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Gradient descent computed by backpropagation (BP) is a widely used learning method for training artificial neural networks but has several limitations: it is computationally demanding, requires frequent manual tuning of the network architecture, and is prone to catastrophic forgetting when learning incrementally. To address these issues, we introduce a brain-mimetic developmental spiking neural network (BDNN) that mimics the postnatal development of neural circuits. We validate its performance through a neuromorphic tactile system capable of learning to recognize objects through grasping. Unlike traditional BP-based methods, BDNN exhibits strong knowledge transfer, supporting efficient incremental learning of new tactile information. It requires no hyperparameter tuning and dynamically adapts to incoming data. Moreover, compared to the BP-based counterpart, it achieves classification accuracy on par with BP while learning over ten times faster in ideal conditions and up to two or three orders of magnitude faster in practical settings. These features make BDNN well-suited for fast data processing on edge devices., Comment: 24 pages, 8 figures, 2 tables

Ninety gravitational wave events have been detected by the LIGO-Virgo-KAGRA network and are released in the Gravitational-Wave Transient Catalog. Among these events, 83 cases are definitely binary black hole mergers since the masses of all the objects involved significantly exceed the upper limit of neutron stars. The black holes in these merger events naturally form two interesting samples, a pre-merger sample that includes all the black holes before the mergers and a post-merger sample that consists of the black holes generated during the merging processes. The former represents black holes that once existed in the Universe, while the latter represents newly born black holes. Here we present a statistical analysis on these two samples. The non-parametric $\tau$ statistic method is adopted to correct for the observational selection effect. The Lynden-Bell's $C^{-}$ method is further applied to derive the mass distribution and density function of black holes. It is found that the mass distribution can be expressed as a broken power-law function. More interestingly, the power-law index in the high mass region is comparable for the two samples. The number density of black holes is found to depend on redshift as $\rho(z) \propto z^{-2.06}$-$z^{-2.12}$ based on the two samples. Implications of these findings on the origin of black holes are discussed., Comment: 14 pages, 5 figures, 1 table

Fast Radio Bursts (FRBs) are bright radio transients with millisecond durations which typically occur at extragalactic distances. The association of FRB 20200428 with the Galactic magnetar SGR J1935+2154 strongly indicates that they could originate from neutron stars, which naturally leads to the expectation that periodicity connected with the spinning of magnetars should exist in the activities of repeating FRBs. However, previous studies have failed to find any signatures supporting such a conjecture. Here we perform a thorough search for short timescale periodicity in the five most active repeating sources, i.e. FRBs 20121102A, 20180916B, 20190520B, 20200120E, and 20201124A. Three different methods are employed, including the phase folding algorithm, the Schuster periodogram and the Lomb-Scargle periodogram. For the two most active repeaters from which more than 1600 bursts have been detected, i.e. FRB 20121102A and FRB 20201124A, more in-depth period searches are conducted by considering various burst properties such as the pulse width, peak flux, fluence, and the brightness temperature. For these two repeaters, we have also selected those days on which a large number of bursts were detected and performed periodicity analysis based on the single-day bursts. No periodicity in a period range of 1 ms-1000 s is found in all the efforts, although possible existence of a very short period between 1 ms-10 ms still could not be completely excluded for FRBs 20200120E and 20201124A due to limited timing accuracy of currently available observations. Implications of such a null result on the theoretical models of FRBs are discussed., Comment: 22 pages, 23 figures, 1 table

Empirical correlations between various key parameters have been extensively explored ever since the discovery of gamma-ray bursts (GRBs) and have been widely used as standard candles to probe the Universe. The Amati relation and the Yonetoku relation are two good examples that enjoyed special attention. The former reflects the connection between the peak photon energy (Ep) and the isotropic $\gamma$-ray energy release (Eiso), while the latter links Ep with the isotropic peak luminosity (Lp), both in the form of a power-law function. Most GRBs are found to follow these correlations well, but a theoretical interpretation is still lacking. Some obvious outliers may be off-axis GRBs and may follow correlations that are different from those at the on-axis. Here we present a simple analytical derivation for the Amati relation and the Yonetoku relation in the framework of the standard fireball model, the correctness of which is then confirmed by numerical simulations. The off-axis Amati relation and Yonetoku relation are also derived. They differ markedly from the corresponding on-axis relation. Our results reveal the intrinsic physics behind the radiation processes of GRBs, and they highlight the importance of the viewing angle in the empirical correlations of GRBs., Comment: 12 pages, 7 figures, 2 tables. A&A accepted

A plateau phase in the X-ray afterglow is observed in a significant fraction of gamma-ray bursts (GRBs). Previously, it has been found that there exists a correlation among three key parameters concerning the plateau phase, i.e., the end time of the plateau phase in the GRB rest frame ($T_{a}$), the corresponding X-ray luminosity at the end time ($L_{X}$) and the isotropic energy of the prompt GRB ($E_{\gamma,\rm{iso}}$). In this study, we systematically search through all the \emph{Swift} GRBs with a plateau phase that occurred between 2005 May and 2018 August. We collect 174 GRBs, with redshifts available for all of them. For the whole sample, the correlation between $L_{X}$, $T_{a}$ and $E_{\gamma,\rm{iso}}$ is confirmed, with the best fit relation being $L_{X}\propto T_{a}^{-1.01}E_{\gamma,\rm{iso}}^{0.84}$. Such an updated three-parameter correlation still supports that the central leftover after GRBs is probably a millisecond magnetar. It is interesting to note that short GRBs with duration less than 2 s in our sample also follow the same correlation, which hints that the merger production of two neutron stars could be a high mass magnetar, but not necessarily a black hole. Moreover, GRBs having an "internal" plateau (i.e., with a following decay index being generally smaller than -3) also obey this correlation. It further strengthens the idea that the internal plateau is due to the delayed collapse of a high mass neutron star into a black hole. The updated three-parameter correlation indicates that GRBs with a plateau phase may act as a standard candle for cosmology study., Comment: 35 pages, 8 figures, 3 tables, accepted by AAS Journal

Currently, FRB 121102 is the only fast radio burst source that was observed to give out bursts repeatedly. It shows a high repeating rate, with more than one hundred bursts being spotted, but with no obvious periodicity in the activities. Thanks to its repetition, the source was well localized with a subarcsecond accuracy, leading to a redshift measurement of about 0.2. FRB 121102 is a unique source that can help us understand the enigmatic nature of fast radio bursts. In this study, we analyze the characteristics of the waiting times between bursts from FRB 121102. It is found that there is a clear bimodal distribution for the waiting times. While most waiting times cluster at several hundred seconds, a small portion of the waiting times are strikingly in the range of 2--40 millisecond. More interestingly, it is found that the waiting time does not correlate with the burst intensity, either for the preceding burst or for the subsequent burst. It strongly indicates that the repeating bursts should be generated by some external mechanisms, but not internal mechanisms. As a result, the models involving collisions between small bodies and neutron stars could be competitive mechanisms for this interesting source., Comment: 11 pages, 3 figures, accepted for publication in International Journal of Cosmology, Astronomy and Astrophysics

The curvature of the $\gamma$-ray spectrum in blazars may reflect the intrinsic distribution of the emitting electron distribution, which will further give some information on the possible acceleration and cooling processes in the emitting region. The $\gamma$-ray spectra of Fermi blazars are normally fitted either by a single power-law (PL) or a log-normal (call Logarithmic Parabola, LP) form. The possible reason for this differnece is not unclear. We statistically explore this issue based on the different observational properties of 1419 Fermi blazars in the 3LAC Clean sample. We find that the $\gamma$-ray flux (100 MeV-100 GeV) and variability index follow bimodal distributions for PL and LP blazars, where $\gamma$-ray flux and variability index show {a positive correlation}. However, the distributions of the $\gamma$-ray luminosity and redshift follow a unimodal distribution. Our results suggest that the bimodal distribution of $\gamma$-ray flux for LP and PL blazars may be not intrinsic and all blazars may have an intrinsic curved $\gamma$-ray spectrum and the PL spectrum is just caused by the fitting effect due to the less photons., Comment: Accepted for publication in RAA. 9 pages, 1 figure, 2 table

Superluminal motion has been found to occur in many kinds of celestial bodies with the relativistic ejecta, especially for some active galactic nuclei (AGNs), gamma-ray bursts (GRBs) and micro-quasars, although these objects are largely different in their lifetimes, sizes and features. We compare the apparent superluminal motions of GRBs with AGNs and different sub-classes of AGNs (e.g., Radio galaxies, BL Lac objects, and Quasars). Particularly, we focus on two low luminosity GRBs, namely 060218 and 170817A, that are ultra-long and short bursts associated with supernova and gravitational wave, respectively. The apparent transverse velocity ($\beta_{app}$) of Swift and pre-Swift GRBs are tightly correlated with the Doppler factor $\delta$ as $\beta_{app}\propto\delta^{0.5}$, while all AGNs distribute around the line of $\beta_{app}= \delta$ behaving a weak correlation of $\beta_{app}$ with $\delta$ . In contrast, $\beta_{app}$ is positively correlated with Lorenz factor $\gamma$ or $\gamma^2(1+z)^{-1}$, not for GRBs but for AGNs. $\beta_{app}$ and $1+z$ are independent for neither GRBs nor AGNs, but apparently exhibit a positive correlation of $\beta_{app}$ with $1+z$ from AGNs to GRBs, showing a cosmological effect of evolution with redshift. I also found that GRB 170817A and GRB 060218 are outliers of the above correlations. Superluminal properties of GRBs are significantly different from those of AGNs. However, there are no obvious differences between radio galaxies, BL Lac objects, and quasars in terms of their superluminal motion. In despite of radiation mechanism, beaming effect and cosmological expanding would play the same roles on the superluminal motion for AGNs and GRBs., Comment: 8 pages, 5 figures and 1 table

Using Gaussian Mixture Model (GMM) and Expectation Maximization Algorithm, we perform an analysis of time duration ($T_{90}$) for \textit{CGRO}/BATSE, \textit{Swift}/BAT and \textit{Fermi}/GBM Gamma-Ray Bursts. The $T_{90}$ distributions of 298 redshift-known \textit{Swift}/BAT GRBs have also been studied in both observer and rest frames. Bayesian Information Criterion has been used to compare between different GMM models. We find that two Gaussian components are better to describe the \textit{CGRO}/BATSE and \textit{Fermi}/GBM GRBs in the observer frame. Also, we caution that two groups are expected for the \textit{Swift}/BAT bursts in the rest frame, which is consistent with some previous results. However, \textit{Swift} GRBs in the observer frame seem to show a trimodal distribution, of which the superficial intermediate class may result from the selection effect of \textit{Swift}/BAT., Comment: This paper has been withdrawn by the author due to a crucial error on the method of resampling analysis

Considering the contribution of the emission from the host galaxies of gamma-ray bursts (GRBs) to the radio afterglows, we investigate the effect of host galaxies on observations statistically. For the three types of events, e.g. low-luminosity, standard and high-luminosity GRBs, it is found that a tight correlation exists between the ratio of the radio flux (RRF) of host galaxy to the total radio peak emission and the observational frequency. Especially, toward lower frequencies, the contribution from the host increases significantly. The correlation can be used to get a useful estimate for the radio brightness of those host galaxies which only have very limited radio afterglow data. Using this prediction, we re-considered the theoretical radio afterglow light curves for four kinds of events, i.e. high-luminosity, low-luminosity, standard and failed GRBs, taking into account the contribution from the host galaxies and aiming at exploring the detectability of these events by the Five-hundred-meter Aperture Spherical radio Telescope (FAST). Lying at a typical redshift of $z=1$, most of the events can be detected by FAST easily. For the less fierce low-luminosity GRBs, their radio afterglows are not strong enough to exceed the sensitivity limit of FAST at such distances. However, since a large number of low luminosity bursts actually happen very near to us, it is expected that FAST will still be able to detect many of them., Comment: 10 pages, 5 figures and 4 tables; accepted for publication in MNRAS

Using the generic hydrodynamic model of Gamma-Ray Burst (GRB) afterglows, we calculate the radio afterglow light curves of low luminosity, high luminosity, failed and standard GRBs in different observational bands of FAST's energy window. The GRBs are assumed to be located at different distances from us. Our results rank the detectability of GRBs in descending order as high luminosity, standard, failed and low luminosity GRBs. We predict that almost all types of radio afterglows except that of low luminosity GRBs could be observed by the large radio telescope as long as the domains of time and frequency are appropriate. It is important to note that FAST can detect relatively weak radio afterglows at a higher frequency of 2.5 GHz for very high redshift up to z=15 or even more. Radio afterglows of low luminosity GRBs can be detected only after the completion of the 2nd phase of FAST. FAST is expected to significantly expand the sample of GRB radio afterglows in the near future., Comment: 16 pages, 8 figures (2 new figs added), 1 table; accepted by Research in Astronomy and Astrophysics

We have tested a relative spectral lag (RSL) method suggested earlier as a luminosity/redshift (or distance) estimator, using the generalized method by Schaefer & Collazzi. We find the derivations from the luminosity/redshift-RSL (L/R-RSL) relation are comparable with the corresponding observations. Applying the luminosity-RSL relation to two different GRB samples, we find that there exist no violators from the generalized test, namely the Nakar & Piran test and Li test. We also find that about 36 per cent of Schaefer's sample are outliers for the L/R-RSL relation within 1$\sigma$ confidence level, but no violators at 3$\sigma$ level within the current precision of L/R-RSL relation. An analysis of several potential outliers for other luminosity relations shows they can match the L/R-RSL relation well within an acceptable uncertainty. All the coincident results seem to suggest that this relation could be a potential tool for cosmological study., Comment: 7 pages, 6 figures and 1 table; Comments are welcome

We report the systematic analysis of the durations for Swift gamma-ray bursts (GRBs) and compare the results with those of pre-Swift data. For 95 GRBs with known redshift, we show that the observed durations have two lognormal distributions that are clearly divided at $T_{90}\simeq2$ s. This is consistent with the earlier BATSE results. The intrinsic durations also show a bimodal distribution but shift systematically toward the smaller value and the distribution exhibits a narrower width compared with the observed one. We find that the intrinsic distributions of long GRBs between Swift and pre-Swift are significantly different particularly in the width and the median value. In addition, the Swift data exhibit a wider dynamic range of duration. Our present study not only confirms the spectra of short GRBs are in general harder than the long GRBs in the observer frame but also shows this trend becomes weaker in the source frame., Comment: 5 pages, 4 figures and 2 table; Accepted to A&A with minor changes; Note that our previously main conclusions are unchanged

Using 64 ms count data for long gamma-ray bursts ($T_{90}>$2.6s), we analyze the quantity, relative spectral lag (RSL), which is defined as $\tau_{31}/FWHM_{(1)}$, where $\tau_{31}$ is the spectral lag between energy bands 1 and 3, and $FWHM_{(1)}$ denotes full width at half maximum of the pulse in energy channel 1. To get insights into features of the RSLs, we investigate in detail all the correlations between them and other parameters with a sub-sample including nine long bursts. The general cross-correlation technique is adopted to measure the lags between two different energy bands. We can derive the below conclusions. Firstly, the distribution of RSLs is normal and oncentrates on around the value of 0.1. Secondly, the RSLs are weakly correlated with $FWHM$, asymmetry, peak flux ($F_{p}$), peak energy ($E_{p}$) and spectral indexes ($\alpha$ and $\beta$), while they are uncorrelated with $\tau_{31}$, hardness-ratio ($HR_{31}$) and peak time ($t_m$). The final but important discovery is that redshift ($z$) and peak luminosity ($L_{p}$) are strongly correlated with the RSLs which can be measured easily and directly. We find that the RSL is a good redshift and peak luminosity estimator., Comment: 16 pages, 5 figures, accepted for publication in ChJAA

In this paper, the effect of the intrinsic distribution of cosmological candles is investigated. We find that, in the case of a narrow distribution, the deviation of the observed modulus of sources from the expected central value could be estimated within a ceratin range. We thus introduce a lower and upper limits of $\chi ^{2}$, $\chi_{\min}^{2}$ and $ \chi_{\max}^{2}$, to estimate cosmological parameters by applying the conventional minimizing $\chi ^{2}$ method. We apply this method to a gamma-ray burst (GRB) sample as well as to a combined sample including this GRB sample and an SN Ia sample. Our analysis shows that: a) in the case of assuming an intrinsic distribution of candles of the GRB sample, the effect of the distribution is obvious and should not be neglected; b) taking into account this effect would lead to a poorer constraint of the cosmological parameter ranges. The analysis suggests that in the attempt of constraining the cosmological model with current GRB samples, the results tend to be worse than what previously thought if the mentioned intrinsic distribution does exist., Comment: 6 pages,4 figures,1 tables.Data updated. Main conclusion unchanged

In this paper, we derive in a much detail the formula of count rates, in terms of the integral of time, of gamma-ray bursts in the framework of fireballs, where the Doppler effect of the expanding fireball surface is the key factor to be concerned. Effects arising from the limit of the time delay due to the limited regions of the emitting areas in the fireball surface and other factors are investigated. Our analysis shows that the formula of the count rate of fireballs can be expressed as a function of $\tau $ which is the observation time scale relative to the dynamical time scale of the fireball. The profile of light curves of fireballs depends only on the relative time scale, entirely independent of the real time scale and the real size of the objects. It displays in detail how a cutoff tail, or a turn over, feature (called a cutoff tail problem) in the decay phase of a light curve can be formed. This feature is a consequence of a hot spot in the fireball surface, moving towards the observer, and was observed in a few cases previously. By performing fits to the count rate light curves of six sample sources, we show how to obtain some physical parameters from the observed profile of the count rate of GRBs. In addition, the analysis reveals that the Doppler effect of fireballs could lead to a power law relationship between the $FWHM$ of pulses and energy, which were observed previously by many authors., Comment: 38 pages, 10 figures; accepted for publication in ApJ (10 December 2004, v617)