Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

: In this article, the authors propose an algorithmic approach to building a model of the dynamics of economic and, in particular, innovation processes. The approach under consideration is based on a complex algorithm that includes (1) decomposition of the time series into components using singular spectrum analysis; (2) recognition of the optimal component model based on fuzzy rules, and (3) creation of statistical models of individual components with their combination. It is shown that this approach corresponds to the high uncertainty characteristic of the tasks of the dynamics of innovation processes. The proposed algorithm makes it possible to create effective models that can be used both for analysis and for predicting the future states of the processes under study. The advantage of this algorithm is the possibility to expand the base of rules and components used for modeling. This is an important condition for improving the algorithm and its applicability for solving a wide range of problems.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

Anomaly detection plays a significant role in helping gas turbines run reliably and economically. Considering collective anomalous data and both sensitivity and robustness of the anomaly detection model, a sequential symbolic anomaly detection method is proposed and applied to the gas turbine fuel system. A structural Finite State Machine is to evaluate posterior probabilities of observing symbolic sequences and most probable state sequences they may locate. Hence an estimating based model and a decoding based model are used to identify anomalies in two different ways. Experimental results indicates that these two models have both ideal performance overall, and estimating based model has a strong ability in robustness, while decoding based model has a strong ability in accuracy, particularly in a certain range of length of sequence. Therefore, the proposed method can well facilitate existing symbolic dynamic analysis based anomaly detection methods especially in gas turbine domain.

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.

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.

With the great development of intelligent transportation systems (ITS), travel time prediction has attracted the attentions of many researchers and a large number of prediction methods have been developed. However, as an unavoidable topic, the predictability of travel time series is the basic premise for travel time prediction has received less attention than the methodology. Based on the analysis of the complexity of travel time series, this paper defines travel time predictability to express the probability of correct travel time prediction and proposes an entropy-based method to measure the upper bound of travel time predictability. Multiscale entropy is employed to quantify the complexity of travel time series, and the relationships between entropy and the upper bound of travel time predictability are presented. Empirical studies are made with vehicle trajectory data in an express road section. The effectiveness of time scales, tolerance, and series length to entropy and travel time predictability are analysis, and some valuable suggestions about the accuracy of travel time predictability are discussed. Finally, the comparisons between travel time predictability and actual prediction results from two prediction models, ARIMA and BPNN, are conducted. Experimental results demonstrate the validity and reliability of the proposed travel time predictability.

The available direct gas dynamic tables provide the area ratio and the Prandtl-Meyer(P-M) angle of isentropic expansion of gas as functions of the Mach number. But finding the value of the Mach number in terms of area ratio or P-M angle requires an inverse function. Currently, the Mach number is determined by either interpolation from the direct gas dynamics tables, or the application of non-linear equation solvers using numerical methods. Both methods are approximate. In this paper inverse functions for Mach number in the form of Taylor’s series expansions are reported to develop the so-called inverse tables. The advantage of this approach is that the Mach number with a greater accuracy, referred to as nearly exact can be obtained by reading from the inverse table. In the presentation, the necessary equations and new tables that can be used by the scientific community will be disseminated. The data and computer programs are made available on GitHub through https://github.com/anillals/Inverse-gas-dynamic-tables- and-codes. A paper describing the complete mathematical steps in the derivation of the equations can be found at https://rdcu.be/dgrlf

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.

Four methods in two different families have been constructed to derive the exact solutions to Benjamin-Bona-Mahony equation in two space dimensions. Simply defined hyperbolic tangent, hyperbolic secant and hyperbolic cosecant ansatzes and the expansion method based on the Sine-Gordon equation in two dimensions are directly substituted into the governing ODE reduced from the two dimensional BBM equation. Classical algebraic method is used to find the relations among the target parameters representing the nonzero coefficients in the predicted solutions and the wave transform parameters. Some complex and real solutions have been constructed in explicit forms.

The futures market plays a significant role in hedging and speculating by investors. Although various models and instruments are developed for real-time trading, it is difficult to realize profit by processing and trading a vast amount of real-time data. This study proposes a real-time index futures trading strategy that uses the pattern of KOSPI 200 index futures time series data. We construct a pattern matching trading system (PMTS) based on a dynamic time warping algorithm that recognizes patterns of market data movement in the morning and determines the afternoon's clearing strategy. We adopt 13 and 27 representative patterns and conduct simulations with various ranges of parameters to find optimal ones. Our experimental results show that the PMTS provides stable and effective trading strategies with relatively low trading frequencies. Investor communities that have sustained financial markets are able to make more efficient investments by using the PMTS. In this sense, the system developed in this paper is a sustainable investment technique and helps financial markets achieve efficient sustainability.

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.

In this work, a novel approach is presented for the multivariate prediction of hydrological variables, employing a specialized type of recurrent neural network (RNN) known as the long-term memory network (LSTM).The central objective is to develop a flood prediction model using data collected from two hydrological stations situated along the Atrato River in the Choc´o Department, Colombia. The interconnected variables of water level, water flow, and water precipitation are analyzed in this model to enhance flood prediction accuracy. The LSTM model, integrated into an RNN structure, is designed to capture the complex dynamics and cross-correlations inherent in these hydrological variables. Validation involves a comparison with linear and nonlinear Nonlinear AutoRegressive with eXogenous input (NARX) models, considering factors such as estimation error and computational time. Additionally, the study conducts further analysis for water level prediction under two scenarios: utilizing only outflow and inflow measurements or predicting outflow alongside measuring inflow, with the objective of utilizing the proposed approach as a flood early warning system. † This article is a revised and expanded version of a paper entitled Multivariable NARX based Neural Networks Models for Short-term Water Level Forecasting, which was presented at International Conference on Time Series and Forecasting (ITISE-2023), Gran Canaria, Spain, 12th-14th July, 2023.

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%

The electrical energy supply relies on the satisfactory operation of insulators. The ultrasound recorded from insulators in different conditions has a time series output, which can be used to classify faulty insulators. The random convolutional kernel transform (Rocket) algorithms use convolutional filters to extract various features from time series data. This paper proposes the combination of Rocket algorithms, machine learning classifiers, and empirical mode decomposition (EMD) methods, such as complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), empirical wavelet transform (EWT), and variational mode decomposition (VMD). The results show that the EMD methods combined with MiniRocket, significantly improve the accuracy of logistic regression in insulator fault diagnosis. The proposed strategy achieves respectively an accuracy of 0.992 using CEEMDAN, 0.995 with EWT, and 0.980 with VMD. These results highlight the potential of incorporating EMD methods in insulator failure detection models to enhance the safety and dependability of power systems.

Most of existing fuzzy forecasting models partition historical training time series into fuzzy time series and build fuzzy-trend logical relationship groups to generate forecasting rules. The determination process of intervals is complex and uncertainty. In this paper, we present a novel fuzzy forecasting model based on high-order fuzzy-fluctuation trends and the fuzzy-fluctuation logical relationships of the training time series. Firstly, we compare each data with the data of its previous day in historical training time series to generate a new fluctuation trend time series(FTTS). Then, fuzzify the FTTS into fuzzy-fluctuation time series(FFTS) according to the up, equal or down range and orientation of the fluctuations. Since the relationship between historical FFTS and the fluctuation trend of future is nonlinear, Particle Swarm Optimization (PSO) algorithm is employed to estimate the required parameters. Finally, use the acquired parameters to forecast the future fluctuations. In order to compare the performance of the proposed model with that of the other models, we apply the proposed method to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) time series datasets. The experimental results and the comparison results show that the proposed method can be successfully applied in stock market forecasting or such kinds of time series. We also apply the proposed method to forecast Shanghai Stock Exchange Composite Index (SHSECI) to verify its effectiveness and universality.

Off-road vehicles and transportation are vital for agricultural economics, yet the transition to green energies is challenging. To make this application easier, a tool that enables the testing of heavy-duty off-road vehicles in various scenarios was created. Based on the methods of the World Harmonized Transient Cycle, a new Hybrid Operational Cycle that reflects the features of agricultural work was created and applied in a graphical model simulation. This was a newly developed methodology. The cycle and the model were based on gathered research data. A numerical model of a medium-power tractor with an internal combustion engine and a series-hybrid setup was created, and simulations were performed in Matlab and AVL Cruise. The research compared both diesel and hybrid vehicles in terms of their power production, fuel consumption, and efficiency in fieldwork and transportation scenarios. The research showed that a series-hybrid transmission can achieve an efficiency similar to that of tractors with a continuously variable transmission (CVT), but with the use of an electric powertrain, there is still an opportunity to exploit energy regeneration in transportation and under low-load conditions. The designed model also may be used for the development of control algorithms for hybrid drives and the improvement of the efficiency thereof.

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.

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.

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.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

This paper describes the successful application of the Transformer model used in the natural language processing and vision tasks as a means of processing the time series of signals from gyroscope and accelerometer sensors for the classification of human activities. The Transformer model is based on deep neural networks with many layers which can generalize well on signals. All measured signals come from a smartphone placed in a waist bag. Activity prediction is sequence-to-sequence, each time step of the signal is assigned a designation of the performed activity. Emphasis is placed on attention mechanisms, which express individual dependencies between signal values within a time series. In comparison with another recent result, the recognition precision was improved from 89.67 percent to 99.2 percent. The transformer model should in the future be included among the top options in machine learning methods for human activity recognition.

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.

Satellite communication (Satcom) is an artificial geostationary satellite that facilitates a wide range of telecommunications. Considering its quality of service (QoS) and security is crucial in government/military applications. The most challenging situation for efficient Satcom is radio frequency interference (RFI) environment. Thus, it is necessary to ensure that transmissions are incorruptible or at least sense the quality of its spectrum. This paper presents a new method to recognize received signal characteristics using a hierarchical classification in a multi-layer perceptron neural network. We consider signal modulation and the type of RFI as the characteristics of a real-time video stream transmitted in the direct broadcast satellite. Four different modulation types are investigated in this study. Moreover, the combination of the communication signal with various kinds of interference and their effects on the classification method widely have been analyzed. Besides, two robust feature selection techniques have been developed to reduce the data-set dimensional, which leads to optimizing the classification process. The results show that the Genetic Algorithm (GA) slightly outperforms Principal Component Analysis (PCA) for feature selection. Furthermore, the robustness of the proposed techniques is assessed to detect unknown signals at different signal to noise ratios.

It is unavoidable that the characteristics of the robot system alter inexactly or cannot be correctly determined during movement and are impacted by external disturbances. There are many adaptive control methods, such as sliding control or neural control, to improve the quality of trajectory tracking for robot motion systems. Still, those methods require a large amount of computation related to solving the problem of constrained nonlinear optimization problem. The article presents some techniques for determining an intelligent controller's online learning function parameters, including two circuits: the inner circuit is a state feedback linearized controller, and the outer course is an Interactive learning controller and does not use the robot's mathematical mode with function parameters online optimal learning and intelligent online learning closely following the joint model to stabilize the robot system. Finally, the 2-DOF planar robot simulation is performed on Matlab software R2022b. The findings indicate that outstanding tracking performance is achievable.

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.

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.

Hybrid forecasting methods have emerged as a solution surpassing the limitations of both statistical and deep learning approaches. While the first emphasize the significance of variables, they often produce worse forecasting results when compared to newer techniques. In contrast, deep learning models remain enigmatic "black boxes" in terms of interpretability, although achieving better results in forecasting. This article introduces the Comprehensive Cross-Correlation and Lagged Linear Regression Deep Learning (CCLR-DL) framework, designed to harness the best of both approaches, enhancing forecasting accuracy while retaining model interpretability through a feature selection process. CCLR-DL blens cross-correlation analysis, lagged multiple linear regression and granger's causality procedures with deep learning architectures based on LSTM. In a practical demonstration, CCLR-DL was applied to a real database of clinical visits associated to diagnoses in Catalonia, Spain (tracking a population of 6.3 million patients during 10 years). Predicting visits enables the healthcare managers to be ready for future demand shifts. Results demonstrate a consistent and substantial improvement over standalone statistical and deep learning methods when predicting healthcare demand. This hybrid approach not only showcases its efficacy but also offers a promising solution to the challenge of balancing predictive accuracy with model explicability. In this context, this work aims to design and validate a method for feature selection and forecasting of multivariate high dimensional time series datasets not only to improve prediction accuracy but also to model transparency by identifying a subset of variables that improve predictions and G-cause the target variable.

We report on the fabrication and electrical characteristics of zinc-oxide (ZnO) based metal-insulator-semiconductor (MIS) type Schottky barrier diodes (SBHs). ZnO thin layer on the p-type silicon substrate was fabricated by atomic layer deposition (ALD). The structure and surface properties of the thin film were characterized by X-ray diffraction (XRD), atomic force microscope (AFM) and secondary ion mass spectrometer (SIMS). The current-voltage (I-V) characteristics of Al/ALD-grown ZnO/p-Si diodes were measured under dark at room temperature. The electrical parameters such as ideality factor (n), series resistance (R_s) and barrier height (ϕ_b) of the diodes were analyzed using standard thermionic emission (TE) theory, Norde and Cheung method. The barrier height value obtained from I-V and Cheung method was found to be 0.73 eV and 0.76 eV, respectively. The interface state density (Dit) of the diodes was determined from the I-V characteristics. The nonideal behavior of measured parameters suggested the presence of interface states. The obtained results showed that the prepared diode can be used for NIR Schottky photodetector applications.

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.

We study the divisibility properties of the constant terms of certain meromorphic modular forms for Hecke groups. We relate those properties to those of some sequences that have already appeared in the literature. For possible use in later drafts, we show how to invert the map taking a Laurent series $f(x) = 1/x + \sum_{n=0}^{\infty}a_{n+1} x^n$ to the sequence of constant terms of its positive powers. At the end of the article, we construct from elementary arithmetic functions some meromorphic but not necessarily modular functions and study their constant terms.

Wildfires are important natural drivers of forest stands dynamics, strongly influencing on their natural regeneration and ecosystem services. This paper presents a comprehensive analysis of spatiotemporal burnt area (BA) patterns over the period 2000–2022 in the Middle Volga region of the Russian Federation on the base of remote sensing time series, considering the impact of cli-matic factors on forest fires. The temporal trends were assessed with the Mann-Kendall nonpara-metric statistical test and Theil-Sen’s slope estimator using the LandTrendr algorithm on the Google Earth Platform (GEE). The accuracy assessment indicated a high overall accuracy (> 84%) and F-score value (> 82%) for forest burnt area detection as evaluated against 581 test sites of ref-erence data. The results revealed that the fire occurrences in the region were mainly irregular with the highest frequency of 7.3 over a 22-year period. The total forest BA was about 280 thousand ha, which equals to 1.7% of the land surface area or 4.0% of the total forested area under study in the Middle Volga region. The coniferous forest stands are the most fire-prone ecosystems accounting for 59.0 % of the total BA; deciduous stands accounts for 25.1%; and insignificant fire occurrences were registered in young forests and shrub lands. On a seasonal scale, temperature generally has a greater impact on the BA than precipitation and wind speed.

InSAR and associated analytic methods enable relative surface deformation measurements from low Earth orbit with a potential accuracy of centimeters to millimeters. However, assessing the actual accuracy can be quite difficult. The analytic methods are complicated enough that naive analytic error propagation is infeasible, and, in many settings, InSAR practitioners lack sufficient ground truth to assess results. Phase noise due to partial decorrelation from changes in the scattering properties of the ground is a prominent source of accuracy loss. In this paper we present a method to assess the loss of precision due to this component of phase noise. The proposed method consists of generating synthetic data stacks whose statistical properties match those of the actual input SAR data stacks, and then using the synthetic data for an ensemble calculation. The spread of the results of the ensemble calculation indicates the loss of precision. We show examples of the ensemble analysis at a mining operation in South Africa, and demonstrate the ability to estimate the precision of two InSAR deformation retrieval methods on a point-by-point and epoch-by-epoch basis.

The Doubly-Fed Induction Generator (DFIG) has significant features in comparison with Fixed Speed Wind Turbine (FSWT), which has popularized its application in power system. Due to partial rated back-to-back converters in the DFIG, Fault Ride-Through (FRT) capability improvement is one of the great subjects regarding new grid code requirements. To enhance the FRT capability of the DFIG, many studies have been carried out. Fault current limiting devices as one of the techniques are utilized to limit the current level and protect switches of the back-to-back converter from over-current damage. In this paper, a review is done based on fault current limiting characteristic of the proposed fault current limiting devices Therefore, Fault Current Limiters (FCLs) and Series Dynamic Braking Resistors (SDBRs) are mainly taken into account. Operation of all configurations including their advantages and disadvantages is explained. Impedance type and the fault current limiting devices’ location are two important factors, which significantly affect the DFIG behaviour in the fault condition. These two factors are basically studied by the simulation and their effects on the key parameters of the DFIG are investigated. Finally, future works in respect to the FCL application in the FRT improvement of the DFIG have also been discussed.

An accurate outbreak prediction of COVID-19 can successfully help to get insight into the spread and consequences of infectious diseases. Recently, machine learning (ML) based prediction models have been successfully employed for the prediction of the disease outbreak. The present study aimed to engage an artificial neural network-integrated by grey wolf optimizer for COVID-19 outbreak predictions by employing the Global dataset. Training and testing processes have been performed by time-series data related to January 22 to September 15, 2020 and validation has been performed by time-series data related to September 16 to October 15, 2020. Results have been evaluated by employing mean absolute percentage error (MAPE) and correlation coefficient (r) values. ANN-GWO provided a MAPE of 6.23, 13.15 and 11.4% for training, testing and validating phases, respectively. According to the results, the developed model could successfully cope with the prediction task.

This paper aims to analyze arbitrarily loaded isotropic rectangular thin plates with two opposite edges supported (simply supported or clamped), from which one or both are clamped, and the other edges have arbitrary support conditions. Rectangular thin plates with two opposite edges simply supported are routinely analyzed using for the deflection the simple trigonometric series of Lévy or the double trigonometric series of Navier, while the loads are expanded in Fourier series. In this paper the flexibility method (or force method) of the linear beam theory was applied whereby the unknowns were the bending moments along the opposite edges; in this regard, the primary system was the plate simply supported along the above-mentioned opposite edges and subjected to the external loads, system solved using the Lévy solution, and the redundant system was the plate simply supported along the opposite edges and subjected to bending moments along those edges. In the redundant system, a modified Lévy solution was introduced to account for the edge moments. The compatibility equations (vanishing of the slopes at selected positions of the opposite edges) were set to determine the unknowns and so the efforts in the plate. The results obtained were in good agreement with the exact results.

The ability of thermoresponsive polymers to respond to temperature with a reversible conformational change makes them promising ‘smart’ materials for solutions in medical and biotechnological applications. In this work, two such polymers and structural isomers were studied: poly(N-isopropyl acrylamide) (PNiPAm) and poly(2-isopropyl-2-oxazoline) (PiPOx). We compare the critical solution temperatures (CST) of these polymers in D2O and H2O in the presence of Hofmeister series salts, as results obtained under these different solvent conditions are often compared. D2O has a higher dipole moment and electronegativity than H2O, which could significantly alter the CST transition. We used two complementary methods to measure the CST, dynamic light scattering (DLS) and differential scanning calorimetry (DSC), and found that the CST decreased significantly in D2O compared to H2O. In the presence of highly concentrated kosmotropes, the CST of both polymers decreased in both solvents. The influence of the kosmotropic anions was smaller than the water isotope effect at low ionic strengths but considerably higher at physiological ionic strengths. However, the Hofmeister anion effect was quantitatively different in H2O than in D2O, with the largest relative differences observed for Cl-, where the CSTs in D2O decreased more than in H2O measured by DLS but less by DSC. PiPOx was more sensitive than PNiPAm to the presence of chaotropes. It exhibited much higher transition enthalpies and multistep transitions, especially in aqueous solutions. Our results highlight that measurements of thermoresponsive polymer properties in D2O cannot be compared directly or quantitatively to application conditions or even measurements performed in H2O.

This study compared the performance of five Family Generalized Auto-Regressive Conditional Heteroscedastic (fGARCH) models (sGARCH, gjrGARCH, iGARCH, TGARCH and NGARCH) in the presence of high positive autocorrelation. To achieve this, financial time series was simulated with autocorrelated coefficients as ρ = (0.8, 0.85, 0.9, 0.95, 0.99), at different time series lengths (as 250, 500, 750, 1000, 1250, 1500) and each trial was repeated 1000 times carried out in R environment using rugarch package. And the performance of the preferred model was judged using Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). Results from the simulation revealed that these GARCH models performances varies with the different autocorrelation values and at different time series lengths. But in the overall, NGARCH model dominates with 62.5% and 59.3% using RMSE and MAE respectively. We therefore recommended that investors, financial analysts and researchers interested in stock prices and asset return should adapt NGARCH model when there is high positive autocorrelation in the financial time series data.

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights in quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows to extract high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo which enables calculations on large finite systems. Finite-size scaling can then be used to determine physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

This study investigates the mean annual water temperature trends at the confluence of the Sava and Danube Rivers, along with air temperature trends at the Belgrade meteorological station, spanning from 1956 to 2020. Results reveal a consistent increase in temperature across all three measuring stations, with the Danube experiencing a rise of 0.34°C/10 years, the Sava at 0.44°C/10 years, and Belgrade's air temperature increasing by 0.39°C/10 years. Employing the RAPS method, sharp rises in water temperature were pinpointed in 1989 for the Sava and 1990 for the Danube, while Belgrade's air temperature surge began in 1998. The highest intensity of air temperature increase within the recent period (1998-2020) was observed at the Belgrade observatory, reaching 0.76°C/10 years. Notably, the Sava exhibited a faster increase in water temperature over the last thirty years compared to the Danube. August marked the peak average water temperature for both rivers, while July recorded the highest average air temperature in Belgrade. Despite differing flow rates, both rivers exhibit similar hydrological regimes, with maximum flows occurring in April and minimum flows in August for the Sava, and October for the Danube. Seasonal temperature increases were most pronounced in summer, notably in August, with the smallest rises occurring during cold periods. Additionally, an inverse proportional relationship between mean annual water temperatures and discharges was observed at both river stations.

There is a serious concern regarding framing rules and guidelines to regulate the content on OTT platforms that needs urgent attention. In the Current Scenario, the use of vulgar language in the public domain on OTT platforms needs to take seriously. Some OTT platforms heavenly use foul language, which is open to children that cause a huge psychological impact on them. The use of vulgar language, including profanity and bad words, has to be regulated strictly. Web series uses obscene, abusive words and foul language with excessive usage. This review paper highlights the excessive use of swear words, profane language, and vulgar expletives on OTT platforms.

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.

It is a common practice to detect outliers in a financial time series in order to avoid the adverse effect of additive outliers. This paper investigated the performance of GARCH family models (sGARCH; gjrGARCH; iGARCH; TGARCH and NGARCH) in the presence of different sizes of outliers (small, medium and large) for different time series lengths (250, 500, 750, 1000, 1250 and 1500) using root mean square error (RMSE) and mean absolute error (MAE) to adjudge the models. In a simulation iteration of 1000 times in R environment using rugarch package, results revealed that for small size of outliers, irrespective of the length of time series, iGARCH dominated, for medium size of outliers, it was sGARCH and gjrGARCH that dominated irrespective of time series length, while for large size of outliers, irrespective of time series length, gjrGARCH dominated. The study further leveled that in the presence of additive outliers on time series analysis, both RMSE and MAE increased as the time series length increased.

Introduction Pharmacovigilance may detect safety issues after marketing of medications, and this can result in regulatory action such as direct healthcare professional communications (DHPC). DHPC can be effective in changing prescribing behaviour, however the extent to which prescribers vary in their response to DHPC is unknown. This study aims to explore changes in prescribing and prescribing variation among GP practices following a DHPC on the safety of mirabegron, a medication to treat overactive bladder (OAB). Methods This is an interrupted time series study of English GP practices from 2014-2017. NHS Digital provided monthly statistics on aggregate practice-level prescribing and practice characteristics (practice staff and registered patient profiles, Quality & Outcomes Framework indicators, and deprivation of the practice area). The primary outcome was monthly mirabegron items as a percentage of all OAB drug items. The exposure was a DHPC issued by the European Medicines Agency in September 2015. Variation between practices in mirabegron prescribing before and after the DHPC was assessed using the systematic component of variation (SCV). Multilevel segmented regression with random effects quantified the change in level and trend of prescribing after the DHPC. Practice characteristics were assessed for their association with a reduction in prescribing following the DHPC. Results This study included 7,408 practices. During September 2015, 88.9% of practices prescribed mirabegron and mirabegron composed a mean of 8.2% (SD 6.8) of OAB items. Variation between practices was classified as very high and the median SCV did not change significantly (p=0.11) in the 6 months after the September 2015 DHPC (12.4) compared to before (11.6). Before the DHPC, there was a monthly trend of 0.294 (95%CI, 0.287, 0.301) percentage points increase in mirabegron percentage. There was no significant change in the month immediately after the DHPC (-0.023, 95% CI -0.105 to 0.058) however there was a significant reduction in trend (-0.036, 95% CI -0.049 to -0.023). Higher numbers of registered patients and patients aged ≥65 years, and practice area deprivation were associated with having a significant decrease in level and slope of mirabegron prescribing post-DHPC. Conclusion Variation in mirabegron prescribing was high over the study period and did not change substantively following the DHPC. There was no immediate prescribing change post-DHPC, although the monthly growth did slow. Knowledge of the degree of variation in and determinants of response to safety communications may allow those that do not change prescribing to be provided with additional supports.

Global models have been developed to tackle the challenge of forecasting sets of series that are related or share similarities, but not for heterogeneous datasets. Various methods of partitioning by relatedness have been introduced to enhance the similarities of the set, resulting in improved forecasting accuracy but often at the cost of a reduced sample size, which could be harmful. To shed light on how the relatedness between series impacts the effectiveness of global models in real-world demand forecasting problems we perform an extensive empirical study using the M5 competition dataset. We examined cross-learning scenarios driven by the product hierarchy commonly employed in retail planning, which allow global models to capture interdependencies across products and regions more effectively. Our findings show that global models outperform state-of-the-art local benchmarks by a considerable margin, indicating that they are not inherently more limited than local models and can handle unrelated time series data effectively. The accuracy of data partitioning approaches increases, as the size of the data pools and the models' complexity decrease. However, there is a trade-off between data availability and data relatedness. Smaller data pools lead to increased similarity among time series, making it easier to capture cross-product and cross-region dependencies, but this comes at the cost of a reduced sample, which may not be beneficial. Finally, it's worth noting that the successful implementation of global models for heterogeneous datasets can significantly impact forecasting practice.

This paper aims to discuss the relationship between financial development and inflation in Kenya using time series data between 1973 and 2021. The short- and long-run impact of financial development on inflation remains an important issue in the empirical and theoretical literature especially for country specific, but has yet to receive significant research consideration. For this purpose, the paper uses an ARDL analysis method, which is considered an advanced analytical model. Empirical findings confirmed that financial development has a significant long-run impact on inflation in Kenya. On the contrary, results confirmed that there is no significant short-run effect of financial development on inflation. In addition, there is significant long-run and short-run negative relationship between interest rate and inflation. The results indicate significant long-run Granger and ARDL causality from financial development to inflation. The main policy implications of the empirical results of this paper suggest supervision of financial sector must be directed in a way that would stimulate a stable and a moderate inflation rate. In particular, both financial institution and government should enhance the infrastructures of the financial market and promote the utilisation of financial services.

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.

In this article, we discuss the concept of infinity (∞), infinitesimals □ , and a new mathematical operation that expands calculations into the realm of the infinite. This breakthrough allows for the computation of infinite numbers, leading to new possibilities for mathematical research and practical applications. By introducing infinite numbers, numerous advantages arise, such as accurately representing limits, divergences in integrals and infinite series, and extending calculations to infinity. This mathematical advancement opens doors to exploring uncharted territories, offering valuable insights and breakthroughs.

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.

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.

Through the half-unit circle area computation using the integration of the corresponding curve power series representation, we deduce a slow converging positive infinite series to $\pi$. However, by studying the remainder of that series we establish sufficiently close inequalities with equivalent lower and upper bound terms allowing us to estimate, more precisely, how the series approaches $\pi$. We use the obtained inequalities to compute up to four-digit denominator, what are in this sense, the best rational numbers that can replace $\pi$. It turns out that the well-known convergents of the continued fraction of $\pi$, $22/7$ and $355/113$ called, respectively, Yuel\"{u} and Mil\"{u} in China are the only ones found. Thus we apply a similar process to find rational estimations to $\pi+e$ where $e$ is taken as the power series of the exponential function evaluated at $1$. For rational numbers with denominators less than $2000$, the convergent $920/157$ of the continued fraction of $\pi+e$ turns out to be the only rational number of this type.

For a given set of plasma parameters, along a single series (Lyman, Balmer etc) the lines with higher principal quantum number(n) lines get progressively wider, closer to each other, and start merging for a certain critical n. In the present work four different codes(with further options) are used to calculate the entire Balmer series for moderate and high electron densities. Particular attention is paid to the relevant physics, such as the cutoff criteria, strong and penetrating electron collisions.

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.

With a longer-term goal of addressing the comparative behavior of the aqueous halides F$^-$, Cl$^-$, Br$^-$, and I$^-$ on the basis of quasi-chemical theory (QCT), here we study structures and free energies of hydration clusters for those anions. We confirm that energetically optimal $(\mathrm{H_2O})_n\mathrm{X}$ clusters, with X = Cl$^-$, Br$^-$, and I$^-$, exhibit \emph{surface} hydration structures. Computed free energies based on optimized surface hydration structures utilizing a harmonic approximation, typically (but not always) disagree with experimental free energies. To remedy the harmonic approximation, we utilize single-point electronic structure calculations on cluster geometries sampled from an AIMD (\emph{ab initio} molecular dynamics) simulation stream. This \emph{rough-landscape} procedure is broadly satisfactory and suggests unfavorable ligand crowding as the physical effect corrected. Nevertheless, this procedure can break down when $n \gtrsim 4$, with the characteristic discrepancy resulting from a relaxed definition of clustering in the identification of $(\mathrm{H_2O})_n\mathrm{X}$ clusters, including ramified structures natural in \emph{physical cluster theories.} With ramified structures, the central equation for the present rough-landscape approach can acquire some inconsistency. Extension of these physical cluster theories in the direction of QCT should remedy that issue, and should be the next step in this research direction.

Recently, a layer-stacked ESN model named deep echo state Network (DeepESN) has been established. As an interactional model of recurrent neural network and deep neural network, investigations of DeepESN are of significant importance in both areas. Optimizing the structure of neural networks remains a common task in artificial neural networks, and the question of how many neurons should be used in each layer of DeepESN must be stressed. In this paper, our aim is to solve the problem of choosing the optimized size of DeepESN. Inspired by the sensitive iterative pruning algorithm, a neuronal similarity-based iterative pruning merging algorithm (NS-IPMA) is proposed to iteratively prune or merge the most similar neurons in DeepESN. Two chaotic time series prediction tasks are applied to demonstrate the effectiveness of NS-IPMA. The results show that the DeepESN pruned by NS-IPMA outperforms unpruned DeepESN with the same network size, and NS-IPMA is a feasible and superior approach to improving the generalization performance of DeepESN.

(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 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.

Divergences have become a very useful tool for measuring similarity (or dissimilarity) between probability distributions. Depending on the field of application a more appropriate measure may be necessary. In this paper we introduce a family of divergences we call gamma-divergences. They are based on the convexity property of the functions that generate them. We demonstrate that these divergences verify all the usually required properties, and we extend them to weighted probability distribution. We investigate their properties in the context of kernel theory. Finally, we apply our findings to the analysis of simulated and real time series.

Accurate detection and quantification of regional vegetation trends is essential for understanding the dynamics of landscape ecology and vegetation distribution. We applied a comprehensive trend analysis to satellite data to describe geo-spatial changes in vegetation along the Pacific slope of Peru and northern Chile, from sea level to the continental divide, a region characterised by biologically unique and highly sensitive arid and semi-arid environments. Our statistical analyses show broad regional patterns of positive trends in EVI, called “greening” alongside patterns of “browning” where trends are negative between 2000 and 2020. The coastal plain and foothills, up 1000m, contain notable greening of the coastal Lomas and newly irrigated agricultural lands occurring alongside browning trends related to changes in land use practices and urban development. Strikingly, the precordilleras show a distinct ’greening strip’ which extends from approximately 6°S to 22°S, with an altitudinal trend; ascending from the tropical lowlands (170-780 m) in northern Peru, to the subtropics (1000-2800 m) in central Peru, and temperate zone (2600-4300 m) in southern Peru and northern Chile. We find that the geographical characteristics of the greening strip do not match climate zones previously established by Köppen and Geiger. Greening and browning trends in the coastal deserts and the high Andes lie within well defined climatic and life zones, producing variable but identifiable trends. However, the distinct Pacific slope greening presents an unexpected distribution with respect to the regional Köppen-Geiger climate and life zones. This work provides insights on understanding the effects of climate change on Peru’s diverse ecosystems in highly sensitive, biologically rich arid and semi-arid environments on the Pacific slope.

This study addresses the causal links between external factors and the main hydro-climatic variables. There is a gap in the literature on the description of a complete chain in addressing the structures of direct causal links of solar activity on the terrestrial variables. This is why, the present study uses the extensive facilities of the application of information theory in view of recent advances in different fields. Also, by other methods (e.g. neural networks) first are tested the existence non-linear links of solar-terrestrial influences on hydro-climate system. The results are promising related to the solar impact on terrestrial phenomena which is discriminant in space-time domain. The implications prove robust for determining the causal measure of climate variables under direct solar impact which makes it easier to consider solar activity in climate models, by appropriate parametrizations. This study found that hydro-climatic variables are sensitive to solar impact only for certain frequencies (periods) and these have a coherence with the Solar-Flux only for some lags of the Solar-Flux (in advance).

The Bessel function of the first kind J_N(kx) is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind I_N(kx) . Known polynomial approximations for the range −3≤x≤3 (having five-digit accuracy) are compared with those arising from this Legendre series and substitute versions are given with twice the number of terms and range (with five-digit accuracy or having fifteen-digit accuracy over −3≤x≤3). It is shown that infinite series of like-powered contributors (involving _2F_3 hypergeometric functions) extracted from the Fourier-Legendre series may be summed, having values that are inverse powers of the first five primes 1/(2^i 3^j 5^k 7^l 11^mm) for powers of order x24.

Hepatocellular carcinoma (HCC) is the most frequent type of primary liver cancer. Low numbers of HCC patients being suitable for liver resection or transplantation and multidrug resistance development during pharmacotherapy leads to high death rates for HCC patients. Understanding the molecular mechanisms of HCC aetiology contributes to development of novel therapeutic strategies for prevention and treatment of HCC. UDP-glucose ceramide glycosyltransferase (UGCG), a key enzyme in glycosphingolipid metabolism, generates glucosylceramide (GlcCer), which is the precursor for all glycosphingolipids (GSLs). Since UGCG gene expression is altered in 0.8 % of HCC tumors, GSLs may play a role in cellular processes in liver cancer cells. Here, we discuss current literature about GSLs and their abundance in normal liver cells, Gaucher disease and HCC. Furthermore, we review the involvement of UGCG/GlcCer in multidrug resistance development, globosides as a potential prognostic marker for HCC, gangliosides as a potential liver cancer stem cell marker, and the role of sulfatides in tumor metastasis. Only a limited number of molecular mechanisms executed by GSLs in HCC are known, which we summarize here briefly.

We examine a nonlinear initial value problem both singularly perturbed in a complex parameter and singular in complex time at the origin. The study undertaken in this paper is the continuation of a joined work with A. Lastra published in 2015. A change of balance between the leading and a critical subdominant term of the problem considered in our previous work is performed. It leads to a phenomenon of coalescing singularities to the origin in the Borel plane w.r.t time for a finite set of holomorphic solutions constructed as Fourier series in space on horizontal complex strips. In comparison to our former study, an enlargement of the Gevrey order of the asymptotic expansion for these solutions relatively to the complex parameter is induced.

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.

Data can be illustrated in shapes, and the shapes could provide insight for data modeling and information extraction. Topological data analysis provides an alternative insight in biomedical data analysis and knowledge discovery with the algebra topology tools. In present work, we study the application of topological data analysis for personalized electrocardiographic signal classification toward arrhythmia analysis. Using phase space reconstruction technique, the signal samples are converted into point clouds for topological analysis facility. With topological techniques the persistence landscapes from the point clouds are extracted as features to perform the arrhythmia classification task. We find that the proposed method is robust to the training set size, with only a training set size of 20% percents, the normal heartbeat class are 100% recognized, ventricular beats for 97.13%, supra-ventricular beats for 94.27% and fusion beats for 94.27% within the corresponding experiments. The property of keeping high performance when using smaller training sample proves that the proposed method is especially applicable to personalized analysis. With the present study, we show that the topological data analysis technique could be a useful tool in biomedical signal analysis, and provide powerful ability in personalized analysis.

The concept of graphs with clique-width at most was first introduced by Courcelle et al.to be the graphs that can be characterized using -expressions derived from graph operations that use labels of vertices. If the clique-width for some graph is bounded then a grand number of algorithmic problems, in general NP-hard, can be solved in polynomial time when restricted to this graph. This important fact motivated the researchers to prove that the clique-width of certain graphs is bounded. Following this research direction, we prove in this paper that the clique-width of series-parallel digraphs is at most 6 and we present an time algorithm to construct a 6-expression for this class of digraphs. In another part, we present a linear time recognition algorithm for a similar class of series-parallel digraphs and prove that the clique-width of this class is at most 3.

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.

This article presents the results of reviewing the predictive capacity of Google trends for national elections in Chile. The electoral results of the elections between Michelle Bachelet and Sebastián Piñera in 2006, Sebastián Piñera and Eduardo Frei in 2010, Michelle Bachelet and Evelyn Matthei in 2013, Sebastián Piñera and Alejandro Guillier in 2017, and Gabriel Boric and José Antonio Kast in 2021 were reviewed. The time series analysed were organised on the basis of relative searches between the candidacies, assisted by R software, mainly with the gtrendsR and forecast libraries. With the series constructed, forecasts were made using the ARIMA technique to check the weight of one presidential option over the other. The ARIMA analyses were performed on 3 ways of organising the data: the linear series, the series transformed by moving average and the series transformed by Hodrick-Prescott. The result indicates that the method offers optimal pre-dictive ability.

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.

The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. A spectral observer can be catalogued as an online algorithm for time-frequency analysis because is a method that can compute on the fly the Fourier transform (FT) of a signal, without having the entire signal available from the start. In this regard, this paper presents a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1) the reconstruction of a simple periodical signal, (2) the approximation of both a square and a triangular signal, (3) the edge detection in signals by using the Fourier coefficients, (4) the fitting of the historical Bitcoin market data from 2014-12-01 to 2018-01-08 and (5) the estimation of a input force acting upon a Duffing oscillator. To round out this paper, we present a detailed discussion about the results of the applications as well as a comparative analysis of the proposed spectral observer vis-à-vis the Short Time Fourier Transform (STFT), which is a well-known method for time-frequency analysis.

An earthquake of Mw6.4 hit the coastal zone of Albania on 26 November 2019, at 02:54:11 UTC. It was intensively felt at about 34km far away, in Tirana City, where damages and lives lost occurred. To emphasize a geomagnetic signature before the onset of this earthquake, the data collected on the interval 15 October–30 November 2019, at the Panagjurishte (PAG)-Bulgaria and Surlari (SUA)-Romania observatories are analyzed by using both the polarization parameter (BPOL)-time invariant in non-seismic conditions, becoming unstable before this seismic event, and the strain effect for geomagnetic signal identification. Consequently, BPOL time series and its standard deviations are performed for the both sites using ULF-FFT band-pass filtering. A statistical analysis, based on a standardized random variable equation, was applied to emphasize on the BPOL*(PAG) and ABS BPOL*(PAG) time series the anomalous signal’s singularity and, to differentiate the transient local anomalies due to Mw6.4earthquake, from the internal and external parts of the geomagnetic field, taken PAG observatory as reference. Finally, the ABS BPOL*(PAG-SUA) time series are obtained on the interval 1-30 November, 2019, where a geomagnetic signature greater than 2.0, was detected on 23 November and the lead time was 3 days before the onset of Mw6.4earthquake.

Deep learning has been applied in many areas that have had a significant impact on applications that improves real-life challenges. The success of deep learning in a wide range of areas is due in part to the use of activation functions, which are particularly effective at solving non-linear problems. Activation functions are a key focus for researchers in artificial intelligence who aim to improve the performance of neural networks. This article provides a comprehensive explanation and comparison of different activation functions, with a focus on the arc tangent and its variations specifically. The paper presents experimental results that show that variations of the arc tangent using irrational numbers such as pi, the golden ratio, and Euler’s number, as well as a self-arctan function, produce promising results. Since we experimented with promising activation functions on two different problems, and datasets, we reached a result that different irrationals work well for different problems. In other words, arctan ϕ gives the best results mostly for multiclass classification and arctan e gives the best results for time series prediction problems. The paper focuses on a multiclass classification problem applied to the Reuters Newswire dataset and a time-series prediction problem on Türkiye energy trade value to show the impacts of activation functions.

Significant changes to the new National College Entrance Examination (NCEE) and the implementation of the “Double First-Class” (DFC) initiative in China are coincidentally in the national spotlight and fall within the same policy window. However, few studies have investigated the effects of the new NCEE on the quality of students in DFC universities. By leveraging the 2018-2022 college admission data from Shandong Province, these effects are examined via the interrupted time-series technique. Weighted rankings for liberal arts and science disciplines and the admission ranking coefficient are adopted to ensure comparability before and after the reform. The findings reveal that after the reform, the quality of students in both world-class universities and first-class discipline universities improved, with greater improvements seen in world-class universities. Focusing on urban differences, the quality of students in DFC universities located in second-tier cities is found to have experienced a higher increase as compared with students in the first-tier and new first-tier cities. In addition, the reform has had different impacts on the quality of students in different majors. Furthermore, when selecting postsecondary institutions, high-scoring students prioritize the quality of universities and majors over urban factors. Finally, the implications of the new NCEE in relation to a sustainable development of DFC universities for research, policy, and practice are further discussed.

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 assessment of photovoltaic devices, which convert light energy into electricity, becomes significantly relevant due to the aspiration to reduce pollution on a global scale. In this context, the pursuit of optimizing the efficiency in converting light energy into electrical energy involves exhaustive studies and structural analyses of solar cells, all directed toward achieving this goal. This study introduces a research proposal aimed at analyzing the losses associated with series resistance (Rs). The analysis takes into account each component comprising this resistance, pro-posing a network of resistances that precisely models each of these elements. The aforementioned research focused on simple-structured crystalline silicon cells. During this investigation, the junction depth (xj) of n-p materials was varied with the aim of achieving efficiencies in the range of 12%. However, in the pursuit of this desired efficiency, a significant impact on series resistance was observed when analyzing the I-V curves of the cells obtained in each manufacturing process.

Reservoir computing is a machine learning method that uses the response of a dynamical system to a certain input in order to solve a task. As the training scheme only involves optimising the weights of the responses of the dynamical system, this method is particularly suited for hardware implementation. Furthermore, the inherent memory of dynamical systems which are suitable for use as reservoirs mean that this method has the potential to perform well on time series prediction tasks, as well as other tasks with time dependence. However, reservoir computing still requires extensive task dependent parameter optimisation in order to achieve good performance. We demonstrate that by including a time-delayed version of the input for various time series prediction tasks, good performance can be achieved with an unoptimised reservoir. Furthermore, we show that by including the appropriate time-delayed input, one unaltered reservoir can perform well on six different time series prediction tasks at a very low computational expense. Our approach is of particular relevance to hardware implemented reservoirs, as one does not necessarily have access to pertinent optimisation parameters in physical systems but the inclusion of an additional input is generally possible.

We evaluate various sums involving the powers of Fibonacci and Lucas numbers.

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 semi-nonparametric (SNP) modeling of the return distribution has been proved to be a flexible and accurate methodology for portfolio risk management that allows two-step estimation of the dynamic conditional correlation (DCC) matrix. For this SNP-DCC model, we propose a stepwise procedure to compute pairwise conditional correlations under bivariate marginal SNP distributions, overcoming the curse of dimensionality. The procedure is compared to the assumption of Dynamic Equicorrelation (DECO), which is a parsimonious model when correlations among the assets are not significantly different but requires joint estimation of the multivariate SNP model. The risk assessment of both methodologies is tested for a portfolio on cryptocurrencies by implementing backtesting techniques and for different risk measures: Value-at-Risk, Expected Shortfall and Median Shortfall. The results support our proposal showing that the SNP-DCC model has better performance for a smaller confidence level than the SNP-DECO model, although both models perform similarly for higher confidence levels.

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.

New q-series in the spirit of Jacobi have been found in a publication rst published in 1884 written in Russian and translated into English in 1928. This work was found by chance and appears to be almost totally unknown. From these entirely new q-series, fresh lattice sums have been discovered and are presented here.

Deep learning has been applied in many areas that have had a significant impact on applications that improves real-life challenges. The success of deep learning in a wide range of areas is due in part to the use of activation functions, which are particularly effective at solving non-linear problems. Activation functions are a key focus for researchers in artificial intelligence who aim to improve the performance of neural networks. This article provides a comprehensive explanation and comparison of different activation functions, with a focus on the arc tangent and its variations specifically. The paper presents experimental results that show that variations of the arc tangent using irrational numbers such as pi, the golden ratio, and Euler’s number, as well as a self-arctan function, produce promising results. Since we experimented with promising activation functions on two different problems, and datasets, we reached a result that different irrationals work well for different problems. In other words, arctan ϕ gives the best results mostly for multiclass classification and arctan e gives the best results for time series prediction problems. The paper focuses on a multi-class classification problem applied to the Reuters Newswire dataset and a time-series prediction problem on Türkiye energy trade value to show the impacts of activation functions.

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.

A family of linear singularly perturbed Cauchy problems is studied. The equations defining the problem combine both partial differential operators together with the action of linear fractional transforms. The exotic geometry of the problem in the Borel plane, involving both sectorial regions and strip-like sets, gives rise to asymptotic results relating the analytic solution and the formal one through Gevrey asymptotic expansions. The main results lean on the appearance of domains in the complex plane which remain intimately related to Lambert W function, which turns out to be crucial in the construction of the analytic solutions. On the way, an accurate description of the deformation of the integration paths defining the analytic solutions and the knowledge of Lambert W function are needed in order to provide the asymptotic behavior of the solution near the origin, regarding the perturbation parameter. Such deformation varies depending on the analytic solution considered, which lies in two families with different geometric features.

A nonlinear singularly perturbed Cauchy problem with confluent fuchsian singularities is examined. This problem involves coefficients with polynomial dependence in time. A similar initial value problem with logarithmic reliance in time has been investigated by the author in a recent work, for which sets of holomorphic inner and outer solutions were built up and expressed as a Laplace transform with logarithmic kernel. Here, a family of holomorphic inner solutions are constructed by means of exponential transseries expansions containing infinitely many Laplace transforms with special kernel. Furthermore, asymptotic expansions of Gevrey type for these solutions relatively to the perturbation parameter are established.

Cities exposed their vulnerabilities during COVID-19 pandemic. Unprecedented policies restricted human activities but left an unique opportunity to quantify anthropogenic effects on urban air pollution. This study aimed to address the key questions of urban development behind the restrictions with the goal of supporting sustainable transition. Data from ground stations and Sentinel-5P satellite were used to assess the temporal and spatial anomalies of NO2. Beijing China was selected for a case study because this mega city maintained a “dynamic zero-COVID” policy with adjusted restrictions, allowing us better to track the effects. The time-series decomposition and prediction regression model were employed to estimate the normal NO2 levels in 2020. The anomalies between the observations and predictions as the deviation were identified due to the policy interventions and quantified different effects using spatial stratified heterogeneity statistics. The top three restrictions showing dominant effects were workplace closures, restricted public transport usage, and school closures, accounting for 54.8%, 52.3%, and 46.4% of NO2 anomalies, respectively; and they are directly linked to the mismatch of employment and housing (deter-mining the commuting patterns), educational inequality and the long-term unsolved road con-gestion. Promoting the transformation of urban spatial structure will effectively alleviate air pollution.

This paper draws upon the theory of turbulence in physics to explore the similarities and differences between volatility in financial markets and turbulent phenomena at a statistical physics level. By analogizing the dynamics of financial markets with fluid turbulence, we have developed an innovative analytical framework aimed at deepening the understanding of the complexity inherent in financial markets. Our research methodology includes a comparative analysis of simulated time series data for the Standard & Poor's 500 Index and fully developed turbulent velocity time series. We focus on the similarities in key statistical physical properties, including probability distributions, correlation structures, and power spectral densities. Furthermore, we have established a model of capital flow in financial markets and proposed corresponding solutions. Through computational simulations and data analysis, we find that while financial market volatility shares some statistical characteristics with turbulent phenomena, significant differences exist in the shapes of probability distributions and the temporal scales of correlations. This suggests that although financial markets exhibit patterns akin to turbulence, the behavior of this complex, multi-variable driven system does not completely correspond to natural turbulence, highlighting the limitations of directly applying turbulence theory to financial market analysis. Our study offers a new perspective for the theories of financial markets and the field of econophysics, providing fresh insights into the complexity of financial markets and contributing to the prevention and management of financial risk.

The distribution laws of various natural and anthropogenic processes in the world around us are stochastic in nature. The development of mathematics and, in particular, of stochastic modelling allows us to study regularities in such processes. In practice, stochastic modelling finds a huge number of applications in various fields, including finance and economics. In this work, some particular applications of stochastic processes in finance are examined in the conditions of financial crisis. More specifically, Autoregressive Integrated Moving Average (ARIMA) models and Modified Ordinary Differential Equations (ODE) models, which have been previously developed by the authors to predict assets’ prices of four Bulgarian companies, are validated on a time period during the crisis. Estimated rates of return are calculated from the models for one period ahead. The errors are estimated and the models are compared. The predicted return values with each of the two approaches are used to derive optimal risk portfolios based on the Markowitz Model. The resulting portfolios are compared in terms of distribution (weights of the stocks), risk and rate of return.

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.

Retailers must have accurate sales forecasts to operate their businesses efficiently and effectively and to remain competitive in the marketplace. Global forecasting models like RNNs can be a powerful tool for forecasting in retail settings, where multiple time series are often interrelated and influenced by a variety of external factors. By including covariates in a forecasting model, we can better capture the various factors that can influence sales in a retail setting. This can help improve the accuracy of our forecasts and enable better decision-making for inventory management, purchasing, and other operational decisions. In this study we investigate how the accuracy of global forecasting models is affected by the inclusion of different potential demand covariates. To ensure the significance of the study's findings, we used the M5 forecasting competition's openly accessible and well-established dataset. The results obtained from the DeepAR models, which were trained on various combinations of features including time, price, events, and IDs, suggest that individually only the features corresponding to IDs improve the baseline model. However, when all the features are used together, the best performance is achieved, indicating that the individual relevance of each feature is emphasized when the information is given jointly. Comparing the model with features to the model without features, there is an improvement of 1.76\% for MRMSSE and 6.47\% for MMASE.

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.

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.

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.

We study the problem of predicting time series data using the autoregressive integrated moving average (ARIMA) model in an online manner. Existing algorithms require model selection, which is time consuming and inapt for the setting of online learning. Using adaptive online learning techniques, we develop algorithms for fitting ARIMA models with fewest possible hyperparameters. We analyse the regret bound of the proposed algorithms and examine their performance using experiments on both synthetic and real world datasets

The present study analyzed light emitting diodes (LEDs) as an output load and used a Taylor series to describe the characteristic curve based on the exponential characteristic of voltage and current. A prototype circuit of a flyback LED driver system was established to verify whether the theory is consistent with actual results. This study focused on the exponential relationship of LED voltage and current. Conventional simulations usually used linear models to present LED loads. However, the linear model resulted in considerable error between simulation and actual characteristics. Therefore, this study employed a Taylor series to describe the nonlinear characteristic of an LED load. Through precise calculations with Mathcad computation software, the error was effectively reduced. Moreover, the process clarified the influence of temperature on LEDs, which benefited the characteristic analysis of the entire system. Finally, a realized circuit of 120-W flyback LED drivers was established for conducting theory verification, including theoretic analysis and evaluation of the system design process of the flyback converter. The circuit simulation software SIMPLIS was used to demonstrate the system model, which enabled quick understanding of the system framework established in this study. Regarding LEDs, a commercially available aluminum luminaire was used as the output load. The measured results of the actual circuit and the simulation results were remarkably consistent. For the same system at the same temperature, the error between the simulation and actual results was less than 3%, which proved the reliability of the Taylor series simulation.

A method for measuring the mechanical parameters of viscoelastic polymers by nanoindentation technology was proposed and verified. Through the mechanical response of load-displacement curves at different loading rates, then creep compliances and relaxation modulus were fitted. Polyimide thin film was employed in this research and experiments for five different loading rates were conducted. The fitting load-displacement loading curves obtained by the inversion method were identical to the experimental curves at five different loading rates，confirming the validity of the method. Moreover, with the loading rates increased，the fitting curves were more consistent commensurately with the nanoindentation experiment. DMA experiments were tested, and the generalized Kelvin/ Maxwell model were used for fitting experiment data. Results from DMA tests generally agree well with data from nanoindentation method, thereby verifying the feasibility of the method. The Prony series obtained by the two methods were used to simulate the creep experiments, which further verified the method.

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.

The morphology and the activity of a submarine caldera, Avyssos, at the northern part of Nisyros volcano in the South Aegean Sea (Greece), has been studied by means of remotely operated underwater vehicle dives. The recorded time series of temperature and conductivity over the submarine volcano have been analyzed in terms of the Generalized Moments Method. The findings of the mathematical analysis shed light on the volcanic activity, but also on the morphology (shape) of the submarine volcano. The conductivity time series indicates the volcano is at rest in agreement with other types of observations. On the other hand, temperature fluctuations, which in general describe a multifractal process, show that the submarine caldera operates as an open system that interacts with its surroundings. This type of analysis can be used as an indicator for the state of activity and the morphological structure (closed or open system) of a submarine volcano.

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.