Multiple Bursts Research Articles

The slow clock is the master

AbstractWe investigate the synchronization and stability of mutually coupled oscillators through small impacts and explore both master–master and master–slave synchrony. The synchronization behaviour between two oscillators, one operating at a frequency $$ \omega $$ ω and the other at a frequency near a multiple of the first one, $$ n \omega $$ n ω where $$ n $$ n is an integer greater than 1, is investigated. It is observed that such systems tend to exhibit a consistent pattern of master–slave relationship. This phenomenon is geometrically elucidated by considering the interaction dynamics: while the multiple bursts of the faster oscillator tend to cancel each other out upon impacting the slower oscillator, the single burst of the slower oscillator on the faster has a secular effect. We propose that this synchronization pattern, arising from perturbative impacts, is prevalent across various physical systems. Further experimental validation of these findings could contribute to a deeper understanding of synchronization phenomena and their implications in natural and technological domains.

Follow-up Observations of Apparently One-off Sources from the Parkes Telescope

A small fraction of fast radio bursts (FRBs) have been observed with multiple bursts, whereas most Galactic sources emitting radio pulses are known to repeat. Here we present the results of follow-up observations of two FRBs and four rotating radio transients (RRATs). Among these, only one RRAT has been observed with repeating pulses, with an estimated period of around 1.297047 s. For comparison, we reanalysed the Parkes archival follow-up observations in CSIRO’s data archive for all apparently one-off sources discovered by the Parkes telescopes, including 13 RRATs and 29 FRBs. In total, 3 RRATs are suggested to be repeaters, but no repeating signals were detected from the other sources. Reporting details of the nondetection observations for the apparently one-off sources would help investigate their origins, and catastrophic scenarios are worth proposing for both extragalactic and Galactic sources.

Multi-iron subpopulations in Liller 1 from high-resolution H-band spectroscopy

We present a high-resolution chemical study of a representative sample of 21 luminous giant stars in Liller 1, a complex stellar system in the Galactic bulge, based on H-band spectra acquired with the Near-Infrared Spectrograph at KeckII. In this sample, we found fifteen stars with a subsolar iron abundance and enhanced alpha /Fe and Al/Fe likely older, having formed early and quickly from gas mainly enriched by type II supernovae, and six stars with supersolar iron and roughly solar-scaled alpha /Fe and Al/Fe likely younger, having formed at later epochs from gas also enriched by type Ia supernovae. Moreover, both subpopulations show enhanced N/Fe as in the bulge field, approximately solar-scaled V/Fe and depletion of C/Fe and 12C/13C with respect to the solar values, indicating the occurrence of significant mixing in the stellar interiors of these evolved stars. Our study also reveals that the subsolar subpopulation shows some structuring, and the presence of a third subcomponent with iron content and intermediate alpha /Fe enhancement, in between that of the metal-poor and metal-rich main subpopulations, has been statistically assessed, providing the chemical signature of both an extended star formation with multiple bursts and some self-enrichment.

Memristors-coupled neuron models with multiple firing patterns and homogeneous and heterogeneous multistability

Abstract Memristors are extensively used to estimate the external electromagnetic stimulation and synapses for neurons. In this paper, two distinct scenarios, i.e., an ideal memristor serves as external electromagnetic stimulation and a locally active memristor serves as a synapse, are formulated to investigate the impact of a memristor on a two-dimensional Hindmarsh–Rose neuron model. Numerical simulations show that the neuronal models in different scenarios have multiple burst firing patterns. The introduction of the memristor makes the neuronal model exhibit complex dynamical behaviors. Finally, the simulation circuit and DSP hardware implementation results validate the physical mechanism, as well as the reliability of the biological neuron model.

Spallation Neutron Source Hydrogen Relief Analysis for the Cryogenic Moderator System

The Spallation Neutron Source at Oak Ridge National Laboratory operates the Cryogenic Moderator System (CMS) which provides hydrogen cooling at 20K to three neutron moderators. Each hydrogen loop is protected by multiple burst discs and reclosing relief valves. As a result of the Proton Power Upgrade project, the CMS moderator loops will hold more hydrogen and thus require piping modifications. Operational experience has demonstrated that transient pressure increases in these hydrogen loops occasionally result in the rupture of the burst discs. The causes for pressure transients in the system that might lead to hydrogen venting are varied and complex, for example loss of vacuum or cooling. Dynamic simulation and analysis of the parameters considered as the worst-case relief venting scenario were performed and will be presented.

Intrinsic Emission of PSR B1937+21 at 327 MHz

At 327 MHz, the observed emission of PSR B1937+21 is greatly affected by scattering in the interstellar medium, on a timescale of order the pulse period. We use the bright impulsive giant pulses emitted by the pulsar to measure the impulse response of the interstellar medium and then recover the intrinsic emission of the pulsar by deconvolution—revealing fine structure on timescales not normally observable. We find that the intrinsic widths of the main pulse and interpulse in the pulse profile are similar to those measured at higher frequencies. We detect 60,270 giant pulses, which typically appear as narrow, ∼100 ns bursts consisting of one to a few nanoshots with widths ≲ 10 ns. However, about 10% of the giant pulses exhibit multiple bursts that seem to be causally related to each other. We also report the first detection of giant micropulses in PSR B1937+21, primarily associated with the regular main pulse emission. These are distinct from giant pulses not only in the phases at which they occur, but also in their larger widths, of order a microsecond, and steeper energy distribution. These measurements place useful observational constraints on emission mechanisms for giant pulses as well as the regular radio emission of millisecond pulsars.

Prospective Six-Month Analysis of Multiarea Burst Spinal Cord Stimulation: Correlating Intraoperative Neuromonitoring With Postoperative Programming and Clinical Outcomes

IntroductionDeRidder burst spinal cord stimulation (SCS) has shown superior relief from overall pain to traditional tonic neurostimulation therapies and a reduction in back and leg pain. However, nearly 80% of patients have two or more noncontiguous pain areas. This affects the ability to effectively program stimulation and deliver long-term efficacy of the therapy. Multiple DeRidder burst region programming is an option to treat multisite pain by interleaving stimulation at multiple areas along the spinal cord. Previous intraoperative neuromonitoring studies have shown that DeRidder burst stimulation provides broader myotomal coverage at a lower recruitment threshold. The goal of this study is to correlate intraoperative electromyogram (EMG) threshold and postsynaptic excitability with postoperative paresthesia thresholds and optimal burst stimulation programming. Materials and MethodsNeuromonitoring was performed during permanent implant of SCS leads in ten patients diagnosed with chronic intractable back and/or leg pain. Each patient underwent the surgical placement of a Penta Paddle electrode through laminectomy at the T8–T11 spinal levels. Subdermal electrode needles were placed into lower extremity muscle groups, in addition to the rectus abdominis muscles, for EMG recording. Evoked responses were compared across multiple trials of burst stimulation in which the number of independent burst areas was varied. After intraoperative data collection, all patients were programmed with single- and multiarea DeRidder burst. Intermittent dosing was delivered at 30:90, 120:360, 120:720, and 120:1440 (seconds ON/OFF) intervals. Numerical rating scale (NRS) and Patient Global Impression of Change scores were evaluated at one, two, three, four, and six months after permanent implant. ResultsThe thresholds for EMG recruitment after DeRidder burst differed across all patients owing to anatomical and physiological variations. After a 30-second dose of stimulation, the average decrease in thresholds was 1.25 mA for two-area and 0.9 mA for four-area DeRidder burst. Furthermore, a 30-second dose of multisite DeRidder burst produced a 0.25 mA reduction in the postoperative paresthesia thresholds. Across all patients, the baseline NRS score was 6.5 ± 0.5, and the NRS score after single or multiarea DeRidder burst therapy was 2.87 ± 1.50. Eight of ten patients reported a ≥50% decrease in their pain scores through the six-month follow-up visit. Pain outcomes using intermittent multiarea stimulation with longer OFF times (120:360, 120:720, 120:1440) were comparable to those using single-area DeRidder burst at 30:90 up to six months after implant with patient preference being two-area DeRidder burst. ConclusionsThis study aims to evaluate the use of intraoperative neuromonitoring to optimize stimulation programming for multisite pain and correlate it with postoperative programming and efficacy. These results suggest that multisite programming can be used to further customize DeRidder burst stimulation to each individual patient and improve outcomes and quality of life for patients receiving SCS therapy for multisite pain.

Exploring the nature of ultra-luminous X-ray sources across stellar population ages using detailed binary evolution calculations

Context. Ultra-luminous X-ray sources (ULXs) are sources observed to have extreme X-ray luminosities exceeding the Eddington limit of a stellar-mass black hole (BH). A fraction of ULXs show X-ray pulsations, which are evidence for accreting neutron stars (NSs). Theoretical studies have suggested that NSs, rather than BHs, dominate the compact objects of intrinsic ULX populations, even though the majority of the observed sample is non-pulsating, implying that X-ray pulses from many NS ULXs are unobservable. Aims. We simulate populations of X-ray binaries covering a range of starburst ages spanning from 5 to 1000 Myr with the aim of comparing the properties of observed ULXs at the different ages. Additionally, we compare two models describing different assumptions for the physical processes governing binary evolution. Methods. We used the new population synthesis code POSYDON to generate multiple populations of ULXs spanning multiple burst ages. We employed a model for geometrically beamed emission from a super-Eddington accretion disk in order to estimate the luminosities of ULXs. Following theoretical predictions for the alignment of the spin axis of an NS with the accretion disk due to mass transfer, we estimated the required mass to be accreted by the NSs in the ULX populations so that the alignment suppresses observable X-ray pulses. Results. While we find that the properties of ULX populations are sensitive to model assumptions, there are certain trends that the populations follow. Generally, young and old stellar populations are dominated by BH and NS accretors, respectively. The donor stars go from being massive H-rich main-sequence stars in young populations (< 100 Myr) to low-mass post-main sequence H-rich stars in older populations (> 100 Myr), with stripped He-rich giant donors dominating the populations at around 100 Myr. In addition, we find that NS ULXs exhibit stronger geometrical beaming than BH ULXs, leading to an underrepresentation of NS accretors in observed populations. Coupled with our finding that X-ray pulses are suppressed in at least 60% of the NS ULXs, we suggest that the observed fraction of ULXs with detectable X-ray pulses is very small, in agreement with observations. Conclusions. We show that geometrical beaming and the mass-accretion phase are critical aspects of understanding ULX observations. Our results suggest that even though most ULXs have accreting NSs, those with observable X-ray pulses would be very few.

A genome assembly of ginger (Zingiber officinale Roscoe) provides insights into genome evolution and 6-gingerol biosynthesis.

Ginger is cultivated in tropical and subtropical regions and is one of the most crucial spices worldwide owing to its special taste and scent. Here, we present a high-quality genome assembly for 'Small Laiwu Ginger', a famous cultivated ginger in northern China. The ginger genome was phased into two haplotypes, haplotype A (1.55Gb), and haplotype B (1.44Gb). Analysis of Ty1/Copia and Ty3/Gypsy LTR retrotransposon families revealed that both have undergone multiple retrotransposon bursts about 0-1 million years ago. In addition to a recent whole-genome duplication event, there has been a lineage-specific expansion of genes involved in stilbenoid, diarylheptanoid, and gingerol biosynthesis, thereby enhancing 6-gingerol biosynthesis. Furthermore, we focused on the biosynthesis of 6-gingerol, the most important gingerol, and screened key transcription factors ZoMYB106 and ZobHLH148 that regulate 6-gingerol synthesis by transcriptomic and metabolomic analysis in the ginger rhizome at four growth stages. The results of yeast one-hybrid, electrophoretic mobility shift, and dual-luciferase reporter gene assays showed that both ZoMYB106 and ZobHLH148 bind to the promoters of the key rate-limiting enzyme genes ZoCCOMT1 and ZoCCOMT2 in the 6-gingerol synthesis pathway and promote their transcriptional activities. The reference genome, transcriptome, and metabolome data pave the way for further research on the molecular mechanism underlying the biosynthesis of 6-gingerol. Furthermore, it provides precious new resources for the study on the biology and molecular breeding of ginger.

Mechanosensory encoding of forces in walking uphill and downhill: force feedback can stabilize leg movements in stick insects.

Force feedback could be valuable in adapting walking to diverse terrains, but the effects of changes in substrate inclination on discharges of sensory receptors that encode forces have rarely been examined. In insects, force feedback is provided by campaniform sensilla, mechanoreceptors that monitor forces as cuticular strains. We neurographically recorded responses of stick insect tibial campaniform sensilla to "naturalistic" forces (joint torques) that occur at the hind leg femur-tibia (FT) joint in uphill, downhill, and level walking. The FT joint torques, obtained in a previous study that used inverse dynamics to analyze data from freely moving stick insects, are quite variable during level walking (including changes in sign) but are larger in magnitude and more consistent when traversing sloped surfaces. Similar to vertebrates, insects used predominantly extension torque in propulsion on uphill slopes and flexion torques to brake forward motion when going downhill. Sensory discharges to joint torques reflected the torque direction but, unexpectedly, often occurred as multiple bursts that encoded the rate of change of positive forces (dF/dt) even when force levels were high. All discharges also showed hysteresis (history dependence), as firing substantially decreased or ceased during transient force decrements. These findings have been tested in simulation in a mathematical model of the sensilla (Szczecinski NS, Dallmann CJ, Quinn RD, Zill SN. Bioinspir Biomim 16: 065001, 2021) that accurately reproduced the biological data. Our results suggest the hypothesis that sensory feedback from the femoro-tibial joint indicating force dynamics (dF/dt) can be used to counter the instability in traversing sloped surfaces in animals and, potentially, in walking machines.NEW & NOTEWORTHY Discharges of sensory receptors (campaniform sensilla) in the hind legs of stick insects can differentially signal forces that occur in walking uphill versus walking downhill. Unexpectedly, sensory firing most closely reflects the rate of change of force (dF/dt) even when the force levels are high. These signals have been replicated in a mathematical model of the receptors and could be used to stabilize leg movements both in the animal and in a walking robot.

Effect of Hydride Morphology on Fracture behavior of Zr-2.5%Nb Pressure Tube Material

Hydrogen generated due to corrosion reaction is partly absorbed by Zr-2.5%Nb pressure tube (PT) material during service in the Pressurized Heavy Water Reactors (PHWRs). Hydrogen present in excess of the solubility limit get precipitated and embrittles the host PT material. The degree of embrittlement of the host PT matrix is governed by the morphology of the hydride precipitates. An experimental setup was designed, fabricated and used to form hydrides of different morphologies using internal pressurization. The internal pressure during the treatment was sufficient to induce hoop stresses more than the threshold for stress for re-orientation of hydrides in the PT spool. The design of the setup ensured constant pressure inside the PT spool while cooling from hydrogen solutionizing temperature. Metallographic examination of the hydrogen charged PT spool after the reorientation treatment revealed formation of stress reoriented hydrides. Series of burst tests were carried out on the PT spools with varying hydride morphology. The burst pressure as well as the final crack extension were found to be function of hydride morphology. This paper summarizes multiple full scale burst tests performed on as received Zr-2.5%Nb PT spools as well as on PT spools with varying hydride content and morphology.

Multiple bursts in non-native and native English: Evidence from twelve L1s

Voiceless plosives are frequently produced with multiple bursts (MBs), a phenomenon that has substantial implications for voice onset time measurement (VOT) of these consonants. MBs have been noted in previous research, but have not been systematically quantified. The objective of this study was to analyze MBs in non-native English (with data from twelve first languages) and native English, and to discern the effect of MBs on VOT measurement. Further, the potential effects of place of articulation (PoA), gender, speech rate, and age on MBs were explored. Results showed that VOT measurement method in the presence of MBs had a significant effect on the VOT values obtained for the plosives. In addition, MBs were influenced to a large extent by PoA, but not by gender, speech rate, or age. Comparisons between non-native English and native English revealed some significant differences, but in both varieties the analyses of MBs showed overall similar tendencies.

Pulse profile modelling of thermonuclear burst oscillations – II. Handling variability

ABSTRACT Pulse profile modelling is a relativistic ray-tracing technique that can be used to infer masses, radii, and geometric parameters of neutron stars. In a previous study, we looked at the performance of this technique when applied to thermonuclear burst oscillations from accreting neutron stars. That study showed that ignoring the variability associated with burst oscillation sources resulted in significant biases in the inferred mass and radius, particularly for the high count rates that are nominally required to obtain meaningful constraints. In this follow-on study, we show that the bias can be mitigated by slicing the bursts into shorter segments where variability can be neglected, and jointly fitting the segments. Using this approach, the systematic uncertainties on the mass and radius are brought within the range of the statistical uncertainty. With about 106 source counts, this yields uncertainties of approximately 10 per cent for both the mass and radius. However, this modelling strategy requires substantial computational resources. We also confirm that the posterior distributions of the mass and radius obtained from multiple bursts of the same source can be merged to produce outcomes comparable to that of a single burst with an equivalent total number of counts.

Sex Differences in the Speech of Persons With and Without Parkinson's Disease.

Sex differences are apparent in the prevalence and the clinical presentation of Parkinson's disease (PD), but their effects on speech have been less studied. Speech acoustics of persons with (34 females and 34 males) and without (age- and sex-matched) PD were examined, assessing the effects of PD diagnosis and sex on ratings of dysarthria severity and acoustic measures of phonation (fundamental frequency standard deviation, smoothed cepstral peak prominence), speech rate (net syllables per second, percent pause ratio), and articulation (articulatory-acoustic vowel space, release burst precision). Most measures were affected by PD (dysarthria severity, fundamental frequency standard deviation) and sex (smoothed cepstral peak prominence, net syllables per second, percent pause ratio, articulatory-acoustic vowel space), but without interactions between them. Release burst precision was differentially affected by sex in PD. Relative to those without PD, persons with PD produced fewer plosives with a single burst: females more frequently produced multiple bursts, whereas males more frequently produced no burst at all. Most metrics did not indicate that speech production is differentially affected by sex in PD. Sex was, however, associated with disparate effects on release burst precision in PD, which deserves further study. https://doi.org/10.23641/asha.24388666.

Genome evolution and initial breeding of the Triticeae grass Leymus chinensis dominating the Eurasian Steppe.

Leymus chinensis, a dominant perennial grass in the Eurasian Steppe, is well known for its remarkable adaptability and forage quality. Hardly any breeding has been done on the grass, limiting its potential in ecological restoration and forage productivity. To enable genetic improvement of the untapped, important species, we obtained a 7.85-Gb high-quality genome of L. chinensis with a particularly long contig N50 (318.49 Mb). Its allotetraploid genome is estimated to originate 5.29 million years ago (MYA) from a cross between the Ns-subgenome relating to Psathyrostachys and the unknown Xm-subgenome. Multiple bursts of transposons during 0.433-1.842 MYA after genome allopolyploidization, which involved predominantly the Tekay and Angela of LTR retrotransposons, contributed to its genome expansion and complexity. With the genome resource available, we successfully developed a genetic transformation system as well as the gene-editing pipeline in L. chinensis. We knocked out the monocot-specific miR528 using CRISPR/Cas9, resulting in the improvement of yield-related traits with increases in the tiller number and growth rate. Our research provides valuable genomic resources for Triticeae evolutionary studies and presents a conceptual framework illustrating the utilization of genomic information and genome editing to accelerate the improvement of wild L. chinensis with features such as polyploidization and self-incompatibility.

Brightness and mass accretion rate evolution during the 2022 burst of EX Lupi

Context. EX Lupi is the prototype by which EXor-type outbursts have been defined. It has experienced multiple accretion-related bursts and outbursts throughout the past decades, and the study of these events has greatly extended our knowledge about their effects. Notably, this star experienced a new burst in 2022. Aims. We aim to investigate whether the recent brightening was caused by temporarily increased accretion or by a brief decrease in the extinction and study the evolution of the EX Lupi system throughout this event. Methods. We used multi-band photometry to create color-color and color-magnitude diagrams to exclude the possibility that the brightening could be explained by a decrease in extinction. We obtained spectra using the X-shooter instrument of the Very Large Telescope (VLT) to determine the Lacc and Ṁacc during the peak of the burst and after its return to quiescence using two different methods: empirical relationships between line luminosity and Lacc, and a slab model of the whole spectrum. We examined the 130-yr light curve of EX Lupi to provide statistics on the number of outbursts experienced during this period of time. Results. Our analysis of the data taken during the 2022 burst confirmed that a change in extinction is not responsible for the brightening. Our two approaches in calculating the Ṁacc were in agreement and resulted in values that are two orders of magnitude above what had previously been estimated for EX Lupi using only a couple of individual emission lines, thus suggesting that EX Lupi is a strong accretor even when in quiescence. We determined that in 2022 March, the Ṁacc increased by a factor of seven with respect to the quiescent level. We also found hints that even though the Ṁacc had returned to near pre-outburst levels, certain physical properties of the gas (i.e., temperature and density) had not returned to the quiescent values. Conclusions. We found that the mass accreted during this three-month event was 0.8 lunar masses, which is approximately half of what is accreted during a year of quiescence. We calculated that if EX Lupi remains as active as it has been for the past 130 yr, during which it has experienced at least three outbursts and ten bursts, then it will deplete the mass of its circumstellar material in less than 160 000 yr.

Bolt tightness monitoring using multiple reconstructed narrowband Lamb waves combined with piezoelectric ultrasonic transducer

Narrowband tone burst excitation with a carefully selected frequency is generally utilized to generate Lamb waves for mode purity, dispersion diminution and signal interpretability. Narrowband excitation exhibits saturation phenomenon and even non-monotonic trends with the development of bolt looseness. In this research, a piezoelectric ultrasonic transducer with high signal-to-noise ratio is designed and fabricated for bolt tightness monitoring. The chirp signal is utilized to drive the actuator to generate broadband Lamb waves in the connected plate, and a transfer function-based signal reconstruction algorithm is innovatively proposed to extract narrowband tone burst responses with different center frequencies from the broadband chirp response for bolt tightness monitoring. The leaked wave energy-based bolt tightness indexes (TIs) are calculated based on the extracted multiple tone burst responses and a feature-level data fusion strategy is proposed to combine the TIs for exploiting the merits of different-frequency inspecting waves for different bolt tightness conditions. The fused TI not only presents a monotonic tendency with the increasing of bolt tightness, but also tackles the low sensitivity of narrowband Lamb waves for embryo bolt looseness. The proposed method contributes a novel and stable scheme for bolt tightness monitoring and opens a new perspective for damage evaluation of structures.

Calculation and Uncertainty of Fast Radio Burst Structure Based on Smoothed Data

Studies of the time-domain structure of fast radio bursts (FRBs) require an accurate estimate of the FRB dispersion measure in order to recover the intrinsic burst shape. Furthermore, the exact dispersion measure is itself of interest when studying the time evolution of the medium through which multiple bursts from repeating FRBs propagate. A commonly used approach to obtain the dispersion measure is to take the value that maximizes the FRB structure in the time domain. However, various authors use differing methods to obtain this structure parameter and do not document the smoothing method used. Furthermore, there are no quantitative estimates of the error in this procedure in the FRB literature. In this article, we present a smoothing filter based on the discrete cosine transform, and show that computing the structure parameter by summing the squares of the derivatives and taking the square root (that is, the 2-norm, ) immediately lends itself to the calculation of the uncertainty of the structure parameter. We illustrate this with FRB 20181112A and FRB 20210117A data, which were detected by the Australian Square Kilometre Array Pathfinder, and for which high-time-resolution data are available.

Temporal integration of infrasound at threshold.

Infrasounds are signals with frequencies below the classical audio-frequency range, i.e., below 20 Hz. Several previous studies have shown that infrasound is audible as well, provided that the sound level is high enough. Hence, the sound pressure levels at threshold are much higher than those in the classical audio-frequency range. The present study investigates how the duration and the shape of the temporal envelope affect thresholds of infrasound stimuli in quiet. Two envelope types were considered: one where the duration of the steady state was varied (plateau bursts) and one where the number of consecutive onset-offset bursts was varied (multiple bursts). Stimuli were presented monaurally to human listeners by means of a low-distortion sound reproduction system. For both envelope types, thresholds decrease with increasing duration, a phenomenon often referred to as temporal integration. At the same duration, thresholds for plateau-burst stimuli are typically lower than those for multiple-burst stimuli. The data are well described by a slightly modified version of a model that was previously developed to account for temporal integration in the classical audio-frequency range. The results suggest similar mechanisms underlying the detection of stimuli with frequencies in the infrasound and in the classical audio-frequency range. Since the model accounts for the effect of duration and, more generally, the shape of the envelope, it can be used to enhance the comparability of existing and future datasets of thresholds for infrasounds with different temporal stimulus parameters.

The Assembly of Black Hole Mass and Luminosity Functions of High-redshift Quasars via Multiple Accretion Episodes

The early evolution of the quasar luminosity function (QLF) and black hole mass function (BHMF) encodes key information on the physics determining the radiative and accretion processes of supermassive black holes (BHs) in high-z quasars. Although the QLF shape has been constrained by recent observations, it remains challenging to develop a theoretical model that explains its redshift evolution associated with BH growth self-consistently. In this study, based on a semianalytical model for the BH formation and growth, we construct the QLF and BHMF of the early BH population that experiences multiple accretion bursts, in each of which a constant Eddington ratio is assigned following a Schechter distribution function. Our best-fit model to reproduce the observed QLF and BHMF at z ≃ 6 suggests that several episodes of moderate super-Eddington accretion occur and each of them lasts for τ ≃ 20–30 Myr. The average duty cycle in super-Eddington phases is ≃15% for massive BHs that reach ≳108 M ⊙ by z ≃ 6, which is nearly twice that of the entire population. We find that the observed Eddington ratio distribution function is skewed to a lognormal shape owing to detection limits of quasar surveys. The predicted redshift evolution of the QLF and BHMF suggests a rapid decay of their number and mass density in a cosmic volume toward z ≳ 6. These results will be unveiled by future deep and wide surveys with the James Webb Space Telescope, Roman Space Telescope, and Euclid.