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Sharding technology is widely regarded as an effective way to solve blockchain scalability limitations, such as lower throughput and longer delay time. However, sharding encounters challenges related to high cross-shard transaction proportion and complex cross-shard transaction verification. Therefore, a transaction sharding algorithm based on account-weighted graph is proposed. Firstly, an account-based transaction sharding model is established from the viewpoint of data sharding. Secondly, based on this model, an account-weighted graph is constructed with accounts as nodes and transaction frequency between accounts as weights for the long-term accumulated transaction data of blockchain. The community discovery algorithm is adopted, and the accounts with the largest modularity gain are selected and merged according to the association relationship between the accounts, so a multi-shard blockchain is formed initially. Finally, the multi-shard blockchain is adjusted and rebuilt by splitting and merging. The proposed algorithm is compared with the modular sharding algorithm and the random sharding algorithm under the sharding granularity of 10. The cross-shard transaction proportion is reduced by 78.8% and 78.7%, the average cross-shard transaction delay of accounts is reduced by 36.1% and 44.5%, and the transaction throughput is increased by 93.1% and 122.1%. Under the other sharding granularities, the proposed algorithm also outperforms the two algorithms in terms of cross-shard transaction proportion and account transaction delay. In conclusion, this method effectively reduces the cross-shard transaction proportion and minimizes cross-shard transaction delay.

We study a sample of 14 spectroscopically confirmed Ly α emitters (LAEs) in the late era of reionization (at redshift z ≈ 6) based on the JWST/NIRCam imaging data set. These LAEs with high Ly α luminosity of L (Ly α ) ∼10 ^42.4 –10 ^43.4 erg s ^−1 have been covered by the (ongoing) COSMOS-Web survey over 0.28 deg ^2 in four NIRCam bands (F115W, F150W, F277W, and F444W). With JWST/NIRCam imaging, we determine the UV continua with M _UV ranging from −20.5 to −18.5 mag. The UV slopes have a median value of β ≈ −2.35, and the steepest slopes can reach β < −3. Under the excellent spatial resolution of JWST, we identify three objects in the sample as potential merging/interacting systems. The 14 LAEs (and their components) are compact in morphology, residing substantially below the mass–size relation of high- z galaxies. We further investigate their physical properties, including the stellar mass ( M _* ) and star formation rates (SFRs). Most of the LAEs lie on the SFR– M _* main-sequence relation, while two of them, featured as “little red dots,” likely host active galactic nuclei (AGNs), implying a ∼10% AGN fraction. Moreover, we reveal that a new correlation may exist between Ly α equivalent width and the offset between Ly α and UV emission (Δ d _Ly _α ), with a median Δ d _Ly _α ∼ 1 kpc. This could be explained by the Ly α radiative transfer process in both the interstellar medium and circumgalactic medium. The results usher in a new era of detailed analysis on high- z LAEs with the JWST capability.

The James Webb Space Telescope provides an unprecedented opportunity for unbiased surveys of H α -emitting galaxies at z > 4 with the NIRCam's wide-field slitless spectroscopy (WFSS). In this work, we present a census of Ly α escape fraction ( f _esc,Ly _α ) of 165 star-forming galaxies at z = 4.9–6.3, utilizing their H α emission directly measured from FRESCO NIRCam/WFSS data. We search for Ly α emission of each H α -emitting galaxy in the Very Large Telescope/MUSE data. The overall f _esc,Ly _α measured by stacking is 0.090 ± 0.006. We find that f _esc,Ly _α displays a strong dependence on the observed UV slope ( β _obs ) and E ( B − V ), such that the bluest galaxies ( β _obs ∼ −2.5) have the largest escape fractions ( f _esc,Ly _α ≈ 0.6), indicative of the crucial role of dust and gas in modulating the escape of Ly α photons. f _esc,Ly _α is less well related to other parameters, including the UV luminosity and stellar mass, and the variation in f _esc,Ly _α with them can be explained by their underlying coupling with E ( B − V ) or β _obs . Our results suggest a tentative decline in f _esc,Ly _α at z ≳ 5, implying increasing intergalactic medium attenuation toward higher redshift. Furthermore, the dependence of f _esc,Ly _α on β _obs is proportional to that of the ionizing photon escape fraction ( f _esc,LyC ), indicating that the escape of Ly α and ionizing photon may be regulated by similar physical processes. With f _esc,Ly _α as a proxy to f _esc,LyC , we infer that UV-faint ( M _UV > −16) galaxies contribute >70% of the total ionizing emissivity at z = 5–6. If these relations hold during the epoch of reionization, UV-faint galaxies can contribute the majority of UV photon budget to reionize the Universe.

We present a study of a sample of 45 spectroscopically confirmed, UV luminous galaxies at z ∼ 6. They were selected as bright Lyman-break galaxies (LBGs) using deep multiband optical images in more than 2 deg ^2 of the sky, and subsequently identified via their strong Ly α emission. The majority of these LBGs span an absolute UV magnitude range from −22.0 to −20.5 mag with Ly α equivalent width (EW) between ∼10 and ∼200 Å, representing the most luminous galaxies at z ∼ 6 in terms of both UV continuum emission and Ly α line emission. We model the spectral energy distributions of 10 LBGs that have deep infrared observations from Hubble Space Telescope, JWST, and/or Spitzer, and find that they have a wide range of stellar masses and ages. They also have high star formation rates ranging from a few tens to a few hundreds of solar mass per year. Five of the LBGs have JWST or HST images, and four of them show compact morphology in these images, including one that is roughly consistent with a point source, suggesting that UV luminous galaxies at this redshift are generally compact. The fraction of our photometrically selected LBGs with strong Ly α emission (EW > 25 Å) is about 0.2, which is consistent with previous results and supports a moderate evolution of the intergalactic medium opacity at the end of cosmic reionization. Using deep X-ray images, we do not find evidence of strong active galactic nucleus (AGN) activity in these galaxies, but our constraint is loose, and we are not able to rule out the possibility of any weak AGN activity.

We present a study of seven spectroscopically confirmed (Ly α -emitting) galaxies at redshift z ≃ 6 using the JWST/NIRCam imaging data. These galaxies, with a wide range of Ly α luminosities, were recently observed in a series of NIRCam broad and medium bands. We constrain the rest-frame UV/optical continua and measure the H α line emission of the galaxies using the combination of JWST/NIRCam and archival HST/WFC3 infrared photometry. We further estimate the escape fractions of their Ly α photons ( ${f}_{\mathrm{esc}}^{\mathrm{Ly}\alpha }$ ) and the production efficiency of ionizing photons ( ξ _ion ). Among the sample, six out of seven galaxies have Ly α escape fractions of ≲10%, which might be the status for most of the star-forming galaxies at z ≃ 6. One UV-faint Ly α galaxy with an extremely blue UV slope has a large value of ${f}_{\mathrm{esc}}^{\mathrm{Ly}\alpha }$ reaching ≃50%. These galaxies have a broad range of ξ _ion over log _10 ξ _ion,0 (Hz erg ^−1 ) ∼ 25.0–26.5. We find that UV-fainter galaxies with bluer UV-continuum slopes likely have higher escape fractions of Ly α photons. We also find that galaxies with higher Ly α line emission tend to produce ionizing photons more efficiently. The most Ly α -luminous galaxy in the sample has a very high ξ _ion,0 of log _10 ξ _ion,0 (Hz erg ^−1 ) > 26. Our results support the scenario that Ly α galaxies may have served as an important contributor to cosmic reionization. Blue and bright Ly α galaxies are excellent targets for JWST follow-up spectroscopic observations.

We report the detection of diffuse halos (LAHs) around star-forming galaxies at z ∼ 5.7 by stacking 310 spectroscopically confirmed emitters (LAEs). The majority of the LAEs are identified from our spectroscopic survey of galaxies at z > 5.5. They are all located in well-studied fields with deep narrowband and broadband imaging data. We combine the LAE sample and its subsamples in the narrowband NB816 (i.e., the band) and z band (i.e., the continuum band). By comparing the stacked objects with their corresponding point-spread functions, we clearly detect extended LAHs around these LAEs. We perform sophisticated simulations and analyses on statistical and systematic errors, and confirm that the detected halos are not caused by errors. The scale lengths of the LAHs, when described by a double-component model, range from 1.2 to 5.3 kpc with a typical value of ∼2 kpc. The LAH sizes from our sample are in agreement with those of individual LAEs at the similar redshift measured by Very Large Telescope/MUSE but are relatively smaller than those of photometrically selected LAEs in previous studies. We also find that LAEs with higher luminosities, higher UV-continuum luminosities, or smaller equivalent widths tend to have larger LAH sizes. Our results are consistent with a scenario that LAHs originate from the scattered light of the central galaxies by H i gas in the circumgalactic medium. [ABSTRACT FROM AUTHOR]