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 $\pm 2\sigma$. This method enables precise analysis of intense transients and other high-flux events, overcoming limitations imposed by instrumental effects in traditional analyses.
Over the last year, kinematic Sunyaev--Zel'dovich (kSZ) velocity reconstruction -- the measurement of the large-scale velocity field using the anisotropic statistics of the small-scale kSZ-galaxy overdensity correlation -- has emerged as a statistically significant probe of the large-scale Universe. In this work, we perform a 2-dimensional tomographic reconstruction using ACT DR6 CMB data and DESI legacy luminous red galaxies (LRGs). We measure the cross-correlation of the kSZ-reconstructed velocity $v^{\mathrm{kSZ}}$ with the velocity inferred from the continuity equation applied to the DESI LRGs $v^{\mathrm{cont}}$ at the $\sim 10 \sigma$ level, detecting the signal with an amplitude with respect to our theory of $b_v = 0.339\pm 0.034$. We fit a scale-dependent galaxy bias model to our measurement in order to constrain local primordial non-Gaussianity $f_{\mathrm{NL}}^{\mathrm{loc}}$, finding {$f_{\mathrm{NL}}^{\mathrm{loc}}=-180^{+61}_{-86}$} at 67\% confidence, with $f_{\mathrm{NL}}^{\mathrm{loc}}$ consistent with zero at 95\% confidence. We also measure an auto spectrum at $2.1\sigma$ significance which provides a constraint on $b_v$ of $b_v=0.26_{-0.05}^{+0.11}$, which is consistent with the measurement from the cross spectrum. Our combined measurement is $b_v=0.33\pm0.03$, an $11\sigma$ measurement. We find a good fit of our model to the data in all cases. Finally, we use different ACT frequency combinations to explore foreground contamination, finding no evidence for foreground contamination in our velocity cross correlation. We compare to a similar measurement where $v^{\mathrm{kSZ}}$ is directly cross correlated with the large-scale galaxy field, and find signs of foreground contamination which is contained in the equal-redshift spectra.
this https URL for codes and some of the data used. 14 pages, 14 figures