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Due to event-triggered sampling in a system, or maybe with the aim of reducing data storage, tracking many applications will encounter irregular sampling time. By calculating the matrix exponential using an inverse Laplace transform, this paper transforms the irregular sampling tracking problem to the problem of tracking with time-varying parameters of a system. Using the common Kalman filter, the developed method is used to track a target for the simulated trajectory and video tracking. The results of simulation experiments have shown that it can obtain good estimation performance even at a very high irregular rate of measurement sampling time.

Quasars are bright and unobscured active galactic nuclei (AGN) thought to be powered by the accretion of matter around supermassive black holes at the centers of galaxies. The temporal variability of a quasar’s brightness contains valuable information about its physical properties. The UV/optical variability is thought to be a stochastic process, often represented as a damped random walk described by a stochastic differential equation (SDE). Upcoming wide-field telescopes such as the Rubin Observatory Legacy Survey of Space and Time (LSST) are expected to observe tens of millions of AGN in multiple filters over a ten year period, so there is a need for efficient and automated modeling techniques that can handle the large volume of data. Latent SDEs are machine learning models well suited for modeling quasar variability, as they can explicitly capture the underlying stochastic dynamics. In this work, we adapt latent SDEs to jointly reconstruct multivariate quasar light curves and infer their physical properties such as the black hole mass, inclination angle, and temperature slope. Our model is trained on realistic simulations of LSST ten year quasar light curves, and we demonstrate its ability to reconstruct quasar light curves even in the presence of long seasonal gaps and irregular sampling across different bands, outperforming a multioutput Gaussian process regression baseline. Our method has the potential to provide a deeper understanding of the physical properties of quasars and is applicable to a wide range of other multivariate time series with missing data and irregular sampling.

Home-range estimation is an important application of animal tracking data that is frequently complicated by autocorrelation, sampling irregularity, and small effective sample sizes. We introduce a novel, optimal weighting method that accounts for temporal sampling bias in autocorrelated tracking data. This method corrects for irregular and missing data, such that oversampled times are downweighted and undersampled times are upweighted to minimize error in the home-range estimate. We also introduce computationally efficient algorithms that make this method feasible with large data sets. Generally speaking, there are three situations where weight optimization improves the accuracy of home-range estimates: with marine data, where the sampling schedule is highly irregular, with duty cycled data, where the sampling schedule changes during the observation period, and when a small number of home-range crossings are observed, making the beginning and end times more independent and informative than the intermediate times. Using both simulated data and empirical examples including reef manta ray, Mongolian gazelle, and African buffalo, optimal weighting is shown to reduce the error and increase the spatial resolution of home-range estimates. With a conveniently packaged and computationally efficient software implementation, this method broadens the array of data sets with which accurate space-use assessments can be made.

The combined University of Michigan Radio Astronomy Observatory and Owens Valley Radio Observatory blazar monitoring programs at 14.5/15 GHz provide uninterrupted light curves of ∼ 46–50 yr duration for 83 blazars, selected from among the brightest and most rapidly flaring blazars north of declination −20°. In a search for supermassive black hole binary (SMBHB) candidates, we carried out tests for periodic variability using generalized Lomb–Scargle (GLS), weighted wavelet-Z, and sine-wave fitting analyses of this sample. We used simulations to test the effects of the power-law spectrum of the power spectral density (PSD) on our findings, and show that the irregular sampling in the observed light curves has very little effect on the GLS spectra. Apparent periodicities and putative harmonics appear in all 83 of the GLS spectra of the blazars in our sample. We tested the reality of these apparent periodicities and harmonics with simulations, and found that in the overwhelming majority of cases, they must be due to the steep slope of the PSD and the random nature of blazar flares, implying that, in general, apparent periodicities and harmonics in blazar light curves observed in any energy band should be treated with great caution. We find one new SMBHB candidate: PKS 1309+1154, which exhibits a 17.9 yr periodicity. The fraction of SMBHB candidates in our sample is 2.4−0.8+3.2% .

UV and optical continuum reverberation mapping is a powerful tool for probing the accretion disk and inner broad-line region. However, recent reverberation mapping campaigns in the X-ray, UV, and optical have found lags consistently longer than those expected from the standard disk reprocessing picture. The largest discrepancy to date was recently reported in Mrk 335, where UV/optical lags are up to 12 times longer than expected. Here, we perform a frequency-resolved time lag analysis of Mrk 335, using Gaussian processes to account for irregular sampling. For the first time, we compare the Fourier frequency-resolved lags directly to those computed using the popular interpolated cross-correlation function method applied to both the original and detrended light curves. We show that the anticipated disk reverberation lags are recovered by the Fourier lags when zeroing in on the short-timescale variability. This suggests that a separate variability component is present on long timescales. If this separate component is modeled as reverberation from another region beyond the accretion disk, we constrain a size scale of roughly 15 lt-days from the central black hole. This is consistent with the size of the broad-line region inferred from Hβ reverberation lags. We also find tentative evidence for a soft X-ray lag, which we propose may be due to light travel time delays between the hard X-ray corona and distant photoionized gas that dominates the soft X-ray spectrum below 2 keV.

Time‐series data missing is a common problem, which often happens with irregular sampling in sensor device failure in human‐cyber‐physical systems (HCPSs). The generation of networked time‐series data is conducive to achieving real‐time perception in HCPSs. Many methods exist for imputing random or non‐random missing data, but their accuracy is often inadequate at high missing rates. We propose a cross‐modality approach using dense spatio‐temporal transformer networks (DSTTN) to impute high‐rate missing data in time series. The DSTTN merges the spatio‐temporal modal data by cross‐modality data fusion technique, and then constructs an end‐to‐end transformer pipeline with dense skip connections to recover the corrupted data accurately. We have conducted many comparative experiments to assess DSTTN imputation performance in the MAR and missing not at random (MNAR). Cross‐modality data fusion offers a new solution for complete data missing, a specific case of MNAR. Furthermore, we also compare and analyse the various recent models, and the particularities between them. Based on the comparative analysis, the application value and working conditions of the DSTTN are demonstrated in detail by the results of rich experiments. We propose a cross‐modality approach using dense spatio‐temporal transformer networks (DSTTN) to impute high‐rate missing data in time series. The DSTTN merges the spatio‐temporal modal data by cross‐modality data fusion technique, and construct an end‐to‐end transformer pipeline with dense skip connections to recover the corrupted data accurately.

Understanding the variability of Sagittarius A* (Sgr A*) requires coordinated, multiwavelength observations that span the electromagnetic spectrum. In this work, we focus on data from four key observatories: Chandra in the X-ray (2–8 keV), GRAVITY on the Very Large Telescope in the near-infrared (2.2 μm), Spitzer in the infrared (4.5 μm), and the Atacama Large Millimeter/submillimeter Array in the submillimeter (340 GHz). These multiband observations are essential for probing the physics of accretion and emission near the black hole’s event horizon, yet they suffer from irregular sampling, band-dependent noise, and substantial data gaps. These limitations complicate efforts to robustly identify flares and measure cross-band time lags, key diagnostics of the physical processes driving variability. To address this challenge, we introduce a diffusion-based generative model, for interpolating sparse, multivariate astrophysical time series. This represents the first application of score-based diffusion models to astronomical time series. We also present the first transformer-based model for light-curve reconstruction that includes calibrated uncertainty estimates. The models are trained on simulated light curves constructed to match the statistical and observational characteristics of real Sgr A* data. These simulations capture correlated multiband variability, realistic observation cadences, and wavelength-specific noise. We compare our models against a multi-output Gaussian process. The diffusion model achieves superior accuracy and competitive calibration across both simulated and real datasets, demonstrating the promise of diffusion models for high-fidelity, uncertainty-aware reconstruction of multiwavelength variability in Sgr A*.

A key science goal of large sky surveys such as those conducted by the Vera C. Rubin Observatory and precursors to the Square Kilometre Array is the identification of variable and transient objects. One approach is analyzing time series of the changing brightness of sources, namely, light curves. However, finding adequate statistical representations of light curves is challenging because of the sparsity of observations, irregular sampling, and nuisance factors inherent in astronomical data collection. The wide diversity of objects that a large-scale survey will observe also means that making parametric assumptions about the shape of light curves is problematic. We present a Gaussian process (GP) regression approach for characterizing light-curve variability that addresses these challenges. Our approach makes no assumptions about the shape of a light curve and, therefore, is general enough to detect a range of variable and transient source types. In particular, we propose using the joint distribution of GP amplitude hyperparameters to distinguish variable and transient candidates from nominally stable ones and apply this approach to 6394 radio light curves from the ThunderKAT survey. We compare our results with two variability metrics commonly used in radio astronomy, namely ην and Vν, and show that our approach has better discriminatory power and interpretability. Finally, we conduct a rudimentary search for transient sources in the ThunderKAT data set to demonstrate how our approach might be used as an initial screening tool. Computational notebooks in Python and R are available to help deploy this framework to other surveys.

The hot metal silicon content is a key indicator of the thermal state in the blast furnace and it needs to be kept within a pre-defined range in order to ensure efficient operations. Effective monitoring of silicon content is challenging due to the harsh environment in the furnace and irregularly sampled measurements. Data-driven approaches have been proposed in the literature to predict silicon content using process data and overcome the sparsity of silicon content measurements. However, these approaches rely on the selection of hand-crafted features and ad hoc interpolation methods to deal with irregular sampling of the process variables, adding complexity to model training and optimisation, and requiring significant effort when tuning the model over time to keep it to the required level of accuracy. This paper proposes an improved framework for the prediction of silicon content using a novel deep learning approach based on Phased LSTM. The model has been trained using 3 years of data and validated over a 1-year period using a robust walk-forward validation method, therefore providing confidence in the model performance over time. The Phased LSTM model outperforms competing approaches due to its in-built ability to learn from event-based sequences and scalability for real-world deployments. This is the first time that Phased LSTM has been applied to real-world datasets and results suggest that the ability to learn from event-based data can be beneficial for the process industry where event-driven signals from multiple sensors are common.

Abstract In seismic exploration, the acquisition of ideal seismic data is often hindered by various constraints such as high costs and environmental limitations, leading to compromised imaging quality. Compressive sensing (CS) offers novel theories and tools to analyze and guide the acquisition and processing of seismic data. This paper explores the technical advantages and physical mechanisms of CS seismic exploration techniques in direct imaging of irregularly acquired data and imaging of reconstructed data compared to traditional acquisition methods. Our research findings demonstrate that irregular acquired data based on CS acquisition inherently possesses anti-aliasing capabilities in migration imaging, converting strong regular migration noise generated by regular sampling into noise with a random distribution, and through stacking processes suppress migration noise, thereby effectively enhancing the signal-to-noise ratio of imaging. Furthermore, irregularly acquired data exhibits reconstruction advantages, enabling the reconstruction of regular high-density seismic data that yields superior imaging effects. Hence, CS seismic exploration technology is conducive to improving the imaging quality of seismic data.