Sequential Correlation Research Articles

Applying Sequential Correlation to Identify Order Dependent Activity Pairs

Mining sequential patterns has been one of the most useful fields in data mining. For example, one recent application of sequential pattern mining is analyzing logs of activity to predict and recognize activities. This is used for both daily life activities and virtual activities. However, only patterns are not always enough to represent the truly interesting information to the end user, especially when the support threshold is low and the number of frequent patterns is huge. A correlation measure is necessary to decipher the relationship between the logged activities. This data is generally collected as a sequence and there is no widely popular correlation measure for elements in sequential patterns. Therefore, we define Sequential Correlation, a novel correlation measure, for discovering important knowledge in sequential patterns and the corresponding full method, SCMine, to classify patterns based on the measure. We employed the measure to establish either a unidirectional or bidirectional association among the activities within a sequence and subsequently classified the sequences based on order dependency. Moreover, an efficient implementation approach for our measure is also discussed. Our performance study shows that, a significant number of activity patterns can be pruned when degree of order among the activities is important. So, it is also useful for classifying or pruning less significant activity patterns from a vast number of frequent sequential patterns. DUJASE Vol. 8 (1) 51-61, 2023 (January)

Dense Continuous-Time Optical Flow From Event Cameras.

We present a method for estimating dense continuous-time optical flow from event data. Traditional dense optical flow methods compute the pixel displacement between two images. Due to missing information, these approaches cannot recover the pixel trajectories in the blind time between two images. In this work, we show that it is possible to compute per-pixel, continuous-time optical flow using events from an event camera. Events provide temporally fine-grained information about movement in pixel space due to their asynchronous nature and microsecond response time. We leverage these benefits to predict pixel trajectories densely in continuous time via parameterized Bézier curves. To achieve this, we build a neural network with strong inductive biases for this task: First, we build multiple sequential correlation volumes in time using event data. Second, we use Bézier curves to index these correlation volumes at multiple timestamps along the trajectory. Third, we use the retrieved correlation to update the Bézier curve representations iteratively. Our method can optionally include image pairs to boost performance further. To the best of our knowledge, our model is the first method that can regress dense pixel trajectories from event data. To train and evaluate our model, we introduce a synthetic dataset (MultiFlow) that features moving objects and ground truth trajectories for every pixel. Our quantitative experiments not only suggest that our method successfully predicts pixel trajectories in continuous time but also that it is competitive in the traditional two-view pixel displacement metric on MultiFlow and DSEC-Flow. Open source code and datasets are released to the public.

Outlier detection in temporal and spatial sequences via correlation analysis based on graph neural networks

Outlier detection is essential for identifying patterns that deviate from expected normal representations in data. Real-world challenges such as the lack of labeled data, noise, and high dimensionality significantly impact the effectiveness of existing methods. Understanding the temporal or spatial correlation of normal data is crucial for detecting or forecasting anomalous patterns. In this paper, we introduce UOSC-GNN, a novel Unsupervised Outlier detection architecture by Sequential Correlation analysis with Graph Neural Network. The architecture includes a deviation generation module to measure the variance between expected and actual states of sequential data. This module incorporates a Generic Feature Extraction component to extract intrinsic features from outliers and normal instances tailored to specific tasks, and an Expected State Estimator component based on Graph Neural Network to learn sequential patterns. To ensure the forecast of outliers with high confidence and improve alarm accuracy, an Outlier Probability Assessment module is introduced. This module combines a rule-based index derived from expert knowledge and a statistical index calculated based on generated deviations. Our method is evaluated on two real-world tasks: medical imaging analysis utilizing spatial-related data and early fault detection of instruments leveraging temporal-related data. The results show that our method triggers alarms about 70 min earlier than the best models on the run-to-failure bearing dataset and achieves an accuracy of 92.82% and a sensitivity of 88.51% on the wireless capsule endoscopy image dataset, outperforming traditional outlier detection algorithms consistently.

Algorithmic Foundation of Federated Learning with Sequential Data

The current analysis of federated optimization algorithms for training deep neural networks assumes that the data is non-sequential (e.g., images), which incurs a smooth loss objective. In contrast, edge devices generate lots of sequential data every day, where these sequences exhibit significant sequential correlation at different time stamps (e.g., text messages). In order to learn from such sequential data, people typically use a class of neural networks that is inherently nonsmooth, with a potentially unbounded smoothness parameter. Examples include recurrent neural networks, long-short-term memory networks, and transformers. It remains unclear how to design provably efficient algorithms for training these neural networks to learn from sequential data. My goal is to lay the algorithmic foundation of federated learning with sequential data, which contributes novel algorithms for learning from a range of real-world sequential data (e.g., natural language, electronic health record, transportation, time series, etc.) using state-of-the-art deep neural networks. In this talk, I will first motivate the problem by showing that the transformer, which is widely used for sequential data learning, has an unbounded smooth landscape. Then, I will introduce provably efficient federated deep learning algorithms in the presence of unbounded smoothness. In particular, I will introduce a few efficient algorithms for various settings of federated learning, including homogeneous data, heterogeneous data, and partial client participation. The main result is twofold. First, we show that the designed algorithms provably small computational and communication complexities. Second, we establish fundamental hardness results in the unbounded smoothness setting. Ultimately, I will discuss the future challenges of extending our research framework from small-scale neural networks to large language models.

Study on modes of occurrence and selective leaching of lithium in coal gangue via grinding-thermal activation

Lithium (Li), an important strategic metal, has been paid attention to by researchers, entrepreneurs, and political circles, especially its recovery from coal-based solid waste. In this paper, the occurrence modes of Li in coal gangue (CG) have been studied through sequential chemical extraction, distribution correlation, and intercalation-leaching test. The CG was pretreated via grinding-thermal activation to selectively leach Li. The correlation between Li and magnesium (Mg) during the leaching process was also investigated. Finally, the migration mechanism of Li during the grinding-thermal activation process was analyzed using solid-state nuclear magnetic resonance for the first time. The results of the first three experiments demonstrated that Li primarily exists within the kaolinite. The extraction of Li from CG after grinding-thermal activation is 44.82 % using 0.2 M (NH4)2SO4 (pH = 4.0), while aluminum (Al) was almost insoluble, exhibiting the selective leaching of Li. 84.76 % of Li and 17.63 % of Al are obtained at pH = 1.0. The correlation analysis result suggests that lithium ions (Li+) exist in the octahedron of the lattice as charge compensation. The migration mechanism is explained by the chemical shift of Li+, which moves from −0.196 ppm (raw, in the octahedron) to −0.319 ppm (ground, octahedral destruction) and further to −0.564 ppm (thermal activation, out of the octahedron). This paper can provide a theoretical basis for the occurrence of Li and a new method for selective extraction of Li from CG.

DFLOWFS: Deep Fast-Learning Optimal Weight Fuzzy System with bottom-up hierarchical structure for high-dimensional data regression

As a model for reasoning and decision-making based on fuzzy rules, fuzzy systems have high interpretability. However, when the data dimension increases, the fuzzy system will face the problem of “rule explosion”, making it difficult to learn and predict effectively. In this paper, the fuzzy system trained by the FLOWFS (Fast-Learning with Optimal Weights for Fuzzy Systems) algorithm is used as sub-module in the deep fuzzy system, and the deep fuzzy system DFLOWFS (Deep FLOWFS) is constructed from the bottom-up hierarchical structure as the following three steps. 1) The FLOWFS algorithm assigns weight attributions to each fuzzy rule, and the rule weights are trained by the least square method with regularization terms to shorten training time and improve accuracy. 2) Three strategies of dividing high-dimensional inputs into multiple low-dimensional inputs are proposed as sequential division, random division and correlation division. Then, it is verified by experiments that the correlation division has the best performance. 3) The sub-module discarding method is proposed to discard the sub-modules with poor performance to have a maximum improvement of 13.8% compared to the DFLOWFS without using the sub-module discarding method. Then, the optimized DFLOWFS is verified and compared with the other three classic regression models on the three UCI datasets. Experiments show that with the increase of the data dimension, DFLOWFS not only have good interpretability but also have good accuracy. Furthermore, DFLOWFS performs best among all models in comprehensive scores, with good learning ability and generalization ability. Therefore, the proposed strategies with hierarchical structure for optimal shallow fuzzy systems are effective, which give a new insight for fuzzy system research.

Source-Free Domain Adaptation via Target Prediction Distribution Searching

Existing Source-Free Domain Adaptation (SFDA) methods typically adopt the feature distribution alignment paradigm via mining auxiliary information (eg., pseudo-labelling, source domain data generation). However, they are largely limited due to that the auxiliary information is usually error-prone whilst lacking effective error-mitigation mechanisms. To overcome this fundamental limitation, in this paper we propose a novel Target Prediction Distribution Searching (TPDS) paradigm. Theoretically, we prove that in case of sufficient small distribution shift, the domain transfer error could be well bounded. To satisfy this condition, we introduce a flow of proxy distributions that facilitates the bridging of typically large distribution shift from the source domain to the target domain. This results in a progressive searching on the geodesic path where adjacent proxy distributions are regularized to have small shift so that the overall errors can be minimized. To account for the sequential correlation between proxy distributions, we develop a new pairwise alignment with category consistency algorithm for minimizing the adaptation errors. Specifically, a manifold geometry guided cross-distribution neighbour search is designed to detect the data pairs supporting the Wasserstein distance based shift measurement. Mutual information maximization is then adopted over these pairs for shift regularization. Extensive experiments on five challenging SFDA benchmarks show that our TPDS achieves new state-of-the-art performance. The code and datasets are available at https://github.com/tntek/TPDS.

High-Resolution Tracking of Multiple Distributions in Metallic Nanostructures: Advanced Analysis Was Carried Out with Novel 3D Correlation Thermal Field-Flow Fractionation.

Multifunctional metallic nanostructures are essential in the architecture of modern technology. However, their characterization remains challenging due to their hybrid nature. In this study, we present a novel photoreduction-based protocol for augmenting the inherent properties of imidazolium-containing ionic polymers (IIP)s through orthogonal functionalization with gold nanoparticles (Au NPs) to produce IIP_Au NPs, as well as novel and advanced characterization via three-dimensional correlation thermal field-flow fractionation (3DCoThFFF). Coordination chemistry is applied to anchor Au3+ onto the nitrogen atom of the imidazolium rings, for subsequent photoreduction to Au NPs using UV irradiation. Thermal field-flow fractionation (ThFFF) and the localized surface plasmon resonance (LSPR) of Au NPs are both dependent on size, shape, and composition, thus synergistically co-opted herein to develop mutual correlation for the advanced analysis of 3D spectral data. With 3DCoThFFF, multiple sizes, shapes, compositions, and their respective distributions are synchronously correlated using time-resolved LSPR, as derived from multiple two-dimensional UV-vis spectra per unit ThFFF retention time. As such, higher resolutions and sensitivities are observed relative to those of regular ThFFF and batch UV-vis. In addition, 3DCoThFFF is shown to be highly suitable for monitoring and evaluating the thermostability and dynamics of the metallic nanostructures through the sequential correlation of UV-vis spectra measured under incremental ThFFF temperature gradients. Comparable sizes are measured for IIP and IIP_Au NPs. However, distinct elution profiles and UV-vis absorbances are recorded, thereby reaffirming the versatility of ThFFF as a robust tool for validating the successful functionalization of IIP with Au to produce IIP_Au NPs.

Ensemble Learning for Breast Cancer Lesion Classification: A Pilot Validation Using Correlated Spectroscopic Imaging and Diffusion-Weighted Imaging.

The main objective of this work was to evaluate the application of individual and ensemble machine learning models to classify malignant and benign breast masses using features from two-dimensional (2D) correlated spectroscopy spectra extracted from five-dimensional echo-planar correlated spectroscopic imaging (5D EP-COSI) and diffusion-weighted imaging (DWI). Twenty-four different metabolite and lipid ratios with respect to diagonal fat peaks (1.4 ppm, 5.4 ppm) from 2D spectra, and water and fat peaks (4.7 ppm, 1.4 ppm) from one-dimensional non-water-suppressed (NWS) spectra were used as the features. Additionally, water fraction, fat fraction and water-to-fat ratios from NWS spectra and apparent diffusion coefficients (ADC) from DWI were included. The nine most important features were identified using recursive feature elimination, sequential forward selection and correlation analysis. XGBoost (AUC: 93.0%, Accuracy: 85.7%, F1-score: 88.9%, Precision: 88.2%, Sensitivity: 90.4%, Specificity: 84.6%) and GradientBoost (AUC: 94.3%, Accuracy: 89.3%, F1-score: 90.7%, Precision: 87.9%, Sensitivity: 94.2%, Specificity: 83.4%) were the best-performing models. Conventional biomarkers like choline, myo-Inositol, and glycine were statistically significant predictors. Key features contributing to the classification were ADC, 2D diagonal peaks at 0.9 ppm, 2.1 ppm, 3.5 ppm, and 5.4 ppm, cross peaks between 1.4 and 0.9 ppm, 4.3 and 4.1 ppm, 2.3 and 1.6 ppm, and the triglyceryl-fat cross peak. The results highlight the contribution of the 2D spectral peaks to the model, and they demonstrate the potential of 5D EP-COSI for early breast cancer detection.

STA-TCN: Spatial-temporal Attention over Temporal Convolutional Network for Next Point-of-interest Recommendation

Recent years have witnessed a vastly increasing popularity of location-based social networks (LBSNs), which facilitates studies on the next Point-of-Interest (POI) recommendation problem. A user’s POI visiting behavior shows the sequential transition correlation with previous successive check-ins and the global spatial-temporal correlation with those check-ins that happened a long time ago at a similar time of day and in geographically close areas. Although previous POI recommendation methods attempted to capture these two correlations, several limitations remain to be solved: (1) RNNs are widely adopted to capture the sequential transition correlation, whereas training an RNN is rather time-consuming given the long input check-in sequence. (2) The pairwise proximities on time of day and geographical area of check-ins are crucial for global spatial-temporal correlation learning, but have not been comprehensively considered by previous methods. To tackle these issues, we propose a novel next POI recommendation framework named STA-TCN. Specifically, instead of RNNs, STA-TCN augments the Temporal Convolutional Network with gated input injection to learn sequential transition correlation. Furthermore, STA-TCN fuses two novel grid-difference and time-sensitivity learning mechanisms with attention network to learn the pairwise spatial-temporal proximities among a user’s check-ins. Extensive experiments are conducted on two large-scale real-world LBSN datasets, and the results show that STA-TCN outperforms the best state-of-the-art baseline with an average improvement of 9.71% and 7.88% on hit rate and normalized discounted cumulative gain, respectively.

Deep Learning for Waveform Level Receiver Design With Natural Redundancy

High-speed information transmission system demands more powerful communication receivers. In this paper, we integrate deep learning algorithms into constructing waveform level receiver, which is capable of harnessing natural redundancy (NR) in raw message sources. Owing to end-to-end learning paradigm of neural network (NN), the proposed NN receiver can accomplish joint symbol timing synchronization and demodulation based on oversampled waveform sequences directly. The prevalent bidirectional LSTM (BiLSTM) and Transformer structures, suitable for excavating sequential correlation of complex sources and waveform sequences, are considered as the backbone of NN receivers. Under the cases of clean label and noisy label, we conceive two novel training algorithms and interpret their principles in theory. The clean label bits are accessible from original source encoding schemes, while noisy label bits are available from the decision results of canonical receivers with independently noised waveform sequences. When noisy labels possess sufficiently small error rates, optimized NN receiver is competitive with that adopting the accurate labels. As for Markov sources and natural language text sources, simulation results show that the proposed NN receivers’ performances are superior to the classical receivers without a priori knowledge, especially when high spectral efficiency modulation schemes are encountered and random noise is significant.

Statistical Analysis of Descending Open Cycles of Collatz Function

Collatz dynamic systems present a statistical space that can be studied rigorously. In a previous study, the author presented Collatz space in a unique dynamic numerical mode by tabulating a sequential correlation pattern of division by 2 of Collatz function’s even numbers until the numbers became odd with a consecutive occurrence, following an attribute of a 50:50 probability of division by 2 once (ascending behavior) as opposed to division by 2 more than once (descending behavior). In this paper, we describe the path of the Collatz function as sequences comprised of groups of the function’s iterates (open cycles) that end up with the first odd integer that is less than the starting odd integer. The descending behavior of the open cycles is attributed to a deterministic factor as observation of the cycles’ sequences shows. We do statistical analysis on 4 large samples of open cycles and orbits to 1. We define R(n) as the cycles’ deterministic variable defined as the ratio of division by 2 once to division by 2 more than once. We use statistical analysis to study the randomness of the orbits of the cycles’ starting odd positive integers as well as orbits to 1 up to 1,002,097,149.

Geochemical Characteristics of Rare-Metal, Rare-Dispersed, and Rare-Earth Elements and Depositional Environments in the Shanxi Formation Coal, Huainan Coalfield, Anhui, China

Coal, being one of the major energy sources for power generation, contains several critical trace elements. There is a growing scarcity and expense of these critical elements as a result of the increased demand and limitation of mining sources. To explore the geochemical characteristics of the rare-metal, rare-dispersed (scattered), and rare-earth elements (TREs) in coal, 25 coal seam samples of the Shanxi Formation in the Huainan coalfield were collected. The major element oxides, minerals, and TREs were analyzed by X-ray fluorescence spectroscopy (XRF), X-ray diffraction (XRD), and inductively coupled plasma-mass spectrometry (ICP-MS). The results revealed that the coal of the Shanxi Formation had ultra-low moisture and low ash yield and was medium-high-volatility with low sulfur content and high calorific value. Concerning minerals, the coal was mainly composed of kaolinite, illite, quartz, calcite, dolomite, and pyrite. Compared with Chinese coal and world hard coal, rare-metal element Li and rare-dispersed element Se were enriched, whereas Ga and Ta were only slightly enriched. The average content of REYs was 51.34 μg/g, which is lower than the average content of REYs in Chinese coal. It has the enrichment characteristics of light REYs. In the vertical direction, the content of most TREs was higher in the roof and floor of the coal seam and the parting, indicating that the sedimentary microenvironment plays an important role in controlling the migration and enrichment of elements. The experimental results of sequential chemical extraction and correlation analysis showed that the TREs in the Shanxi Formation coal mainly exist in a residual and carbonate bound state, and occur in clay minerals and carbonate minerals. The enrichment of Se may be due to its high organic form ratio. The C-value, B content, w(Sr)/w(Ba), and REY geochemical parameters indicated that the Shanxi Formation Coal seam was developed in a transitional, semi-saline, deltaic sedimentary environment. With their development affected by seawater, REYs in coal are greatly supplied by terrigenous clastics. The complex sedimentary environment is an important reason for the varying occurrence states of TREs in the Shanxi Formation coals.

GPU accelerated grouped magnetic resonance fingerprinting using clustering techniques

Magnetic Resonance Fingerprinting (MRF) is a new quantitative technique of Magnetic Resonance Imaging (MRI). Conventionally, MRF requires sequential correlation of the acquired MRF signals with all the signals of (a large sized) MRF dictionary. This is a computationally intensive matching process and is a major challenge in MRF image reconstruction. This paper introduces the use of clustering techniques (to reduce the effective size of MRF dictionary) by splitting MRF dictionary into multiple small sized MRF dictionary components called MRF signal groups. The proposed method has been further optimized for parallel processing to reduce the computation time of MRF pattern matching. A multi-core GPU based parallel framework has been developed that enables the MRF algorithm to process multiple MRF signals simultaneously. Experiments have been performed on human head and phantom datasets. The results show that the proposed method accelerates the conventional MRF (MATLAB based) reconstruction time up to 25× with single-core CPU implementation, 300× with multi- core CPU implementation and 1035× with the proposed multi-core GPU based framework by keeping the SNR of the resulting images in a clinically acceptable range. Furthermore, experimental results show that the memory requirements of MRF dictionary get significantly reduced (due to efficient memory utilization) in the proposed method.

Applying Feature Detection to XPCS Image Processing

Sequential X-ray photon correlation spectroscopy (XPCS) reveals sample dynamics by analyzing a series of coherent scattering images, which is often time-consuming. For applications like real-time XPCS analysis, high efficiency is desired. Pixel binning is a straightforward strategy to reduce the processing time, but over-binning may result in an insufficient signal-to-noise ratio. In this work, feature detection is applied to obtain the optimal binning factor for the XPCS image processing. Results show that under optimal binning, the processing time is reduced by more than one order of magnitude. In addition, it is illustrated that feature detection could potentially be applied to other coherent imaging and scattering techniques such as coherent diffraction imaging (CDI).

Supervised learning-assisted modeling of flow-based domains in European resource adequacy assessments

• This paper aims to enhance the modeling of cross-border energy exchanges in adequacy study. • Novel supervised learning-based models in single- and two-step set-ups are proposed. • Accuracy, scalability, and computational complexity of adequacy study are improved. • It can have high implication for policy makers and be of a great interest of academics. To represent the cross-border exchange capacities defined by the flow-based approach in the European resource adequacy assessments, transmission system operators currently employ a data-driven methodology that consists of sequential clustering and correlation steps. This methodology entails assumptions and simplifications within both clustering and correlation analyses that may lead to an erroneous representation of import–export capacities in the subsequent adequacy assessments. While the first stage of this methodology can be improved by leveraging a clustering technique tailored to adequacy assessments, the correlation step presents a poor performance in terms of accuracy and scalability. To address the latter challenges, this paper proposes a supervised learning-based model that can enhance the mapping between several relevant explanatory variables and the pre-clustered flow-based domains, leading to a more accurate representation of the flow-based domains in adequacy assessments. Furthermore, the current paper leverages supervised learning to develop a single-step approach that directly maps the selected explanatory variables to the flow-based domains using the K-Nearest Neighbors algorithm, eliminating the clustering step. This circumvents inaccuracies introduced by the significant intra-cluster discrepancies due to numerous shapes and forms of the flow-based domains and enables an enhanced modeling of the flow-based domains in adequacy assessments. In an extensive case study, we demonstrate that the proposed single-step model can significantly improve the accuracy of adequacy assessments, compared to the best-in-class result obtained by the two-step set-up. Moreover, the proposed single-step model involves no hyper-parameters, eliminates the computational complexity of the two-step set-up, and efficiently upscales to integrate the new zones joining to the flow-based market coupling.

Safety analysis of marine nuclear reactor in severe accident with dynamic fault trees based on cut sequence method

Dynamic fault tree (DFT) and its related research methods have received extensive attention in safety analysis and reliability engineering. DFT can perform reliability modelling for systems with sequential correlation, resource sharing, and cold and hot spare parts. A technical modelling method of DFT is proposed for modelling ship collision accidents and loss-of-coolant accidents (LOCAs). Qualitative and quantitative analyses of DFT were carried out using the cutting sequence (CS)/extended cutting sequence (ECS) method. The results show nine types of dynamic fault failure modes in ship collision accidents, describing the fault propagation process of a dynamic system and reflect the dynamic changes of the entire accident system. The probability of a ship collision accident is 2.378 × 10−9 by using CS. This failure mode cannot be expressed by a combination of basic events within the same event frame after an LOCA occurs in a marine nuclear reactor because the system contains warm spare parts. Therefore, the probability of losing reactor control was calculated as 8.125 × 10−6 using the ECS. Compared with CS, ECS is more efficient considering expression and processing capabilities, and has a significant advantage considering cost.

Diagnostic and prognostic performance of Mxa and transfer function analysis-based dynamic cerebral autoregulation metrics

Dynamic cerebral autoregulation is often assessed by continuously recorded arterial blood pressure (ABP) and transcranial Doppler-derived mean cerebral blood flow velocity followed by analysis in the time and frequency domain, respectively. Sequential correlation (in the time domain, yielding e.g., the measure mean flow index, Mxa) and transfer function analysis (TFA) (in the frequency domain, yielding, e.g., normalised and non-normalised gain as well as phase in the low frequency domain) are commonly used approaches. This study investigated the diagnostic and prognostic performance of these metrics. We included recordings from 48 healthy volunteers, 19 patients with sepsis, 36 with traumatic brain injury (TBI), and 14 patients admitted to a neurorehabilitation unit. The diagnostic (between healthy volunteers and patients) and prognostic performance (to predict death or poor functional outcome) of Mxa and the TFA measures were assessed by area under the receiver-operating characteristic (AUROC) curves. AUROC curves generally indicated that the measures were ‘no better than chance’ (AUROC ∼0.5) both for distinguishing between healthy volunteers and patient groups, and for predicting outcomes in our cohort. No metric emerged as superior for distinguishing between healthy volunteers and different patient groups, for assessing the effect of interventions, or for predicting mortality or functional outcome.

Suppression of Deception-False-Target Jamming for Active/Passive Netted Radar Based on Position Error

Owing to the shortcomings of single view angle and insufficient information in the monostatic radar, it is difficult to effectively suppress the deception-false-target (FT) jamming. To counter the range-velocity compound deception jamming, a suppression method based on the radar position error (RPE) is proposed for active <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$/$ </tex-math></inline-formula> passive netted radar on different moving platforms. In this algorithm, FTs are discriminated in the two stages of track initiation and target tracking. Firstly, in the track initiation stage, the RPE is taken into consideration to construct the error covariance matrix of the Mahalanobis distance. Then, the chi-square test is used to make the measurement correlation based on the azimuth and pitch angle information, which eliminates some FTs. Secondly, the measurements in active radar, which has been successfully correlated, are regarded as the supplementary for track initiation of passive radar. The FTs are discriminated again based on the radial velocity information. Finally, in the target tracking stage, the targets are tracked independently in active radar and passive radar. The sequential track correlation method is adapted to eliminate the remaining FTs that have been maintained in active radar. Simulation results verify that the proposed method improves the discrimination probability of FTs under the condition of ensuring the high discrimination probability of the physical target (PT).

Comment on: Laser corneal enhancement after trifocal intraocular lens implantation in eyes that had previously undergone photoablative corneal refractive surgery.

We congratulate Mayordomo-Cerdá et al. on their valuable observations in a large group of patients after sequential trifocal intraocular lens (IOL) implantation and laser corneal enhancement (LCE) after primary laser corneal refractive surgery (LCRS) for hyperopia or myopia.1 This is an increasingly frequent clinical problem as more patients with prior LCRS develop presbyopia and/or cataract yet still seek spectacle independence. We highlight some points of discussion, which may benefit the design of further studies aimed at optimizing outcomes in this challenging group. The reported rate of dissatisfaction of 10% to 20% is higher than that typically observed in studies of primary trifocal IOL implantation (∼2%).2 It would be interesting to know to what extent this disparity relates to residual refractive error or higher-order aberrations (HOAs): both are more likely after LCRS. Separating these factors may identify the main source of dissatisfaction and guide onward management of individual patients. A diffractive trifocal IOL adds negative spherical aberration to eyes with a wider defocus curve, which may be further modified by the original LCRS and subsequent LCE. While this may be desirable after myopic laser in situ keratomileusis (LASIK), it can have an adverse effect on quality of vision after hyperopic LCRS. The presentation of defocus curves may have facilitated the understanding of the presented outcomes, particularly in this relatively complex optical system. Furthermore, certain LCE techniques may be better suited to the original LCRS method used. Consequently, it would be of interest to know how HOAs varied between myopic and hyperopic subgroups after sequential treatments and correlation with final visual outcomes. As the number of post-LCRS patients with presbyopia and/or cataract increases, data on visual outcomes and safety are likely to increase across a range of treatment options such as monovision, small-aperture IOLs, or combination of trifocal and low-addition bifocal IOLs, with or without LCE.3 Alternatively, in the absence of cataract (45% in this study), additional LCE with or without presbyopic protocols may be considered instead of presbyopic refractive lens exchange. Since some degree of corneal multifocality is present after LASIK, especially with older laser protocols and myopic treatments, individuals with larger pupils may benefit from the spherical aberration–induced increased depth of focus. Current studies may yield more favorable results simply because lens technology has developed (ie, toric trifocal IOLs are now available), laser platforms have improved, and IOL calculation formulas for post-LCRS eyes have evolved.4,5 This study reported quite high cylindrical refractive error after primary LCRS for which toric trifocal IOL implantation may have prevented the need for subsequent LCE. The predominant method of LCE was photorefractive keratectomy (PRK) (72%), which is more likely to delay recovery with postoperative haze and ocular surface symptoms. Some surgeons favor LASIK or small-incision lenticule extraction for laser retreatments for these reasons. The preferred LCE protocol (topography-guided vs wavefront-guided treatment) is not clarified in the study, which could aid the interpretation of postoperative satisfaction. Information on LCE modality according to the type of primary treatment (myopic vs hyperopic) would also add further value to this welcome and valuable study.