrödinger equation serves as the fundamental equation for quantum mechanics. In this article, we consider the theoretical and numerical solutions of Schrödinger’s linear equations. This is achieved using the new semi-analytical approach as an alternative to the classical Adomian Decomposition Method (ADM). The new method is referred to as Telescoping Decomposition Method. Some cases are considered; the results obtained display high level of convergence to their exact forms. The improved version is very useful and reliable; it requires less analytical effort, even without giving up precision. Thus, it is also highly recommended for the solution of related linear and nonlinear differential models in the fields of applied research.

RESEARCH OF TWO SYSTEMS E2/H2/1 WITH ORDINARY AND SHIFTED DISTRIBUTIONS BY THE SPECTRAL DECOMPOSITION METHOD

ABSTRACT Context. In the queueing theory, the studies of G/G/1 systems are relevant because it is impossible to obtain solutions for the waiting time in the final form in the general case with arbitrary laws of distributions of the input flow and of the service time. Therefore, the study of such systems for particular cases of input distributions is important. The problem of deriving a solution for the average waiting time in a queue in closed form for a pair of systems with ordinary and with shifted Erlang and hyperexponential input distributions is considered.Objective. Obtaining a solution for the main system characteristic – the average waiting time in queue for two queuing systems of type G/G/1 with conventional and with shifted second-order Erlang and Hyperexponential input distributions.Method. To solve this problem, we used the classical spectral decomposition method for solving the Lindley integral equation, which plays an important role in the theory of G/G/1 systems. This method allows obtaining a solution for the average waiting time for the considered systems in a closed form. For the practical application of the obtained results, the well-known probability theory moments method is used.Results. For the first time, spectral expansions of the solution of the Lindley integral equation are obtained for two systems, with the help of which the formulas for the average waiting time in the queue are derived in closed form.Conclusions. Spectral expansions of the solution of the Lindley integral equation for the systems under consideration are obtained and their complete coincidence is proved. Consequently, the formulas for the average waiting time in the queue for these systems are the same, but with modified parameters. It is shown that in the system with a delay in time, the average waiting time is less than in a conventional system. The resulting for waiting time formulas expand and supplement the known queuing theory incomplete formula for the average waiting time for G/G/1 systems with arbitrary laws distributions of input flow and service time. This approach allows us to calculate the average latency for these systems in mathematical packages for a wide range of traffic parameters. All other characteristics of the systems are derived from the waiting time. In addition to the average waiting time, such an approach makes it possible to determine also moments of higher orders of waiting time. Given the fact that the packet delay variation (jitter) in telecommunications is defined as the spread of the waiting time from its average value, the jitter can be determined through the variance of the waiting time. The results are published for the first time.

Hybrid tensor decomposition in neural network compression

Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for computational resources especially the storage consumption is growing due to that the increasing sizes of models are being required for more and more complicated applications. To address this problem, several tensor decomposition methods including tensor-train (TT) and tensor-ring (TR) have been applied to compress DNNs and shown considerable compression effectiveness. In this work, we introduce the hierarchical Tucker (HT), a classical but rarely-used tensor decomposition method, to investigate its capability in neural network compression. We convert the weight matrices and convolutional kernels to both HT and TT formats for comparative study, since the latter is the most widely used decomposition method and the variant of HT. We further theoretically and experimentally discover that the HT format has better performance on compressing weight matrices, while the TT format is more suited for compressing convolutional kernels. Based on this phenomenon we propose a strategy of hybrid tensor decomposition by combining TT and HT together to compress convolutional and fully connected parts separately and attain better accuracy than only using the TT or HT format on convolutional neural networks (CNNs). Our work illuminates the prospects of hybrid tensor decomposition for neural network compression.