The anomaly detection task is very important in computer science. And there are a lot of anomaly detection methods. Different from some thresholding methods, some unsupervised methods could make us get more accurate and faster result, which is the object of the project. In this paper, I tried to use EWMA and some other methods in two datasets: Webank time consuming indicators dataset and AIOps Challenge dataset. The paper consists nine parts: background of the project, related work, description of algorithms, implementation details, experimental setup and data sets used, experimental results and discussion, future directions, reference and meeting notes.

While increasing empirical evidence suggests that global time series forecasting models can achieve better forecasting performance than local ones, there is a research void regarding when and why the global models fail to provide a good forecast. This paper uses anomaly detection algorithms and Explainable Artificial Intelligence (XAI) to answer when and why a forecast should not be trusted. To address this issue, a dashboard was built to inform the user regarding (i) the relevance of the features for that particular forecast, (ii) which training samples most likely influenced the forecast outcome, (iii) why the forecast is considered an outlier, and (iv) provide a range of counterfactual examples to understand value changes, in the feature vector or the predicted value, can lead to a different outcome. Moreover, a modular architecture and a methodology were developed to iteratively remove noisy data instances from the train set, to enhance the overall global time series forecasting model performance. Finally, to test the effectiveness of the proposed approach, it was validated on two publicly available real-world datasets.

Time series data are significant and are derived from temporal data, which involve real numbers representing values collected regularly over time. Time series have a great impact on many types of data. However, time series have anomalies. We introduce hybrid algorithm named novel matrix profile (NMP) to solve the all-pairs similarity search problem for time series data. The proposed NMP inherits the features from two state-of-the art algorithms: similarity time-series automatic multivariate prediction (STAMP), and short text online microblogging protocol (STOMP). The proposed algorithm caches the output in an easy-to-access fashion for single- and multidimensional data. The proposed NMP algorithm can be used on large data sets and generates approximate solutions of high quality in a reasonable time. The proposed NMP can also handle several data mining tasks. It is implemented on a Python platform. To determine its effectiveness, it is compared with the state-of-the-art matrix profile algorithms i.e., STAMP and STOMP. The results confirm that the proposed NMP provides higher accuracy than the compared algorithms.

The removal of non-climatic biases, so-called inhomogeneities, from long climatic records needs sophistically developed statistical methods. One principle is that usually the differences between a candidate series and its neighbour series are analysed instead of directly the candidate series, in order to neutralize the possible impacts of regionally common natural climate variation on the detection of inhomogeneities. In most homogenization methods, two main kinds of time series comparisons are applied, i.e. composite reference series or pairwise comparisons. In composite reference series the inhomogeneities of neighbour series are attenuated by averaging the individual series, and the accuracy of homogenization can be improved by the iterative improvement of composite reference series. By contrast, pairwise comparisons have the advantage that coincidental inhomogeneities affecting several station series in a similar way can be identified with higher certainty than with composite reference series. In addition, homogenization with pairwise comparisons tends to facilitate the most accurate regional trend estimations. A new time series comparison method is presented here, which combines the use of pairwise comparisons and composite reference series in a way that their advantages are unified. This time series comparison method is embedded into the ACMANT homogenization method, and tested in large, commonly available monthly temperature test datasets.

Time irreversibility, i.e. the lack of invariance of the statistical properties of a system under time reversal, is a fundamental property of all systems operating out of equilibrium. Time reversal symmetry is associated with important statistical and physical properties and is related to the predictability of the system generating the time series. Over the past fifteen years, various methods to quantify time irreversibility in time series have been proposed, but these can be computationally expensive. Here we propose a new method, based on permutation entropy, which is essentially parameter-free, temporally local, yields straightforward statistical tests, and has fast convergence properties. We apply this method to the study of financial time series, showing that stocks and indices present a rich irreversibility dynamics. We illustrate the comparative methodological advantages of our method with respect to a recently proposed method based on visibility graphs, and discuss the implications of our results for financial data analysis and interpretation.

In this paper, we study the usage of machine learning models for sales time series forecasting. The effect of machine learning generalization has been considered. A stacking approach for building regression ensemble of single models has been studied. The results show that using stacking technics, we can improve the performance of predictive models for sales time series forecasting.

We define a new seasonal forecasting method based on fuzzy transforms. We use the best interpolating polynomial for extracting the trend of the time series and generate the inverse fuzzy transform on each seasonal subset of the universe of discourse for predicting the value of a an assigned output. Like first example, we use the daily weather dataset of the municipality of Naples (Italy) starting from data collected from 2003 till to 2015 making predictions on the following outputs: mean temperature, max temperature and min temperature, all considered daily. Like second example, we use the daily mean temperature measured at the weather station “Chiavari Caperana” in the Liguria Italian Region. We compare the results with our method, the average seasonal variation, ARIMA and the usual fuzzy transforms concluding that the best results are obtained under our approach in both examples.

Deep learning methods have been widely applied to time series classification tasks. Although deep learning methods perform excellently on these tasks, they require much training data. Labeling time series data for training is very time-consuming and labor-intensive. Active learning can be used to select the most informative data for labeling in time series classification tasks to save human labeling efforts. In this paper, we propose a new active learning (AL) framework for time series data. First, a temporal classifier for pixel-level temporal classification tasks is designed. Next, We propose an effective active learning method to select informative time series samples for labeling, which combines representativeness and uncertainty. For representativeness, We use the K-shape method to cluster time series data. For uncertainty, we construct an auxiliary deep network to evaluate the uncertainty of unlabeled data. The features of the middle hidden layer with rich temporal information of the classifier will be fed into the auxiliary deep network, which is equipped with a self-attention mechanism to utilize the temporal dependencies of time series data fully. Then, we define a new loss function with the aim of improving the deep model’s performance. Finally, the proposed method in this paper was evaluated on two temporal remote-sensing image datasets. The results demonstrate a significant advantage of our method over other approaches to time series data. Code is available at https://github.com/Fighting-Golion/time_series_active_learning

Traditional applications of Interferometric Synthetic Aperture Radar (InSAR) data involved inverting an interferogram stack to determine the average displacement velocity. While this approach has useful applications in continuously deforming regions, much information is lost by simply fitting a line through the time series. Thanks to regular acquisitions across most of the the world by the ESA Sentinel-1 satellite constellation, we are now in a position to explore opportunities for near-real time deformation monitoring. In this paper we present a simple statistical approach for detecting offsets and gradient changes in InSAR time series. Our key assumption is that 5 years of Sentinel-1 data is sufficient to calculate the population standard deviation of the detection variables. Our offset detector identifies statistically significant peaks in the first, second and third difference series. The gradient change detector identifies statistically significant movements in the second derivative series. We exploit the high spatial resolution of Sentinel-1 data and the spatial continuity of geophysical deformation signals to filter out false positive detections that arise due to signal noise. When combined with near-real time processing of InSAR data these detectors, particularly the gradient change, could be used to detect incipient ground deformation associated with geophysical phenomena, for example from landslides or volcanic eruptions.

The study of order patterns of three equally spaced values $x_t,x_{t+d},x_{t+2d}$ in a time series is a powerful tool. The lag $d$ is changed in a wide range so that differences of frequencies of order patterns become autocorrelation functions. Similar to a spectrogram in speech analysis, four ordinal autocorrelation functions are used to visualize big data series, as for instance heart and brain activity over many hours. The method applies to real data without preprocessing, outliers and missing data do not matter. On the theoretical side, we study properties of order correlation functions and show that the four autocorrelation functions are orthogonal in a certain sense. An analysis of variance of a modified permutation entropy can be performed with four variance components associated with the functions.

In recent years, transformer-based models have gained prominence in multivariate long-term time series forecasting (LTSF), demonstrating significant advancements despite facing challenges such as high computational demands, difficulty in capturing temporal dynamics, and managing long-term dependencies. The emergence of LTSF-Linear, with its straightforward linear architecture, has notably outperformed transformer-based counterparts, prompting a reevaluation of the transformer's utility in time series forecasting. In response, this paper presents an adaptation of a recent architecture termed extended LSTM (xLSTM) for LTSF. xLSTM incorporates exponential gating and a revised memory structure with higher capacity that has good potential for LTSF. Our adopted architecture for LTSF termed as xLSTMTime surpasses current approaches. We compare xLSTMTime's performance against various state-of-the-art models across multiple real-world datasets, demonstrating superior forecasting capabilities. Our findings suggest that refined recurrent architectures can offer competitive alternatives to transformer-based models in LTSF tasks, potentially redefining the landscape of time series forecasting.

Machine learning methods have widely been applied to detect anomalies in machine and cutting tool behavior during lathe or milling. However, detecting anomalies in the workpiece itself did not get the same attention by researchers. That is why in this article, the authors present a pub-licly available multivariate time series dataset which was recorded during milling of 16MnCr5. Due to artificially introduced, though realistic anomalies in the workpiece the dataset can be ap-plied for anomaly detection. By using a convolutional autoencoder as a first model good results in detecting the location of the anomalies in the workpiece were achieved. Furthermore, milling tools with two different diameters where used which led to a dataset eligible for transfer learn-ing. The objective of this article is to provide researchers with a real-world time series dataset of the milling process which is suitable for modern machine learning research topics like anomaly detection and transfer learning.

In this paper, we study the asymptotic behavior of the sequential empirical process and the sequential empirical copula process, both constructed from residuals of multivariate stochastic volatility models. Applications for the detection of structural changes and specification tests of the distribution of innovations are discussed. It is also shown that if the stochastic volatility matrices are diagonal, which is the case if the univariate time series are estimated separately instead of being jointly estimated, then the empirical copula process behaves as if the innovations were observed; a remarkable property. As a by-product, one also obtains the asymptotic behavior of rank-based measures of dependence applied to residuals of these time series models.

Hand and arm gesture recognition using radio frequency (RF) sensing modality proves valuable in man-machine interface and smart environment. In this paper, we use time series analysis method for accurately measuring the similarity of the micro-Doppler (MD) signatures between the training and test data, thus providing improved gesture classification. We characterize the MD signatures by the maximum instantaneous Doppler frequencies depicted in the spectrograms. In particular, we apply the dynamic time warping (DTW) method and compare its performance with that of the long short-term memory (LSTM) network. Both methods take into account the values as well as the temporal evolution and trends of time series data. It is shown that the DTW method achieves high gesture classification rates and is robust to time misalignment.

Noise model selection criteria has a significant impact on identifying the stochastic noise proper-ties of any GNSS daily coordinate time series. The low-frequency random walk noise existing in these time series could lead to overestimation of the tectonic rate, so it is of great significance to accurately detect the random walk component. This study focuses on noise model estimation cri-terion (BIC_tp) derived from the AIC and the BIC by introducing 2π factors. It is more sensitive to abnormal steps (random jumps). Using observation data from 72 GNSS stations from 1992 to 2022 and simulated data, four combined noise models are used to explore the impacts of time se-ries lengths (ranging from2 to 24 years) and data loss (between 2% and 30%) on noise models and velocity estimation. The results show that as the time length increased, the selected optimal noise model, and the estimated uncertainty of the tectonic trend with different data gap, gradually con-verge. When the time length is short (less than 8 years), it could lead to the FNRWWN, FNWN, and PLWN models being mistakenly estimated as GGMWN models, thereby affecting the accura-cy of determining the station velocity parameters. When the time length is 12 years, the RW noise component is more probably detected, As the time length increases, the impact of RW on velocity uncertainty is weakened. Finally, we conclude that for a time series with a minimum time length of 12 years, both the selection of the optimal stochastic noise model and the estimation of the ve-locity parameters are reliable.

We propose a novel tensor-based formalism for inferring causal structures from time series. An information theoretical analysis of transfer entropy (TE), shows that TE results from transmission of information over a set of communication channels. Tensors are the mathematical equivalents of these multi-channel causal channels. A multi-channel causal channel is a generalization of a discrete memoryless channel (DMC). We consider a DMC as a single-channel causal channel. Investigation of a system comprising three variables shows that in our formalism, bivariate analysis suffices to differentiate between direct and indirect relations. For this to be true, we have to combine the output of multi-channel causal channels with the output of single-channel causal channels. We can understand this result when we consider the role of noise. Subsequent transmission of information over noisy channels can never result in less noisy transmission overall. This implies that a Data Processing Inequality (DPI) exists for transfer entropy.

Modern energy systems collect high volumes of data that can provide valuable information about energy consumption. Electric companies can now use historical data to make informed decisions on energy production by forecasting the expected demand. Many deep learning models have been proposed to deal with these type of time series forecasting problems. Deep neural networks, such as recurrent or convolutional, can automatically capture complex patterns in time series data and provide accurate predictions. In particular, Temporal Convolutional Networks (TCN) are a specialised architecture that has advantages over recurrent networks for forecasting tasks. TCNs are able to extract long-term patterns using dilated causal convolutions and residual blocks, and can also be more efficient in terms of computation time. In this work, we propose a TCN-based deep learning model to improve the predictive performance in energy demand forecasting. Two energy-related time series with data from Spain have been studied: the national electric demand, and the power demand at charging stations for electric vehicles. An extensive experimental study has been conducted, involving more than 1900 models with different architectures and parametrisations. The TCN proposal outperforms the forecasting accuracy of Long Short-Term Memory (LSTM) recurrent networks, which are considered the state-of-the-art in the field.

Time series forecasting has been a challenging area in the field of Artificial Intel-ligence. Various approaches such as linear Neural Networks, Recurrent Linear Neural Networks, Convolutional Neural Networks and recently Transformers have been attempted for the time series forecasting domain. Although, Trans-former-based architectures have been outstanding in the Natural Language Pro-cessing domain, especially in autoregressive language modeling, the initial at-tempts to use transformers in the time series arena have met with mixed success. One of the recent papers demonstrated that modeling the multi-variate time se-ries problem as independent channels on a transformer architecture produced lower mean square and mean absolute errors on benchmarks, however, another recent paper claimed that a simple linear neural network out-performs previous approaches including transformer-based designs. We investigate this paradox in detail comparing the linear Neural Network and Transformer based designs, provide insights to why a certain approach may be better for a particular type of problem. We also improve upon the recently proposed simple linear Neural Network based architecture by using dual pipelines with batch normalization and reversible instance normalization. Our enhanced architecture outperforms all existing architectures for time series forecasting on majority of the popular benchmarks.

Industrial data scarcity is one of the largest factors holding back the widespread use of machine learning in manufacturing. To overcome this problem, the concept of transfer learning was developed and it achieved high attention in recent industrial research. Our paper focuses on the problem of time series segmentation and presents the first in-depth research about transfer learning for deep-learning based time series segmentation on the example of industrial end-of-line pump testing. In particularly, we investigate if the performance of deep learning models can be increased by pretraining the network with data from other domains. Three different scenarios are analyzed: source and target data being closely related, source and target data being distantly related, and source and target data being non-related. The results demonstrate that transfer learning can enhance the performance of time series segmentation models in respect to accuracy and training speed. The benefit is most clearly seen in scenarios where source and training data are closely related and the number of target training data samples is lowest. However, in the scenario of non-related datasets, cases of negative Transfer Learning were observed as well. Thus, the research emphasizes the potential, but also the challenges of industrial Transfer Learning.

This paper has three objectives, the first is to present a detailed overview in the form of a tutorial for the developments of several key quantile time series modelling approaches. The second objective is to develop a general framework to represent such quantile models in a unifying manner in order to easily develop extensions and connections between existing models that can then be developed to further extend these models in practice. In this regard, the core theme of the paper is to provide perspectives to a general audience of core components that go into construction of a quantile time series model and then to explore each of these core components in detail. The paper is not addressing the concerns of estimation of these models, as there is existing literature on these aspects in many settings, we provide references to relevant works on these aspects in several classes of model. Instead, the focus is rather to provide a unified framework to construct such models for practitioners, therefore the focus is instead on the properties of the models and links between such models from a constructive perspective. The third objective is to compare and discuss the application of the different quantile time series models on several sets of interesting demographic and mortality based time series data sets of relevance to life insurance analysis. The exploration included detailed mortality, fertility, births and morbidity data in several countries with more detailed analysis of regional data in England, Wales and Scotland.

A continuous Deep Belief Network (cDBN) with two hidden layers is proposed in this paper, focusing on the problem of weak feature learning ability when dealing with continuous data. In cDBN, the input data is trained in an unsupervised way by using continuous version of transfer functions, the contrastive divergence is designed in hidden layer training process to raise convergence speed, an improved dropout strategy is then implemented in unsupervised training to realize features learning by de-cooperating between the units, and then the network is fine-tuned using back propagation algorithm. Besides, hyper-parameters are analysed through stability analysis to assure the network can find the optimal. Finally, the experiments on Lorenz chaos series, CATS benchmark and other real world like CO2 and waste water parameters forecasting show that cDBN has the advantage of higher accuracy, simpler structure and faster convergence speed than other methods.

The purpose of this project is to explore the potential of Long Short-Term Memory (LSTM), a type of recurrent neural network (RNN), as a tool for making directional predictions for assets. The focus will be on using LSTM for classifying up/down moves in stock indices, stocks, and FX rates (EUR/USD). Various financial ratios, advanced technical indicators, and volatility estimators will be used as features to enhance the predictive power of the model. Incorporating credit spreads and news indicators can also improve the model. The advantage of LSTM is its ability to handle sequences of arbitrary length, which means that longer time frames such as 5-day, 10-day, or 1-week returns can be used for prediction. Before using RNNs, exploratory data analysis (EDA) will be performed to understand the underlying patterns in the data. This may include dimensionality reduction techniques such as autoencoding, self-organizing maps, or decision tree regression. The results of the EDA will be used to guide the selection of features for the LSTM model. It is important to note that long memory and stationarity are common characteristics of time series data, such as interest rates or economic indicators. Power-law autocorrection, Hurst exponent fractional, or Markov processes may be used to model these data. Predicting 5-day, 10-day returns for equities or 1-week, 1-month returns for financial factors presents two challenges. First, a large amount of data is required, typically 7–10 years of data. Second, positive autocorrelation in the 5-day or 10-day returns in equity time series must be isolated.

This study explores the shear-induced reversible gel behavior of suspensions containing silica na-noparticles and poly(ethylene oxide) (PEO). When subjected to vigorous shaking, these mixtures exhibit interesting shear thickening, transitioning from low-viscosity fluids to 'shake-gels' and then reverts to liquid after some time. Rheological measurements conducted at constant shear rates re-veal a significant increase in viscosity by several orders of magnitude occurring at specific time points during the process. Followed by the lowering of the shear rate implemented to understand the relaxation behavior. The investigation specifically examines the influence of various ions from the Hofmeister series on the gelation and relaxation dynamics of these suspensions. Results indicate that salts positioned on the right-hand side of the Hofmeister series, known as salting-in agents, facilitate quicker gelation and slower relaxation of the shake-gels. Conversely, salts on the left-hand side, referred to as salting-out agents, lead to slower gelation and faster relaxation. These observa-tions are attributed to the distinct effects that different salts exert on the conformation of PEO chains. Salting-in agents induce swelling of the polymer chains, enhancing their ability to interact and bridge between silica nanoparticles effectively, thus promoting rapid gelation and sustaining the gel structure for extended periods. In contrast, salting-out agents cause the polymer chains to collapse, reducing their bridging efficiency and resulting in delayed gelation along with a more rapid return to the fluid state during relaxation. Understanding the role of specific ions in modu-lating the gelation and relaxation behavior of colloidal-polymer suspensions provides valuable in-sights for tailoring material properties in various applications, including drug delivery, oil drilling, environmental restoration, coatings, and soft matter engineering.

Time series (TS)-based predictions are made by examining the behaviour of historical data to forecast future values. Multiple industries; such as stock market trading, power load forecasting, medical monitoring, and intrusion detection; frequently use it. Several variables; such as the performance of other markets as well as the economic situation of a country which affect its market performance; significantly affect the prediction of stock market prices. Therefore, this present study uses numerous variables; such as the opening, lowest, highest, and closing prices; to predict the indices of the stock market of the Kingdom of Saudi Arabia (KSA). Successfully accomplishing an investment goal largely depends on choosing the right stocks to buy, sell, or maintain. The project's output is the projected closing prices (regression) over the next seven days, which helps investors make the best decisions. This present study used exponential smoothing (ES) to remove noise from the input data obtained from the Saudi Stock Exchange, or Tadawul, before using a multivariate long short-term memory (LSTM) deep learning (DL) algorithm to forecast stock market prices. The proposed multivariate LSTMDL model had satisfactory prediction rates of 97.49% and 92.19% for the univariate model. Therefore, it can be used to effectively predict stock market prices. The results also indicate that DL as well as multiple sources of information can be used to accurately predict stock markets.

This work focuses on analyzing acoustic emission (AE) signals as a means to predict failure in structures. Two main approaches are considered: (i) long-range correlation analysis using both the Hurst (H) and the Detrended Fluctuation Analysis (DFA) exponents, and (ii) natural time domain (NT) analysis. These methodologies are applied to the data collected from two application examples: a glass fiber reinforced polymeric plate and a spaghetti bridge model, where both structures were subjected to increasing loads until collapse. A traditional (AE) signal analysis is also performed to reference the study of the other methods. Results indicate that the proposed methods yield a reliable indication of failure in the studied structures.

Fractal analysis of time series aims to extract the hidden or complex structures issued from the associated real data, such as scaling laws, non-stationary, dynamics, and so on. In the present work, the air quality index and its components are considered as time series owing fractal structures. To understand their underlying dynamics, wavelet multifractal approach is applied starting with a wavelet multifractal spectrum test to confirm the multifractality of the underlying data. Next, a new model is introduced improving the classical minmax one, provided with a statistical measure for the adequacy of the new model. The theoretical findings are applied to the north west Tabuk region of Saudi Arabia for environmental and climate data related to pollutants and factors involved in the estimation of the air quality index.

Landslide is a sliding movement of rock mass, debris and soil along the slope under the action of gravity. Small Baseline Subset (SBAS) is an established method for the investigation and monitoring of landslide moments. This study focuses on monitoring the long-temporal displacement of mountainous terrain in Danba County, Sichuan Province via SBAS technique, based on 31 scenes of L-band ALOS/PALSAR data from Feb. 2007 to Oct. 2010.The results show that the largest velocity rates in LOS direction are ±120 mm/yr and maximum accumulated displacement is up to -300, which indicates fast movement of the mountainous terrain during the observation time. These results get good consistency against the results of previous study. This demonstrates the strong potential of SBAS technique for monitoring the landslides geohazard.

Background: Digital clinical measures collected via various digital sensing technologies such as smartphones, smartwatches, wearables, ingestible, and implantable are increasingly used by individuals and clinicians to capture health outcomes or behavioral and physiological characteristics of individuals. Time series classification (TSC) is very commonly used in modeling digital clinical measures. While deep learning models for TSC are very common and powerful, there exist some fundamental challenges. This review presents non-deep learning models commonly used for time series classification in biomedical applications that achieve high performance. Objective: We performed a systematic review to characterize the techniques used in time series classification of digital clinical measures throughout all stages of data processing and model building. Methods: We conducted a literature search on PubMed, and the Institute of Electrical and Electronics Engineers (IEEE), Web of Science, and SCOPUS databases using a range of search terms to retrieve peer-reviewed articles reporting academic research on digital clinical measures in the five year period between June 2016 and June 2021. We identified and categorized research studies based on the types of classification algorithms and sensor input types. Results: We found 452 papers in total from four different databases: PubMed, IEEE, Web of Science Database, and SCOPUS. After removing duplicates and irrelevant papers, 135 articles remained for detailed review and data extraction. Among these, engineered features using time series methods that were subsequently fed into widely-used machine learning classifiers was the most commonly used technique and also most frequently achieved the best performance metrics (77 out of 135 articles). Statistical modeling (24 out of 135 articles) algorithms were the second most common and also second best classification technique. Wavelet-based classification models (8 out of 135 articles) were also common. Electroencephalogram (29 out of 135 articles) was the most common data type used as an input. Accuracy was the most commonly reported performance metric, with 67.65% of articles reporting on accuracy. In this review paper, we provide summaries of signal pre-processing methods, feature engineering and selection methods, time series models, as well as model interpretations. Importantly, we found that about 50% of the papers only report one performance metric, which may result in a skewed view of overall performance. Conclusion: While high time series classification performance has been achieved in digital clinical, physiological, or biomedical measures, no standard benchmark datasets, modeling methods, or reporting methodology exist. There is no single widely used method for time series model development or feature interpretation– many different methods have proven successful.

Landsat and Sentinel-2 data archives provide ever-increasing amounts of satellite data for studying land cover and land use change (LCLUC) over the past four decades. However, the availability of cloud-, shadow-, and snow-free observations varies spatially and temporally due to climate and satellite data acquisition schemes. Spatio-temporal heterogeneity poses a major issue for some time-series analysis approaches, but can be addressed with pixel-based compositing that generates temporally equidistant cloud-free or near-cloud free synthetic images. Although much consideration is given to methods identifying the ‘best’ pixel value for each composite, determining the aggregation period receives less attention and is often done arbitrary, or based on expert intuition. Here, we evaluated data compositing windows ranging from five days to one year for 1984-2021 Landsat and 2015-2021 Sentinel‑2 time series across Europe. We considered separate and joint use of both data archives and analyzed spatio-temporal availability of composites during each calendar year and pixel-specific growing season. We reported mean annual composites’ availability investigating differences among biogeographical regions, checked feasibility of pan‑European analyses for three LCLUC applications based on annual, monthly and 10-day composites, and analyzed the shortest feasible compositing window ensuring ≥50% temporal data availability and interpolation of the remaining composites for individual years and across a variety of medium- and long‑term time windows. Our results highlighted low data coverage in the 1980s, 1990s, and in 2012, as well as spatial variability in data availability driven by climate and orbit overlaps, which altogether impact spatio-temporal consistency of medium- and long-term time series, limiting feasibility of some LCLUC analyses. We demonstrated that prior to 2011 monthly composites ensured overall 50-62% data coverage for each calendar year, and ~75% afterwards, with further increase to ~82% when Landsat and Sentinel-2 were combined. Temporal consistency of monthly composites was overall low and temporal interpolation augmenting up to 50% missing data each year and across a time window of interest, ensured feasibility of analyses. Applications based on shorter than monthly composites were challenging without joining Landsat and Sentinel‑2 archives after 2015, and beyond the Mediterranean biogeographical region. Using pixel-specific growing season data typically boosted data availability in most geographies and diminished most of the latitudinal differences, but feasibility of complete time series with sub-monthly compositing windows was still restricted to the most recent years, and required data interpolation. Overall, our analyses provided a detailed assessment of Landsat and Sentinel-2 data availability over Europe, and based on selected application examples, highlighted often lacking spatio-temporal consistency of time series with sub-monthly compositing windows and long-time periods, which might hinder feasibility of some LCLUC applications.

Today, there is a time series analysis that has gained significant popularity across various industries to provide effective solutions for any specific challenges. Artificial intelligence logic is generally used to solve time-series problems with the help of various frameworks that are available for the development of AI-based applications. Currently, there is a significant framework in Python that is driven by its comprehensive libraries and their practical implementations. Time series analysis can be built with the help of some specific models that give results to differentiate the efficiency and domains of great work. This paper focuses on three diverse libraries of Python to predict the Gulf stock exchange market. These libraries are prediction models that are helpful in predicting future values. These models utilized include SARIMA (Seasonal Auto-Regressive Integrated Moving Average), Neural Prophet Model, and Fb Prophet model. Each model is trained using the provided datasets, which are followed by evaluation parameters such as MSE, RMSE, recall, MDAPE, accuracy, precision, etc. The main purpose of using these three models for stock market prediction is to find the better-suited models. In the past few decades, the stock market industry has seemed to have promising growth after 2022 onwards. This paper will help us make a significant decision about model usage for addressing such complex challenges. Especially, the research findings indicate that all three models demonstrate in different domains. SARIMA can perform well in overall prediction tasks, while the Prophet model works great with smaller datasets that contain seasonality trends.

This article explores the required amount of time series points from a high-speed traffic network to accurately estimate the Hurst exponent. The methodology consists in designing an experiment using estimators that are applied to time series, followed by addressing the minimum amount of points required to obtain accurate estimates of the Hurst exponent in real-time. The methodology addresses the exhaustive analysis of the Hurst exponent considering bias behavior, standard deviation, mean square error, and convergence using fractional Gaussian noise signals with stationary increases. Our results show that the Whittle estimator successfully estimates the Hurst exponent in series with few points. Based on the results obtained, a minimum length for the time series is empirically proposed. Finally, to validate the results, the methodology is applied to real traffic captures in a high-speed network based on the IEEE 802.3ab standard.

GNSS time series prediction plays a significant role in monitoring crustal plate motion, landslide detection, and maintenance of the global coordinate framework. Long Short-Term Memory (LSTM), a deep learning model has been widely applied in the field of high-precision time series prediction especially when combined with Variational Mode Decomposition (VMD) to form the VMD-LSTM hybrid model. To further improve the prediction accuracy of the VMD-LSTM model, this paper proposes a dual variational modal decomposition long short-term memory (DVMD-LSTM) model to effectively handle the noise in GNSS time series prediction. This model extracts fluctuation features from the residual terms obtained after VMD decomposition to reduce the prediction errors associated with residual terms in the VMD-LSTM model. Daily E, N, and U coordinate data recorded at multiple GNSS stations between 2000 and 2022 are used to validate the performance of the proposed DVMD-LSTM model. The experimental results demonstrate that compared to the VMD-LSTM model, the DVMD-LSTM model achieves significant improvements in prediction performance across all measurement stations. The average RMSE is reduced by 9.86%, and the average MAE is reduced by 9.44%. Furthermore, the average accuracy of the optimal noise model for the predicted results is improved by 36.50%, and the average speed accuracy of the predicted results is enhanced by 33.02%. These findings collectively attest to the superior predictive capabilities of the DVMD-LSTM model, thereby enhancing the reliability of the predicted results.

Rapid growth and domestic migration to capital city, Kathmandu Metropolitan City (KMC), Nepal have amplified land-use transition to unmanaged and unplanned urbanization have exacerbated problems of Urban Heat Island (UHI) Effect. Increasing built up surfaces, means of transport and industrial activities are major results for increasing temperature in the city area as compared to other areas. This study focuses on forecasting Land Surface Temperature (LST) using both univariate and multivariate time series models. The primary goal is to predict the impact of climatic factors on the Urban Heat Island (UHI) effect, utilizing data from 1981 to 2019. We analyzed key factors including - (i) relative humidity, (ii) surface pressure, (iii) specific humidity, and (iv) wind speed sourced from the MEERA-2 dataset. A univariate model using exponential smoothing achieved a Mean Absolute Error (MAE) of 3.17°C and an R² score of 0.94, highlighting strong predictive accuracy. Additionally, the multivariate Prophet model, which incorporates trend and seasonal components, further refined the forecasting by integrating multiple climatic factors. This study aims provides valuable information via prediction for sustainable urban planning and landscape design in KMC and other 61 districts.

The future of the Colorado River water supply (WS) affects millions of people and the U.S. economy. A recent study suggested a cross-basin correlation between the Colorado River and its neighboring Great Salt Lake (GSL). Following that study, the feasibility of using the previously developed multi-year prediction of the GSL water level to forecast the Colorado River WS was tested. Time-series models were developed to predict the changes in WS out to 10 years. Regressive methods and the GSL water level data were used for the depiction of decadal variability of the Colorado River WS. Various time-series models suggest a decline in the 10-year-averaged WS since 2013 before starting to increase around 2020. Comparison between this WS prediction and the WS projection published in a 2012 government report (derived from climate models) reveals a widened imbalance between supply and demand by 2020. Further research to update similar multi-year prediction of the Colorado River WS is needed. Such information could aid in management decision making in the face of future water shortages.

Solar flares are characterized by sudden bursts of electromagnetic radiation from the Sun’s surface, and caused by the changes in magnetic field states in solar active regions. Earth and its surrounding space environment can suffer from various negative impacts caused by solar flares ranging from electronic communication disruption to radiation exposure-based health risks to the astronauts. In this paper, we address the solar flare prediction problem from magnetic field parameter-based multivariate time series (MVTS) data using multiple state-of-the-art machine learning classifiers that include MINImally RandOm Convolutional KErnel Transform (MINIROCKET), Support Vector Machine (SVM), Canonical Interval Forest (CIF), Multiple Representations SEQuence Learner (Mr-SEQL), and Long Short-Term Memory (LSTM)-based deep learning model. Our experiment is conducted on the on the Space Weather ANalytics for Solar Flares (SWAN-SF) benchmark data set, which is a partitioned collection of MVTS data of active region magnetic field parameters spanning over 9 years of operation of the Solar Dynamics Observatory (SDO). The MVTS instances of the SWAN-SF dataset are labeled by GOES X-ray flux-based flare class labels, and attributed to extreme class imbalance because of the rarity of the major flaring events (e.g., X and M). As a performance validation metric in this class-imbalanced dataset, we used the true skill statistic (TSS) score. Finally, we demonstrate the advantages of the MVTS learning algorithm MINIROCKET, which outperformed the aforementioned classifiers without the need for essential data preprocessing steps such as normalization, statistical summarization, and class imbalance handling heuristics.

We have implemented quantum modeling mainly based on Bohmian Mechanics to study time series that contain strong coupling between their events. Compared to time series with normal densities, such time series are associated with rare events. Hence, employing Gaussian statistics drastically underestimates the occurrence of their rare events. The central objective of this study is to investigate the effects of rare events in the probability densities of time series from the point of view of quantum measurements. For this purpose, we first model the non-Gaussian behavior of time series using the multifractal random walk (MRW) approach. Then, we examine the role of the key parameter of MRW, λ, which controls the degree of non-Gaussianity, in quantum potentials derived for time series. Our Bohmian quantum analysis shows that the derived potential takes some negative values in high frequencies (its mean values), then substantially increases, and the value drops again for rare events. Thus, rare events can generate a potential barrier in the high-frequency region of the quantum potential, and the effect of such a barrier becomes prominent when the system transverses it. Finally, as an example of applying quantum potential beyond the microscopic world, we compute quantum potentials for the S&P financial market time series to verify the presence of rare events in the non-Gaussian densities and demonstrate deviation from the Gaussian case.

Vegetation status assessment is crucial for agricultural monitoring and management. Vegetation indices derived from high resolution image time series can be used to derive key phenological parameters for annual crops. In this work, we propose a procedure for the estimation of these parameters and their associated uncertainties. The approach uses Bayesian inference through Markov Chain Monte Carlo in order to obtain the full joint posterior distribution of the phenological parameters given the satellite observations. The proposed algorithm is quantitatively validated on synthetic data. Its use on real data is presented together with an application to real-time within season estimation allowing for phenology forecasting.

Changes in sea level exhibit nonlinearity, nonstationarity, and multivariable characteristics, making traditional time series forecasting methods less effective in producing satisfactory results. To enhance the accuracy of the predictions of changes in sea level, this study introduced an improved VMD–EEMD–LSTM hybrid model. This model decomposes satellite altimetry data from near the Dutch coast using VMD, resulting in components of the Intrinsic Mode Function (IMF) with various frequencies and a residual sequence. EEMD further dissects the residual sequence obtained from VMD into second-order components. These IMFs decomposed by VMD and EEMD are utilized as features in the LSTM model for making predictions, culminating in the final forecasted results. The experimental results demonstrated significant improvements in the predictive performance compared with the VMD–LSTM model. The RMSE (root mean square error) decreased by an average of 58.68%, the MAE (mean absolute error) reduced by an average of 59.96%, and the R2 (coefficient of determination) increased by an average of 49.85% compared with the VMD–LSTM model. In comparison with the EEMD–LSTM model, the RMSE decreased by an average of 26.95%, the MAE decreased by an average of 28.00%, and the R2 increased by an average of 6.53%. The VMD–EEMD–LSTM model exhibited significantly improved predictive performance.

Extensive, but remote oil and gas fields of the United States, Canada, and Russia require the construction and operation of extremely long pipelines. Global warming and local heating effects lead to rising soil temperatures and thus a reduction in the sub-grade capacity of the soils; this causes changes in the spatial positions and forms of the pipelines, consequently increasing the number of accidents. Oil operators are compelled to monitor the soil temperature along the routes of the remoted pipelines in order to be able to perform remedial measures in time. They are therefore seeking methods for the analysis of volumetric diagnostic information. To forecast soil temperatures at the different depths we propose compiling a multidimensional dataset, defining descriptive statistics; selecting uncorrelated time series; generating synthetic features; robust scaling temperature series, tuning the additive regression model to forecast soil temperatures.

To improve the monitoring of the electrical power grid it is necessary to evaluate the influence of contamination in relation to leakage current and its progression to a disruptive discharge. In this paper, insulators were tested in a saline chamber to simulate the increase of salt contamination on their surface, and to evaluate the supportability of these components. From the time series forecasting of the leakage current, it is possible to evaluate the development of the fault before a flashover occurs. Choosing which method to use is always a difficult task since some models may have higher computational effort. In this paper, for a complete evaluation, the long short-term memory (LSTM), group method of data handling (GMDH), adaptive neuro-fuzzy inference system (ANFIS), bootstrap aggregation (bagging), sequential learning (boosting), random subspace, and stacked generalization (stacking) ensemble learning models are analyzed. A review and comparison of these well-established methods for time series forecasting is performed. From the results of the best structure of the model, the hyperparameters are evaluated and the Wavelet transform is used to obtain an enhanced model.

The environmental issues we are currently facing require long-term prospective efforts for sustainable growth. Renewable energy sources seem to be one of the most practical and efficient alternatives in this regard. Understanding a nation's pattern of energy use and renewable energy production is crucial for developing strategic plans. No previous study has been performed to explore the dynamics of power consumption with the change in renewable energy production on a country-wide scale. In contrast, a number of deep learning algorithms demonstrated acceptable performance while handling sequential data in the era of data-driven predictions. In this study, we developed a scheme to investigate and predict total power consumption and renewable energy production time series for eleven years of data using a Recurrent Neural Network (RNN). The dynamics of the interaction between the total annual power consumption and renewable energy production are investigated through extensive Exploratory Data Analysis (EDA) and a feature engineering framework. The performance of the model is found satisfactory through the comparison of the predicted data with the observed data, visualization of the distribution of the errors and Root Mean Squared Error (RMSE) value of 0.084. Higher performance is achieved through the increase in the number of epochs and hyperparameter tuning. The proposed framework can be used and transferred to investigate the trend of renewable energy production and power consumption and predict the future scenarios for different communities. Incorporation of the cloud-based platform into the proposed pipeline may lead to real-time forecasting.

The prediction of stock prices is a challenging task, particularly for retail investors who may lack the resources and expertise to perform sophisticated quantitative trading. This study focuses on enhancing stock price prediction for retail investors by employing advanced machine learning techniques on data from the stock exchange market. We utilize a comprehensive methodology that includes data preprocessing to handle missing values and outliers, feature engineering, cross-validation, and parameter tuning. The techniques applied include Keras Deep Neural Networks (DNN), LightGBM, LSTM, GRU, and linear regression (LR). Our proposed ensemble model, which combines time series and deep learning models, demonstrates superior performance compared to individual models. This integration of methods leads to significant improvements in prediction accuracy, providing a robust solution for retail investors.

(1) Introduction: The unprecedented coronavirus disease 2019 (COVID-19) epidemic has caused millions of infections worldwide and represents a significant challenge facing modern health care systems. This study was conducted to investigate the impact of lockdown measures on regional neonate services, which might be used to predict the long-term effects of medical behavior. (2) Methods: Using hospital information system (HIS) Statistics data from 4 January 2019 to 27 August 2020, an interrupted time-series analysis was employed to compare changes and trends in hospital admissions and disease spectrum before and after the lockdown interventions. Furthermore, this study was designed to evaluate whether the pandemic influenced newborns' healthcare behavior. (3) Results: Overall, 13,540 infants were admitted to the NICU during the pre-COVID period (n = 12082) and COVID-impacted period (n =4558). The patients' age at admission were younger than that of the pre-COVID-19 period (median age 5d vs. 6d after birth, p＜0.001). The overall number of neonate visits consistently decreased from the first days of the lockdown measures (24 January 2020). The disease spectrum for respiratory system, infectious diseases, and gastrointestinal disease indicated no declined immediately after intervention(p =0.079, p =0.113, p =0.060, respectively). There was an immediate decline in the volume of Jaundice-related conditions (p<0.001) after lockdown measures. The percentage of patients who suffer from respiratory system and infectious diseases has decreased (p =0.005 and p =0.002). However, a relatively high percentage of patients admitted to the neonatal intensive care unit (NICU) presented with Jaundice-related conditions (p <0.001). (4) Conclusions: In summary, the COVID-19 pandemic profoundly impacted the regional neonate services. However, it is still unclear what might be the effect of long-term effects from pandemic.

The enhanced multi-objective symbolic discretization for time series (eMODiTS) method employs a flexible discretization scheme using different value cuts for each non-equal time interval, which requires a computational cost for evaluating each objective function. Therefore, surrogate models were implemented to minimize this disadvantage. Nevertheless, each solution found by eMODiTS is a different-sized vector, so the surrogate model must be able to handle data sets under this characteristic. Consequently, this work's contribution lies in analyzing the surrogate models' implementation on the time series discretization, where each potential scheme is a real-number different-sized vector. For this reason, the surrogate model proposed was k-nearest Neighbors for regression with Dynamic Time Warping as a distance measure. Results suggest our proposal finds a suitable approximation to the final eMODiTS solutions with a functions evaluation reduction rate between 15% and 95%. However, according to Pareto front performance measures, the proposal Pareto front is competitive compared to the eMODiTS Pareto front, reaching an average Generational Distance (GD) between 0.0447 and 0.0536. Moreover, the average Hypervolume Ratio (HVR) ranges between 0.334 and 0.3891. Finally, our proposal compared against SAX-based methods presents a similar behavior regarding classification tasks and statistical tests.

This study investigates the impact of Foreign Direct Investment (FDI) on economic growth and examines the causality between FDI and economic growth in Bangladesh during 1972-2013. Gross Domestic Product (GDP), export performance (EXP), Foreign Direct Investment (FDI), and Gross Fixed Capital Formation (GFCF) are considered to capture the objective of the study. The study methodology includes some systematic steps. As the data used in the study is time-series in nature, the author employs unit root tests, and in this case, Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests are used. Then Johansen’s cointegration test, Granger causality test, regression with Newey-West Standard Error and Vector Error Correction Model (VECM) are applied. By using the ADF and PP test the study reveals that the variables of four-time series are integrated of I (1) i.e. they are stationary at first difference. Regression analysis result demonstrates that FDI has a positive effect on economic growth. The Granger Causality test discloses that there is a unidirectional relationship between FDI and economic growth. But the VECM estimation finds that in the long run FDI negatively affects economic growth.

When dealing with limited sample sizes or missing values in time series data, achieving high accuracy in forecasting becomes challenging. This challenge is particularly common in wind energy forecasting, where many wind farms lack complete data. In this paper, we employ the widely-used ARIMA (Autoregressive Integrated Moving Average) model for time series forecasting. To address the difficulties posed by limited sample sizes and missing values, we adopt a unique approach by utilizing multiple ARIMA models for different datasets. A key distinction from other multiple models methods for time series forecasting lies in each model within our approach using its own dataset, making the fusion process more intricate. To overcome this, we incorporate neural networks and two techniques for model fusion: direct fusion with a learning mechanism and compensation for missing data through training. For each ARIMA model, we introduce a noise estimation method to circumvent the white noise assumptions inherent in ARIMA models. Finally, we apply these methods to wind energy prediction, and our experimental results showcase a significant enhancement in forecasting accuracy.

In Portugal, cork oak (Quercus suber L.) stands cover 737 Mha, being the most predominant species of the montado agroforestry system, contributing for the economic, social and environmental development of the country. Cork oak decline is a known problem since the late years of the 19th century that has recently worsen. The causes of oak decline seem to be a result of slow and cumulative processes, although the role of each environmental factor is not yet established. The availability of Sentinel-2 high spatial and temporal resolution dense time series enables gradual processes monitoring. These processes can be monitored using spectral vegetation indices (VI) once their temporal dynamics are expected to be related with green biomass and photosynthetic efficiency. The Normalized Difference Vegetation Index (NDVI) is sensitive to structural canopy changes, however it tends to saturate at moderate-to-dense canopies. Modified VI have been proposed to incorporate the reflectance in the red-edge spectral region, which is highly sensitive to chlorophyll content while largely unaffected by structural properties. In this research, in-situ data on the location and vitality status of cork oak trees are used to assess the correlation between chlorophyll indices (CI) and NDVI time series trends and cork oak vitality at the tree level. Preliminary results seem to be promising since differences between healthy and unhealthy (diseased/dead) trees were observed.

Continuous and uncontrolled extraction of groundwater often creates tremendous pressure on groundwater levels. As a part of the sustainable planning and effective management of water resources, it is crucial to assess the existing as well as future groundwater level (GWL) condition. In the current study, an attempt was made to model and forecast GWL using artificial neural networks (ANN) and multivariate time series models. Autoregressive integrated moving average (ARIMA) and ARIMA incorporating exogenous variables (ARIMAX) were adopted as the time series models. Kushtia district in Bangladesh was selected as the case study area, and GWL data of five monitoring wells in the study are used to demonstrate the modeling exercise. Rainfall was taken as the exogeneous variable to explore whether its inclusion enhanced the performance of GWL forecasting using the developed models. The performance of each time series and ANN model was assessed based on various model evaluation criteria. It was evident from the results that the multivariate ARIMAX model (SSE of 15.361) performed better than the univariate ARIMA model with an SSE of 17.217 for GWL forecasting. This demonstrates the fact that the multivariate time series models generated enhanced forecasting of GWL compared to the univariate time series models. When comparing the time series and ANN models, it was found that the ANN-based model outperformed the time series models with the enhanced forecasting accuracy (SSE of 9.894). Results also exhibit a significant correlation coefficient value R of 0.995 (ANN 6-8-1) for the existing and predicted data. The current study conclusively proves the superiority of ANN over the time series models for the enhanced forecasting of GWL in the study area. Thus, the ANN approach was not only carried out for model building and simulation but also to provide a valuable tool for managing water resources amidst changing environmental conditions.

Accurate forecasting and efficient management of commodities are crucial for stakeholders in the industry, given the volatile nature of these markets. This study addresses these needs by leveraging advanced forecasting techniques and machine learning models to predict prices and enhance supply chain efficiency. TThe focus is on utilizing ARIMA, SARIMAX, and LSTM models to analyze historical trading data for commodities such as cocoa, coffee, and sugar sourced from Kaggle’s comprehensive dataset. The research applies ARIMA and SARIMAX models to forecast price trends, overcoming initial challenges related to data index frequency and seasonality. LSTM models are employed for more nuanced demand forecasting, particularly for random-length lumber, demonstrating the model's capability to predict future market trends accurately. The study highlights significant improvements in prediction accuracy and supply chain management through meticulous feature engineering and model optimization, offering valuable insights for strategic decision-making in the supply chain sector.

We present and benchmark FilterNet, a flexible deep learning architecture for time series classification tasks, such as activity recognition via multichannel sensor data. It adapts popular CNN and CNN-LSTM motifs which have excelled in activity recognition benchmarks, implementing them in a many-to-many architecture to markedly improve frame-by-frame accuracy, event segmentation accuracy, model size, and computational efficiency. We propose several model variants, evaluate them alongside other published models using the Opportunity benchmark dataset, demonstrate the effect of model ensembling and of altering key parameters, and quantify the quality of the models’ segmentation of discrete events. We also offer recommendations for use and suggest potential model extensions. FilterNet advances the state of the art in all measured accuracy and speed metrics on the benchmarked dataset, and it can be extensively customized for other applications.

Air sampling using vortex air samplers combined with species specific amplification of pathogen DNA, was carried out over two years in four or five locations in the Salinas Valley of California. The resulting time series data for the abundance of pathogen DNA trapped per day displayed complex dynamics with features of both deterministic (chaotic) and stochastic dynamics. Methods of nonlinear time series analysis developed for the reconstruction of low dimensional attractors provided new insights into the complexity of the pathogen abundance data, but also indicated that practicality may limit the capacity for definitively classifying the dynamics of air borne plant pathogen inoculum. Over the two years of the study five location/year combinations were classified as having stochastic linear dynamics and four were not. Calculation of entropy values for either the number of pathogen DNA copies or for a binary string indicating the pathogen abundance data were increasing or not, revealed (1) some robust differences in the dynamics between seasons that were not obvious in the time series data themselves, and also (2) that the series were almost all at their theoretical maximum entropy value when considered from the simple perspective of whether instantaneous change along the sequence is positive or not.

Due to its flexibility, cloud computing has become essential in modern operational schemes. However, the effective management of cloud resources to ensure cost-effectiveness and maintain high performance presents significant challenges. The pay-as-you-go pricing model, while convenient, can lead to escalated expenses and hinder long-term planning. Consequently, FinOps advocates proactive management strategies, with resource usage prediction emerging as a crucial optimization category. In this research, we introduce the multi-time series forecasting system (MSFS), a novel approach for data-driven resource optimization alongside the hybrid ensemble anomaly detection algorithm (HEADA). Our method prioritizes the concept-centric approach, focusing on factors such as prediction uncertainty, interpretability and domain-specific measures. Furthermore, we introduce the similarity-based time-series grouping (STG) method as a core component of MSFS for optimizing multi-time series forecasting, ensuring its scalability with the rapid growth of the cloud environment. The experiments performed demonstrate that our group-specific forecasting model (GSFM) approach enabled MSFS to achieve a significant cost reduction of up to 44%.

In order to reduce the environmental impact of energy enterprises, it is important to promptly identify cases of possible changes in the quality of wastewater generated at power plants, that is cases of exceeding the maximum permissible concentrations of pollutants in wastewater. The goal of the method for detecting complex anomalies in multidimensional time series obtained from smart energy station’s sensor channels is to increase the accuracy of detecting pollution levels in industrial wastewater. To achieve this goal, the following tasks were solved: methods for detecting time series anomalies were analyzed, the method for detecting complex anomalies was developed, software implementation of the algorithm was carried out and experiments were conducted. The developed method is proposed to be used in an smart energy monitoring system.

Accurate prediction of crop production is essential in effectively managing agricultural countries' food security and economic resilience. This study evaluates the performance of statistical and machine learning-based methods for large-scale crop production forecasting. We predict the quarterly production of 325 crops (including fruits, vegetables, cereals, non-food, and industrial crops) across 83 provinces in the Philippines. Using a comprehensive dataset of 10,949 time series over 13 years, we demonstrate that a global forecasting approach using a state-of-the-art deep learning architecture, the transformer, significantly outperforms traditional local forecasting approaches built on statistical and baseline methods. By leveraging cross-series information, our proposed way is scalable and works well even with time series that are short, sparse, intermittent, or exhibit structural breaks/regime shifts. The results of this study further advance the field of applied forecasting in agricultural production and provide a practical and effective decision-support tool for policymakers that oversee the farm sector on a national scale.

Time-series analysis is a widely used technique across various fields and industries, as it helps in understanding, predicting, and forecasting the behavior of data points over time. These fields include but are not limited to finance, economics, healthcare, transportation, etc. In the case of this paper, we have focused on finance. Predicting future values of financial time series offers several benefits. Accurate forecasts can help investors make better decisions about their investments. To predict future values, deep learning algorithms are commonly used since it is an effective method with complex data. In this study, we conduct a study that investigates the use of different data pre-processing techniques on deep learning algorithms in predicting the time series values. To conduct this experimental study, we utilize an open source software, which using long short-term memory technique as the representative deep learning technique, published in github software code repository platform. With this study, we investigate the effects of autoencoder and discrete wavelet transform data pre-processing techniques in time-series prediction. We discuss the details of the experimental study and report our results. The results show that time series prediction (using backtesting methodology) without any data pre-processing leads to 12.6% for mean absolute percentage error. The results also show that, time series prediction with the data preprocessing techniques (Wavelet Transform and Stacked Autoencoder) lead to 3.4%

Background: Coronavirus disease 2019 (COVID-19) pandemic are causing significant damages to many nations. For mitigating its risk, Japan’s Prime Minister called on all elementary, junior high and high schools nationwide to close beginning March 1, 2020. However, its effectiveness in decreasing disease burden has not been investigated. Methods: We used daily data on the report of COVID-19 and coronavirus infection incidence in Japan until March 31, 2020. Time series analysis were conducted using Bayesian method. Local linear trend models with interventional effect were constructed for number of newly reported cases of COVID-19, including asymptomatic infections. We considered that the effects of intervention start to appear 9 days after the school closure; i.e., on March 9. Results: The intervention of school closure did not appear to decrease the incidence of coronavirus infection. If the effectiveness of school closure began on March 9, mean coefficient α for effectiveness of the measure was calculated to be 0.08 (95% credible interval -0.36 to 0.65), and the actual reported cases were more than predicted, yet with rather wide credible interval. Sensitivity analyses using different dates also showed similar results. Conclusions: School closure carried out in Japan did not show the effectiveness to mitigate the transmission of novel coronavirus infection.

This paper realizes early bearing fault warning through bearing fault time series prediction, and proposes a bearing fault time series prediction model based on optimized maximum correlation kurtosis deconvolution (MCKD) and long short-term memory (LSTM) recurrent neural network to ensure bearings operation reliability. The model is based on lifecycle vibration signal of the bearing, to begin, the cuckoo search (CS) is utilized to optimize the parameter filter length L and deconvolution period T of MCKD, taking into account the influence and periodicity of the bearing time series, the fault impact component of the optimized MCKD deconvolution time series is improved. Then select the LSTM learning rate α depending on deconvolution time series. Finally, the dataset obtained through various preprocessing approaches are used to train and predict the LSTM model. The average prediction accuracy of the optimized MCKD-LSTM model is 26 percent higher than that of the original time series, proving the efficiency of this method, and the prediction results track the real fault data well, according to the XI'AN JIAOTONG University XJTU-SY bearing dataset.

Land Surface Temperature (LST) is a basic parameter in energy exchange between the land and atmosphere and is frequently used in many sciences such as climatology, hydrology, agriculture, ecology, etc. LST time series data have usually deficient, missing and unacceptable data caused by the presence of clouds in images, presence of dust in atmosphere and sensor failure. In this study, Singular Spectrum Analysis (SSA) algorithm was used to resolve the problem of missing and outlier data caused by cloud cover. The region studied in the present research included an image frame of MODIS with horizontal number 22 and vertical number 05 (h22v05). This image involved a large part of Iran and Turkmenistan and Caspian Sea. In this study, MODIS LST sensor (MOD11A1) was used during 2015 with 1×1 Km spatial resolution and day/night LST data (daily temporal resolution). The results of the data quality showed that cloud cover caused 36.37% of missing data in the studied time series with 730 day/night LST images. Further, the results of SSA algorithm in reconstruction of LST images indicated the Root Mean Square Error (RMSE) of 2.95 K between the original and reconstructed data in LST time series in the study region. In general, the findings showed that SSA algorithm using spatio-temporal interpolation in LST time series can be effectively used to resolve the problem of missing data caused by cloud cover.

The aerospace industry develops prognosis and health management algorithms to ensure better safety on board. Particularly for in-flight controls where jamming is dreaded. For that, vibration signals are monitored to predict future defect occurrences. However, time series are not labeled according to severity level, and the user can only assess the system health from the data mining procedure. To that extent, we developed a clustering algorithm using a deep neural network core. We encoded the time series into pictures to be feed into an artificially trained neural network: U-NET. From the segmented output, one-dimensional information on cluster frontiers is extracted and filtered without any parameter selection. Then, a kernel density estimation finally transforms the signal into an empirical density. Ultimately, a Gaussian mixture model extracts the latter independent components. The method empowered us to reveal different degrees of severity faults in the studied data, with their respective likelihood without prior knowledge. We compared it to state-of-the-art machine learning algorithms. However, internal clustering results evaluation for time series is an open question. As state-of-the-art indexes were not producing relevant results, we built a new indicator to fulfill this task. We applied the whole method to an actuator consisting of an induction machine linked to a ball screw. This study lays the groundwork for future training of diagnosis and prognosis structures in the health management framework.

In an epoch characterized by the swift pace of digitalization and urbanization, the essence of community well-being hinges on the efficacy of urban management. As cities burgeon and transform, the need for astute strategies to navigate the complexities of urban life becomes in-creasingly paramount. This study employs time series analysis to scrutinize citizen interactions with the coordinate-based problem mapping platform in the Municipality of Patras in Greece. The research explores the temporal dynamics of reported urban issues, with a specific focus on identifying recurring patterns through the lens of seasonality. The analysis, employing the sea-sonal decomposition technique, dissects time series data to expose trends in reported issues and areas of the city that might be obscured in raw big data. It accentuates a distinct seasonal pattern, with concentrations peaking during the summer months. The study extends its approach to forecasting, providing insights into the anticipated evolution of urban issues over time. Projec-tions for the coming years show a consistent upward trend in both overall city issues and those reported in specific areas, with distinct seasonal variations. This comprehensive exploration of time series analysis and seasonality provides valuable insights for city stakeholders, enabling informed decision-making and predictions regarding future urban challenges.

One of the key components of application performance monitoring (APM) software is 2 AI/ML empowered data analytics for predictions, anomaly detection, event correlations and root 3 cause analysis. Time series metrics, logs and traces are three pillars of observability and the valuable 4 source of information for IT operations. Accurate, scalable and robust time series forecasting and 5 anomaly detection are desirable capabilities of the analytics. Approaches based on neural networks 6 (NN) and deep learning gain increasing popularity due to their flexibility and ability to tackle complex 7 non-linear problems. However, some of the disadvantages of NN-based models for distributed cloud 8 applications mitigate expectations and require specific approaches. We demonstrate how NN-models 9 pretrained on a global time series database can be applied to customer specific data using transfer 10 learning. In general, NN-models adequately operate only on stationary time series. Application 11 to non-stationary time series requires multilayer data processing including hypothesis testing for 12 data categorization, category specific transformations into stationary data, forecasting and backward 13 transformations. We present the mathematical background of this approach and discuss experimental 14 results from the productized implementation in Wavefront by VMware (an APM software) while 15 monitoring real customer cloud environments.

This paper addresses the evolving landscape of electricity markets in Europe, with a focus on the integration of Renewable Energy Communities as introduced by the Renewable Energy Directive 2018/2001. Residents within a postal code area are highly incentivized to join a community, which enables them to exchange energy among themselves at lower procurement costs. Thereby, energy management systems optimize the operation of respective energy systems, with electrical load forecasting playing a key role. Given that prosumers may switch between communities on a daily basis, electricity demands within these groups will vary, leading to data that is non-stationary, discontinuous as well as non-identical and independently distributed. To encounter this issue, we propose a sophisticated forecasting model that applies federated learning, using informations from various distributed communities to learn domain-invariant features. To achieve this, we initially utilize synthetic electrical load time series at district level and aggregate them to profiles of Renewable Energy Communities with dynamic portfolios. Subsequently, we develop a forecasting model that accounts for the composition of residents of a Renewable Energy Community, adapt data pre-processing in accordance with the time series process, and detail a federated learning algorithm that incorporates weight averaging and data sharing. Following the training of various experimental setups, we ultimately evaluate their effectiveness. The findings suggest that our proposed framework is capable of effectively forecast non-stationary and discontinuous time series and that it can be applied to new, unseen data through the integration of knowledge from multiple sources.

The global demand for energy has been steadily increasing due to population growth, urbanization, and industrialization. Numerous researchers worldwide are striving to create precise forecasting models for predicting energy consumption to manage supply and demand effectively. In this research, a time-series forecasting model based on multivariate multilayered long short-term memory (LSTM) is proposed for forecasting energy consumption and tested using data obtained from commercial buildings in Melbourne, Australia: the Advanced Technologies Center, Advanced Manufacturing and Design Center, and Knox Innovation, Opportunity, and Sustainability Center buildings. This research specifically identifies the best forecasting method for subtropical conditions and evaluates its performance by comparing it with the most used methods at present, including LSTM, bidirectional LSTM, and linear regression. The proposed multivariate multilayered LSTM model was assessed by comparing mean average error (MAE), root-mean-square error (RMSE), and mean absolute percentage error (MAPE) values with and without labeled time. Results indicate that the proposed model exhibits optimal performance with improved precision and accuracy. Specifically, the proposed LSTM model achieved a decrease in MAE by 30%, RMSE by 25%, and MAPE by 20% compared to the LSTM method. Moreover, it outperformed the bidirectional LSTM method with a reduction in MAE by 10%, RMSE by 20%, and MAPE by 18%. Furthermore, the proposed model surpassed linear regression with a decrease in MAE by 2%, RMSE by 7%, and MAPE by 10%. These findings highlight the significant performance increase achieved by the proposed multivariate multilayered LSTM model in energy consumption forecasting.

For more than ten years, Central Chile faces drought conditions, which impact crop production and quality, increasing food security risk. Under this scenario, implementing management practices that allow increasing water use efficiency is urgent. The study was carried out in kiwifruit trees, located in the O’Higgins region, Chile; for season 2018-2019 and 2019-2020. We evaluate nine vegetation indices in the VNIR and SWIR regions derived from Sentinel-2 (A/B) satellites to know how much variability in the canopy water status could explain. Over the study's site were installed sensors that continuously measure the leaf's turgor pressure (Yara Water-Sensor). A strong correlation between turgor pressure and vegetation indices was obtained with the Spearman's rho coefficient ($\rho$). However, the NIR range's indices were influenced by the vegetative development of the crop rather than its water status. Red-edge showed better performance as the vegetative growth did not affect it. It is necessary to expand the study to consider higher variability in kiwifruit's water conditions and incorporate the sensitivity of different wavelengths.

Mapping forest composition using multiseasonal optical time series is still challenging. Highly contrasted results are reported from one study to another suggesting that drivers of classification errors are still under-explored. We evaluated the performances of single-year Formosat-2 time series to discriminate tree species in temperate forests in France and investigated how predictions vary statistically and spatially across multiple years. Our objective was to better estimate the impact of spatial autocorrelation in the validation data on measurement accuracy and to understand which drivers in the time series are responsible for classification errors. The experiments were based on ten Formosat-2 image time series irregularly acquired during the seasonal vegetation cycle from 2006 to 2014. Due to lot of clouds in the year 2006, an alternative 2006 time series using only cloud-free images has been added. Thirteen tree species were classified in each single-year dataset based on the SVM algorithm. The performances were assessed using a spatial leave-one-out cross validation (SLOO-CV) strategy, thereby guaranteeing full independence of the validation samples, and compared with standard non-spatial leave-one-out cross-validation (LOO-CV). The results show relatively close statistical performances from one year to the next despite the differences between the annual time series. Good agreements between years were observed in monospecific tree plantations of broadleaf species versus high disparity in other forests composed of different species. A strong positive bias in the accuracy assessment (up to 0.4 of Overall Accuracy) was also found when spatial dependence in the validation data was not removed. Using the SLOO-CV approach, the average OA values per year ranged from 0.48 for 2006 to 0.60 for 2013, which satisfactorily represents the spatial instability of species prediction between years.

Astronomy is entering an unprecedented era of Big Data science, driven by missions like the ESA's Gaia telescope, which aims to map the Milky Way in three dimensions. Gaia's vast dataset presents a monumental challenge for traditional analysis methods. The sheer scale of this data exceeds the capabilities of manual exploration, necessitating the utilization of advanced computational techniques. In response to this challenge, we developed a novel approach leveraging deep learning to estimate the metallicity of fundamental mode (ab-type) RR Lyrae stars from their light curves in the Gaia optical G-band. Our study explores applying deep learning techniques, particularly advanced neural network architectures, in predicting photometric metallicity from time-series data. Moreover, our deep learning models demonstrated notable predictive performance over experimentation and analysis. Through GRU-based models we achieved a low mean absolute error of 0.056 and a high $R^2$ regression performance of 0.9401 measured by cross-validation, showcasing the effectiveness of our approach in accurately estimating metallicity values. Our work underscores the importance of deep learning in astronomical research, particularly with large datasets from missions like Gaia. By harnessing the power of deep learning methods, we can provide precision in analyzing vast datasets, contributing to more precise and comprehensive insights into complex astronomical phenomena.

Satellite Image Time Series (SITS) is a data set which includes satellite images across several years with a high acquisition rate. Radiometric normalization is a fundamental and important preprocessing method for remote sensing applications using SITS due to the radiometric distortion caused by noise between images. Normalizing the subject image based on the reference image is a general strategy when using traditional radiometric normalization methods to normalize multi-temporal imagery (usually two scenes or three scenes in different time phases). However, these methods are not suitable for calibrating SITS because they cannot minimize the radiometric distortion between any pair of images in SITS. The existing relative radiometric normalization methods for SITS are based on linear assumptions which cannot effectively reduce nonlinear radiometric distortion caused by continuously changing noise in SITS. To overcome this problem and obtain a more accurate SITS, this study proposed a Nonlinear Radiometric Normalization Model (named NMAG) for SITS based on Artificial Neural Networks (ANN) and Greedy Algroithm (GA) . In this method, GA was used to determine the correction order of SITS and calculate the error between the image to be corrected and normalized images, which avoided the selection of a single reference image. ANN was used to obtain the optimal solution of error function, which minimized the radiometric distortion between different images in SITS. SITS composed of 21 Landsat-8 images in Tianjin City from October 2017 to January 2019 were selected to test the method. We compared NMAG with other two contrasting method (refered as CM1 and CM2), and found that the average of root mean square error $(\mu_{RMSE})$ of NMAG $(497.22)$ was significantly smaller than those of CM1 $(641.39)$ and CM2 $(543.47)$, and the accuracy of normalized SITS obtained by using NMAG has increased by 22.4\% and 8.5\% toward CM1 and CM2, respectively. These experimental results confirmed the effectiveness of NMAG in the reduction of radiometric distortion caused by continuously changing noise between images in SITS.

A vast majority of the countries is under the economic and health crises due to the current epidemic of coronavirus disease 2019 (COVID-19). The present study analyzes the COVID-19 using time series, which is an essential gizmo for knowing the enlargement of infection and its changing behavior, especially the trending model. We have considered an autoregressive model with a non-linear time trend component that approximately converted into the linear trend using the spline function. The spline function split the COVID-19 series into different piecewise segments between respective knots and fitted the linear time trend. First, we obtain the number of knots with its locations in the COVID-19 series and then the estimation of the best-fitted model parameters are determined under Bayesian setup. The results advocate that the proposed model/methodology is a useful procedure to convert the non-linear time trend into a linear pattern of newly coronavirus case for various countries in the pandemic situation of COVID-19.

The evaluation of geometric defects is necessary in order to maintain the integrity of structures over time. These assessments are designed to detect damages of structures and ideally help inspectors to estimate the remaining life of structures. Current methodologies for monitoring structural systems, while providing useful information about the current state of a structure, are limited in the monitoring of defects over time and in linking them to predictive simulation. This paper presents a new approach to the predictive modeling of geometric defects. A combination of segmented from point clouds are parametrized using the convex hull algorithm to extract features from detected defects, and a stochastic dynamic model is then adapted to these features to model the evolution of the hull over time. Describing a defect in terms of its parameterized hull enables consistent temporal tracking for predictive purposes, while implicitly reducing data dimensionality and complexity as well. In this study, 2D point clouds analogous to information derived from point clouds were first generated over simulated life-cycles. The evolutions of point cloud hull parameterizations were modeled as stochastic dynamical processes via autoregressive integrated moving average (ARIMA) and vectorized autoregression (VAR) and compared against ground truth. The results indicate that this convex hull approach provides consistent and accurate representations of defect evolution across a range of defect topologies and is reasonably robust to noisy measurements, however assumptions regarding the underlying dynamical process play a significant the role in predictive accuracy. The results were then validated on experimental data from fatigue testing with high accuracy. Longer term, the results of this work will support finite element model updating for predictive analysis of structural capacity.

Inland lake variations are considered sensitive indicators of global climate change. However, human activity is playing as a more and more important role in inland lake area variations. Therefore, it is critical to identify whether anthropogenic activity or natural event is playing as the dominant factor in inland lake surface area change. In this study, we proposed a Douglas-Peucker simplification algorithm and bend simplification algorithm combined method to locate major lake surface area disturbances; these disturbances were then characterized to extract the time series change features according to documented records; and the disturbances were finally classified into anthropogenic or natural. We took the nine lakes in Yunnan Province as test sites, a 31 years long (from 1987 to 2017) time series Landsat TM/OLI images and HJ-1A/1B used as data sources, the official records was used as references to aid the feature extraction and disturbance identification accuracy. Results of our method for both disturbance location and the disturbance identification could be concluded as follows: 1) The method can accurately locate the main lake changing events based on the time series lake surface area curve. The accuracy of this model for segmenting the lake area time series curves in our study area was 95.24%. 2) Our proposed method achieved an overall accuracy of 91.67%, with F-score of 94.67 for anthropogenic disturbances and F-score of 85.71 for natural disturbances. 3) According to our results, lakes in Yunnan Provence, China, have undergone extensive disturbances, and the human-induced disturbances occurred almost twice as often as natural disturbances, indicating intensified disturbances caused by human activities. This inland lake area disturbance identification method is expected to uncover whether a disturbance to inland lake area is human activity-induced or natural event.

Advances in the availability of multitemporal and global built-/human-settlements datasets as derived from Remote Sensing (RS) can now provide globally consistent definitions of “human-settlement” at unprecedented spatial fineness. Yet, these data only provide a time-series of past extents and urban growth/expansion models have not had parallel advances at high-spatial resolution. We present a flexible modelling framework for producing annual built-settlement extents in the near future past last observed extents as provided by RS-based data. Using a random forest and autoregressive temporal models with short time-series of built-settlement extents and subnational level data, we predict annual 100m resolution binary settlement extents five years beyond the last observations. We applied this framework within varying contexts and predicted annual extents from 2010 to 2015. We found that our model framework preformed consistently across all sample countries and, when compared to time-specific imagery, demonstrated the capacity to capture human-settlement missed by the input time-series and validation extents. When comparing building footprints of small settlements to forecast extents, we saw that the modelling framework had a 12 percent increase in ground-truth accuracy. This framework shows promise for predicting near-future settlement extents, and provides a foundation for forecasts further into the future.

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for a) describing the dynamics and b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and non-linearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of non-linearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.

Rift Valley Fever (RVF), is a viral zoonotic disease predominant in East Africa and transmitted by Aedes mosquitoes carrying the virus. Using the systematic literature review approach, the present study evaluated machine learning techniques and time series approaches to find literature on the impact of climatic changes on RVF outbreaks published between 1930 and 2024. The literature search involved databases including PubMed, PLOS ONE, JSTOR, Web of Science, Google Scholar, and SCOPUS (Kenmoe et al., 2023).The results show that most of the articles were published between 2018 and 2022, and most of the articles were from United States, France, and Kenya. We conducted a detailed review of the articles using the PRISMA 2020 flow chart, screening and qualifying 10,015 articles. Some articles revealed significant gaps in both internal and external validation. Therefore, future research should focus on developing multi-disciplinary models that incorporate climatic condition, geographical, biological, and social factors.

The Vaal Dam catchment, which is the source of potable water for Gauteng province, holds various human activities including mining, urbanization, agricultural and industrial activities coupled with high fluxes of nutrients from different areas within the catchment. This situation led to an enhancement of Harmful Algal Blooms (HABs) in the dam reservoir. Phosphorus and Nitrogen are the limiting nutrients for HABs in many eutrophic aquatic systems when their concentrations are raised in such waters. In this study, multi-time-series plot types and scutter plots were analysed to reveal the relationship between HABs proxy chlorophyll-a (Chl-a) and the potential nutrients. Also (Chl-a) data extracted from landsat-8 satellite images were visualised to show the spatial distribution of HABs in the reservoir. The results showed that the Vaal Dam HABs productivity is a function of the total phosphorus (TP) and the organic nitrogen (KJEL_N) levels, which were positively correlated with chlorophyll-a (Chl-a) concentration. The long-term analysis of Chl-a in-situ data (1986 – 2022) measured at one point within the reservoir showed an average of 11.25μg/l but at some stochastic dates, the Chl-a concentration jumped to very high values reaching the maximum value of 452.8μg/l. Such high values are associated with high records of TP and KJEL_N concentrations at the same dates which clearly reveals their effect on the productivity levels. The decadal time series and its trend analysis showed that the average productivity level of Chl-a increased during the studded period from 4.75μg/l in the first decade (1990 – 2000) to 10.51μg/l in the second decade (2000 – 2010) reaching 16.7 during the last decade (2010 – 2020). The increasing averages of the decadal values are associated with the increasing decadal average of its driving factors, TP from 0.1043 to 0.1096 to 0.1119mg/l for the three decades, respectively and KJEL_N from 0.80mg/l in the first decade to 1.14mg/l in the last decade. The decadal average of temperature showed no significant increase, 17.9 °C in the first decade and 18 °C in the last decade which suggests that temperature is not the only enhancing factor of the HABs productivity in the Vaal Dam. The satellite data analysis during the last decade revealed that the HABs spatial dynamics is a function of the dam geometry and the levels of the discharges from its two feeding rivers. Higher concentrations were observed where the reservoir is meandering and within the areas of restricted water circulation.

Satellite Crop Detection technologies are focused on detection of different types of crops on the field in the early stage before harvesting. Crop detection is usually done on a time series of satellite data by classification of the desired fields. Currently, data obtained from Remote Sensing (RS) are used to solve tasks related to the identification of the type of agricultural crops, also modern technologies using AI methods are desired in the postprocessing part. In this challenge Sentinel-1 and Sentinel-2 time series data were used due to their periodic availability. Our focus was to develop methodology for classification of time series of Sentinel 2 and Sentinel 1 data and compare how accuracy of classification can be increased, but also how to guarantee availability of data. We analyse phenology of single crops and on the basis of this analysis we started to provide crop classification. Original crop classifications were made from Enhanced Vegetation Index (EVI) layers made from Sentinel-2 time-series data and then we added also . To increase accuracy we also integrate into the process parcel borders and provide classification of fields..

This study presents a novel approach for predicting hierarchical short time series. In this article, our objective was to formulate long-term forecasts for household natural gas consumption by considering the hierarchical structure of territorial units within a country's administrative divisions. For this purpose, we utilized natural gas consumption data from Poland. The length of the time series was an important determinant of the data set. We contrast global techniques, which employ a uniform method across all time series, with local methods that fit a distinct method for each time series. Furthermore, we compare the conventional statistical approach with a machine learning (ML) approach. Based on our analyses, we devised forecasting methods for short time series that exhibit exceptional performance. We have demonstrated that global models provide better forecasts than local models. Among ML models, neural networks yielded the best results, with the MLP network achieving comparable performance to the LSTM network while requiring significantly less computational time.

The variability of meteorological parameters such as temperature and precipitation, and climatic conditions such as intense droughts, are known to impact vegetation health over southern Africa. Thus, understanding large-scale ocean–atmospheric phenomena like the El Niño/Southern Oscillation (ENSO) and Indian Ocean Dipole/Dipole Mode Index (DMI) is important as these factors drive the variability of temperature and precipitation. In this study, 16 years (2002–2017) of Moderate Resolution Imaging Spectroradiometer (MODIS) Terra/Aqua 16-day normalized difference vegetation index (NDVI), extracted and processed using JavaScript code editor in the Google Earth Engine (GEE) platform in order to analyze the response pattern of the oldest proclaimed nature reserve in Africa, the Hluhluwe-iMfolozi Park (HiP), during the study period. The MODIS-enhanced vegetation index and burned area index were also analyzed for this period. The area-averaged Modern Retrospective Analysis for Research Application (MERRA) model maximum temperature and precipitation were also extracted using the JavaScript code editor in the GEE platform. This procedure demonstrated a strong reversal of both the NDVI and Enhanced Vegetation Index (EVI), leading to signs of a sudden increase of burned areas (strong BAI) during the strongest El Niño period. Both the Theilsen method and the Mann–Kendall test showed no significant greening or browning trends over the whole time series, although the annual Mann–Kendall test, in 2003 and 2014–2015, indicated significant browning trends due to the most recent strongest El Niño. Moreover, a multi-linear regression model seems to indicate a significant influence of both ENSO activity and precipitation. Our results indicate that the recent 2014–2016 drought altered the vegetation condition in the HiP. We conclude that it is vital to exploit freely available GEE resources to develop drought monitoring vegetation systems, and to integrate climate information for analyzing its influence on protected areas, especially in data-poor counties.

Multivariate Time Series Classification (MTSC) is one of most important tasks in time series analysis, aiding in activities such as human motion recognition and medical diagnostics. Existing methods for MTSC do not explicitly model temporal differences and generalize the idea of temporal difference into a efficient temporal module. Additionally, existing methods are not yet able to capture cross-variable relationships well during network training. As a result, they are unable to achieve convincing feature representation, leading to suboptimal classification accuracy. In this paper, we propose a novel MTSC model called Temporal Difference and Cross-variate Fusion Network (TDCFN), which integrates a two-stream differential LSTM network and a cross-variate feature extraction network to enhance feature representation. TDCFN achieves superior classification accuracy by capturing dynamic temporal evolution and inter-variable relationships. The experimental results show that TDCFN can achieve competitive performance with state-of-the-art multivariate time series classification approaches.

For more than half a century, Manfred Deistler has been contributing to the construction of the rigorous theoretical foundations of the statistical analysis of time series and more general stochastic processes. Half a century of unremitting activity is not easily summarized in a few pages. In this short note, we chose to concentrate on a relatively little-known aspect of Manfred's contribution which nevertheless had quite an impact on the development of one of the most powerful tools of contemporary time series and econometrics: dynamic factor models.

Snow is a vital environmental parameter and dynamically responsive to climate change, particularly in mountainous regions. Snow cover can be monitored at variable spatial scales using Earth Observation (EO) data. Long-lasting remote sensing missions enable the generation of multi-decadal time series and thus the detection of long-term trends. However, there have been few attempts to use these to model future snow cover dynamics. In this study, we therefore explore the potential of such time series to forecast the Snow Line Elevation (SLE) in the European Alps. We generate monthly SLE time series from the entire Landsat archive (1985-2021) in 43 Alpine catchments. Positive long-term SLE change rates are detected, with the highest rates (5-8 m/y) in the Western and Central Alps. We utilize this SLE dataset to implement and evaluate seven uni-variate time series modeling and forecasting approaches. The best results were achieved by Random Forests, with a Nash-Sutcliffe efficiency (NSE) of 0.79 and a Mean Absolut Error (MAE) of 258 m, Telescope (0.76, 268 m), and seasonal ARIMA (0.75, 270 m). Since the model performance varies strongly with the input data, we developed a Combined forecast based on the best performing methods in each catchment. This approach was then used to forecast the SLE for the years 2022-2029. In the majority of the catchments the shift of the forecast median SLE level retained the sign of the long-term trend. In cases where a deviating SLE dynamic is forecast a discussion based on the unique properties of the catchment and past SLE dynamics is required. In the future, we expect major improvements in our SLE forecasting efforts by including external predictor variables in a multi-variate modeling approach.

High-rise building machines (HBMs) play a critical role in the successful construction of super-high skyscrapers, providing essential support and ensuring safety. The HBM’s climbing system relies on a jacking mechanism consisting of several independent jacking cylinders. A reliable control system is imperative to maintain a smooth posture of the construction steel platform (SP) under the action of the jacking mechanism. This research introduces three multivariate time series neural network models—namely, Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Temporal Convolutional Network (TCN)—to predict the posture of HBM. The models take pressure and stroke measurements from the jacking cylinders as inputs, and their outputs determine the levelness of the SP and the posture of the HBM at various climbing stages. The development and training of these neural networks are based on historical on-site data, with the predictions subjected to thorough comparative analysis. All proposed neural network models exhibit the capability to dynamically predict the posture of the HBM during the climbing process, using data from sensors. Notably, the GRU model shows better predictive performance.

Suitable measures of grazing impacts on ground cover, that enable separation of the effects of climatic variations, are needed to inform land managers and policy makers across the arid rangelands of the Northern Territory of Australia. This work developed and tested a time-series, change-point detection method for application to time series of vegetation fractional cover derived from Landsat data to identify irregular and episodic ground-cover growth cycles. These cycles were classified to distinguish grazing impacts from that of climate variability. A measure of grazing impact was developed using a multivariate technique to quantify the rate and degree of ground cover change. The method was successful in detecting both long term (> 3 years) and short term (< 3 years) growth cycles. Growth cycle detection was assessed against rainfall surplus measures indicating a relationship with high rainfall periods. Ground cover change associated with grazing impacts was also assessed against field measurements of ground cover indicating a relationship between both field and remotely sensed ground cover. Cause and effects between grazing practices and ground cover resilience can now be explored in isolation to climatic drivers. This is important to the long term balance between ground cover utilisation and overall landscape function and resilience.

Accurately predicting electrical signals of three-phase Direct Torque Control (DTC) induction motors is crucial for optimal motor performance and effective condition monitoring. However, multiple DTC motors’ complexity and operating conditions’ variations pose challenges for traditional prediction methods. To overcome these challenges, we propose an innovative approach that combines Fast Fourier Transform (FFT) to transform electrical motor simulation data and a Bi-directional Long Short-Term Memory (Bi-LSTM) network to forecast processed motor data. By transforming the DTC induction motor signals from the time domain to the frequency domain, we enhance the capability of learning models to capture subtle differences and generate various input features. The Bi-LSTM model effectively captures both forward and backward dependencies in time series data, enabling accurate prediction of electrical signals. We evaluate the proposed approach using our simulated dataset and compare the proposed method to a state-of-the-art model, the Gated Recurrent Unit (GRU), demonstrating its effectiveness in improving the accuracy and reliability of induction motor signals forecasting. The finding provides valuable insights for advancing motor control and operation in industrial applications.

In 2019, Chinese government implemented the first round of National Centralized Drug Procurement (NCDP) pilot (so-called "4+7" policy) in mainland China, achieved a prominent price reduction of 52% on average for 25 bidding winning products. Under cross-price elasticity theory, the price behavior of pharmaceutical enterprises for policy-related drugs might change. This study used drug purchasing data from the Centralized Drug Procurement Survey in Shenzhen 2019, and applied single-group Interruption Time Series (ITS) design to examine the impact of "4+7" policy on the drug price index (DPI) of policy-related drugs. The ITS analysis showed that the DPI of winning (-0.183 per month, p&lt;0.0001) and non-winning (-0.034 per month, p=0.046) products significantly decreased after the implementation of "4+7" policy. No significant difference was found for the immediate change of DPI for alternative drugs (p=0.537), while a significant decrease in change trend was detected in the post-"4+7" policy period (-0.003 per month, p=0.014). The DPI of the overall policy-related drugs significantly decreased (-0.261 per month, p&lt;0.0001) after "4+7" policy. These findings indicate that the price behavior of pharmaceutical enterprises changed under NCDP policy, while the price linkage effect is still limited. It is necessary to further expand the scope of centralized purchased drugs and strengthen the monitoring of related drugs regarding price change and consumption structure.

This paper explores the application of machine learning in financial time series analysis, focusing on predicting trends in financial enterprise stocks and economic data. It begins by distinguishing stocks from stocks and elucidates risk management strategies in the stock market. Traditional statistical methods such as ARIMA and exponential smoothing are discussed in terms of their advantages and limitations in economic forecasting. Subsequently, the effectiveness of machine learning techniques, particularly LSTM and CNN-BiLSTM hybrid models, in financial market prediction is detailed, highlighting their capability to capture nonlinear patterns in dynamic markets. The study demonstrates the advancements in predictive accuracy and robustness achieved by deep learning methods through empirical analysis and model validation. The findings contribute significantly to academic discourse and offer practical insights for investors, financial analysts, and policymakers navigating market volatility and optimizing investment strategies. Finally, the paper outlines prospects for machine learning in financial forecasting, laying a theoretical foundation and methodological framework for achieving more precise and reliable economic predictions.

Abstract: This paper presents a comprehensive analysis of links between satellite-measured vegetation vigor and climate variables in Armenian mountain grassland ecosystems in years 1984–2018. NDVI is derived from MODIS and Landsat data, temperature and precipitation data are from meteorological stations. Two study sites were selected, representing arid and semi-arid grassland vegetation types, respectively. Various trend estimators including Mann-Kendall (MK) and derivatives were combined for vegetation change analysis at different time scales. Results suggest that temperature and precipitation had negative and positive impacts on vegetation growth, respectively, in both areas. NDVI-to-precipitation correlation was significant but with an apparent time-lag effect that was further investigated. No significant general changes were observed in vegetation along the observed period. Further comparisons between results from corrected and uncorrected data led us to conclude that MODIS and Landsat data with BRDF, topographic and atmospheric corrections applied are best suited for analyzing relationships between NDVI and climatic factors for the 2000-2018 period in grassland at a very local scale, but in the absence of correction tools and information, uncorrected data can still provide meaningful results. Future refinements will include removal of anthropogenic impact, and deeper investigation of time-lag effects of climatic factors on vegetation dynamics.

In the steel industries, workers are exposed to heat and ambient thermal stresses on a daily basis, leading to discomfort and limited performance. In this study, the main purpose is to investigate the effect of climate heat stress on the rate of accidents in the workplace for workers for 5 consecutive years. The data of this study were received without any sampling through the HSE Center for Steel Industry and meteorological data from 2015 to 2019 from Isfahan Meteorological station. The daily number of casualties among workers in the steel industry during 2015-2019 by adjusting seasonal patterns, months, effects of the day of the week and other meteorological factors on the average daily temperature using the studied model has a decreasing effect. Eviews software (version 8) was used to model and investigate the relationship between events and meteorological variables. The mean temperature was at least 40.2-2 and at most 70.34 ° C, respectively. In the time-series study for the main model, the number of accidents shows a direct relationship with the average temperature and wind speed. Climatic indices of humidity and rainfall have the least impact on accidents compared to temperature and wind speed. A strong correlation was shown between the increase in average ambient temperature and the rate of accidents over the past 5 years. Given the fundamental differences in studies of environmental exposure and wind speed over heat stress, further analysis in workers should be considered.

The goal of VAR or BVAR is the characterization of the dynamics and endogenous relationships among time series. Also the VAR models are known for their applications to forecasting and policy analysis. This paper compare the performance of VAR and Sims-Zha Bayesian VAR models when the multiple time series are jointly influenced by different levels of collinearity and autocorrelation in the short term (T=16, 32, 64 and 128). Five levels (-0.9,-0.5, 0,+0.5,+0.9) of collinearity and autocorrelation were considered and the results from the simulation study revealed that VAR(2) model dominated for no and moderate levels of autocorrelation (-0.5, 0, +0.5) irrespective of the collinearity level except in few cases when T=16. While the BVAR models dominated for high autocorrelation levels (-0.9 and +0.9) irrespective of the collinearity level except in few cases when T=128. The performance of the models varies at different levels of the collinearity and autocorrelated error, and also varies with the short term periods. Furthermore, the values of the RMSE and MAE criteria decrease as a result of increase in the time series length. In conclusion, the performance of the forecasting models depend on the time series data structure and the time series length. It is therefore recommended that the data structure and series length should be considered in using an appropriate model for forecasting.

Drinking water quality is a major concern, especially in African countries. This manuscript aims to analyze the chemical composition of Lioua’s groundwater in order to determine the geological processes influencing the chemical elements' composition and origin. Therefore, chemometrics techniques such as multivariate statistical analysis (MSA) and time series methods (TSM) are used. Indeed, MSA includes a component analysis (PCA) and a cluster analysis (CA), while au-tocorrelation analysis (AA) supplemented by simple spectral density analysis (SDA) is used for TMS. PCA displays three main factors explaining a total variance (TV) of 85.01 %. Factors 1, 2, and 3 are 68.72%, 11.96%, and 8.89 % of TV, respectively. In the CA, three groups were controlled by TDS and EC. G1 reveals a close association between SO42−, K+, Ca2+, and TDS; G2 reveals a close association between Na+, Cl−, Mg2+, and EC; G3 shows the dissociation of bicarbonates HCO3− and NO3− from other chemical elements. AA shows a linear interrelationship of EC, Mg2+, Na+, K+, Cl−, and SO42−. However, NO3− and HCO3− indicate uncorrelated characteristics with other parameters. For SDA, the correlograms of Mg2+, Na+, K+, Cl−, and SO42− have a similar trend with EC. None-theless, pH, Ca2+, HCO3− and NO3− exhibit multiple peaks related to the presence of several dis-tinct cyclic mechanisms. The methods enabled the authors to conclude that the geochemical processes influencing the chemical composition are: (i) dissolution of evaporated mineral depos-its, (ii) water-rock interaction, and (iii) evaporation process. In addition, Groundwater exhibits two bipolar characteristics, one recorded with negative and positive charges on pH and Ca+ and another recorded only with negative charges on HCO3− and NO3−. On the other hand, SO42-, K+, Ca2+, and TDS are the major predominant elements in the groundwater’s chemical composition. The major participation of salts and chlorides is in the electrical conductivity of water. The dominance of the lithological factor in the overall mineralization of the Plio-Quaternary surface aquifer waters. The origins of HCO3− and NO3− are different. Indeed, carbonated for HCO3- has a carbonate origin, whereas NO3– has an anthropogenic origin. The salinity was affected by Mg2+, SO42-, Cl-, Na+, K+, and EC. Ca2+, HCO3− and NO3− are resulted from human activity fertilizers, the carbonate facies outcrops, and domestic sewage.

Color change is the most obvious characteristic of tomato ripening stage and an important indicator of tomato ripening condition, which directly affects the commodity value of tomato. To visualize the color change of tomato fruit in mature stage, a gated recurrent unit network with an encoder-decoder structure that dynamically simulates tomato growth and development with time-dependent lines using tomato color and shape as real-time data was proposed in this paper. Firstly, the .json file was converted into a mask.png file, the tomato mask was extracted, and the tomato was separated from the complex background environment, and the tomato growth and development data set was successfully constructed. Then, a network of gated recurrent units with encoder-decoder structure was constructed to predict the future growth trend of tomato under different greenhouse temperatures. The experimental results showed that for the gated recurrent unit network of encoder-decoder structure proposed, when the hidden layer number was 1 and hidden layer number was 512, a high consistency and similarity between the model predicted image sequence and the actual growth and development image sequence would be realized, and the structural similarity index measure was 0.746. It was proved that when the average temperature was 24.93℃, the average soil temperature was 24.06℃, and the average light intensity was 11.26 Klux, the environment was the most suitable for tomato growth. The environmental data-driven tomato growth model was constructed to explore the growth status of tomato under different environmental conditions, thus to understand the growth status of tomato in time. The statement provided a theoretical foundation for determining the optimal greenhouse environmental conditions to achieve tomato maturity. And it offered recommendations for investigating the growth cycle of tomatoes, as well as technical assistance for standardized cultivation in solar greenhouses.

In this research, univariate and bivariate statistical methods were applied to rainfall, river and piezometric level datasets belonging to 24 years long time series (1986-2009). These methods, that often are used to understand the effects of precipitation on rivers and karstic springs discharge, have been used to assess, piezometric level response to rainfall and river level fluctuations in a porous aquifer. A rain gauge, a river level gauge and three wells, located in Central Italy along the lower Pescara river valley in correspondence of its important alluvial aquifer, provided the data. The statistical analysis has been used within a known hydrogeological framework, which has been refined by mean of a photo-interpretation and a GPS survey. Water-groundwater relationships were identified following the autocorrelation and cross-correlation analyses; the spectral analysis and mono-fractal features of time series were assessed, in order to provide information on multy-year variability, data distributions, their fractal dimension and the distribution return time within the historical time series. The statistical-mathematical results were interpreted through field work that identified distinct groundwater flowpaths within the aquifer and enabled the implementation of a conceptual model, improving the knowledge on water resources management tools.

The Covid-19 pandemic and the subsequent implementation of lockdown measures have significantly impacted global electricity consumption, necessitating accurate energy consumption forecasts for optimal energy generation and distribution during a pandemic. In this study, we propose a new forecasting model called the Multivariate Multilayered LSTM with Covid-19 case injection ($\proposedModel$) for improved energy forecast during the next occurrence of a similar pandemic. We utilize data from commercial buildings in Melbourne, Australia during the Covid-19 pandemic to predict energy consumption and evaluate the model's performance against commonly used methods such as LSTM, Bi-LSTM, Linear Regression, Support Vector Machine and the previously published work of Multilayered LSTM (M-LSTM). The proposed forecasting model was analyzed using the following metrics of mean percent absolute error (MPAE), normalized root mean square error (NRMSE), and $R^2$ score values. The model $\proposedModel$ demonstrates superior performance, achieving the lowest MPAE values of 0.061, 0.093, and 0.158 for data sets from 3 different buildings, respectively. Our results highlight the improved precision and accuracy of the model, providing valuable information for energy management and decision-making during the challenges posed by the occurrence of a pandemic like Covid-19 in the future.

We reduplicate the Book “Dark Energy” by M. Li, X-D. Li, and Y. Wang, given zero-point energy calculation with an unexpected “length’ added to the ‘width’ of a graviton wave just prior to specifying the creation of ‘gravitons’, using the Rosen and Israelit model of a nonsingular universe. In doing so we are in addition to obtaining a wavelength 10^30 times greater than Planck’s length so we can calculate DE, may be able to with the help of the Rosen and Israelit model have a first approximation as to the arrow of time, and a universe with massive gravity. We have left the particulars of the nonsingular starting point undefined but state that the Rosen and Israelit model postulates initial temperatures of 10^-180 Kelvin and also a value of about Planck temperature, at 10^-3 centimeters radii value which may satisfy initial conditions asked by t’Hooft for describing an arrow of time. A key assumption is that the DE is formed at 10^-3 cm, after an expansion of 10^30 times in radii, from the Planck length radius nonsingular starting point. The given starting point for DE in this set of assumptions is where there is a change in the cosmic acceleration, to a zero value, according to Rosen and Israel, with time t = 1.31 times 10^-42 seconds. Which may be where we may specify a potential magnitude, V, which has ties into inflaton physics. The particulars of the model from Rosen and Israelit allow a solution to be found, without discussion of where that nonsingular starting point came from, a point the author found in need of drastic remedies and fixes.

The aim of this study was to assess the ability of multiscale sample entropy (MSE), refined composite multiscale entropy (RCMSE), and complexity index (CI) to characterize gait complexity through trunk acceleration patterns in subjects with Parkinson's disease (swPD) and healthy subjects, regardless of age or gait speed. The trunk acceleration patterns of 51 swPD and 50 HS were acquired using a lumbar-mounted magneto-inertial measurement unit during their walking. MSE, RCMSE, and CI were calculated on 2000 data points, using scale factors (τ) 1-6. Differences between swPD and HS were calculated at each τ, and the area under the receiver operating characteristics, optimal cutoff points, post-test probabilities, and diagnostic odds ratios were calculated. MSE in the antero-posterior direction at τ 4 and τ 5, and MSE in the ML direction at τ 4 outperformed the other entropy measures in terms of discriminative ability and characterized the gait of swPD with 79%, 82%, and 78% probabilities, respectively, and correlated with the motor disability, pelvic kinematics, and stance phase. Using a time series of 2000 data points, a scale factor of 4 or 5 in the MSE procedure can be considered as a marker of gait variability and complexity in swPD.

Background: Pediatric Rapid Response Teams (RRTs) are expected to significantly lower pediatric mortality in healthcare settings. This study evaluates RRTs' effectiveness in decreasing cardiac arrests and unexpected Pediatric Intensive Care Unit (PICU) admissions. Methods: A quasi-experimental study (2014-2017) at King Abdulaziz University Hospital, Jeddah, Saudi Arabia, involved 3,261 pediatric inpatients, split into pre-intervention (1,604) and post-intervention (1,657) groups. The intervention entailed pediatric specialists collaboratively managing acute decompensations following set protocols. Results: RRT was activated 471 times, primarily for respiratory distress (29.30%), sepsis (22.30%), clinical anxiety (13.80%), and hematological abnormalities (6.7%). Family concerns triggered 0.1% of activations. Post-RRT implementation, unplanned PICU admissions significantly reduced (RR = 0.552, 95% CI 0.485-0.628, P < 0.0001), and non-ICU cardiac arrests were eliminated (RR = 0). Patient care improvement was notable, with a -9.61 coefficient for PICU admissions (95% CI: -12.65 to -6.57, P < 0.001) and a -1.641 coefficient for non-ICU cardiac arrests (95% CI: -2.22 to -1.06, P < 0.001). Sensitivity analysis showed mixed results for PICU admissions, while zero-inflation Poisson analysis confirmed a reduction in non-ICU arrests. Conclusions: The deployment of pediatric RRTs is associated with fewer unexpected PICU admissions and non-ICU cardiopulmonary arrests, indicating improved PICU management. Further research using robust scientific methods is necessary to conclusively determine RRTs' clinical benefits.

Einstein’s publication of the Special Theory of Relativity in 1905 gave birth to the space-time model as a fundamental arena of the universe. Time has become 4th dimension of space and theoretically one could move backward and forward in time. Hypothetical time travel has been a hot topic of scientific discussion since Kurt Gödel published his article about closed time-like curves (CTC) in 1949. He was aware that his CTC model confirms that there is no physical time. Physicists understood his model as a theoretical frame for time travel. Recent research confirmed that universal space is time-invariant. Motion happens only in space and time is the duration of motion. Nobody can travel in time because time has no physical existence. Time as duration is an emergent physical quantity entering existence in the process of measurement of the duration of material change with clocks. The universal space is utterly timeless. There is no physical time in the universe.

.In his groundbreaking 1905 paper on special relativity, Einstein distinguished between local and global time in inertial systems, introducing his famous definition of distant simultaneity to give physical content to the notion of global time. Over the following decade, Einstein attempted to generalize this analysis of relativistic time to include accelerated frames of reference, which, according to the principle of equivalence, should also account for time in the presence of gravity. Characteristically, Einstein's methodology during this period focused on simple, intuitively accessible physical situations, exhibiting a high degree of symmetry. However, in the final general theory of relativity, the a priori existence of such global symmetries cannot be assumed. Despite this, Einstein repeated some of his early reasoning patterns even in his 1916 review paper on general relativity and in later writings. Modern commentators have criticized these arguments as confused, invalid, and inconsistent. Here, we defend Einstein in the specific context of his use of global time and his derivations of the gravitational redshift formula. We argue that a detailed examination of Einstein's early work clarifies his later reasoning and demonstrates its consistency and validity.

Research has shown that emotional states may influence the subjective experience of time. The present study involved 111 healthy adult participants and examined the impact of emotional stimuli on time perception, using a time estimation task with four conditions: in one of the conditions, participants estimated the exposure time of a black screen, wherein the duration could vary be-tween 2 to 7 s (condition without emotional interference); in the other conditions, participants es-timated the exposure time (also ranging from 2 to 7 s) of images that would induce pleasant, un-pleasant, or neutral emotions, to which participants were instructed to focus their attention (pleasant, unpleasant, or neutral emotions). The results showed that participants estimated “shorter” time intervals (underestimation) for pleasant and unpleasant images compared to the condition without interference, but no significant differences were found between the neutral condition and the condition without interference. It is suggested that increased attention to an ex-ternal stimuli, regardless of its emotional valence, produces an underestimated perception of time.

We consider the problem of scheduling $n$ jobs with identical processing times and given release as well as delivery times on $m$ uniform machines. The goal is to minimize the makespan, i.e., the maximum full completion time of any job. This problem is well-known to have an open complexity status even if the number of jobs is fixed. We present a polynomial-time algorithm for the problem which is based on the earlier introduced algorithmic framework blesscmore (``branch less and cut more''). We extend the analysis of the so-called behavior alternatives developed earlier for the version of the problem with identical parallel machines and show how the earlier used technique for identical machines can be extended to the uniform machine environment if a special condition on the job parameters is imposed. The time complexity of the proposed algorithm is $O(\gamma m^2 n\log n)$, where $\gamma$ can be either $n$ or the maximum job delivery time $q_{\max}$. This complexity can even be reduced further by using a smaller number $\kappa<n$ in the estimation describing the number of jobs of particular types. However, this number $\kappa$ becomes only known when the algorithm has terminated.

In Einstein’s Special Relativity(SR), time is treated as one of the four dimensions within spacetime and is relative in nature. Typically, a photon clock serves as the illustrative device in the time dilation thought experiment, featuring a single photon bouncing between two mirrors. However, the present paper identifies a fundamental flaw in this thought experiment, hence challenging its validity. Contrary to SR, this paper asserts that time is a consequence of motion. Space and time should be treated differently as proposed by classical mechanics. Importantly, this stance does not challenge the concept of curved space in General Relativity (GR), but rather questions the idea of relative time, as employed in both SR and GR. The absence of time dilation also dispels the twin paradox, prompting a necessary reassessment of the second postulate of relativity to ensure a more precise depiction of relativistic effects.