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.

Precision Agriculture is the ability to handle variations in productivity within a field and maximize financial return, optimize resource utilization and minimize impact of the environment. It is also the process of automated data collection, cloud storage and utilization to build robust decision support system. In case of Ethiopia, due to poor communication infrastructure coverage and absence of the state-of-the-art technology in the agriculture sector, implementing precision farming system is a challenging tasks in the domain area. In this work, we proposed a fusion of multiple sensors using IOT and IIOT infrastructure to collect critical data from farming fields to develop precision farming facility for decision makers. The main purpose was to monitor weather variability, automate irrigation process, extract critical soil properties. In addition, we have used time series data collected from sensor devices to build forecasting model. Fusion of multiple IoT device provide a mechanism in the agriculture area to deal with real-time monitoring of crops. It is cost-effective technology and required low-energy with edge computing sensor device. We employed the Message Queuing Telemetry Transport (MQTT) protocol to connect the Industrial/Internet of Things (I/IoT) to the cloud server. The communication between system user and sensor device has been done via cloud using Node-RED platform, web android APIs. The cloud-based Eco-system allows us to aggregate, visualize, and analyze live streams output from each sensor in real-time manner. Finally, we have built time series forecasting model using records collected by each sensor device. Using the multi-variate time series data-set, we have obtained about 99 forecasting accuracy on some important variables. Finally, we have developed mobile and web-based application for the end-user to monitor the proposed system remotely.

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.

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.

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

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.

Abstract The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the cosine function. Here we generalize this MBF to include a fractional parameter, such that the exponential in the previously mentioned integral is replaced by a Mittag-Leffler function. The necessity for this generalization arises from a problem of communication in networks. We find the power series representation of the fractional MBF of the first kind, as well as some differential properties. We give some examples of its utility in graph/networks analysis and mention some fundamental open problems for further investigation.

During disaster response, clouds or darkness can prevent the use of optical images for detecting consequences of natural disasters, including landslides. In these situations, radar images can be used to detect changes more rapidly. However, Synthetic Aperture Radar (SAR) backscatter intensity images are underutilized for landslide detection. Unfortunately, there remains a lack of understanding about how to interpret landslide signatures in SAR imagery. In this study, we investigate how the morphometric features and material properties of landslides, and preexisting land cover, control their expression in SAR backscatter intensity change images. Trends in the spatial and temporal signatures of over 1000 landslides in 30 diverse case studies are investigated, using multi-temporal composites and dense time-series of Sentinel-1 C-band SAR backscatter intensity data. The results show that the orientation of landslide surfaces relative to the sensor, pre-existing land cover, and the roughness of the landslide surface, determine whether landslides will produce an increase or decrease in backscatter intensity values. In certain cases, we can identify morphometric features of landslides (e.g. scarps, transit zone, deposits, ponding) and material properties. Generally, we see that landslides appear most clearly with a strong increase in intensity when they occur in herbaceous vegetation or non-vegetated ground surfaces, due to an increase in surface roughness. While in forested or densely vegetated areas, landslides produce a more complex signature with both decreases due to radar shadow and vegetation removal, and an adjacent edge of increased intensity due to double bounce and direct return from vertical tree trunks and convex edges. In most cases, rough deposits produce an increase in intensity, while smooth deposits (e.g. from mudslides) exhibit specular reflection, and thus show decreased values. Landslides are less visible in cases with pre-event very rough ground, or mixed vegetation conditions. The conceptual model developed can aid interpretation of landslides in SAR imagery, and provide domain knowledge needed to train models for automatic landslide detection.

Since the early 1990s, the European (ESA) and Italian (ASI) space agencies have managed and distributed a huge amount of satellite-recorded SAR data to the research community and private industries. Moreover, the availability of advanced cloud computing services implementing different multi-temporal SAR interferometry techniques allows the generation of deformation time series from massive SAR images. We exploit the information provided by a large PS dataset to determine the temporal trend of ground deformation and the relative deformation rate with millimetric accuracy to analyse the spatial and temporal distribution of land subsidence induced by water pumping from a deep confined aquifer in the Northern Valle Umbra Basin (Central Italy), exploiting 24 years of Permanent Scatterers – Interferometric SAR data archives. The SAR images were acquired between 1992 and 2016 by satellite ERS1/2, ENVISAT and Sentinel 1 ESA missions, and the COSMO-SkyMed ASI mission). We observe ground velocities and deformation geometries between 1992 and 2016, with displacements of more than 70 cm and velocities of up to 55 mm/yr and the results suggest that the shape and position of the surface ground displacement are controlled by the fault activity hidden under the valley deposits.

The design of torsional springs for Series Elastic Actuators (SEAs) is challenging, especially when it comes to balancing good stiffness characteristics and efficient torque robustness. This study focuses on the design of a lightweight, low-cost, and compact torsional spring for use in rotary series elastic actuator (ES-RSEA) of lumbar support exoskeleton. The exoskeleton is used as an assistive device to prevent lower back injuries. The torsion spring was designed following design for manufacturability (DFM) principles, focusing on minimal space and weight. The design process consisted of determining the potential topology and optimizing the selected topology parameters through finite element method (FEM) to reduce equivalent stress. The prototype was made using a waterjet cutting process with low-cost material (AISI-4140-alloy) and tested using a custom-made test rig. The results showed that the torsion spring had a linear torque-displacement relationship with 99% linearity, and the deviation between FEM simulation and experimental measurements was less than 2%. The torsion spring has a maximum torque capacity of 45.7 Nm and a stiffness of 440 Nm/rad. The proposed torsion spring is a promising option for lumbar support exoskeletons and similar applications requiring high stiffness, low weight-to-torque ratio, and cost-effectiveness.

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.

The adoption of digital health technologies accelerated during Covid-19, with concerns over the equity of access due to digital exclusion. Using data from a text-based online mental health service for children and young people we explore the impact of the pandemic on service access and presenting concerns and whether differences were observed by sociodemographic characteristics in terms of access (gender, ethnicity and deprivation). We used interrupted time-series models to assess whether there was a change in the level and rate of service use during the Covid-19 pandemic (April 2020-April 2021) compared to pre-pandemic trends (June 2019-March 2020). Routinely collected data from 61221 service users were extracted for observation, those represented half of the service population as only those with consent to share their data were used. The majority of users identified as female (74%) and White (80%), with an age range between 13 and 20 years of age,. There was evidence of a sudden increase (13%) in service access at the start of the pandemic (RR 1.13 95% CI 1.02, 1.25), followed by a reduced rate (from 25% to 21%) of engagement during the pandemic compared to pre-pandemic trends (RR 0.97 95% CI 0.95,0.98). There was a sudden increase in almost all presenting issues apart from physical complaints. There was evidence of a step increase in the number of contacts for Black/African/Caribbean/Black British (38% increase; 95% CI: 1%-90%) and White ethnic groups (14% increase; 95% CI: 2%-27%) ), the sudden increase in service use at the start of the pandemic for the most (58% increase; 95% CI: 1%-247%) and least (47% increase; 95% CI: 6%-204%) deprived areas. During the pandemic, contact rates decreased, and referral sources change at the start. Findings on access and service activity align with other studies observing reduced service utilisation. The lack of differences in deprivation levels and ethnicity at lockdown suggests exploring equity of access to the anonymous service. The study provides unique insights into changes in digital mental health use during Covid-19 in the UK.

We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter and singular in a complex time variable at the origin. These equations combine differential operators of Fuchsian type in time and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on the complex parameter known as the formal monodromy around 0. Their coefficients and forcing terms comprise polynomial and logarithmic type functions in time and are bounded holomorphic in space. A set of logarithmic type solutions are shaped by means of Laplace transforms relatively to time and parameter and Fourier integrals in space. Furthermore, a formal logarithmic type solution is modeled which represents the common asymptotic expansion of Gevrey type of the genuine solutions with respect to the complex parameter on bounded sectors at the origin.

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.

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.

We present a custom platform that integrates data from several sensors measuring synchronously different variables of the beehive and wirelessly transmits all measurements to a cloud server. There is a rich literature on beehive monitoring. The choice of our work is not to use ready platforms such as Arduino and Raspberry Pi and to present a low cost and power solution for long term monitoring. We integrate sensors that are not limited to the typical toolbox of beehive monitoring such as gas, vibrations and bee counters. The synchronous sampling of all sensors every 5 minutes allows us to form a multivariable timeseries that serves two-ways: a) it provides immediate alerting in case a measurement exceeds predefined boundaries that are known to characterize a healthy beehive, and b) based on historical data predict future levels that are correlated with hive’s health. Finally, we demonstrate the benefit of using additional regressors in the prediction of the variables of interest. The database, the code and a video of the vibrational activity of two months are made open to the interested readers.

The alteration of natural land cover to impervious surfaces during development increases stormwater runoff. Stormwater Control Measures (SCMs) are used to manage water quantity and enhance water quality by restoring the hydrologic cycle altered by development. Often, SCMs have an outflow pipe to handle overflows or to manage the release of water detained when infiltration is not possible. Traditionally, these are static controls (e.g. a small orifice is used to restrict the volume of outflow), however, these systems can be improved by instituting real-time controls (RTC). RTC improve the functionality of SCMs by dynamically controlling outflows to adjust to environmental conditions. A major impediment to the widespread implementation of RTC is the high cost of installation and operation. This study utilized machine learning methods to develop a forecasting approach for the implementation of low-cost RTC that were implemented on a programmable gate of the outlet structure of a multi-stage basin in southeastern Pennsylvania. The goals were to decrease the peak flow exiting the basin during rain events, increase the volume of water detained, decrease the number of overtopping events, maintain healthy vegetation in the basin, and protect the downstream vegetation from erosion. Multiple popular data science algorithms were evaluated including multiple linear regression and long short-term memory. These algorithms were used with a dataset, which consisted of four years of historical sensor data, collected in 5-minute intervals, to train models to predict water levels to optimize operations. The accuracy of 30 models with three different methods of handling missing values were compared. A long short-term memory model configured with a 30-minute lead time produced the best results. Having an approximate same lag time of 30 minutes for the contributing drainage area of the SCM provided a sufficient RTC functioning period to improve the performance of the outlet structure.

: 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.

This article presents the implementation of a model to estimate the future price of commodities in the Brazilian market from time series of short-term technical evaluation. For this, data from two databases were used, one referring to the foreign market (opening values, maximum, minimum, closing, closing adjustment and volume) and the other, from the Brazilian market (the price of the day), considering commodities, sugar, cotton, corn, soybean and wheat. Subsequently, the technical indicators were calculated from the TA-Lib technical analysis library. Pearson’s correlation coefficient was applied, records with low correlation were removed, and then the database was consolidated. From the pre-processed data, Long Short-Term Memory (LSTM) recurrent neural networks were used to perform data prediction at the one and three day interval. These models were evaluated using the mean square error (MSE), obtaining results between 0.00010 and 0.00037 on test data one day ahead, and from 0.00017 to 0.00042 three days ahead. However, based on the results obtained, it was observed that the developed model obtained a promising forecasting performance for all the commodities evaluated. As a main contribution, there is the consolidation of databases that can be used in future scientific research. Furthermore, based on its interpretation, it can assist in decision making regarding the buying and selling of commodities to increase financial gains.

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

Care coordination (CC) for children with special healthcare needs and medical complexity (CSHCN-CMC) is challenging, and medication management is especially difficult for providers, parents/caregivers, and patients alike. While numerous strategies for CC have been suggested and implemented, barriers to medication optimization remain. The report describes the creation of a pediatric clinical pharmacotherapy practice, related standard operating procedures to assure consistent application of screening tools and care provision through comprehensive medication management (CMM), and establishment of a collaborative practice agreement (CPA) to guide drug therapy delegation, monitoring, and modification. The methodology of a prospective case series is also presented to highlight drug therapy problems and their resolution in CSHCN-CMC. Future opportunities to expand the practice for engagement in population health management as well as prior authorization activities on behalf of physicians will be discussed.

The reported study was devoted to the investigation of viscoelastic behavior for solid and porous ultra-high-molecular-weight polyethylene (UHMWPE) under compression. The obtained experimental stress curves were interpreted using a two-term Prony series to represent the superposition of two coexisting activation processes corresponding to long molecular (~160 s) and short structural (~20 s) time scales, respectively, leading to good statistical correlation with the observations. In the case of porous polymer, the internal strain redistribution during relaxation was quantified using Digital Image Correlation (DIC) analysis. The strongly inhomogeneous deformation of the porous polymer was found not to affect the relaxation times. In order to generalize the results to three dimensions, X-ray tomography was used to examine the porous structure at the macro- and micro-scale levels. DIC analysis revealed positive correlation between the applied force and relative density. The apparent stiffness variation for UHMWPE foams with mixed open and closed cells was described using a newly proposed three-term expression. Furthermore, the in situ tensile loading and X-ray scattering study was applied for isotropic solid UHMWPE specimens to investigate their parameters of internal structure during orientation and stress relaxation process at another mode.

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 electric power distribution utility is responsible for providing energy to consumers in a continuous and stable way, failures in the electrical power system reduce the reliability indexes of the grid, directly harming its performance. For this reason, there is a need for failure prediction to reestablish power in the shortest possible time. Considering an evaluation of the number of failures over time, this paper proposes to perform a failure prediction during the first year of the pandemic in Brazil (2020) to verify the feasibility of using time series forecasting models for fault prediction. The Long Short-Term Memory (LSTM) model will be evaluated to obtain a forecast result that can be used by the electric power utility to organize the maintenance teams. The Wavelet transform shows to be promising in improving the predictive ability of the LSTM, making the Wavelet LSTM model suitable for the study at hand. The results show that the proposed approach has better results regarding the evaluation of the error in prediction and has robustness when a statistical analysis is performed.

Increasingly measured data in the context of smart cities can be used to develop new and innovative business models to increase efficiency and the value of life. A time-series classification algorithm can support to automatize many different processes such as forecasting services. In order to ensure data security and privacy, Federated Learning trains a global model collaboratively on multiple clients. Having different data-distributions and data-quantities across participating clients, neural networks suffer from slow convergence and overfitting. Based on different data-distributions, data-quantities and number of clients, we develop and evaluate different data-clustering strategies to update global model weights in comparison to the state of the art. We use public time-series data, generate various synthetic datasets and train a Relational-Regularized Autoencoder for classification purposes. Our results show an improvement of model performance concerning generalization.

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

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

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.

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.

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

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

The 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.

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

Context: Anomaly detection in a data center is a challenging task, having to consider different services on various resources. Current literature shows the application of artificial intelligence techniques to either log files or monitoring data: the former created by services at run time, while the latter produced by specific sensors directly on the physical or virtual machine. Objectives: We propose a model that exploits information both in log files and monitoring data to identify patterns and detect anomalies over time. Methods: The key idea is to use on one side natural language processing solutions to detect problems at service level, extracting words that represent anomalies. Clustering and topic modeling techniques have been used to identify patterns and group them with respect to topics. On the other side time series anomaly detection technique has been applied to sensors data in order to combine problems found in the log files with problems stored in the monitoring data. Results: We have tested our approach on a real data center equipped with log files and monitoring data that can characterize the behaviour of physical and virtual resources in production. We have observed a correspondence between anomalies in log files and monitoring data, e.g. an increase in memory usage or machine load. The results are extremely promising. Conclusion: Our model requires to integrate site administrators' expertise in order to consider all critical scenario in the data center and understand results properly.

Lumbar support exoskeletons with active and passive actuators are currently the cutting-edge technology for preventing back injuries in workers while lifting heavy objects. However, many challenges still exist in both types of exoskeletons, including rigid actuators, risks of human-robot interaction, high battery consumption, bulky design, and limited assistance. In this paper, the design of a compact, lightweight energy storage device combined with rotary series elastic (ES-RSEA) is proposed for use in a lumbar support exoskeleton to increase the level of assistance and exploit the human bioenergy during the two stages of the lifting task. ES takes the responsibility to store and release passive mechanical energy while RSEA provides excellent compliance and prevents injury from the human body's undesired movement. The experimental tests on the spiral spring showed excellent linear characteristics (above 99%) with an actual spring stiffness of 9.96 Nm/rad. The results demonstrate that ES-RSEA can provide maximum torque assistance in the ascent phase with 66.6 Nm while generating nearly 21 Nm of spring torque during descent without turning on the DC motor. Ultimately, the proposed design can maximize the energy storage of human energy, exploit the biomechanics of lifting tasks, and reduce the burden on human effort to perform lifting tasks.

Photoplethysmography is a widely used technique to noninvasively assess heart rate, blood pressure, and oxygen saturation. This technique has a large potential for further applications, for example in the field of physiological and mental health monitoring. However, advanced applications of photoplethysmography have been hampered by the lack of accurate and reliable methods to analyze the characteristics of the complex nonlinear dynamics of the photoplethysmogram. Methods of nonlinear time series analysis may be used to estimate the dynamical characteristics of the photoplethysmogram but they are highly influenced by the length of the time series, which is often limited in practical photoplethysmography applications. The aim of this study was to evaluate the error in the estimation of the dynamical characteristics of the photoplethysmogram associated to the limited length of the time series. The dynamical properties were evaluated using recurrence quantification analysis, and the estimation error was computed as a function of the length of the time series. Results demonstrated that properties such as de-terminism and entropy can be estimated with an error lower than 1% even for short photople-thysmogram recordings. Additionally, the lower limit for the time series length to estimate the average prediction time was computed.

In this part of the series of two papers, we extend the theorems discussed in part I for infinite series. We then use these theorems to develop distinct novel results involving the Hurwitz zeta function, Riemann zeta function, Polylogarithm and Fibonacci numbers. In continuation, we obtain some zeros of the newly developed zeta functions and explain their behaviour using plots in complex plane. Furthermore, we provide particular cases for the theorems and corollaries which show that our results generalise the currently available functions and series such as the Riemann zeta function and the geometric series. Finally, we provide four miscellaneous examples to showcase the vast scope of the developed theorems.

We present a novel method for interpolating univariate time series data. The proposed method combines multi-point fractional Brownian bridges, a genetic algorithm, and Takens’ theorem for reconstructing a phase space from univariate time series data. The basic idea is to first generate a population of different stochastically interpolated time series data, and secondly, to use a genetic algorithm to find the pieces in the population which generate the smoothest reconstructed phase space trajectory. A smooth trajectory curve is hereby found to have a low variance of second derivatives along the curve. For simplicity, we refer to the developed method as PhaSpaSto-interpolation, which is an abbreviation for phase-space-trajectory-smoothing stochastic interpolation. The proposed approach is tested and validated with a univariate time series of the Lorenz system, five non-model data sets and tested against a cubic spline interpolation and a linear linear interpolation. We find that the criterion for smoothness guarantees low errors on known model and non-model data. Finally, we interpolate the discussed non-model data sets, and show the corresponding improved phase space portraits. The proposed method is useful for interpolating low-sampled time series data sets for, e.g., machine learning, regression analysis, or time series prediction approaches.

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 family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

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.

Demographic change is leading to the aging of German society. As long as the baby boom co-horts are still of working age, the working population will also age - and decline as soon as this baby boom generation gradually reaches retirement age. At the same time, there has been a trend towards increasing absenteeism (times of inability to work) in companies since the zero years, with the number of days of absence increasing with age. We present a novel stochastic forecast approach that combines population forecasting with forecasts of labor force participation trends, considering epidemiological aspects. For this, we combine a stochastic Monte Carlo-based cohort-component forecast of the population with projections of labor force participation rates and morbidity rates. This article examines the purely demographic effect on the economic costs associated with such absenteeism due to the inability to work. Under expected future employment patterns and constant morbidity patterns, absenteeism is expected by close to 5 percent by 2050 relative to 2020, associated with increasing economic costs of almost 3 percent. Our results illustrate how strongly the pronounced baby boom/ baby bust phenomenon determines demographic development in Germany in the midterm.

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

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

Commercial buildings are a significant consumer of energy worldwide. Logistics facilities, and specifically warehouses, are a common building type yet under-researched in the demand-side energy forecasting literature. Warehouses have an idiosyncratic profile when compared to other commercial and industrial buildings with a significant reliance on a small number of energy systems. As such, warehouse owners and operators are increasingly entering in to energy performance contracts with energy service companies (ESCOs) to minimise environmental impact, reduce costs, and improve competitiveness. ESCOs and warehouse owners and operators require accurate forecasts of their energy consumption so that precautionary and mitigation measures can be taken. This paper explores the performance of three machine learning models (Support Vector Regression (SVR), Random Forest, and Extreme Gradient Boosting (XGBoost)), three deep learning models (Recurrent Neural Networks (RNN), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU)), and a classical time series model, Autoregressive Integrated Moving Average (ARIMA) for predicting daily energy consumption. The dataset comprises 8,040 records generated over an 11-month period from January to November 2020 from a non-refrigerated logistics facility located in Ireland. The grid search method was used to identify the best configurations for each model. The proposed XGBoost models outperform other models for both very short load forecasting (VSTLF) and short term load forecasting (STLF); the ARIMA model performed the worst.

We developed a novel approach in the field of spatiotemporal modelling, based on the spatialisation of time: the Timescape algorithm. It is especially aimed at sparsely distributed datasets in ecological research, whose spatial and temporal variability is strongly entangled. The algorithm is based on the definition of a spatiotemporal distance that incorporates a causality constraint and that is capable of accommodating the seasonal behaviour of the modelled variable as well. The actual modelling is conducted exploiting any established spatial interpolation technique, substituting the ordinary spatial distance with our Timescape distance, thus sorting, from the same input set of observations, those causally related to each estimated value at a given site and time. The notion of causality is expressed topologically and it has to be tuned for each particular case. The Timescape algorithm originates from the field of stable isotopes spatial modelling (isoscapes), but in principle it can be used to model any real scalar random field distribution.

Background: Jerusalem artichoke (Helianthus tuberosus L.) is tolerant to salinity stress and has high economic value. The salt tolerance mechanisms of Jerusalem artichoke are still unclear. Especially in the early stage of Jerusalem artichoke exposure to salt stress, the plant physiology, biochemistry and gene transcription are likely to undergo large changes. Elucidating these changes may be of great significance to understanding the salt tolerance mechanisms of it. Results: We obtained high-quality transcriptome from leaves and roots of Jerusalem artichoke exposed to salinity (300 mM NaCl) for 0 h, 6 h, 12 h, 24 h and 48 h, with 150,129 unigenes and 9023 DEGs (Differentially Expressed Genes). The RNA-seq data were clustered into time-dependent groups (nine clusters each in leaves and roots); gene functions were distributed evenly among the groups convergence. KEGG enrichment analysis showed the genes related to plant hormone signal transduction were enriched in almost all treatment comparisons. Under salt stress, genes belongs to PYL (abscisic acid receptor PYR / PYL family), PP2C (Type 2C protein phosphatases), GH3 (Gretchen Hagen3), ETR (ethylene receptor), EIN2/3 (ethylene-insensitive protein 2/3), JAZ (Genes such as jasmonate ZIM-domain gene) and MYC2 (Transcription factor MYC2) had extremely similar expression patterns. The results of qPCR of 12 randomly selected genes confirmed the accuracy of RNA-seq. Conclusions: Under the impact of high salinity (300mM) environment, Jerusalem artichoke in the seedling stage was difficult to survive for a long time, and the phenotype was severe in the short term. Based on the expression of genes on the time scale, we found that the distribution of gene functions in time is relatively even. Upregulation of the phytohormone signal transduction had a crucial role in the response of Jerusalem artichoke seedlings to salt stress, the genes of abscisic acid, auxin, ethylene, and jasmonic acid had the most obvious change pattern.

We examine a family of linear partial differential equations both singularly perturbed in a complex parameter and singular in complex time at the origin. These equations entail forcing terms which combine polynomial and logarithmic type functions in time and that are bounded holomorphic on horizontal strips in one complex space variable. A set of sectorial holomorphic solutions are built up by means of complete and truncated Laplace transforms w.r.t time and parameter and Fourier inverse integral in space. Asymptotic expansions of these solutions relatively to time and parameter are investigated and two distinguished Gevrey type expansions in monomial and logarithmic scales are exhibited.

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.

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

The work consisted in identifying possible effects from heavy metals (HMs) pollution due to waste disposal activities in three potentially polluted sites located in Basilicata (Italy), where a release of pollutants with values over the thresholds allowed by the Italian legislation was detected. The potential variations in the physiological efficiency of vegetation have been analyzed through the multitemporal processing of satellite images. In detail, Landsat 5 Thematic Mapper (TM) and Landsat 8 Operational Land Imager (OLI) images were used to calculate the Normalized Difference Vegetation Index (NDVI) trend over the years. Then, the multitemporal trends were analyzed using the median of Theil-Sen, a non-parametric estimator particularly suitable for the treatment of remote sensing data, being able to minimize the outlier effects due to exogenous factors. Finally, the subsequent application of the Mann-Kendall test on the trends identified by Theil-Sen slope allowed the evaluation of trends significance and, therefore, the areas characterized by the effects of contamination on vegetation. The application of the procedure to the three survey sites led to the exclusion of the presence of significant effects of HMs contamination on the vegetation surrounding the sites during the years of waste disposal activities.

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.

Physical processes play important roles in controlling eutrophication and oligotrophication. In stratified lakes, internal waves can cause vertical transport of heat and nutrients without breaking the stratification, through boundary mixing events. Such is the case in tropical Valle de Bravo (VB) lake, where strong diurnal winds drive internal waves, boundary mixing and hypolimnetic warming during stratification periods. We monitored VB during 18 years (2001-2018) when important water-level fluctuations (WLF) occurred, affecting mixing and nutrient flux. Mean hypolimnetic temperature increase (0.06–1.04°C month-1) occurred in all the stratifications monitored. We analyzed temperature distributions and modeled the hypolimnion heat budget to assess vertical mixing between layers (26,618–140,526 m-3h-1), vertical diffusivity coefficient KZ (6.2x10-7–3.3x10-6 m2s-1) and vertical nutrient entrainment to epilimnion on monthly scale. Stability also varied as a function of WLF. Nutrient flux to the epilimnion ranged 0.36–5.99 mg m-2d-1 for soluble reactive phosphorus (SRP) and 5.8–97.1 mg m-2d-1 for dissolved inorganic nitrogen (DIN). During low water-level years, vertical nutrient fluxes increase and can account for up to >40% of the total external nutrients load to the lake. Vertical mixing changes related to WLF affect nutrient recycling, their flux to sediments, ecosystemic metabolic balance and planktonic composition of VB.

We investigate the power of time series analysis based on a variety of information-theoretic approaches from statistics (AIC, BIC) and machine learning (Minimum Message Length) - and we then compare their efficacy with traditional time series model and with hybrids involving deep learning. More specifically, we develop AIC, BIC and Minimum Message Length (MML) ARMA (autoregressive moving average) time series models - with this Bayesian information-theoretic MML ARMA modelling already being new work. We then study deep learning based algorithms in time series forecasting, using Long Short Term Memory (LSTM), and we then combine this with the ARMA modelling to produce a hybrid ARMA-LSTM prediction. Part of the purpose of the use of LSTM is to seek capture any hidden information in the residuals left from the traditional ARMA model. We show that MML not only outperforms earlier statistical approaches to ARMA modelling, but we further show that the hybrid MML ARMA-LSTM models outperform both ARMA models and LSTM models.

A major task in Functional Time Series Analysis is measuring the dependence within and between processes, for which lagged covariance and cross-covariance operators have proven to be a practical tool in well-established spaces. This article deduces estimators and asymptotic upper bounds of the estimation errors for lagged covariance and cross-covariance operators of processes in Cartesian products of abstract Hilbert spaces for fixed and increasing lag and Cartesian powers. We allow the processes to be non-centered, and to have values in different spaces when investigating the dependence between processes. Also, we discuss features of estimators for the principle components of our covariance operators.

Ho Chi Minh City (HCMC), the most crowded city and economic hub of Viet Nam, has been experiencing land subsidence over the past decades. This effort aims to contribute the spatial distribution of subsidence in HCMC in its horizontal and vertical components using synthetic aperture radar interferometry (InSAR) time series. To this purpose, an advanced Persistent Scatterers and Distributed Scatterers (PSDS) InSAR technique was applied to two European Space Agency (ESA) Sentinel-1 datasets consisting of 96 ascending and 202 descending images, acquired from 2014 to 2020 over the HCMC area. A time series of 33 COSMO-SkyMed ascending images was also used for comparison. The combination of ascending and descending satellite passes is used to decompose the light of sight velocities into horizontal east-west and vertical components. Taking into account the presence of east-west horizontal motion, our findings indicate that the accuracy of the decomposed vertical velocity can be improved by up to 3 mm/year for Sentinel-1 data. The obtained results revealed that subsidence is most pronounced in the areas along the Sai Gon River, in the northwest-southeast axis, and in the southwest of the city, with a maximum value of 80 mm/yr, which is in accordance with the findings of the literature. The amplitude of east-west horizontal velocities is relatively small and large-scale eastward movement can be observed in the west of the city at a rate of 3-5 mm/yr. This confirmed that the displacement in Ho Chi Minh City area is mainly vertical downward. Together, these results reinforced the remarkable suitability of ESA's SAR Sentinel-1 for subsidence applications, even for non-European countries such as Vietnam and Southeast Asia.

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.

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.

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.

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 evaluate some binomial cubic Fibonacci sums.

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

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

Nighttime lights (NTL) are a popular type of data for evaluating economic performance of regions and economic impacts of various shocks and interventions. Several validation studies use traditional statistics on economic activity like national or regional Gross Domestic Product (GDP) as a benchmark to evaluate the usefulness of NTL data. Many of these studies rely on dated and imprecise Defence Meteorological Satellite Program (DMSP) data and use aggregated units such as nation-states or the first sub-national level. Yet applied researchers who draw support from validation studies to justify their use of NTL data as a proxy for economic activity increasingly focus on smaller and lower level spatial units. This study uses a 2001-19 time-series of GDP for over 3100 US counties as a benchmark to examine the usefulness of the recently released version 2 VIIRS nighttime lights (V.2 VNL) products as proxies for local economic activity. Contrasts are made between cross-sectional predictions for GDP differences between areas and time-series predictions of GDP changes within areas. Disaggregated GDP data for various industries are used to examine what types of economic activity are best proxied by NTL data and comparisons are also made with the predictive performance of earlier NTL data products.

The design flood concept (DF) provides for an essential tool in designing the hydraulic works, in defining the reservoir operation programs and for a reliable flood hazard identification. Under a simplified approach, the maximum discharge and the floods volume are statistically processed to reasonably define the DF. Yet, the integral hydrograph provides additional key temporal and quantitative details of important significance for flood management and particularly for the res-ervoirs operation and associated risks of failures. The procedure presented in this paper (as applied on a set of compatibly shaped hydrographs) involves the following key stages: (i) normalize the floods, (ii) define similar flood shape classes and (iii) evaluate the average dimensionless flood (ADF) for each class. The ADFs are finally transformed into a set of (DF)s. Many statistical distributions approximate acceptably the frequent values of the maximum discharges or the flood volumes, yet displaying a significant spread for medium or rare probabilities of exceedance (PE). This scattering, which can be explained by the epistemic uncertainty, defines an area of uncertainty both for measured and extrapolated values. In considering upper and lower values of the uncertainty in-tervals as limits for maximum discharges and flood volumes, then by combining them compatibly, a set of DFs - as completely defined hydrographs, with different shapes - results for each PE. The herein proposed procedure defines both one peak DF and multi-peaks DF. Subsequently, such DFs do assist water managers in examining and establishing tailored approaches for a variety of input hydrographs. Among the DFs that would correspond to a same PE, the most compact floods arise a special interest, for they are basic in defining the set of safe operation rules for hydraulic structures.

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.

The use of Artificial Neural Networks (ANN) is a great contribution to medical studies since the application of forecasting concepts allows the analysis of future diseases propagations. In this context, this paper presents a study of the new coronavirus SARS-COV-2 with a focus on verifying the virus propagation associated with mitigation procedures and massive vaccination campaigns. There were proposed two methodologies to predict 28 days ahead the number of new cases, deaths, and ICU patients of five European countries: Portugal, France, Italy, United Kingdom, and Germany, and a case study of the results of massive immunization in Israel. The data input of cases, deaths, and daily ICU patients was normalized to reduce discrepant numbers due to the countries size, and the cumulative vaccination values by the percentage of population immunized, at least with one dose of vaccine. As a comparative criterion, the calculation of the mean absolute error (MAE) of all predictions presents the best methodology and targets other possibilities of use for the proposed method. The best architecture achieved a general MAE for the 1 to 28 days ahead forecast lower than 30 cases, 0,6 deaths and 2,5 ICU patients by million people.

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

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

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.

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).

Since December 2019, the coronavirus disease (COVID-19) has rapidly spread worldwide. The Mexican government has implemented public safety measures to minimize the spread of the virus. In this paper, the authors use statistical models in two stages to estimate the total number of coronavirus (COVID-19) cases per day at the state and national level in Mexico. Two types of models are proposed: first, a polynomial model of the growth for the first part of the outbreak until the inflection point of the pandemic curve and then a second nonlinear growth model is used to estimate the middle and the end of the outbreak. Model selection will be performed using Vuong’s test. The proposed models show overall fit similar to predictive models (e.g. time series, and machine learning); however, the interpretation of parameters is less complex for decision-makers and the residuals follow the expected distribution when fitting the models without autocorrelation being an issue.

A signal analysis of the genoma sequenced of coronavirus variants: B.1.1.7, B.1.135, B.1.429-B.1.427, B.1.525 and P1 is presented. We deal with a certain type of finite alternating sum series having independently distributed terms associated with binary (0,1) indicators for the nucleotide bases A,C,G,T. This method provides additional information to conventional Similarity comparisons and Power Spectrum approaches. It leads to uncover distinctive patterns regarding the intrinsic data organization of genomic sequences according to its progression along the nucleotide bases position. Hence, the method could be useful for survelliance of genoma variants.

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<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<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.

For analysis tasks, time counts are of interest — values recorded at some, usually equidistant, points in time. The calculation can be performed at various intervals: after a minute, an hour, a day, a week, a month, or a year, depending on how much detail the process should be analyzed. In time series analysis problems, we deal with discrete-time, when each observation of a parameter forms a time frame. The same can be said about the behavior of Covid-19 over time.In this paper, we solve the problem of predicting Covid-19 diseases in the world using neural networks. This approach is useful when it is necessary to overcome difficulties related to non-stationarity, incompleteness, unknown distribution of data, or when statistical methods are not completely satisfactory. The problem of forecasting is solved with the help of the analytical platform Deductor Studio, developed by specialists of the company Intersoft Lab of the Russian Federation. When solving this problem, appropriate methods were used to clean the data from noise and anomalies, which ensured the quality of building a predictive model and obtaining forecast values for tens of days ahead. The principle of time series forecasting was also demonstrated: import, seasonal detection, cleaning, smoothing, building a predictive model, and predicting Covid-19 diseases in the world using neural technologies for 30 days ahead.

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

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.

We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.

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.

(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.

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

Natural circulation loop (NCL) systems are buoyancy-driven heat exchangers that are used in various industrial applications. The concept of passive heat exchange in NCL systems is attractive, because there is no need for an externally driven equipment (e.g., a pump) to maintain the fluid circulation. However, relying on buoyancy as the sole driving force may lead to several potential difficulties, one of which is generation of (possibly) time-varying nonlinearities in the dynamical system, where a difference in the time scales of heat transfer and fluid flow causes the flow to change from a steady-state regime to either an oscillatory regime or a flow-reversal regime, both of which are undesirable. In this paper, tools of symbolic time series analysis (e.g., probabilistic finite state automata (PFSA)) are proposed to identify selected regimes of operation in NCL systems, where the underlying principle is built upon the concept of pattern classification from measurements of fluid-flow dynamics. The proposed method is shown to be capable of identifying the current regime of operation from the initial time response under a given set of operational parameters. The efficacy of regime classification is demonstrated by testing on two data sets, generated from numerical simulation of a MATLAB SimuLink model that has previously been validated with experimental data. The results of the proposed PFSA-based classification are compared with those of a hidden Markov model (HMM) that serves as the baseline.

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.

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.

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 spatiotemporal variability of vegetation in the Middle East was investigated for the period 2001–2019 using the Moderate Resolution Imaging Spectroradiometer (MODIS) 16-day/500 m composites of the Normalized Difference Vegetation Index (NDVI; MOD13A1). The results reveal a strong increase in the NDVI coverage in the Middle East during the study period (R = 0.75, p-value = 0.05). In Egypt, the annual coverage exhibits the strongest positive trend (R = 0.99, p-value = 0.05). In Turkey, both the vegetation coverage and density increased from 2001 to 2019, which can be attributed to the construction of some of the biggest dams in the Middle East, such as the Atatürk and Ilisu dams. Significant increases in the annual coverage and maximum and average NDVI in Saudi Arabia are due to farming in the northern part of the country for which groundwater and desalinated seawater are used. The results of this study suggest that the main factors affecting the vegetation coverage in the Middle East are governmental policies. These policies can have a positive effect on the vegetation coverage in some countries such as Egypt, Saudi Arabia, Qatar, Kuwait, Iran, and Turkey.

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

In this article, author performs computational analysis for the generalized zeta functions by using computational software Mathematica. To achieve the purpose recently obtained difference equations are used. These difference equations have a computational power to compute these functions accurately while they can not be computed by using their known integral represenations. Several authors investigated such functions and their analytic properties, but no work has been reported to study the graphical representations and zeors of these functions. Author performs numerical computations to evaluate these functions for different values of the involved parameters. Taylor series expansions are also presented in this research.

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.

Lake Malombe fish stocks have been depleted by chronic overfishing. Various management approaches (co-management, command control, and ecosystem-based management to fisheries) have been used to manage the fishery. However, the lack of an accurate predictive model has hampered their success. Therefore, we developed and tested a time series model for Lake Malombe fishery. The seasonal fish biomass and CPUE trends were first observed and both were non-stationary. The second-order differencing was applied to transform the non-stationary data into stationary. Autocorrelation functions (AC), partial autocorrelation function (PAC), and Akaike information criterion (AIC) were estimated, which led to the identification and construction of autoregressive integrated moving average (ARIMA) models, suitable in explaining the time series and forecasting. The results showed that ARIMA (1,2,1) provided a better prediction than its counterparts. The model satisfactorily predicted that by 2032, both fish biomass and CPUE will decrease to 3204.6 tons and 59.672 respectively, signifying the potential threat to Lake Malombe fishery. The model justified the necessity of taking precautionary measures to avoid the total collapse of the fishery.

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.

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.

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

This paper is a slightly modified, abridged version of a previous work ``Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference ``Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

Monitoring drought impacts in forest ecosystems is a complex process, because forest ecosystems are composed of different species with heterogeneous structural compositions. Even though forest drought status is a key control on the carbon cycle, very few indices exist to monitor and predict forest drought stress. The Forest Drought Indicator (ForDRI) is a new monitoring tool developed by the National Drought Mitigation Center (NDMC) to identify forest drought stress. ForDRI integrates 12 types of data, including satellite, climate, evaporative demand, ground water, and soil moisture, into a single hybrid index to estimate tree stress. The model uses Principal Component Analysis (PCA) to determine the contribution of each input variable based on its covariance in the historical records (2003–2017). A 15-year time series of 780 ForDRI maps at a weekly interval were produced. The ForDRI values at a 12.5km spatial resolution were compared with normalized weekly Bowen ratio data, a biophysically based indicator of stress, from nine AmeriFlux sites. There were strong and significant correlations between Bowen ratio data and ForDRI at sites that had experienced intense drought. In addition, tree ring annual increment data at eight sites in four eastern U.S. national parks were compared with ForDRI values at the corresponding sites. The correlation between ForDRI and tree ring increments at the selected eight sites during the summer season ranged between 0.46 and 0.75. Generally, the correlation between the ForDRI and normalized Bowen ratio or tree ring increment are reasonably good and indicate the usefulness of the ForDRI model for estimating drought stress and providing decision support on forest drought management.

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

There is a lack of knowledge concerning the effects of ambient heat exposure on morbidity in Northern Europe. Therefore, this study aimed to evaluate the relationships of daily summer-time temperature and heatwaves with cardiorespiratory hospital admissions in the Helsinki metropolitan area, Finland. Methods: Time-series models adjusted for potential confounders such as air pollution were used to investigate the associations of daily temperature and heatwaves with cause-specific cardiorespiratory hospital admissions, during summer months of 2001-2017. Daily number of hospitalizations was obtained from the national hospital discharge register, weather information from the Finnish Meteorological Institute. Results: Increased daily temperature was associated with decreased risk of total respiratory hospital admissions and asthma. Heatwave days were associated with 20.5% (95% CI: 6.9, 35.9) increased risk of pneumonia admissions and during long or intense heatwaves also with total respiratory admissions in the oldest age group (≥ 75 years). There were also suggestive positive associations between heatwave days and admissions due to myocardial infarction and cerebrovascular diseases. In contrast, risk of arrhythmia admissions was decreased 20.8% (95% CI: 8.0, 31.8) during heatwaves. Conclusions: Heatwaves, rather than single hot days, are a health threat affecting the morbidity even in a Northern climate.

Conditional heteroskedastic financial time series are commonly modelled by (G)ARCH processes. ARCH(1) and GARCH were recently established in C[0,1] and L^2[0,1]. This article provides sufficient conditions for the existence of strictly stationary solutions, weak dependence and finite moments of (G)ARCH processes for any order in C[0,1] and L^p[0,1]. It deduces explicit asymptotic upper bounds of estimation errors for the shift term, the complete (G)ARCH operators and the projections of ARCH operators on finite-dimensional subspaces. The operator estimaton is based on Yule-Walker equations, and estimating the GARCH operators also involves a result estimating operators in invertible linear processes being valid beyond the scope of (G)ARCH. Moreover, our results regarding (G)ARCH can be transferred to functional AR(MA).

To minimise environmental impact, avoid regulatory penalties, and improve competitiveness, energy-intensive manufacturing firms require accurate forecasts of their energy consumption so that precautionary and mitigation measures can be taken. Deep learning is widely touted as a superior analytical technique to traditional artificial neural networks, machine learning, and other classical time series models due to its high dimensionality and problem solving capabilities. Despite this, research on its application in demand-side energy forecasting is limited. We compare two benchmarks (Autoregressive Integrated Moving Average (ARIMA), and an existing manual technique used at the case site) against three deep learning models (simple Recurrent Neural Networks (RNN), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU)) and three machine learning models (Support Vector Regression (SVM), Random Forest, and K-Nearest Neighbors (KNN)) for short term load forecasting (STLF) using data from a Brazilian thermoplastic resin manufacturing plant. We use the grid search method to identify the best configurations for each model, and then use Diebold-Mariano testing to confirm the results. Results suggests that the legacy approach used at the case site is the worst performing, and that the GRU model outperformed all other models tested.

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.