伽马射线暴及相关高能暂现源观测数据的科学分析方法

doi:10.11871/jfdc.issn.2096-742X.2025.04.009

数据与计算发展前沿 ›› 2025, Vol. 7 ›› Issue (4): 101-117.

CSTR: 32002.14.jfdc.CN10-1649/TP.2025.04.009

doi: 10.11871/jfdc.issn.2096-742X.2025.04.009

• 专刊：空间科学大数据智能算法模型与工具 • 上一篇下一篇

伽马射线暴及相关高能暂现源观测数据的科学分析方法

杨俊^1,^2,^*(),张彬彬^1,²

1.南京大学，天文与空间科学学院，江苏南京 210093
2.南京大学，现代天文与天体物理教育部重点实验室，江苏南京 210093

收稿日期:2025-05-30 出版日期:2025-08-20 发布日期:2025-08-21
通讯作者: 杨俊
作者简介:杨俊，南京大学天文与空间科学学院，博士研究生，主要研究方向为伽马射线暴及相关天体物理现象，其研究主要聚焦于若干特殊的伽马射线暴事件，通过对观测数据的综合分析，揭示它们的物理起源、中心引擎以及辐射机制。
本文主要承担的工作为：（1）设计并开发科学分析流程与关键算法；（2）将所开发科学分析流程应用于实际观测数据；（3）撰写论文初稿。
YANG Jun, is a Ph.D. candidate at the School of Astronomy and Space Science, Nanjing University. His primary research interests include gamma-ray bursts and their associated astrophysical phenomena. Specifically, his research has centered on several peculiar GRBs, revealing their physical origins, central engines, and radiation mechanisms through a comprehensive analysis of observational data.
In this study, he is mainly responsible for designing and implementing the scientific analysis workflow and key algorithms, applying the developed workflow to real observational data, and drafting the manuscript.
E-mail: jyang@smail.nju.edu.cn
基金资助:
国家重点研发计划“高能天体空间观测特征信息提取与知识挖掘”(2022YFF0711404);国家自然科学基金“基于爱因斯坦探针卫星的伽马射线暴研究”(13001106)

Scientific Methods for Analyzing Observational Data of Gamma-Ray Bursts and Related High-Energy Transients

YANG Jun^1,^2,^*(),ZHANG Binbin^1,²

1. School of Astronomy and Space Science, Nanjing University, Nanjing, Jiangsu 210093, China
2. Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Nanjing, Jiangsu 210093, China

Received:2025-05-30 Online:2025-08-20 Published:2025-08-21
Contact: YANG Jun

摘要/Abstract

摘要：

【应用背景】天文学研究高度依赖于观测数据的获取与分析。对于伽马射线暴等高能暂现源而言，其辐射在极短时间尺度内剧烈变化，呈现出显著的时变与能谱演化特征。如何在复杂观测数据中高效且精准地提取此类剧烈爆发现象的时变与能谱信息，已成为当前高能时域天体物理研究中亟待突破的关键技术挑战。【目的】本文旨在构建一套面向伽马射线暴及相关高能暂现源观测数据的科学分析流程，重点聚焦于高效率、高精度的关键算法与核心技术的研发与应用。【方法】在时变分析方面，本文提出一种融合基线矫正、贝叶斯块分割、显著性计算与多项式拟合的自动化信号识别与背景拟合算法；在能谱分析方面，本文构建了一种基于贝叶斯推断的能谱拟合框架，用于实现模型参数及其不确定性的稳健估计。【结果】该分析流程及其核心算法已成功应用于伽马射线暴的实际观测数据分析中，能够有效识别和分离信号与背景，并基于贝叶斯推断算法实现关键能谱参数的可靠估计。【结论】本文提出的数据分析流程显著提升了伽马射线暴及相关高能暂现源观测数据的分析效率与准确性，为高能天体爆发现象的自动化数据分析提供了一种可复用的技术路径，具有广泛的应用前景和科研价值。

关键词: 伽马射线暴, 暂现源, 天文数据处理方法, 信号识别, 贝叶斯推断

Abstract:

[Context] Astronomical research heavily relies on the acquisition and analysis of observational data. For high-energy transients such as gamma-ray bursts (GRBs), radiation undergoes rapid and intense variations over extremely short timescales, characterized by significant temporal and spectral evolution. Efficiently and accurately extracting these dynamic features from complex observational data has become a critical technical challenge in high-energy time-domain astrophysics. [Objective] This study aims to develop a scientific data analysis pipeline tailored for GRBs and related high-energy transient sources, with a particular focus on the development and application of key algorithms and core technologies that ensure high efficiency and precision. [Methods] For temporal analysis, we propose an automated signal identification and background fitting algorithm that integrates baseline correction, Bayesian block segmentation, significance calculation, and polynomial fitting. For spectral analysis, we construct a Bayesian inference-based spectral fitting framework designed to robustly estimate model parameters and their uncertainties. [Results] The proposed analysis pipeline and its key algorithms have been successfully applied to real observational data of GRBs. The approach effectively identifies and separates signal from background and enables reliable estimation of key spectral parameters through a Bayesian inference algorithm. [Conclusion] The data analysis framework presented in this work significantly improves the efficiency and accuracy of observational data analysis for GRBs and related high-energy transient sources. It offers a reusable technical approach for the automated analysis of high-energy astrophysical explosion phenomena and holds substantial potential for broad application and scientific advancement.

Key words: gamma-ray bursts, transient sources, astronomical data processing methods, signal identification, Bayesian inference

杨俊, 张彬彬. 伽马射线暴及相关高能暂现源观测数据的科学分析方法[J]. 数据与计算发展前沿, 2025, 7(4): 101-117.

YANG Jun, ZHANG Binbin. Scientific Methods for Analyzing Observational Data of Gamma-Ray Bursts and Related High-Energy Transients[J]. Frontiers of Data and Computing, 2025, 7(4): 101-117, https://cstr.cn/32002.14.jfdc.CN10-1649/TP.2025.04.009.

图/表 10

表1

表2

算法 1

算法 2

自动化信号识别与背景拟合算法"

自动化信号识别与背景拟合算法
Input：总光变曲线$\mathit{A}\left(\mathit{T}\right)=\left\{\left({\mathit{T}}_{\mathit{i}},{\mathit{R}}_{\mathit{i}}\right)\right\}$
Output：分离出的信号光变曲线$\mathit{S}\left(\mathit{T}\right)$和背景光变曲线$\mathit{B}\left(\mathit{T}\right)$
/* 基线矫正 */
使用DRPLS算法进行基线矫正，得到初步背景估计$\left\{\left({\mathit{T}}_{\mathit{i}},{\mathit{R}}_{\mathit{i},\mathit{b}\mathit{c}}\right)\right\}$
/* 贝叶斯块 */
使用贝叶斯块算法对$\left\{\left({\mathit{T}}_{\mathit{i}},{\mathit{R}}_{\mathit{i}}\right)\right\}$进行自动分段，得到分段边界$\left\{{\mathit{T}}_{\mathit{k}}\right\}$
/* 显著性计算 */
For 每个贝叶斯块$\left[{\mathit{T}}_{\mathit{k}},{\mathit{T}}_{\mathit{k}+1}\right]$ do
计算该时间区间内的总光子数：${\mathit{C}}_{\mathit{k}}=\sum _{{\mathit{T}}_{\mathit{i}}\in \left[{\mathit{T}}_{\mathit{k}},{\mathit{T}}_{\mathit{k}+1}\right]}{\mathit{R}}_{\mathit{i}}\mathrm{\Delta }\mathit{t}$
计算该时间区间内的背景光子数：${\mathit{C}}_{\mathit{k},\mathit{b}\mathit{c}}=\sum _{{\mathit{T}}_{\mathit{i}}\in \left[{\mathit{T}}_{\mathit{k}},{\mathit{T}}_{\mathit{k}+1}\right]}{\mathit{R}}_{\mathit{i},\mathit{b}\mathit{c}}\mathrm{\Delta }\mathit{t}$
计算信号显著性：${\mathit{S}}_{\mathit{k}}=\sqrt{2\mathbf{l}\mathbf{o}\mathbf{g}\frac{{\mathit{L}}_{1}\left({\mathit{\theta }}_{1}^{\mathbf{m}\mathbf{l}\mathbf{e}}\right)}{{\mathit{L}}_{0}\left({\mathit{\theta }}_{0}^{\mathbf{m}\mathbf{l}\mathbf{e}}\right)}}$
If ${\mathit{S}}_{\mathit{k}}\ge {\mathit{S}}_{\mathbf{t}\mathbf{h}}$ then
标记该贝叶斯块为信号区间$\left[{\mathit{T}}_{\mathit{k}}^{\mathit{S}},{\mathit{T}}_{\mathit{k}+1}^{\mathit{S}}\right]$
标记该贝叶斯块内的数据为信号${\left\{\left({\mathit{T}}_{\mathit{i}}^{\mathit{S}},\mathrm{ }{\mathit{R}}_{\mathit{i}}^{\mathit{S}}\right)\right\}}_{{\mathit{T}}_{\mathit{i}}\in \left[{\mathit{T}}_{\mathit{k}},{\mathit{T}}_{\mathit{k}+1}\right]}$
End
Else
标记该贝叶斯块为背景区间$\left[{\mathit{T}}_{\mathit{k}}^{\mathit{B}},\mathrm{ }{\mathit{T}}_{\mathit{k}+1}^{\mathit{B}}\right]$
标记该贝叶斯块内的数据为信号${\left\{\left({\mathit{T}}_{\mathit{i}}^{\mathit{B}},\mathrm{ }{\mathit{R}}_{\mathit{i}}^{\mathit{B}}\right)\right\}}_{{\mathit{T}}_{\mathit{i}}\in \left[{\mathit{T}}_{\mathit{k}},{\mathit{T}}_{\mathit{k}+1}\right]}$
End End
/* 多项式拟合 */
构建m阶多项式$\mathit{f}\left(\mathit{t},\mathrm{ }\mathit{\beta }\right)=\stackrel{\mathit{m}}{\sum _{\mathit{j}=0}}{\mathit{\beta }}_{\mathit{j}}{\mathit{t}}^{\mathit{j}}$拟合背景数据$\left\{\left({\mathit{T}}_{\mathit{i}}^{\mathit{B}},\mathrm{ }{\mathit{R}}_{\mathit{i}}^{\mathit{B}}\right)\right\}$
采用加权最小二乘法求解最优多项式系数$\widehat{\beta }$及其协方差矩阵 $Cov\left(\widehat{\beta }\right)$
生成背景光变曲线$\mathit{B}\left(\mathit{T}\right)=\left\{\left({\mathit{T}}_{\mathit{i}},\mathrm{ }\mathit{f}\left({\mathit{T}}_{\mathit{i}},\mathrm{ }\widehat{\beta }\right)\right)\right\}$
生成信号光变（净光变）曲线$\mathit{S}\left(\mathit{T}\right)=\mathit{A}\left(\mathit{T}\right)-\mathit{B}\left(\mathit{T}\right)$
Return $\mathit{S}\left(\mathit{T}\right)$，$\mathit{B}\left(\mathit{T}\right)$

算法 2

图1

图2

算法 3

伽马射线背景能谱提取算法"

伽马射线背景能谱提取算法
Input：光子事件列表$\left\{\left({\mathit{t}}_{\mathit{i}},\mathrm{ }{\mathit{p}}_{\mathit{i}}\right)\right\}$，时间切片$\left[{\mathit{T}}_{\mathit{l}},\mathrm{ }{\mathit{T}}_{\mathit{r}}\right]$
Output：背景能谱$\left\{\left(\mathit{I},{\mathit{C}}_{\mathit{I}}^{\mathit{B}},{\mathit{\sigma }}_{{\mathit{C}}_{\mathit{I}}^{\mathit{B}}}\right)\right\}$
提取总光变曲线$\mathit{A}\left(\mathit{T}\right)=\left\{\left({\mathit{T}}_{\mathit{i}},\mathrm{ }{\mathit{R}}_{\mathit{i}}\right)\right\}$
应用信号识别与背景拟合算法，确定信号区间$\left\{{\mathit{T}}_{\mathit{i}}^{\mathit{S}}\right\}$和背景区间$\left\{{\mathit{T}}_{\mathit{i}}^{\mathit{B}}\right\}$
For 每一个能道$\mathit{I}\in \left\{1,\mathrm{ }2,\cdots,\mathit{N}\right\}$ do
提取光子事件列表$\left\{\left({\mathit{t}}_{\mathit{i}},\mathrm{ }{\mathit{p}}_{\mathit{i}}\right)\|{\mathit{p}}_{\mathit{i}}=\mathit{I}\right\}$
提取光变曲线${\mathit{A}}_{\mathit{I}}\left(\mathit{T}\right)=\left\{\left({\mathit{T}}_{\mathit{i},\mathrm{ }\mathit{I}},{\mathit{R}}_{\mathit{i},\mathrm{ }\mathit{I}}\right)\right\}$
使用多项式拟合背景区间$\left\{{\mathit{T}}_{\mathit{i}}^{\mathit{B}}\right\}$内的${\mathit{A}}_{\mathit{I}}\left(\mathit{T}\right)$
获取背景光变曲线的多项式模型${\mathit{B}}_{\mathit{I}}\left(\mathit{t}\right)$及其误差${\mathit{\sigma }}_{{\mathit{B}}_{\mathit{I}}}\left(\mathit{t}\right)$
计算背景光子数：${\mathit{C}}_{\mathit{I}}^{\mathit{B}}=\stackrel{{\mathit{T}}_{\mathit{r}}}{\underset{{\mathit{T}}_{\mathit{l}}}{\int }}{\mathit{B}}_{\mathit{I}}\left(\mathit{t}\right)\mathit{d}\mathit{t}$
计算背景光子数的统计误差：${\mathit{\sigma }}_{{\mathit{C}}_{\mathit{I}}^{\mathit{B}}}=\stackrel{{\mathit{T}}_{\mathit{r}}}{\underset{{\mathit{T}}_{\mathit{l}}}{\int }}{\mathit{\sigma }}_{{\mathit{B}}_{\mathit{I}}}\left(\mathit{t}\right)\mathit{d}\mathit{t}$
End
Return $\left\{\left(\mathit{I},{\mathit{C}}_{\mathit{I}}^{\mathit{B}},{\mathit{\sigma }}_{{\mathit{C}}_{\mathit{I}}^{\mathit{B}}}\right)\right\}$

算法 3

算法 4

基于贝叶斯推断的天文能谱拟合算法"

基于贝叶斯推断的天文能谱拟合算法
Input：观测光子计数谱${\mathit{D}}_{\mathit{n},\mathit{g}}\left({\mathit{I}}_{\mathit{n},\mathit{g}},\mathit{t}\right)$，仪器响应矩阵${\mathit{R}}_{\mathit{n},\mathit{g}}\left({\mathit{I}}_{\mathit{n},\mathit{g}},{\mathit{J}}_{\mathit{n},\mathit{g}}\right)$，参数化能谱模型${\mathit{M}}_{\mathit{n}}\left(\mathit{E},\mathit{t},{\mathit{\theta }}_{\mathit{n}}\right)$
Output：参数后验概率分布$\mathit{P}\left(\mathit{\theta }\|\mathit{D},\mathit{M}\right)$
/* 模型构建 */
构建参数化能谱模型${\mathit{M}}_{\mathit{n}}\left(\mathit{E},\mathit{t},{\mathit{\theta }}_{\mathit{n}}\right)$，其中$\mathit{\theta }$为待估参数
/* 数据准备 */
准备观测光子计数谱${\mathit{D}}_{\mathit{n},\mathit{g}}\left({\mathit{I}}_{\mathit{n},\mathit{g}},\mathit{t}\right)$和仪器响应矩阵${\mathit{R}}_{\mathit{n},\mathit{g}}\left({\mathit{I}}_{\mathit{n},\mathit{g}},{\mathit{J}}_{\mathit{n},\mathit{g}}\right)$
/* 贝叶斯推断 */
结合先验认知，设定参数的先验分布$\mathit{P}\left(\mathit{\theta }\right\|\mathit{M})$
根据数据的统计假设，定义似然函数$\mathit{P}\left(\mathit{D}\right\|\mathit{\theta },\mathit{M})$
采样器根据参数先验分布在多维参数空间中进行采样
While 未满足收敛条件do
采样获得当前参数值$\mathit{\theta }$
计算能谱模型${\mathit{M}}_{\mathit{n}}\left(\mathit{E},\mathit{t},{\mathit{\theta }}_{\mathit{n}}\right)$
计算模型预测的光子计数谱${\mathit{D}}_{\mathit{n},\mathit{g}}^{\mathit{p}}\left({\mathit{I}}_{\mathit{n},\mathit{g}},\mathit{t}\right)$
计算拟合统计量$\mathit{S}$
更新采样状态，并检查是否满足收敛条件
End
计算参数后验概率分布$\mathit{P}\left(\mathit{\theta }\|\mathit{D},\mathit{M}\right)$
Return $\mathit{P}\left(\mathit{\theta }\|\mathit{D},\mathit{M}\right)$

算法 4

图3

图4

参考文献 18

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[2]	KIENLIN A, MEEGAN C A, PACIESAS W S, et al. The Fourth Fermi-GBM Gamma-Ray Burst Catalog: A Decade of Data[J]. The Astrophysical Journal, 2020, 893(1): 46.
[3]	LIEN A, SAKAMOTO T, BARTHELMY S D, et al. The Third Swift Burst Alert Telescope Gamma-Ray Burst Catalog[J]. The Astrophysical Journal, 2016, 829(1): 7.
[4]	EILERS P H C. A Perfect Smoother[J]. Analytical Chemistry, 2003, 75(14): 3631-3636. doi: 10.1021/ac034173t pmid: 14570219
[5]	SCARGLE J D, NORRIS J P, JACKSON B, et al. Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations[J]. The Astrophysical Journal, 2023, 764(2): 167.
[6]	PRICE-WHELAN A M, LIM P L, Earl N, et al. The Astropy Project: Sustaining and Growing a Community-oriented Open-source Project and the Latest Major Release (v5.0) of the Core Package[J]. The Astrophysical Journal, 2022, 935(2): 167.
[7]	VIANELLO G. The Significance of an Excess in a Counting Experiment: Assessing the Impact of Systematic Uncertainties and the Case with a Gaussian Background[J]. The Astrophysical Journal Supplement Series, 2018, 236(1): 17.
[8]	WILKS S S. The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses[J]. The Annals of Mathematical Statistics, 1938, 9(1): 60-62.
[9]	LI T P, MA Y Q. Analysis methods for results in gamma-ray astronomy[J]. The Astrophysical Journal, 1983, 272: 317-324.
[10]	BURGESS J M, YU H F, GREINER J, et al. Awakening the BALROG: BAyesian Location Reconstruction Of GRBs[J]. Monthly Notices of the Royal Astronomical Society, 2018, 476(2): 1427-1444.
[11]	BERLATO F, GREINER J, BURGESS J M. Improved Fermi-GBM GRB Localizations Using BALROG[J]. The Astrophysical Journal, 2019, 873(1): 60.
[12]	ARNAUD K A. XSPEC: The First Ten Years[J]. Astronomical Data Analysis Software and Systems, 1996, 101: 17.
[13]	FOREMAN-MACKEY D, HOGG D W, LANG D, et al. Emcee: The MCMC Hammer[J]. Publications of the Astronomical Society of the Pacific, 2013, 125(925): 306.
[14]	FEROZ F, HOBSON M P. Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses[J]. Monthly Notices of the Royal Astronomical Society, 2008, 384(2): 449-463.
[15]	FEROZ F, HOBSON M P, BRIDGES M. MULTINEST: an efficient and robust Bayesian inference tool for cosmology and particle physics[J]. Monthly Notices of the Royal Astronomical Society, 2009, 398(4): 1601-1614.
[16]	BUCHNER J, GEORGAKAKIS A, NANDRA K, et al. X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue[J]. Astronomy & Astrophysics, 2014, 564: A125.
[17]	FEROZ F, HOBSON M P, CAMERON E, et al. Importance Nested Sampling and the MultiNest Algorithm[J]. The Open Journal of Astrophysics, 2019, 2(1): 10.
[18]	CASH W. Parameter estimation in astronomy through application of the likelihood ratio[J]. The Astrophysical Journal, 1979, 228: 939-947.

参数	类型	单位	解释
TIME	8字节实数	s	光子事件的到达时间
PHA	2字节整数	—	脉冲高度分析器通道编号

参数	类型	单位	解释
TIME	8字节实数	s	光子事件的到达时间
X	2字节整数	pixel	光子在天球坐标系中的X坐标
Y	2字节整数	pixel	光子在天球坐标系中的Y坐标
RAWX	2字节整数	pixel	光子在原始探测器坐标系中的 X坐标（未线性化前）
RAWY	2字节整数	pixel	光子在原始探测器坐标系中的 Y坐标（未线性化前）
DETX	2字节整数	pixel	光子在线性化探测器坐标系中的 X坐标
DETY	2字节整数	pixel	光子在线性化探测器坐标系中的 Y坐标
PHA	4字节整数	—	脉冲高度分析器通道编号
PI	4字节整数	—	脉冲不变通道编号
GRADE	2字节整数	—	光子事件的等级
STATUS	16位无类型	—	光子事件的数据质量标志

光变曲线提取算法
Input：光子事件列表${\left\{\left({\mathit{t}}_{\mathit{i}},{\mathit{E}}_{\mathit{i}}\right)\right\}}_{\mathit{i}=1}^{\mathit{n}}$，时间区间$[{\mathit{T}}_{\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{r}\mathbf{t}},{\mathit{T}}_{\mathbf{e}\mathbf{n}\mathbf{d}}]$，能量范围$[{\mathit{E}}_{\mathbf{m}\mathbf{i}\mathbf{n}},\mathrm{ }{\mathit{E}}_{\mathbf{m}\mathbf{a}\mathbf{x}}]$，时间步长$\mathrm{\Delta }\mathit{t}$
Output：光变曲线$\left\{\right({\mathit{T}}_{\mathit{j}},{\mathit{C}}_{\mathit{j}},{\mathit{\sigma }}_{\mathit{j}}\left)\right\}$
计算时间箱的总数：$\mathit{M}=\left[({\mathit{T}}_{\mathbf{e}\mathbf{n}\mathbf{d}}-{\mathit{T}}_{\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{r}\mathrm{t}})/\mathrm{\Delta }\mathit{t}\right]$；
For $\mathit{j}=1$ 到 $\mathit{M}$ do
	计算当前时间箱的时间范围： $\left[{\mathit{T}}_{\mathit{j}}^{1},\mathrm{ }{T}_{\mathit{j}}^{2}\right]=[{\mathit{T}}_{\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{r}\mathbf{t}}+\left(\mathit{j}-1\right)\mathrm{\Delta }\mathit{t},\mathrm{ }{\mathit{T}}_{\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{r}\mathbf{t}}+\mathit{j}\mathrm{\Delta }\mathit{t}]$
	统计落入特定时间范围和能量范围内的光子数：${\mathit{C}}_{\mathit{j}}=\stackrel{\mathit{n}}{\sum _{\mathit{i}=1}}1$，满足${\mathit{T}}_{\mathbf{j}}^{1}\le {\mathit{t}}_{\mathit{i}}<{\mathit{T}}_{\mathit{j}}^{2}$，${\mathit{E}}_{\mathbf{m}\mathbf{i}\mathbf{n}}\le {\mathit{E}}_{\mathit{i}}\le {\mathit{E}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$
	计算当前时间箱的泊松误差：${\mathit{\sigma }}_{\mathit{j}}=\sqrt{{\mathit{C}}_{\mathit{j}}}$
End
Return $\left\{\right({\mathit{T}}_{\mathit{j}},\mathrm{ }{\mathit{C}}_{\mathit{j}},\mathrm{ }{\mathit{\sigma }}_{\mathit{j}}\left)\right\}$

伽马射线暴及相关高能暂现源观测数据的科学分析方法

Scientific Methods for Analyzing Observational Data of Gamma-Ray Bursts and Related High-Energy Transients

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