Series Of Transformations Research Articles

Variable-wise generative adversarial transformer in multivariate time series anomaly detection

Variable-wise generative adversarial transformer in multivariate time series anomaly detection

Lambert series of logarithm, the derivative of Deninger’s function $R(z),$ and a mean value theorem for $\zeta \left (\frac {1}{2}-it\right )\zeta '\left (\frac {1}{2}+it\right )$

AbstractAn explicit transformation for the series $\sum \limits _{n=1}^{\infty }\displaystyle \frac {\log (n)}{e^{ny}-1}$ , or equivalently, $\sum \limits _{n=1}^{\infty }d(n)\log (n)e^{-ny}$ for Re $(y)>0$ , which takes y to $1/y$ , is obtained for the first time. This series transforms into a series containing the derivative of $R(z)$ , a function studied by Christopher Deninger while obtaining an analog of the famous Chowla–Selberg formula for real quadratic fields. In the course of obtaining the transformation, new important properties of $\psi _1(z)$ (the derivative of $R(z)$ ) are needed as is a new representation for the second derivative of the two-variable Mittag-Leffler function $E_{2, b}(z)$ evaluated at $b=1$ , all of which may seem quite unexpected at first glance. Our transformation readily gives the complete asymptotic expansion of $\sum \limits _{n=1}^{\infty }\displaystyle \frac {\log (n)}{e^{ny}-1}$ as $y\to 0$ which was also not known before. An application of the latter is that it gives the asymptotic expansion of $ \displaystyle \int _{0}^{\infty }\zeta \left (\frac {1}{2}-it\right )\zeta '\left (\frac {1}{2}+it\right )e^{-\delta t}\, dt$ as $\delta \to 0$ .

A novel isolated multi‐port interleaved flyback converter operated TPSL‐DVR for smallscale distribution system

SummaryThis study describes a three‐phase six‐level (TPSL) inverter‐based dynamic voltage restorer (DVR) that employs a newly designed isolated multi‐port interleaved flyback converter (IMPIFC). A conventional DVR needs a big and heavy series transformer even for a three‐phase low‐voltage system, which is rated up to 400 V. Power electronic engineers have developed high‐frequency isolated DC–DC converters as a result of the introduction of advanced semiconductor devices and magnetic cores. Control and performance of a low‐voltage DVR utilizing a high‐frequency isolated DC–DC converter are discussed. In the proposed IMPIFC, the high‐frequency (25 kHz) transformer, which is smaller in size than the line‐frequency transformer, is utilized to reduce the size and to integrate multiple energy sources together. In addition, the introduction of a TPSL inverter into the configuration of DVR considerably reduces the injection of harmonic components into the distribution network. The proposed structure of DVR is named as “TPSL‐DVR.” The experimental findings of a three‐phase, three‐wire, 400 V, 50 Hz, 2kW laboratory system validate the boosting ability, feasibility, and efficiency of the system layout.

Mortality prediction using medical time series on TBI patients

Background and objectiveTraumatic Brain Injury (TBI) is one of the leading causes of injury-related mortality in the world, with severe cases reaching mortality rates of 30-40%. It is highly heterogeneous both in causes and consequences making more complex the medical interpretation and prognosis. Gathering clinical, demographic, and laboratory data to perform a prognosis requires time and skill in several clinical specialties. Artificial intelligence (AI) methods can take advantage of existing data by performing helpful predictions and guiding physicians toward a better prognosis and, consequently, better healthcare. The objective of this work was to develop learning models and evaluate their capability of predicting the mortality of TBI. The predictive model would allow the early assessment of the more serious cases and scarce medical resources can be pointed toward the patients who need them most. MethodsLong Short Term Memory (LSTM) and Transformer architectures were tested and compared in performance, coupled with data imbalance, missing data, and feature selection strategies. From the Medical Information Mart for Intensive Care III (MIMIC-III) dataset, a cohort of TBI patients was selected and an analysis of the first 48 hours of multiple time series sequential variables was done to predict hospital mortality. ResultsThe best performance was obtained with the Transformer architecture, achieving an AUC of 0.907 with the larger group of features and trained with class proportion class weights and binary cross entropy loss. ConclusionsUsing the time series sequential data, LSTM and Transformers proved to be both viable options for predicting TBI hospital mortality in 48 hours after admission. Overall, using sequential deep learning models with time series data to predict TBI mortality is viable and can be used as a helpful indicator of the well-being of patients.

A Global Forecasting Approach to Large-Scale Crop Production Prediction with Time Series Transformers

Accurate prediction of crop production is essential in effectively managing the food security and economic resilience of agricultural countries. This study evaluates the performance of statistical and machine learning-based methods for large-scale crop production forecasting. We predict the quarterly production of 325 crops (including fruits, vegetables, cereals, non-food, and industrial crops) across 83 provinces in the Philippines. Using a comprehensive dataset of 10,949 time series over 13 years, we demonstrate that a global forecasting approach using a state-of-the-art deep learning architecture, the transformer, significantly outperforms popular tree-based machine learning techniques and traditional local forecasting approaches built on statistical and baseline methods. Our results show a significant 84.93%, 80.69%, and 79.54% improvement in normalized root mean squared error (NRMSE), normalized deviation (ND), and modified symmetric mean absolute percentage error (msMAPE), respectively, over the next-best methods. By leveraging cross-series information, our proposed method is scalable and works well even with time series that are short, sparse, intermittent, or exhibit structural breaks/regime shifts. The results of this study further advance the field of applied forecasting in agricultural production and provide a practical and effective decision-support tool for policymakers that oversee crop production and the agriculture sector on a national scale.

Network intrusion detection based on the temporal convolutional model

Recurrent networks have been adopted as default architecture in approaches performing sequence modelling of network intrusion detection problems. However, models based on Recurrent Neural Network (RNN) architecture have some limitations regarding computation complexity and detection performance due to information loss. Recent studies suggested that certain convolutional-based architectures that can natively process temporal data outperform recurrent networks in time series modelling, such as speech synthesis and machine translation. Inspired by the success of temporal-based convolutional architectures in other domains, this paper designs and implements four temporal-based convolutional models in network intrusion detection and studies their classification performance. The models are based on MINImally RandOm Convolutional KErnel Transform (MiniRocket), eXplainable Convolutional Neural Network for Multivariate Time Series Classification (XCM), One-Dimensional Convolution Neural Network (OS-CNN), and Time Series Transformer (TST) architecture. We evaluate our models using the effectiveness and efficiency metrics based on CICDDoS2019 and CSE-CIC-IDS2018 datasets. Every model has achieved a high evaluation performance in the range between 98.07% and 99.99% in most considered metrics using the test dataset. MiniRocket and OS-CNN obtained the highest evaluation results regarding the effectiveness metrics. The high evaluation results suggest that they can improve the detection effectiveness of approaches formulating network intrusion detection as a time series task.

Residential energy consumption forecasting using deep learning models

The energy sector plays an important role in socioeconomic and environmental development. Accurately forecasting energy demand across various time horizons can yield substantial advantages, such as better planning and management of energy resources. Different methodologies, including mathematical, statistical, and machine learning models, have been proposed for energy consumption prediction. Nevertheless, some studies claim that deep learning models can outperform other approaches when dealing with time series data characterized by a high level of granularity. There are different implementations of deep learning models, such as recurrent unit layers, dimensional convolutions, or Transformers. Hence, it is interesting to compare the performance of different architectural types using a methodology that utilizes feature selection and model interpretation to underscore the significance of meteorological features and timestamps in the forecasting task. This study presents a comparative methodology of forecasting approaches employing recurrence-based models: Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Time Series Transformer (TST), while exploring the relationship between model performance and resource allocation related with amount of features and time resolution. The findings reveal that the Transformer architecture works better with fewer samples, despite the occurrence of overfitting. In addition, training the models enabled the creation of a voting ensemble, optimized by the Simulated Annealing metaheuristic, resulting in a 23% improvement in hourly granularity.

Performance Evaluation of Biomedical Time Series Transformation Methods for Classification Tasks

The extraction of time series features is essential across various fields, yet it remains a challenging endeavor. Therefore, it's crucial to identify appropriate methods capable of extracting pertinent information that can significantly enhance classification performance. Among these methods are those that translate time series into different domains. This study investigates three distinct time series transformation approaches for addressing time series classification challenges within biomedical data. The first method involves a response vector transformation, while the other two employ image transformation techniques: RandOm Convolutional KErnel Transform (ROCKET), Gramian Angular Fields, and Markov Transition Fields. These transformation methods were applied to five biomedical datasets, exploring various format configurations to ascertain the optimal representation technique and configuration for input, which in turn improves classification performance. Evaluations were conducted on the effectiveness of these methods in conjunction with two classification algorithms. The outcomes underscore the significance of these time series transformation techniques as facilitators for enhanced classification algorithms documented in current literature.

Research on Fault Diagnosis Method of Rotary Machinery Based on Improved Transformer

In modern industry, rotating machinery plays a crucial role. These rotating machines are not only fundamental components of power generation and propulsion systems but also key factors for their efficient operation. Harsh operating environments often lead to failures in critical components like gears and bearings in rotating machinery, which can directly result in equipment malfunction. Therefore, authentic fault diagnosis of these primary building blocks in rotating machinery is of pivotal value for improving its reliability and safety during operation. This research proposes a fault diagnosis strategy for rotating machinery rooted on time series Transformer and validates the effectiveness of the proposed approach. Firstly, a time series Transformer model is designed, which incorporates modules like time series embedding, attention mechanism, and multi-layer perceptron to promptly approach 1D oscillatory motion signal data. Subsequently, the hypothetical model is trained and tested on multiple public datasets, and its fault diagnosis results are compared with existing achievements in the literature. The proficiency of the model is thoroughly verified, and the fault diagnosis performance of this proposed approach surpasses many existing fault diagnosis methods.

Performance of multiple neural networks in predicting lower limb joint moments using wearable sensors.

Joint moment measurements represent an objective biomechemical parameter in joint health assessment. Inverse dynamics based on 3D motion capture data is the current 'gold standard' to estimate joint moments. Recently, machine learning combined with data measured by wearable technologies such electromyography (EMG), inertial measurement units (IMU), and electrogoniometers (GON) has been used to enable fast, easy, and low-cost measurements of joint moments. This study investigates the ability of various deep neural networks to predict lower limb joint moments merely from IMU sensors. The performance of five different deep neural networks (InceptionTimePlus, eXplainable convolutional neural network (XCM), XCMplus, Recurrent neural network (RNNplus), and Time Series Transformer (TSTPlus)) were tested to predict hip, knee, ankle, and subtalar moments using acceleration and gyroscope measurements of four IMU sensors at the trunk, thigh, shank, and foot. Multiple locomotion modes were considered including level-ground walking, treadmill walking, stair ascent, stair descent, ramp ascent, and ramp descent. We show that XCM can accurately predict lower limb joint moments using data of only four IMUs with RMSE of 0.046 ± 0.013 Nm/kg compared to 0.064 ± 0.003 Nm/kg on average for the other architectures. We found that hip, knee, and ankle joint moments predictions had a comparable RMSE with an average of 0.069 Nm/kg, while subtalar joint moments had the lowest RMSE of 0.033 Nm/kg. The real-time feedback that can be derived from the proposed method can be highly valuable for sports scientists and physiotherapists to gain insights into biomechanics, technique, and form to develop personalized training and rehabilitation programs.

Motor Current-Based Degradation Modeling for Tool Wear Hybrid Prognostics in Turning Process

For many machines with turning process systems, the application of economical indirect Tool Condition Monitoring (TCM) is enhanced by utilizing internal encoder spindle motor current signals. In this study, we proposed a novel approach to extract the total harmonic distortion (THD) feature associated with the metal cutting frequency of a specific working tool in the time domain. Our method entailed the application of filtered variational mode decomposition (VMD) combined with envelope analysis to demodulate the motor current signal and define TCM features based on the THD of odd harmonics, which are more related to the motor structure. These features serve as inputs for a hybrid prognostics technique, employing the Geometric Brownian Motion (GBM) to stochastically model the degradation process along with a deep learning transformer-based framework called the time series Transformer (TST) to improve the life prediction. Finally, to validate our approach, we conducted experiments based on 36 sets of tool run-to-wear data extracted from a CNC machine operating under turning process conditions using two different tools. Finally, we compared the degradation models based on the extracted odd-THD and even-THD features.

TSE-Tran: Prediction method of telecommunication-network fraud crime based on time series representation and transformer

Telecom network fraud has become the most common and concerning type of crime and is an important public security incident that threatens urban resilience. Therefore, preventing a continuous rise in telecommunications and network fraud will help establish a resilient urban governance system. Undertaking the spatiotemporal forecasting of telecommunications-network fraud trends is of significant importance for aiding public security agencies in proactive crime prevention and implementing targeted anti-fraud campaigns. This study presents a telecommunication network fraudulent crime prediction method called TSE-Tran, which integrates temporal representation and transformer architecture. The time-series data of telecommunication-network fraud occurrences were input into the TimesNet module, which maps the sequence data to a more precise feature representation tensor that accounts for both intra- and inter-cycle features. Subsequently, the data are fed into the transformer-encoder module for further encoding, capturing long-range dependencies in the time-series data. Finally, occurrences of future telecommunication network frauds are predicted by a fully connected layer. The results of the study demonstrate that the proposed TSE-Tran method outperforms benchmark methods in terms of prediction accuracy. The results of this study are expected to aid in the prevention and control of telecommunications and network frauds effectively strengthen the resilience of urban development and the ability to respond to public security incidents.

The linear and non-linear study of effect of rotation and internal heat source/sink on Bénard convection

The primary objective of this study is to investigate non-linear Bénard convection in a single-walled carbon nanotube suspension saturated in a rotating porous medium with an internal heat sink/source. The modified Buongiorno model is utilized to formulate the governing equations for the flow. Both linear and weak non-linear stability analyses are conducted in this investigation. The linear stability analysis employs the truncated Fourier series transformation, while the weakly non-linear stability analysis utilizes the Lorenz model, assuming weak thermophoresis, porous friction, and small-scale convective motion. The cubic Ginzburg–Landau equation is formulated and subsequently solved to derive the expression for the amplitude. The influence of various parameters, such as the Taylor number, heat sink/source parameter, and viscosity parameter, is discussed in relation to the threshold criteria of convection, as well as heat and mass transport rates. Based on the linear stability analysis, it is determined that the introduction of a rotating frame of reference delays the initiation of convection, whereas the energy supplied to the system accelerates the onset of convection. The heat transfer rate increases by when the nanofluidic system is placed in the rotating frame of reference under the presence of an internal heat source.

INFINITE SERIES CONCERNING HARMONIC NUMBERS AND QUINTIC CENTRAL BINOMIAL COEFFICIENTS

AbstractBy examining two hypergeometric series transformations, we establish several remarkable infinite series identities involving harmonic numbers and quintic central binomial coefficients, including five conjectured recently by Z.-W. Sun [‘Series with summands involving harmonic numbers’, Preprint, 2023, arXiv:2210.07238v7]. This is realised by ‘the coefficient extraction method’ implemented by Mathematica commands.

An Aspect of Basic (q-) Integral for q-Basic Series

In the present aspect, several transformations of q-basic series with bilateral q-basic series have been established by employing the notion of basic (q-) integral. Some of these lead to relationships between the two q-series products. Following from these findings are some highly intriguing modifications of the basic and bilateral basic q-series. This article presents a handful of the numerous outcomes that are illustrative of the many results attained.

Harmonized multi-metric and multi-centric assessment of EEG source space connectivity for dementia characterization.

Harmonization protocols that address batch effects and cross-site methodological differences in multi-center studies are critical for strengthening electroencephalography (EEG) signatures of functional connectivity (FC) as potential dementia biomarkers. We implemented an automatic processing pipeline incorporating electrode layout integrations, patient-control normalizations, and multi-metric EEG source space connectomics analyses. Spline interpolations of EEG signals onto a head mesh model with 6067 virtual electrodes resulted in an effective method for integrating electrode layouts. Z-score transformations of EEG time series resulted in source space connectivity matrices with high bilateral symmetry, reinforced long-range connections, and diminished short-range functional interactions. A composite FC metric allowed for accurate multicentric classifications of Alzheimer's disease and behavioral variant frontotemporal dementia. Harmonized multi-metric analysis of EEG source space connectivity can address data heterogeneities in multi-centric studies, representing a powerful tool for accurately characterizing dementia.

A new approach in forecasting Greek electricity demand: From high dimensional hourly series to univariate series transformation

This article presents a different approach to power consumption forecasting problem. This forecasting can help power supply companies to program their production or purchases. Based on this forecasting the companies take part in auctions that determine the price of the MWh in the electricity market and at the end of the day, the price for the end consumer. So far, the problem of forecasting power supply time series has mainly been dealt with the use of classical time series algorithms or VAR models. In this paper, we use a method from the insurance sector to forecast Greek power consumption hourly values. The innovation in this method is that it allows converting the forecasting of a system of time series (high dimensional time series) into forecasting a single time series and propagating the results back to each time series. It leaves the forecasting algorithm choice to the researcher, making it very flexible and removing the necessity of choosing complex algorithms. We demonstrate the forecasting of the results of this method by applying the ARIMA algorithm.

Classical structural identifiability methodology applied to low-dimensional dynamic systems in receptor theory.

Mathematical modelling has become a key tool in pharmacological analysis, towards understanding dynamics of cell signalling and quantifying ligand-receptor interactions. Ordinary differential equation (ODE) models in receptor theory may be used to parameterise such interactions using timecourse data, but attention needs to be paid to the theoretical identifiability of the parameters of interest. Identifiability analysis is an often overlooked step in many bio-modelling works. In this paper we introduce structural identifiability analysis (SIA) to the field of receptor theory by applying three classical SIA methods (transfer function, Taylor Series and similarity transformation) to ligand-receptor binding models of biological importance (single ligand and Motulsky-Mahan competition binding at monomers, and a recently presented model of a single ligand binding at receptor dimers). New results are obtained which indicate the identifiable parameters for a single timecourse for Motulsky-Mahan binding and dimerised receptor binding. Importantly, we further consider combinations of experiments which may be performed to overcome issues of non-identifiability, to ensure the practical applicability of the work. The three SIA methods are demonstrated through a tutorial-style approach, using detailed calculations, which show the methods to be tractable for the low-dimensional ODE models.

Smoothing method for unit quaternion time series in a classification problem: an application to motion data

Smoothing orientation data is a fundamental task in different fields of research. Different methods of smoothing time series in quaternion algebras have been described in the literature, but their application is still an open point. This paper develops a smoothing approach for smoothing quaternion time series to obtain good performance in classification problems. Starting from an existing method which involves an angular velocity transformation of unit quaternion time series, a new method which employ the logarithm function to transform the quaternion time series to a real three-dimensional time series is proposed. Empirical evidences achieved on real data set and artificially noisy data sets confirm the effectiveness of the proposed method compared with the classical approach based on angular velocity transformation. The R functions developed for this paper will be provided in a Github repository.

Construction of highly non linear component of block cipher based on mclaurin series and mellin transformation with application in image encryption

Construction of highly non linear component of block cipher based on mclaurin series and mellin transformation with application in image encryption