SOME PROPERTIES OF MULTIPLE TAYLOR SERIES AND RANDOM TAYLOR SERIES

Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on any compact set properties of the series may also be studied. For some random multiple are some corresponding properties. Growth and other Taylor series there

The Lower Orders of Dirichlet and Random Dirichlet Series

The formulas of the lower orders of Dirichlet series are given by means of the exponents and the convex regularized sequences of the logarithms and the convex regularized sequences of the logarithms of the moduli of the coefficients. Corresponding results are obtained for some random Dirichlet series.

THE GROWTH OF RANDOM DIRICHLET SERIES (I)

Under the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sigma a(n) Z(n)e(-lambda n) and series' Sigma a(n)e(-lambda ns) a.s. have the same abscissa of convergence, the (R) order, lower order and type.

Analysis of the causes of primary revision after unicompartmental knee arthroplasty: A case series

BACKGROUND Unicompartmental knee arthroplasty(UKA)has great advantages in the treatment of unicompartmental knee osteoarthritis,but its revision rate is higher than that of total knee arthroplasty.AIM To summarize and analyse the causes of revision after UKA.METHODS This is a retrospective case series study in which the reasons for the first revision after UKA are summarized.We analysed the clinical symptoms,medical histories,laboratory test results,imaging examination results and treatment processes of the patients who underwent revision and summarized the reasons for primary revision after UKA.RESULTS A total of 13 patients,including 3 males and 10 females,underwent revision surgery after UKA.The average age of the included patients was 67.62 years.The prosthesis was used for 3 d to 72 months.The main reasons for revision after UKA were improper suturing of the surgical opening(1 patient),osteophytes(2 patients),intra-articular loose bodies(2 patients),tibial prosthesis loosening(2 patients),rheumatoid arthritis(1 patient),gasket dislocation(3 patients),anterior cruciate ligament injury(1 patient),and medial collateral ligament injury with residual bone cement(1 patient).CONCLUSION The causes of primary revision after UKA were gasket dislocation,osteophytes,intra-articular loose bodies and tibial prosthesis loosening.Avoidance of these factors may greatly reduce the rate of revision after UKA,improve patient satisfaction and reduce medical burden.

Time series prediction of reservoir bank landslide failure probability considering the spatial variability of soil properties

Historically,landslides have been the primary type of geological disaster worldwide.Generally,the stability of reservoir banks is primarily affected by rainfall and reservoir water level fluctuations.Moreover,the stability of reservoir banks changes with the long-term dynamics of external disastercausing factors.Thus,assessing the time-varying reliability of reservoir landslides remains a challenge.In this paper,a machine learning(ML)based approach is proposed to analyze the long-term reliability of reservoir bank landslides in spatially variable soils through time series prediction.This study systematically investigated the prediction performances of three ML algorithms,i.e.multilayer perceptron(MLP),convolutional neural network(CNN),and long short-term memory(LSTM).Additionally,the effects of the data quantity and data ratio on the predictive power of deep learning models are considered.The results show that all three ML models can accurately depict the changes in the time-varying failure probability of reservoir landslides.The CNN model outperforms both the MLP and LSTM models in predicting the failure probability.Furthermore,selecting the right data ratio can improve the prediction accuracy of the failure probability obtained by ML models.

The Growth of Dirichlet Series and Random Dirichlet Series of Zero Order and Finite Order

In this paper,we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {Xn {ω}} satisfies the certain condition, in the whole plane, the growth of the random entire function which is determined by the zero order and finite order random Dirichlet series is almost surely same with corresponding growth of random Dirichlet series on any horizontal straight line.

VECTOR-VALUED RANDOM POWER SERIES ON THE UNIT BALL OF C～n

In this article, the authors study the vector-valued random power series on the unit ball of C^n and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between vector-valued random power series and several function spaces are also studied.

BOREL LINES OF RANDOM DIRICHLET SERIES

For some random Dirichlet series of order (R) infinite almost surely every horizontal line is a Borel line of order (R) infinite and without exceptional values

Defect Detection Model Using Time Series Data Augmentation and Transformation

Time-series data provide important information in many fields,and their processing and analysis have been the focus of much research.However,detecting anomalies is very difficult due to data imbalance,temporal dependence,and noise.Therefore,methodologies for data augmentation and conversion of time series data into images for analysis have been studied.This paper proposes a fault detection model that uses time series data augmentation and transformation to address the problems of data imbalance,temporal dependence,and robustness to noise.The method of data augmentation is set as the addition of noise.It involves adding Gaussian noise,with the noise level set to 0.002,to maximize the generalization performance of the model.In addition,we use the Markov Transition Field(MTF)method to effectively visualize the dynamic transitions of the data while converting the time series data into images.It enables the identification of patterns in time series data and assists in capturing the sequential dependencies of the data.For anomaly detection,the PatchCore model is applied to show excellent performance,and the detected anomaly areas are represented as heat maps.It allows for the detection of anomalies,and by applying an anomaly map to the original image,it is possible to capture the areas where anomalies occur.The performance evaluation shows that both F1-score and Accuracy are high when time series data is converted to images.Additionally,when processed as images rather than as time series data,there was a significant reduction in both the size of the data and the training time.The proposed method can provide an important springboard for research in the field of anomaly detection using time series data.Besides,it helps solve problems such as analyzing complex patterns in data lightweight.

Cross-Dimension Attentive Feature Fusion Network for Unsupervised Time-Series Anomaly Detection

Time series anomaly detection is crucial in various industrial applications to identify unusual behaviors within the time series data.Due to the challenges associated with annotating anomaly events,time series reconstruction has become a prevalent approach for unsupervised anomaly detection.However,effectively learning representations and achieving accurate detection results remain challenging due to the intricate temporal patterns and dependencies in real-world time series.In this paper,we propose a cross-dimension attentive feature fusion network for time series anomaly detection,referred to as CAFFN.Specifically,a series and feature mixing block is introduced to learn representations in 1D space.Additionally,a fast Fourier transform is employed to convert the time series into 2D space,providing the capability for 2D feature extraction.Finally,a cross-dimension attentive feature fusion mechanism is designed that adaptively integrates features across different dimensions for anomaly detection.Experimental results on real-world time series datasets demonstrate that CAFFN performs better than other competing methods in time series anomaly detection.

THE VALUE DISTRIBUTION OF RANDOM ANALYTIC DIRICHLET SERIES OF NEUTRAL GROWTH (Ⅱ)

This paper studies the value distribution of random analytic Dirichlet series f(s) = Zn()e-sn, where {Zn} is a sequence of independent random variables, n = 1 with moments zero, such that infE{Zn}/E1/2{Zn2≥ α > 0. Suppose [h*(σ)]2 = n converges for any α > 0, and diverges for = 0. It is shown that if = ρ E (0, ), then with probability one, where β is a constant depending only upon the constant α.

Reservoir characteristics and formation model of Upper Carboniferous bauxite series in eastern Ordos Basin,NW China

Through core observation,thin section identification,X-ray diffraction analysis,scanning electron microscopy,and low-temperature nitrogen adsorption and isothermal adsorption experiments,the lithology and pore characteristics of the Upper Carboniferous bauxite series in eastern Ordos Basin were analyzed to reveal the formation and evolution process of the bauxite reservoirs.A petrological nomenclature and classification scheme for bauxitic rocks based on three units(aluminum hydroxides,iron minerals and clay minerals)is proposed.It is found that bauxitic mudstone is in the form of dense massive and clastic structures,while the(clayey)bauxite is of dense massive,pisolite,oolite,porous soil and clastic structures.Both bauxitic mudstone and bauxite reservoirs develop dissolution pores,intercrystalline pores,and microfractures as the dominant gas storage space,with the porosity less than 10% and mesopores in dominance.The bauxite series in the North China Craton can be divided into five sections,i.e.,ferrilite(Shanxi-style iron ore,section A),bauxitic mudstone(section B),bauxite(section C),bauxite mudstone(debris-containing,section D)and dark mudstone-coal section(section E).The burrow/funnel filling,lenticular,layered/massive bauxite deposits occur separately in the karst platforms,gentle slopes and low-lying areas.The karst platforms and gentle slopes are conducive to surface water leaching,with strong karstification,well-developed pores,large reservoir thickness and good physical properties,but poor strata continuity.The low-lying areas have poor physical properties but relatively continuous and stable reservoirs.The gas enrichment in bauxites is jointly controlled by source rock,reservoir rock and fractures.This recognition provides geological basis for the exploration and development of natural gas in the Upper Carboniferous in the study area and similar bauxite systems.

THE NATURAL BOUNDARY OF SOME RANDOM POWER SERIES

Suppose that {X(n)(omega)} are independent random complex variable sequence, E(X(n)) = 0 and [GRAPHICS] (V(X(n) = sigma(n)2). If reversed capital E-epsilon > 0 such that for all P (H) > 1-epsilon, we have [GRAPHICS] Then the circle {\Z\ = rho} is almost surely a natural boundary of the random series [GRAPHICS]

THE VALUE DISTRIBUTION OF RANDOM ANALYTIC DIRICHLET SERIES OF NEUTRAL GROWTH(I)

This paper deals with the value distribution of random Dirichlet series whose coefficients are a martingale difference sequence, and which is of neutral growth.

Unsupervised Time Series Segmentation: A Survey on Recent Advances

Time series segmentation has attracted more interests in recent years,which aims to segment time series into different segments,each reflects a state of the monitored objects.Although there have been many surveys on time series segmentation,most of them focus more on change point detection(CPD)methods and overlook the advances in boundary detection(BD)and state detection(SD)methods.In this paper,we categorize time series segmentation methods into CPD,BD,and SD methods,with a specific focus on recent advances in BD and SD methods.Within the scope of BD and SD,we subdivide the methods based on their underlying models/techniques and focus on the milestones that have shaped the development trajectory of each category.As a conclusion,we found that:(1)Existing methods failed to provide sufficient support for online working,with only a few methods supporting online deployment;(2)Most existing methods require the specification of parameters,which hinders their ability to work adaptively;(3)Existing SD methods do not attach importance to accurate detection of boundary points in evaluation,which may lead to limitations in boundary point detection.We highlight the ability to working online and adaptively as important attributes of segmentation methods,the boundary detection accuracy as a neglected metrics for SD methods.

Improved Responses with Multitaper Spectral Analysis for Magnetotelluric Time Series Data Processing:Examples from Field Data

In order to attain good quality transfer function estimates from magnetotelluric field data(i.e.,smooth behavior and small uncertainties across all frequencies),we compare time series data processing with and without a multitaper approach for spectral estimation.There are several common ways to increase the reliability of the Fourier spectral estimation from experimental(noisy)data;for example to subdivide the experimental time series into segments,taper these segments(using single taper),perform the Fourier transform of the individual segments,and average the resulting spectra.

Multivariate Time Series Anomaly Detection Based on Spatial-Temporal Network and Transformer in Industrial Internet of Things

In the Industrial Internet of Things(IIoT),sensors generate time series data to reflect the working state.When the systems are attacked,timely identification of outliers in time series is critical to ensure security.Although many anomaly detection methods have been proposed,the temporal correlation of the time series over the same sensor and the state(spatial)correlation between different sensors are rarely considered simultaneously in these methods.Owing to the superior capability of Transformer in learning time series features.This paper proposes a time series anomaly detection method based on a spatial-temporal network and an improved Transformer.Additionally,the methods based on graph neural networks typically include a graph structure learning module and an anomaly detection module,which are interdependent.However,in the initial phase of training,since neither of the modules has reached an optimal state,their performance may influence each other.This scenario makes the end-to-end training approach hard to effectively direct the learning trajectory of each module.This interdependence between the modules,coupled with the initial instability,may cause the model to find it hard to find the optimal solution during the training process,resulting in unsatisfactory results.We introduce an adaptive graph structure learning method to obtain the optimal model parameters and graph structure.Experiments on two publicly available datasets demonstrate that the proposed method attains higher anomaly detection results than other methods.

An Innovative Deep Architecture for Flight Safety Risk Assessment Based on Time Series Data

With the development of the integration of aviation safety and artificial intelligence,research on the combination of risk assessment and artificial intelligence is particularly important in the field of risk management,but searching for an efficient and accurate risk assessment algorithm has become a challenge for the civil aviation industry.Therefore,an improved risk assessment algorithm(PS-AE-LSTM)based on long short-term memory network(LSTM)with autoencoder(AE)is proposed for the various supervised deep learning algorithms in flight safety that cannot adequately address the problem of the quality on risk level labels.Firstly,based on the normal distribution characteristics of flight data,a probability severity(PS)model is established to enhance the quality of risk assessment labels.Secondly,autoencoder is introduced to reconstruct the flight parameter data to improve the data quality.Finally,utilizing the time-series nature of flight data,a long and short-termmemory network is used to classify the risk level and improve the accuracy of risk assessment.Thus,a risk assessment experimentwas conducted to analyze a fleet landing phase dataset using the PS-AE-LSTMalgorithm to assess the risk level associated with aircraft hard landing events.The results show that the proposed algorithm achieves an accuracy of 86.45%compared with seven baseline models and has excellent risk assessment capability.

Periodic signal extraction of GNSS height time series based on adaptive singular spectrum analysis

Singular spectrum analysis is widely used in geodetic time series analysis.However,when extracting time-varying periodic signals from a large number of Global Navigation Satellite System(GNSS)time series,the selection of appropriate embedding window size and principal components makes this method cumbersome and inefficient.To improve the efficiency and accuracy of singular spectrum analysis,this paper proposes an adaptive singular spectrum analysis method by combining spectrum analysis with a new trace matrix.The running time and correlation analysis indicate that the proposed method can adaptively set the embedding window size to extract the time-varying periodic signals from GNSS time series,and the extraction efficiency of a single time series is six times that of singular spectrum analysis.The method is also accurate and more suitable for time-varying periodic signal analysis of global GNSS sites.

A Time Series Short-Term Prediction Method Based on Multi-Granularity Event Matching and Alignment

Accurate forecasting of time series is crucial across various domains.Many prediction tasks rely on effectively segmenting,matching,and time series data alignment.For instance,regardless of time series with the same granularity,segmenting them into different granularity events can effectively mitigate the impact of varying time scales on prediction accuracy.However,these events of varying granularity frequently intersect with each other,which may possess unequal durations.Even minor differences can result in significant errors when matching time series with future trends.Besides,directly using matched events but unaligned events as state vectors in machine learning-based prediction models can lead to insufficient prediction accuracy.Therefore,this paper proposes a short-term forecasting method for time series based on a multi-granularity event,MGE-SP(multi-granularity event-based short-termprediction).First,amethodological framework for MGE-SP established guides the implementation steps.The framework consists of three key steps,including multi-granularity event matching based on the LTF(latest time first)strategy,multi-granularity event alignment using a piecewise aggregate approximation based on the compression ratio,and a short-term prediction model based on XGBoost.The data from a nationwide online car-hailing service in China ensures the method’s reliability.The average RMSE(root mean square error)and MAE(mean absolute error)of the proposed method are 3.204 and 2.360,lower than the respective values of 4.056 and 3.101 obtained using theARIMA(autoregressive integratedmoving average)method,as well as the values of 4.278 and 2.994 obtained using k-means-SVR(support vector regression)method.The other experiment is conducted on stock data froma public data set.The proposed method achieved an average RMSE and MAE of 0.836 and 0.696,lower than the respective values of 1.019 and 0.844 obtained using the ARIMA method,as well as the values of 1.350 and 1.172 obtained using the k-means-SVR method.