Accurate spectral analysis of high-energy astrophysical sources often relies on comparing observed data to incident spectral models convolved with the instrument response. However, for Gamma-Ray Bursts and other high-energy transient events observed at high count rates, significant distortions (e.g., pile-up, dead time, and large signal trailing) are introduced, complicating this analysis. We present a method framework to address the model dependence problem, especially to solve the problem of energy spectrum distortion caused by instrument signal pile-up due to high counting rate and high-rate effects, applicable to X-ray, gamma-ray, and particle detectors. Our approach combines physics-based Monte Carlo (MC) simulations with a model-independent spectral inversion technique. The MC simulations quantify instrumental effects and enable correction of the distorted spectrum. Subsequently, the inversion step reconstructs the incident spectrum using an inverse response matrix approach, conceptually equivalent to deconvolving the detector response. The inversion employs a Convolutional Neural Network, selected for its numerical stability and effective handling of complex detector responses. Validation using simulations across diverse input spectra demonstrates high fidelity. Specifically, for 27 different parameter sets of the brightest gamma-ray bursts, goodness-of-fit tests confirm the reconstructed spectra are in excellent statistical agreement with the input spectra, and residuals are typically within ± 2σ. This method enables precise analysis of intense transients and other high-flux events, overcoming limitations imposed by instrumental effects in traditional analyses.

Earth's radiation belt is filled with high-energy electrons and protons, the particle fluxes distributions and dynamic variations are significantly modulated by solar activities. Based on high-precision China Seismo-Electromagnetic Satellite (CSES) satellite data from 2019 to 2024, a statistical analysis of radiation belt electrons and protons is conducted to investigate their long-term responses to space weather events and solar cycle variations. Firstly, During the solar minimum, high-energy electrons in the outer radiation belt exhibit a pronounced similar to 27-day recurrence, which is strongly correlated with recurrent solar wind speed enhancements. Secondly, Proton fluxes in the inner radiation belt exhibit an inverse correlation with solar activity, primarily due to enhanced atmospheric neutral density and increased Coulomb collisions during solar maximum. Thirdly, the observed day-night asymmetry in proton fluxes is attributed to the interaction between proton gyromotion and the upper atmosphere molecule collision in low-Earth orbit, as well as the satellite's orbital and instrument viewing geometry. Additionally, a distinct and persistent double-peaked structure is reported in the low-energy (2-10 MeV) protons of the inner belt, which differs from traditional radiation belt models, but is consistent with the National Oceanic and Atmospheric Administration (NOAA-19) satellite observations. This structure maybe related to the weakened magnetic field on the southeastern side of the South Atlantic Anomaly (SAA). These results provide new insights for understanding of the dynamic variations and structural complexity of radiation belt particles associated with space weather activities. (c) 2026 China University of Geosciences (Beijing) and Peking University. Published by Elsevier B.V. on behalf of China University of Geosciences (Beijing). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

The randomized Kaczmarz method, the randomized Gauss-Seidel method, the randomized extended Kaczmarz method, and the randomized extended Gauss-Seidel method are four efficient randomized iteration methods for solving large-scale systems of linear equations. In this paper, we point out that the randomized extended Gauss-Seidel method is actually mathematically equivalent to the randomized extended Kaczmarz method, and we find the intrinsic connection between the randomized-Kaczmarz-type methods and the randomized-Gauss-Seidel-type methods. In addition, by classifying a linear system into four cases according to its consistency and the column-rank of its coefficient matrix, we give the preferred method among the four randomized iteration methods in each case. With these results, we can make full use of the most appropriate randomized iteration method to solve the linear system. What is more, we can also obtain new efficient randomized iteration methods based on these analyses.

Among the coronal mass ejections (CMEs) and solar proton events (SPEs) frequently observed by near-Earth spacecraft, the SPE that occurred on 28 October 2021 stands out as a remarkable research event. This is due to the infrequency of reported ground-level enhancements it induced. The CSES (China seismo-electromagnetic satellite) is equipped with high-energy particle detectors, namely, HEPP and HEPD, capable of measuring protons within an energy range of 2 MeV to 143 MeV. These detectors provide valuable opportunities for studying solar activity. By utilizing the Monte Carlo method to simulate the pile-up effect and accounting for the detector’s dead time, with the assistance of real-time incident counting rates, we successfully corrected the spectra in the 10–50 MeV range. The energy spectrum is important for understanding solar proton events. We used the data from the HEPP (high-energy particle package) and HEPD (high-energy particle detector) to obtain the total event-integrated spectrum, which possessed good continuity. Additionally, we compared the observations from the CSES with those from the NOAA satellite and achieved reasonable agreement. We also searched for ground-based responses to this solar activity in China and discovered Forbush decreases detected by the Yang Ba Jing Muon Telescope experiment. In conclusion, the HEPP and HEPD can effectively combine to study solar activity and obtain a smooth and consistent energy spectrum of protons across a very wide energy range.

The central position of the South Atlantic Anomaly (SAA) has been drifting westward or northward, and the drift speeds exhibit a complex relationship with solar activity, which also affects the area of the SAA configuration. Using six years of data from the low-Earth orbit satellite CSES, we analyze the spatiotemporal evolution of the geomagnetic field and high-energy protons within the SAA during Solar Cycle 25. Low-energy protons (2.0–10.0 MeV) exhibit a characteristic double-peak structure, whereas high-energy protons (10.0–20.0 MeV) display a single-peak profile—consistent with observations from NOAA/MEPED. By fitting a Double-Gaussian distribution in both latitude and longitude from January 2019 to April 2024, we find that the center of the SAA proton distribution drifted northward at an average speed of 0.29±0.12°/yr (dayside). At the same time, the SAA proton center drifted westward at speeds of 0.36±0.08°/yr (dayside) and 0.33±0.10°/yr (nightside). Notably, lower-energy protons drift slightly faster. The geomagnetic field variations in the SAA region observed by CSES are generally consistent with the IGRF-13 model. Based on IGRF-13, we calculate drift speeds from 2015 to 2025 to be 0.014±0.002°/yr in the northward (latitudinal) direction and 0.282±0.030°/yr in the westward (longitudinal) direction. Quantitative boundary analysis further indicates that the area of the SAA decreased by 6.09

Earth suffered the attack of the strongest geomagnetic storm in the last 20 years (Kp = 9, Dst −400 nT) occurred on 11 May 2024. Taking advantage of the LEO multi‐parameter CSES satellite (launched in 2018) with a large inclination angle , with the joint observations of NOAA and GOES, we present a comprehensive near‐earth space responses on this super geomagnetic storm and report the precise high energy particle flux enhancements, electric and magnetic field disturbances and plasma density changes. A new proton belt with fluxes exceeding with energy 2.5–14 MeV at L = 1.5 ∼ 2 was formed, which was likely caused by the inward proton penetration from solar proton events(SPEs) and possible energization under the condition of compressed magnetopause in the southward interplanetary magnetic field of subsequent storm sudden commencement(SSC). During this super storm, many kinds of excited electromagnetic (EM) waves, such as ULF waves at several Hz, left‐hand polarized quasi‐periodic waves and magnetosonic waves, were observed in the ionosphere. Simultaneously, the electron and ion density, temperature and the total electron content (TEC) show significantly complicated changes after the storm occurrence. We also investigated the ground influence in western region of China and an obvious Forbush decrease of muon detection by 5 was caused by the storm effect.

The China Seismo-Electromagnetic Satellite (CSES-01) is the first satellite of the space-based observational platform for the earthquake (EQ) monitoring system in China. It aims to monitor the ionospheric disturbances related to EQ activities by acquiring global electromagnetic fields, ionospheric plasma, energy particles, etc., opening a new path for innovative explorations of EQ prediction. This study analyzed 47 shallow strong EQ cases (Ms ≥ 7 and depth ≤ 100 km) recorded by CSES-01 from its launch in February 2018 to February 2023. The results show that: (1) For the majority (90%) of shallow strong EQs, at least one payload onboard CSES-01 recorded discernible abnormal signals before the mainshocks, and for over 65% of EQs, two or three payloads simultaneously recorded ionospheric disturbances; (2) the majority of anomalies recorded by different payloads onboard CSES-01 predominantly manifest within one week before or on the mainshock day, or occasionally about 11–15 days or 20–25 days before the mainshock; (3) typically, the abnormal signal detected by CSES-01 does not directly appear overhead the epicenter, but rather hundreds of kilometers away from the epicenter, and more preferably toward the equatorward direction; (4) the anomaly recognition rate of each payload differs, with the highest rate reaching more than 70% for the Electric Field Detector (EFD), Search-Coil Magnetometer (SCM), and Langmuir Probe (LAP); (5) for the different parameters analyzed in this study, the plasma density from LAP, and electromagnetic field in the ULF band recorded by EFD and SCM, and energetic electrons from the High-Energy Particle Package (HEPP) show a relatively high occurrence of abnormal phenomena during the EQ time. Although CSES-01 has recorded prominent ionospheric anomalies for a significant portion of EQ cases, it is still challenging to accurately extract and confirm the real seismic precursor signals by relying solely on a single satellite. The combination of seismology, electromagnetism, geodesy, geochemistry, and other multidisciplinary means is needed in the future’s exploration to get infinitely closer to addressing the global challenge of EQ prediction.

Based on the observations by the sun-synchronous circular orbit China Seismo-Electromagnetic Satellite(CSES), a typical case of the rising-tone quasiperiodic (QP) emissions with a large period of around 2 min was reported to appear on the dayside on 23 October 2021. The frequency of QP waves ranges from 2,000 similar to 3,000 Hz and the wave spectral structure consists of four elements with right-handed polarization. Three elements of them are located at extremely low L-shells from 2 similar to 3.5. The periodic precipitating fluxes of 100 similar to 400 keV electrons were found in the conjugate region also observed by CSES, which appeared in the same magnetic field lines with the elements of QP waves, respectively. By numerical simulations of quasi-linear diffusion theory, we confirm that QP emissions can effectively precipitate energetic electrons near the loss cone into the atmosphere in the inner radiation belt. To our best knowledge, this is the first evidence that the rising-tone QP whistler waves scatter electrons in the inner radiation belt. This new finding will help to deepen our understanding of the electron precipitation dynamics in radiation belt physics. The whistler-mode quasiperiodic (QP) emissions with a repetition period from several seconds to several minutes have been reported by a large amount of satellites and ground-based detector stations observations, and their generation mechanisms have been studied a lot. However, the reports about diffusion or acceleration effects on the relativistic electrons induced by QP waves are rare and only a little focused on the outer radiation belts. CSES satellite with the sun-synchronous polar orbits at 507 km altitude provides an advantage to study the wave-particle interaction in the extremely low L-shell regions including the inner radiation belts. In this work, we present the rising-tone QP whistler waves observed by CSES satellite in the inner radiation belt. Simultaneously, the periodic precipitating fluxes of 100-400 keV electrons were found in the same magnetic field lines with the elements of QP waves, respectively. To our knowledge, this provides the first evidence that QP emissions can effectively precipitate energetic electrons into the atmosphere in the inner radiation belt. This scenario is confirmed by our numerical simulations of quasi-linear diffusion theory. This new finding will help to deeply understand the electron precipitation dynamics in radiation belt physics. The rising-tone quasi-periodic (QP) whistler waves are observed by CSES satellite in the inner radiation belt100 similar to 400 keV electrons within 30 degrees equatorial pitch angles in the conjugate region was periodically precipitatedQP whistler waves can efficiently diffuse relativistic electrons near the bounce loss cone in extremely low L-shells (L = 2 similar to 3.5)

Earthquakes (EQs) are a significant natural threat to humanity. In recent years, with advancements in space observation technology, it has been put forward that the electromagnetic effects of earthquakes can propagate into space in various ways, causing electromagnetic radiation and plasma disturbances in space and leading to high–energy particle precipitation. The China Seismo-Electromagnetic Satellite (CSES) is specifically designed for monitoring the space electromagnetic environment. In our study, we select 78 strong earthquakes from September 2018 to February 2023 (global earthquakes with M ⩾ 7.0 and the major seismic regions in China with M ⩾ 6.0). We focus on 10∘ of the latitude and longitude around the epicenter, spanning from 15 days before the earthquake to 5 days after, and look for anomalies in spatial evolution and temporal evolution. We present some typical cases of electron flux perturbation and summarize the anomalies of all 78 cases to look for regularity in EQ–related particle anomalies. Notably, we introduce two cases of simultaneous electromagnetic and energetic particle anomalies during earthquakes. And we propose a conjecture that the particle precipitation may be the result of wave–particle interactions triggered by seismic activity.

The Kaczmarz method is a classical while effective iteration method for solving very large-scale consistent systems of linear equations, and the randomized Kaczmarz method is an important and valuable variant of the Kaczmarz method. By theoretically analyzing and numerically experimenting several criteria typically adopted in the non-randomized and the randomized Kaczmarz method for selecting the working row, we derive sharper upper bounds for the convergence rates of some of the correspondingly induced Kaczmarz-type methods including those with respect to the maximal residual, maximal distance, and distance selection rules of the working row, and, for this whole suite of iteration methods consisting of the Kaczmarz methods with respect to the uniform, non-uniform, residual, distance, maximal residual, and maximal distance selection rules of the working row, we reveal their comparable relationships in terms of both mean-squared distance and mean-squared error, and show their computational effectiveness and numerical robustness based upon implementing a large number of test examples. Here the mean-squared distance is defined as the mean-value of the squared Euclidean norm of the current update increment of the iteration, and the mean-squared error is defined as the mean-value of the squared Euclidean norm of the current error that is the difference between the current iterate and the true solution of the target linear system.

In order to improve the convergence property and computational behavior of the randomized extended Kaczmarz method, we propose a multi-step randomized extended Kaczmarz method, in which we repeatedly update the iterate several times at each iteration step, obtaining a nonstationary inner-outer iteration scheme for solving large-scale, sparse, and inconsistent system of linear equations. For this multi-step randomized extended Kaczmarz method, we prove its convergence, derive an upper bound for its convergence rate, and demonstrate that this upper bound can be smaller than that of the randomized extended Kaczmarz method for several typical choices of the numbers of inner iteration steps. Numerical experiments also show that the multi-step randomized extended Kaczmarz method can perform better than the randomized extended Kaczmarz method if we choose the numbers of inner iteration steps appropriately.

Solar eruptions can cause violent effects on the space environment. Electromagnetic radiation from solar flares will be the first to arrive on the Earth at the speed of light, followed by solar energetic charged particles. The last to appear will be coronal mass ejections and geomagnetic storms. Based on observations of ZH-1 satellite, we report three strong disturbed space environment events, all of them with solar proton events (SPEs), and analyze the driving mechanisms: 1) On 29 November 2020, an M4.4 flare accompanied with a full halo CME caused a gradual SPE, which was mainly driven by CME shocks. 2) On 28 May 2021, a C9.4 flare brought an impulsive SPE, which was accelerated by the flare. The heliolongitude of this small flare was 63°W, near the footpoint of the magnetic field line leading from the Sun to the Earth. 3) On 28 October 2021, a full-halo CME accompanied with an X1.1 flare brought a gradual SPE. On 2 November 2021, another fast full halo CME accompanied with flare was ejected. The faster CME of November 2 caught up and swept up the slower CME of November 1, and subsequently caused a severe geomagnetic storm (minimum Dst = -101) and a high-energy electron storm on November 4. The observations of the above three space environmental events confirm that the data quality of the high-energy particle package (HEPP) from ZH-1 is highly reliable and accurate and is highly advantageous to monitoring the variation of energetic particles and X-rays in the radiation belt of the Earth during solar activities.

The high energy particle package (HEPP) onboard the China Seismo‐Electromagnetic Satellite (CSES) consists of three subsystems: HEPP‐H, HEPP‐L, and HEPP‐X. HEPP‐H and HEPP‐L detect 0.1–55 MeV electrons and 2–230 MeV protons. HEPP‐X is used to monitor 0.9–35 keV solar X‐rays. The primary objective of this study is to present the measurement techniques and instrument parameters, show the main features of particle observations recorded by these instruments and evaluate the proton contamination to MeV electrons. Based on CSES observation, we report a typical solar X‐ray and solar proton event and compare with observations from Polar Orbiting Environmental Satellites (POES) and Geostationary Operational Environmental Satellites (GOES) satellite. Based on the observations of solar proton events, we put forward one method to evaluate the proton contamination level using comparatively pure proton samples on high L‐shells where the proton flux is near zero at quiet time. The percentage of protons that are mistakenly identified to be electrons by HEPP‐H is estimated to be approximately 0.022%. The proton contaminations only contribute no more than 10% of the total observed electron populations at L = 4 with energy range 8–9 MeV in the outer radiation belt region. Therefore, we conclude that the on‐orbit performance of HEPP instrument has satisfyingly met the design expectations by providing plenty of high‐quality high energy particle observation data and reference for scientific uses in the fields of space weather research and natural hazard monitoring.

. For solving large-scale sparse inconsistent linear systems by iteration methods, we introduce a relaxation parameter in the probability criterion of the greedy randomized augmented Kaczmarz method, obtaining a class of relaxed greedy randomized augmented Kaczmarz methods. We prove the convergence of these methods and estimate upper bounds for their convergence rates. Theoretical analysis and numerical experiments show that these methods can perform better than the greedy randomized augmented Kaczmarz method if the relaxation parameter is chosen appropriately.

The Gauss-Seidel and Kaczmarz methods are two classic iteration methods for solving systems of linear equations, which operate in column and row spaces, respectively. Utilizing the connections between these two methods and imitating the exact analysis of the mean-squared error for the randomized Kaczmarz method, we conduct an exact closed-form formula for the mean-squared residual of the iterate generated by the randomized Gauss-Seidel method. Based on this new formula, we further estimate an upper bound for the convergence rate of the randomized Gauss-Seidel method. Theoretical analysis and numerical experiments show that this bound measurably improves the existing ones. Moreover, these theoretical results are also extended to the more general extrapolated randomized Gauss-Seidel method.

Matrix is widely used in telecommunication, cryptography, computer science and other field. Especially in wireless sensor network data processing, it is important and necessary to keep data transmitting reliable and resilient. In channel coding and secure communication, matrix is used to realize the coding of transmission information and source information in the channel, which not only reduces the bit error rate of wireless communication, but also realizes the confidentiality of communication. The development of effective algorithms for matrix calculation has been an interesting subject for several centuries and an expanding research field. For some widely used and special matrices, such as sparse matrix and quasi diagonal matrix, there are specific fast algorithms. This paper briefly describes and explains our design of serial algorithms which implementing the sparse matrix multiplication by parallel programming, and also to provide benchmark results to justify the correctness and performance of our design.