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Ying Qin

Publications and source records attributed to Ying Qin.

At least 37 records · Page 2Linked to original sources

PlanMoGPT: Flow-Enhanced Progressive Planning for Text to Motion Synthesis

Recent advances in large language models (LLMs) have enabled breakthroughs in many multimodal generation tasks, but a significant performance gap still exists in text-to-motion generation, where LLM-based methods lag far behind non-LLM methods. We identify the granularity of motion tokenization as a critical bottleneck: fine-grained tokenization induces local dependency issues, where LLMs overemphasize short-term coherence at the expense of global semantic alignment, while coarse-grained tokenization sacrifices motion details. To resolve this issue, we propose PlanMoGPT, an LLM-based framework integrating progressive planning and flow-enhanced fine-grained motion tokenization. First, our progressive planning mechanism leverages LLMs' autoregressive capabilities to hierarchically generate motion tokens by starting from sparse global plans and iteratively refining them into full sequences. Second, our flow-enhanced tokenizer doubles the downsampling resolution and expands the codebook size by eight times, minimizing detail loss during discretization, while a flow-enhanced decoder recovers motion nuances. Extensive experiments on text-to-motion benchmarks demonstrate that it achieves state-of-the-art performance, improving FID scores by 63.8% (from 0.380 to 0.141) on long-sequence generation while enhancing motion diversity by 49.9% compared to existing methods. The proposed framework successfully resolves the diversity-quality trade-off that plagues current non-LLM approaches, establishing new standards for text-to-motion generation.

cs.CV↗

Constraining the initial Lorentz factor of gamma-ray bursts under different circumburst mediums

The initial Lorentz factor ($Γ_{\text{0}}$) plays a crucial role in uncovering the physical characteristics of gamma-ray bursts (GRBs). Previous studies have indicated that the ambient medium density index $k$ for GRBs falls in the range of 0 - 2, rather than exactly equal to 0 (homogeneous interstellar ambient) or 2 (typical stellar wind). In this work, we aim to constrain the $Γ_0$ of GRBs considering their distinct circumburst medium. We select a total of 33 GRBs for our analysis, comprising 7 X-ray GRBs and 26 optical GRBs. Subsequently, by utilizing the deceleration time of fireball $t_{\rm p}$, we derive the $Γ_0$ for the 33 GRBs assuming the radiation efficiency of $η=$ 0.2. The inferred initial Lorentz factor was found to be from 50 to 500, consistent with previous studies. We then investigate the correlation between the $Γ_0$ and the isotropic energy $E_{\rm γ,iso}$ (as well as the mean isotropic luminosity $L_{\rm γ,iso}$), finding very tight correlations between them, i.e., $Γ_0$ $\propto$ $E^{0.24}_{\rm γ,iso,52}$ ($Γ_0$ $\propto$ $L^{0.20}_{\rm γ,iso.49}$) with $η$=0.2. Additionally, we verify the correlation among $Γ_0$, the isotropic energy $E_{\rm γ,iso}$ (or $L_{\rm γ,iso}$) and the peak energy $E_{\rm{p,z}}$, i.e., $E_{\rm γ,iso,52}$ $\propto$ $Γ^{1.36}_0$$E^{0.82}_{\rm{p,z}}$ ($L_{\rm γ,iso,49}$ $\propto$ $Γ^{1.05}_0$$E^{0.66}_{\rm{p,z}}$) under the same radiation efficiency ($η$=0.2).

astro-ph.HE↗

Origin of Black Hole Spin in Lower-Mass-Gap Black Hole-Neutron Star Binaries

During the fourth observing run, the LIGO-Virgo-KAGRA Collaboration reported the detection of a coalescing compact binary (GW230529$_{-}$181500) with component masses estimated at $2.5-4.5\, M_\odot$ and $1.2-2.0\, M_\odot$ with 90\% credibility. Given the current constraints on the maximum neutron star (NS) mass, this event is most likely a lower-mass-gap (LMG) black hole-neutron star (BHNS) binary. The spin magnitude of the BH, especially when aligned with the orbital angular momentum, is critical in determining whether the NS is tidally disrupted. An LMG BHNS merger with a rapidly spinning BH is an ideal candidate for producing electromagnetic counterparts. However, no such signals have been detected. In this study, we employ a detailed binary evolution model, incorporating new dynamical tide implementations, to explore the origin of BH spin in an LMG BHNS binary. If the NS forms first, the BH progenitor (He-rich star) must begin in orbit shorter than 0.35 days to spin up efficiently, potentially achieving a spin magnitude of $χ_{\rm BH} > 0.3$. Alternatively, if a non-spinning BH (e.g., $M_{\rm BH} = 3.6\, M_\odot$) forms first, it can accrete up to $\sim 0.2\, M_\odot$ via Case BA mass transfer (MT), reaching a spin magnitude of $χ_{\rm BH} \sim 0.18$ under Eddington-limited accretion. With a higher Eddington accretion limit (i.e., 10.0 $\Dot{M}_{\rm Edd}$), the BH can attain a significantly higher spin magnitude of $χ_{\rm BH} \sim\,0.65$ by accreting approximately $1.0\, M_\odot$ during Case BA MT phase.

astro-ph.HE↗

Formation of Fast-spinning Neutron Stars in Close Binaries and Magnetar-driven Stripped-envelope Supernovae

Extreme stripped-envelope supernovae (SESNe), including Type Ic superluminous supernovae (SLSNe-I), broad-line Type Ic SNe (SNe Ic-BL), and fast blue optical transients (FBOTs), are widely believed to harbor a newborn fast-spinning highly-magnetized neutron star (``magnetar''), which can lose its rotational energy via spin-down processes to accelerate and heat the ejecta. The progenitor(s) of these magnetar-driven SESNe, and the origin of considerable angular momentum (AM) in the cores of massive stars to finally produce such fast-spinning magnetars upon core-collapse are still under debate. Popular proposed scenarios in the literature cannot simultaneously explain their event rate density, SN and magnetar parameters, and the observed metallicity. Here, we perform a detailed binary evolution simulation that demonstrates that tidal spin-up helium stars with efficient AM transport mechanism in close binaries can form fast-spinning magnetars at the end of stars' life to naturally reproduce the universal energy-mass correlation of these magnetar-driven SESNe. Our models are consistent with the event rate densities, host environments, ejecta masses, and energetics of these different kinds of magnetar-driven SESNe, supporting that the isolated common-envelope formation channel could be a major common origin of magnetar-driven SESNe. The remnant compact binary systems of magnetar-driven SESNe are progenitors of some gravitational-wave transients and galactic systems.

astro-ph.HE↗

Stable Case BB/BC Mass Transfer to Form GW190425-like Massive Binary Neutron Star Mergers

On April 25th, 2019, the LIGO-Virgo Collaboration discovered a Gravitational-wave (GW) signal from a binary neutron star (BNS) merger, i.e., GW190425. Due to the inferred large total mass, the origin of GW190425 remains unclear. We perform detailed stellar structure and binary evolution calculations that take into account mass-loss, internal differential rotation, and tidal interactions between a He-rich star and a NS companion. We explore the parameter space of the initial binary properties, including initial NS and He-rich masses and initial orbital period. We find that the immediate post-common-envelope progenitor system, consisting of a primary $\sim2.0\,M_\odot$ ($\sim1.7\,M_\odot$) NS and a secondary He-rich star with an initial mass of $\sim3.0-5.5\,M_\odot$ ($\sim5.5-6.0\,M_\odot$) in a close binary with an initial period of $\sim0.08-0.5\,{\rm{days}}$ ($\sim 0.08-0.4\,{\rm{days}}$), that experiences stable Case BB/BC mass transfer (MT) during binary evolution, can reproduce the formation of GW190425-like BNS events. Our studies reveal that the secondary He-rich star of the GW190425's progenitor before its core collapse can be efficiently spun up through tidal interaction, finally remaining as a NS with rotational energy even reaching $\sim10^{52}\,{\rm{erg}}$, which is always much higher than the neutrino-driven energy of the supernova (SN) explosion. If the newborn secondary NS is a magnetar, we expect that GW190425 can be the remnant of a magnetar-driven SN, e.g., a magnetar-driven ultra-stripped SN, a superluminous SN, or a broad-line Type Ic SN. Our results show that GW190425 could be formed through the isolated binary evolution, which involves a stable Case BB/BC MT just after the common envelope phase. On top of that, we show the He-rich star can be tidally spun up, potentially forming a spinning magnetized NS (magnetar) during the second SN explosion.

astro-ph.SR↗

Formation of GW230529 from Isolated Binary Evolution

In this {\em{Letter}}, we explore the formation of the mass-gap black hole-neutron star (mgBHNS) merger detected in gravitational wave (GW) event, i.e., GW230529, from the isolated binary evolution channel, and study potential signatures of its electromagnetic counterparts. By adopting the `delayed' supernova prescription and reasonable model realizations, our population synthesis simulation results can simultaneously match the rate densities of mgBHNS and total BHNS mergers inferred from the population analyses, along with the population distribution of the BH mass in BHNS mergers reported by the LIGO-Virgo-KAGRA Collaboration. Because GW230529 contributes significantly to the inferred mgBHNS rate densities, we suggest that GW230529 can be explained through the isolated binary evolution channel. Considering the AP4 (DD2) equation of state, the probability that GW230529 can make tidal disruption is $12.8\%$ ($63.2\%$). If GW230529 is a disrupted event, its kilonova peak apparent magnitude is predicted $\sim23-24\,{\rm{mag}}$, and hence, can be detected by the present survey projects and LSST. Since GW230529 could be an off-axis event inferred from the GW observation, its associated gamma-ray burst (GRB) might be too dim to be observed by $γ$-ray detectors, interpreting the lack of GRB observations. Our study suggests the existence of mgBHNS mergers formed through the isolated binary evolution channel due to the discovery of GW230529, indicating that BHNS mergers are still likely to be multimessenger sources that emit GWs, GRBs, and kilonovae. Although mgBHNS mergers account for $\sim50\%$ cosmological BHNS population, we find that $\gtrsim90\%$ disrupted BHNS mergers are expected to originate from mgBHNS mergers.

astro-ph.HE↗

Resolution enhancement of SOHO/MDI Magnetograms

Research on the solar magnetic field and its effects on solar dynamo mechanisms and space weather events has benefited from the continual improvements in instrument resolution and measurement frequency. The augmentation and assimilation of historical observational data timelines also play a significant role in understanding the patterns of solar magnetic field variation. Within the realm of astronomical data processing, superresolution reconstruction refers to the process of using a substantial corpus of training data to learn the nonlinear mapping between low-resolution and high-resolution images,thereby achieving higher-resolution astronomical images. This paper is an application study in highdimensional non-linear regression. Deep learning models were employed to perform SR modeling on SOHO/MDI magnetograms and SDO/HMI magnetograms, thus reliably achieving resolution enhancement of full-disk SOHO/MDI magnetograms and enhancing the image resolution to obtain more detailed information. For this study, a dataset comprising 9717 pairs of data from April 2010 to February 2011 was used as the training set,1332 pairs from March 2011 were used as the validation set, and 1,034 pairs from April 2011 were used as the test set. After data preprocessing, we randomly cropped 128x128 sub-images as the LR from the full-disk MDI magnetograms, and the corresponding 512x512 sub-images as HR from the HMI full-disk magnetograms for model training. The tests conducted have shown that the study successfully produced reliable 4x super-resolution reconstruction of full-disk MDI magnetograms.The MESR model'sresults (0.911) were highly correlated with the target HMI magnetographs as indicated by the correlation coefficient values. Furthermore, the method achieved the best PSNR, SSIM, MAE and RMSE values, indicating that the MESR model can effectively reconstruct magnetog.

astro-ph.SR↗

Formation of Lower Mass-gap Black Hole--Neutron Star Binary Mergers through Super-Eddington Stable Mass Transfer

Super-Eddington accretion of neutron stars (NSs) has been suggested both observationally and theoretically. In this paper, we propose that NSs in close-orbit binary systems with companions of helium (He) stars, most of which systems form after the common-envelope phase, could experience super-Eddington stable Case BB/BC mass transfer (MT), and can sometimes occur accretion-induced collapses (AICs) to form lower mass-gap black holes (mgBHs). Our detailed binary evolution simulations reveal that AIC events tend to happen if the primaries NS have an initial mass $\gtrsim1.7\,M_\odot$ with an accretion rate of $\gtrsim300$ times the Eddington limit. These mgBHs would have a mass nearly equal to or slightly higher than the NS maximum mass. The remnant mgBH--NS binaries after the core collapses of He stars are potential progenitors of gravitational-wave (GW) source. Multimessenger observation between GW and kilonova signals from a population of high-mass binary NS and mgBH--NS mergers formed through super-Eddington stable MT are helpful in constraining the maximum mass and equation of state of NSs. S230529ay, a mgBH--NS merger candidate recently detected in the fourth observing run of the LIGO-Virgo-KAGRA Collaboration, could possibly originate from this formation scenario.

astro-ph.HE↗

A Channel to Form Fast-spinning Black Hole-Neutron Star Binary Mergers as Multimessenger Sources. II. Accretion-induced Spin-up

In this work, we investigate an alternative channel for the formation of fast-spinning black hole-neutron star (BHNS) binaries, in which super-Eddington accretion is expected to occur in accreting BHs during the stable mass transfer phase within BH-stripped helium (BH--He-rich) star binary systems. We evolve intensive \texttt{MESA} grids of close-orbit BH--He-rich star systems to systematically explore the projected aligned spins of BHs in BHNS binaries, as well as the impact of different accretion limits on the tidal disruption probability and electromagnetic (EM) signature of BHNS mergers. Most of the BHs in BHNS mergers cannot be effectively spun up through accretion, if the accretion rate is limited to $\lesssim10\,\dot{M}_{\rm Edd}$, where $\dot{M}_{\rm Edd}$ is the standard Eddington accretion limit. In order to reach high spins (e.g., $χ_{\rm BH} \gtrsim 0.5$), the BHs are required to be born less massive (e.g., $\lesssim3.0\,M_\odot$) in binary systems with initial periods of $\lesssim0.2-0.3\,{\rm days}$ and accrete material at $\sim100\,\dot{M}_{\rm Edd}$. However, even under this high accretion limit, $\gtrsim6\,M_\odot$ BHs are typically challenging to significantly spin up and generate detectable associated EM signals. Our population simulations suggest that different accretion limits have a slight impact on the ratio of tidal disruption events. However, as the accretion limit increases, the EM counterparts from the cosmological BHNS population can become bright overall.

astro-ph.HE↗

An Exposure Meter of Lijiang Fiber-fed High-Resolution Spectrograph

In 2016, an exposure meter was installed on the Lijiang Fiber-fed High-Resolution Spectrograph to monitor the coupling of starlight to the science fiber during observations. Based on it, we investigated a method to estimate the exposure flux of the CCD in real time by using the counts of the photomultiplier tubes (PMT) of the exposure meter, and developed a piece of software to optimize the control of the exposure time. First, by using flat-field lamp observations, we determined that there is a linear and proportional relationship between the total counts of the PMT and the exposure flux of the CCD. Second, using historical observations of different spectral types, the corresponding relational conversion factors were determined and obtained separately. Third, the method was validated using actual observation data, which showed that all values of the coefficient of determination were greater than 0.92. Finally, software was developed to display the counts of the PMT and the estimated exposure flux of the CCD in real-time during the observation, providing a visual reference for optimizing the exposure time control.

astro-ph.IM↗

Sparsely Shared LoRA on Whisper for Child Speech Recognition

Whisper is a powerful automatic speech recognition (ASR) model. Nevertheless, its zero-shot performance on low-resource speech requires further improvement. Child speech, as a representative type of low-resource speech, is leveraged for adaptation. Recently, parameter-efficient fine-tuning (PEFT) in NLP was shown to be comparable and even better than full fine-tuning, while only needing to tune a small set of trainable parameters. However, current PEFT methods have not been well examined for their effectiveness on Whisper. In this paper, only parameter composition types of PEFT approaches such as LoRA and Bitfit are investigated as they do not bring extra inference costs. Different popular PEFT methods are examined. Particularly, we compare LoRA and AdaLoRA and figure out the learnable rank coefficient is a good design. Inspired by the sparse rank distribution allocated by AdaLoRA, a novel PEFT approach Sparsely Shared LoRA (S2-LoRA) is proposed. The two low-rank decomposed matrices are globally shared. Each weight matrix only has to maintain its specific rank coefficients that are constrained to be sparse. Experiments on low-resource Chinese child speech show that with much fewer trainable parameters, S2-LoRA can achieve comparable in-domain adaptation performance to AdaLoRA and exhibit better generalization ability on out-of-domain data. In addition, the rank distribution automatically learned by S2-LoRA is found to have similar patterns to AdaLoRA's allocation.

eess.AS↗

Statistical Properties of X-Ray Bursts from SGR J1935+2154 Detected by Insight-HXMT

As one class of the most important objects in the universe, magnetars can produce a lot of different frequency bursts including X-ray bursts. In \cite{2022ApJS..260...24C}, 75 X-ray bursts produced by magnetar SGR J1935+2154 during an active period in 2020 are published, including the duration and net photon counts of each burst, and waiting time based on the trigger time difference. In this paper, we utilize the power-law model, $dN(x)/dx\propto (x+x_0)^{-α_x}$, to fit the cumulative distributions of these parameters. It can be found that all the cumulative distributions can be well fitted, which can be interpreted by a self-organizing criticality theory. Furthermore, we check whether this phenomenon still exist in different energy bands and find that there is no obvious evolution. These findings further confirm that the X-ray bursts from magnetars are likely to be generated by some self-organizing critical process, which can be explained by a possible magnetic reconnection scenario in magnetars.

astro-ph.HE↗

Nonlinear Dispersion Relation and Out-of-Plane Second Harmonic Generation in MoSSe and WSSe Janus Monolayers

Janus transition metal dichalcogenides are an emerging class of atomically thin materials with engineered broken mirror symmetry that gives rise to long-lived dipolar excitons, Rashba splitting, and topologically protected solitons. They hold great promise as a versatile nonlinear optical platform due to their broadband harmonic generation tunability, ease of integration on photonic structures, and nonlinearities beyond the basal crystal plane. Here, we study second and third harmonic generation in MoSSe and WSSe Janus monolayers. We use polarization-resolved spectroscopy to map the full second-order susceptibility tensor of MoSSe, including its out-of-plane components. In addition, we measure the effective third-order susceptibility, and the second-order nonlinear dispersion close to exciton resonances for both MoSSe and WSSe at room and cryogenic temperatures. Our work sets a bedrock for understanding the nonlinear optical properties of Janus transition metal dichalcogenides and probing their use in the next-generation on-chip multifaceted photonic devices.

cond-mat.mes-hall↗

Strain Anisotropy Driven Spontaneous Formation of Nanoscrolls from Two-Dimensional Janus Layers

Two-dimensional Janus transition metal dichalcogenides (TMDs) have attracted attention due to their emergent properties arising from broken mirror symmetry and self-driven polarisation fields. While it has been proposed that their vdW superlattices hold the key to achieving superior properties in piezoelectricity and photovoltiacs, available synthesis has ultimately limited their realisation. Here, we report the first packed vdW nanoscrolls made from Janus TMDs through a simple one-drop solution technique. Our results, including ab-initio simulations, show that the Bohr radius difference between the top sulphur and the bottom selenium atoms within Janus M_Se^S (M=Mo, W) results in a permanent compressive surface strain that acts as a nanoscroll formation catalyst after small liquid interaction. Unlike classical 2D layers, the surface strain in Janus TMDs can be engineered from compressive to tensile by placing larger Bohr radius atoms on top (M_S^Se) to yield inverted C scrolls. Detailed microscopy studies offer the first insights into their morphology and readily formed Moiré lattices. In contrast, spectroscopy and FETs studies establish their excitonic and device properties and highlight significant differences compared to 2D flat Janus TMDs. These results introduce the first polar Janus TMD nanoscrolls and introduce inherent strain-driven scrolling dynamics as a catalyst to create superlattices.

cond-mat.mtrl-sci↗

KG-BERTScore: Incorporating Knowledge Graph into BERTScore for Reference-Free Machine Translation Evaluation

BERTScore is an effective and robust automatic metric for referencebased machine translation evaluation. In this paper, we incorporate multilingual knowledge graph into BERTScore and propose a metric named KG-BERTScore, which linearly combines the results of BERTScore and bilingual named entity matching for reference-free machine translation evaluation. From the experimental results on WMT19 QE as a metric without references shared tasks, our metric KG-BERTScore gets higher overall correlation with human judgements than the current state-of-the-art metrics for reference-free machine translation evaluation.1 Moreover, the pre-trained multilingual model used by KG-BERTScore and the parameter for linear combination are also studied in this paper.

cs.CL↗

Potential Subpopulations and Assembling Tendency of the Merging Black Holes

The origins of coalescing binary black holes (BBHs) detected by the advanced LIGO/Virgo are still under debate, and clues may be present in the joint mass-spin distribution of these merger events. Here we construct phenomenological models containing two sub-populations to investigate the BBH population detected in gravitational wave observations. We find that our models can explain the GWTC-3 data rather well, and several constraints to our model are required by the data: first, the maximum mass for the component with a stellar-origin, $m_{\rm max}$, is $39.1^{+2.4}_{-2.7}M_{\odot}$ at 90\% credibility; second, about $15\%$ of the mergers happen in dynamical environments, in which $7-16\%$ of events are hierarchical mergers, and these BHs have an average spin magnitude significantly larger than the first-generation mergers, with ${\rm d}μ_{\rm a} > 0.4 $ at $99\%$ credibility; third, the dynamical component BHs tend to pair with each other with larger total mass and higher mass ratio. An independent analysis focusing on spins is also carried out, and we find that the spin amplitude of component BHs can be divided into two groups according to a division mass $m_{\rm d} = 46.1^{+5.6}_{-5.1}M_{\odot}$. These constraints can be naturally explained by current formation channels, and our results suggest that some of the observed events were likely from AGN disks.

astro-ph.HE↗

iEmoTTS: Toward Robust Cross-Speaker Emotion Transfer and Control for Speech Synthesis based on Disentanglement between Prosody and Timbre

The capability of generating speech with specific type of emotion is desired for many applications of human-computer interaction. Cross-speaker emotion transfer is a common approach to generating emotional speech when speech with emotion labels from target speakers is not available for model training. This paper presents a novel cross-speaker emotion transfer system, named iEmoTTS. The system is composed of an emotion encoder, a prosody predictor, and a timbre encoder. The emotion encoder extracts the identity of emotion type as well as the respective emotion intensity from the mel-spectrogram of input speech. The emotion intensity is measured by the posterior probability that the input utterance carries that emotion. The prosody predictor is used to provide prosodic features for emotion transfer. The timber encoder provides timbre-related information for the system. Unlike many other studies which focus on disentangling speaker and style factors of speech, the iEmoTTS is designed to achieve cross-speaker emotion transfer via disentanglement between prosody and timbre. Prosody is considered as the main carrier of emotion-related speech characteristics and timbre accounts for the essential characteristics for speaker identification. Zero-shot emotion transfer, meaning that speech of target speakers are not seen in model training, is also realized with iEmoTTS. Extensive experiments of subjective evaluation have been carried out. The results demonstrate the effectiveness of iEmoTTS as compared with other recently proposed systems of cross-speaker emotion transfer. It is shown that iEmoTTS can produce speech with designated emotion type and controllable emotion intensity. With appropriate information bottleneck capacity, iEmoTTS is able to effectively transfer emotion information to a new speaker. Audio samples are publicly available https://patrick-g-zhang.github.io/iemotts/

eess.AS↗

Searching for candidates of coalescing binary black holes formed through chemically homogeneous evolution in GWTC-3

The LIGO, Virgo, and KAGRA (LVK) collaboration has announced 90 coalescing binary black holes (BBHs) with $p_{\rm astro} > 50\%$ to date, however, the origin of their formation channels is still an open scientific question. Given various properties of BBHs (BH component masses and individual spins) inferred using the default priors by the LVK, independent groups have been trying to explain the formation of the BBHs with different formation channels. Of all formation scenarios, the chemically homogeneous evolution (CHE) channel has stood out with distinguishing features, namely, nearly-equal component masses and preferentially high individual spins aligned with the orbital angular momentum. We perform Bayesian inference on the BBH events officially reported in GWTC-3 with astrophysically-predicted priors representing different formation channels of the isolated binary evolution (CEE: common-envelope evolution channel; CHE; SMT: stable mass transfer). Given assumed models, we report strong evidence for GW190517\_055101 being most likely to have formed through the CHE channel. Assuming the BBH events in the subsample are all formed through one of the isolated binary evolution channels, we obtain the lower limits on the local merger rate density of these channels at $11.45 ~\mathrm{Gpc^{-3}~yr^{-1}}$ (CEE), $0.18 ~\mathrm{Gpc^{-3}~yr^{-1}}$ (CHE), and $0.63 ~\mathrm{Gpc^{-3}~yr^{-1}}$ (SMT) at $90\%$ credible level.

astro-ph.HE↗