A uniformly accurate (UA) multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime

We propose and rigourously analyze a multiscale time integrator Fourier pseudospectral (MTI-FP) method for the Dirac equation with a dimensionless parameter $\varepsilon\in(0,1]$ which is inversely proportional to the speed of light. In the nonrelativistic limit regime, i.e. $0<\varepsilon\ll 1$, the solution exhibits highly oscillatory propagating waves with wavelength $O(\varepsilon^2)$ and $O(1)$ in time and space, respectively. Due to the rapid temporal oscillation, it is quite challenging in designing and analyzing numerical methods with uniform error bounds in $\varepsilon\in(0,1]$. We present the MTI-FP method based on properly adopting a multiscale decomposition of the solution of the Dirac equation and applying the exponential wave integrator with appropriate numerical quadratures. By a careful study of the error propagation and using the energy method, we establish two independent error estimates via two different mathematical approaches as $h^{m_0}+\frac{\tau^2}{\varepsilon^2}$ and $h^{m_0}+\tau^2+\varepsilon^2$, where $h$ is the mesh size, $\tau$ is the time step and $m_0$ depends on the regularity of the solution. These two error bounds immediately imply that the MTI-FP method converges uniformly and optimally in space with exponential convergence rate if the solution is smooth, and uniformly in time with linear convergence rate at $O(\tau)$ for all $\varepsilon\in(0,1]$ and optimally with quadratic convergence rate at $O(\tau^2)$ in the regimes when either $\varepsilon=O(1)$ or $0<\varepsilon\lesssim \tau$. Numerical results are reported to demonstrate that our error estimates are optimal and sharp. Finally, the MTI-FP method is applied to study numerically the convergence rates of the solution of the Dirac equation to those of its limiting models when $\varepsilon\to0^+$.Comment: 25 pages, 1 figur

Modal Analysis of Cylindrical Gears with Arcuate Tooth Trace

In this paper, the forming principle, meshing features and tooth surface equation were introduced. And the modal parameters distribution of cylindrical gears with arcuate tooth trace was researched. The results show: 1. The modulus was the biggest impact factor for modal and natural frequency of cylindrical gears with arcuate tooth trace, then tooth width, and the radius of tooth line have the minimum influence; 2. When the modulus increased, natural frequency of cylindrical gears with arcuate tooth reduced rapidly; 3. When the tooth width increased, natural frequency of cylindrical gears with arcuate tooth has a tendency to rise except for first-order modal; 4. The influence of radius of tooth line can be basic ignored; 5. The second-order modal and third-order modal, fifth-order modal and sixth-order modal was very close. The research on cylindrical gears with arcuate tooth trace in this paper has a certain reference value on gear design and selection

Unbiased Delayed Feedback Label Correction for Conversion Rate Prediction

Conversion rate prediction is critical to many online applications such as digital display advertising. To capture dynamic data distribution, industrial systems often require retraining models on recent data daily or weekly. However, the delay of conversion behavior usually leads to incorrect labeling, which is called delayed feedback problem. Existing work may fail to introduce the correct information about false negative samples due to data sparsity and dynamic data distribution. To directly introduce the correct feedback label information, we propose an Unbiased delayed feedback Label Correction framework (ULC), which uses an auxiliary model to correct labels for observed negative feedback samples. Firstly, we theoretically prove that the label-corrected loss is an unbiased estimate of the oracle loss using true labels. Then, as there are no ready training data for label correction, counterfactual labeling is used to construct artificial training data. Furthermore, since counterfactual labeling utilizes only partial training data, we design an embedding-based alternative training method to enhance performance. Comparative experiments on both public and private datasets and detailed analyses show that our proposed approach effectively alleviates the delayed feedback problem and consistently outperforms the previous state-of-the-art methods.Comment: accepted by KDD 202

Detection of TiO and VO in the atmosphere of WASP-121b and Evidence for its temporal variation

We report the transit observations of the ultra hot Jupiter WASP-121b using the Goodman High Throughput Spectrograph (GHTS) at the 4-meter ground-based telescope Southern Astrophysical Research Telescope (SOAR), covering the wavelength range $502-900$ nm. By dividing the target and reference star into 19 spectroscopic passbands and applying differential spectrophotometry, we derive spectroscopic transit light curves and fit them using Gaussian process framework to determine transit depths for every passbands. The obtained optical transmission spectrum shows a steep increased slope toward the blue wavelength, which seems to be too steep to be accounted for by the Rayleigh scattering alone. We note that the transmission spectrum from this work and other works differ obviously from each other, which was pointed out previously by \citet{Wilson2021} as evidence for temporal atmospheric variation. We perform a free chemistry retrieval analysis on the optical transmission spectra from this work and the literature HST/WFC3 NIR spectrum. We determine TiO, VO and H$_{2}$O with abundances of $-5.95_{-0.42}^{+0.47}$ dex, $-6.72_{-1.79}^{+0.51}$ dex, and $-4.13_{-0.46}^{+0.63}$ dex, respectively. We compare the abundances of all these three molecules derived from this work and previous works, and find that they are not consistent with each other, indicating the chemical compositions of the terminator region may change over long timescales. Future multi-epoch and high-precision transit observations are required to further confirm this phenomena. We note that when combining the transmission spectra in the optical and in NIR in retrieval analysis, the abundances of V and VO, the NIR-to-optical offset and the cloud deck pressure may be coupled with each other.Comment: 23 pages, 13 figures, 6 tables. Accepted for publication in Research in Astronomy and Astrophysic

Influence on emergency digit replantation and outcome assessment after COVID-19 virus nucleic acid testing normalization

ObjectiveThe study aims to compare the implementation and prognosis of emergency digit replantation surgery before and after normalized corona virus disease 2019 (COVID-19) nucleic acid testing for patients taking emergency operation and to explore the influence of normalized COVID-19 nucleic acid testing on replantation surgery.MethodNormalized COVID-19 nucleic acid testing for patients taking emergency operation has been carried out since 1 August 2021 at our hospital, which means each patient who needs emergency surgical treatment has to obtain either positive or negative results of COVID-19 nucleic acid before entering the operating room. This research reviewed and compared the prognosis of the injured extremity that had emergency severed digit replantation between June and September 2021, at the Shanghai Sixth People's Hospital Affiliated to Shanghai Jiao Tong University School of Medicine, and analyzed the impact of normalized COVID-19 nucleic acid testing on the outcome of the replanted fingers of different severity using disability of arm-shoulder-hand (DASH) and hand injury severity scoring (HISS) scoring systems.ResultsA total of 54 cases with 74 severed replanted phalanges were included replanted by the research group between 1 August and 30 September 2021, without any COVID-19 suspected/confirmed case detected. Compared with previous period (1 June to 31 July, 2021), although the interval between emergency visits and emergency replantation did increase significantly after normalized COVID-19 nucleic acid testing [(3.83 ± 0.94) to (1.77 ± 0.67) h, P &lt; 0.05], we observed no significant difference in the improvement rate of the DASH scoring of the disabled upper extremity 3-month postoperatively (P = 0.538) nor in the complication rate (P = 0.344). Moreover, there was no significant difference in the improvement rate of the DASH scoring of the disabled upper extremity 3-month postoperatively in patients with different traumatic severities before and after normalized COVID-19 nucleic acid testing (moderate P = 0.269, severe P = 0.055, major P = 0.149).ConclusionDespite the preoperative delay, the policy of COVID-19 nucleic acid testing normalization does not have explicit influence on the short-term outcomes of emergency digit replantation surgery. With this evidence, microsurgeons could pay attention to the patients' anxiety and spend more effort in comforting them during the prolonged preoperative wait. These insights may have implications for other emergency department resource management whenever a social crisis occurs

Low self-esteem and the neural basis of attentional bias for social rejection cues: Evidence from the N2pc ERP component

a b s t r a c t Previous studies have indicated that individuals with low self-esteem show an attentional bias toward information concerning social rejection. The present study used event-related potentials (ERPs) to investigate whether task-irrelevant rejection cues could capture the visuo-spatial attention of low self-esteem individuals during a demanding visual detection task. The N2pc ERP component was measured as an index of the allocation of spatial attention. Results revealed that rejection cues induced greater N2pc component responses among individuals with low levels of self-esteem than for those with high levels of self-esteem. These results suggest that task-irrelevant rejection cues are likely to capture the attention of individuals with low self-esteem but not those with high self-esteem. These findings provide direct electrophysiological support for the idea that individuals with low levels of self-esteem show an attentional bias for cues related to social rejection

Cognitive control in belief-laden reasoning during conclusion processing: An ERP study

Belief bias is the tendency to accept conclusions that are compatible with existing beliefs more frequently than those that contradict beliefs. It is one of the most replicated behavioral findings in the reasoning literature. Recently, neuroimaging studies using functional magnetic resonance imaging (fMRI) and event-related potentials (ERPs) have provided a new perspective and have demonstrated neural correlates of belief bias that have been viewed as supportive of dual-process theories of belief bias. However, fMRI studies have tended to focus on conclusion processing, while ERPs studies have been concerned with the processing of premises. In the present research, the electrophysiological correlates of cognitive control were studied among 12 subjects using high-density ERPs. The analysis was focused on the conclusion presentation phase and was limited to normatively sanctioned responses to valid–believable and valid–unbelievable problems. Results showed that when participants gave normatively sanctioned responses to problems where belief and logic conflicted, a more positive ERP deflection was elicited than for normatively sanctioned responses to nonconflict problems. This was observed from −400 to −200 ms prior to the correct response being given. The positive component is argued to be analogous to the late positive component (LPC) involved in cognitive control processes. This is consistent with the inhibition of empirically anomalous information when conclusions are unbelievable. These data are important in elucidating the neural correlates of belief bias by providing evidence for electrophysiological correlates of conflict resolution during conclusion processing. Moreover, they are supportive of dual-process theories of belief bias that propose conflict detection and resolution processes as central to the explanation of belief bias

An open science resource for establishing reliability and reproducibility in functional connectomics

Efforts to identify meaningful functional imaging-based biomarkers are limited by the ability to reliably characterize inter-individual differences in human brain function. Although a growing number of connectomics-based measures are reported to have moderate to high test-retest reliability, the variability in data acquisition, experimental designs, and analytic methods precludes the ability to generalize results. The Consortium for Reliability and Reproducibility (CoRR) is working to address this challenge and establish test-retest reliability as a minimum standard for methods development in functional connectomics. Specifically, CoRR has aggregated 1,629 typical individuals’ resting state fMRI (rfMRI) data (5,093 rfMRI scans) from 18 international sites, and is openly sharing them via the International Data-sharing Neuroimaging Initiative (INDI). To allow researchers to generate various estimates of reliability and reproducibility, a variety of data acquisition procedures and experimental designs are included. Similarly, to enable users to assess the impact of commonly encountered artifacts (for example, motion) on characterizations of inter-individual variation, datasets of varying quality are included

Neural correlates of the perception for novel objects.

Perception of novel objects is of enormous importance in our lives. People have to perceive or understand novel objects when seeing an original painting, admiring an unconventional construction, and using an inventive device. However, very little is known about neural mechanisms underlying the perception for novel objects. Perception of novel objects relies on the integration of unusual features of novel objects in order to identify what such objects are. In the present study, functional Magnetic Resonance Imaging (MRI) was employed to investigate neural correlates of perception of novel objects. The neuroimaging data on participants engaged in novel object viewing versus ordinary object viewing revealed that perception of novel objects involves significant activation in the left precuneus (Brodmann area 7) and the right visual cortex. The results suggest that the left precuneus is associated with the integration of unusual features of novel objects, while the right visual cortex is sensitive to the detection of such features. Our findings highlight the left precuneus as a crucial component of the neural circuitry underlying perception of novel objects

Effect of Ionic Liquids on the Isobaric Vapor-Liquid Equilibrium Behavior of Acetone-Chloroform

Isobaric vapor-liquid equilibrium (VLE) data of the ternary system acetone + chloroform + 1,3-dimethylimidazolium dimethylphosphate ([MMIM][DMP]) or 1-ethyl-3-methylimidazolium diethylphosphate ([EMIM][DEP]) were obtained at 101.3 kPa. Results indicated that the addition of [MMIM][DMP] or [EMIM][DEP] could eliminate the azeotropic point of the binary system of acetone + chloroform when the mole fraction of ionic liquids (ILs) was above 0.15. Besides, the experimental data could be well correlated by the nonrandom two-liquid (NRTL) model. The structures as well as interactions between molecular solvents (acetone, chloroform) and the ion pairs ([MMIM][DMP], [EMIM][DEP]) were studied by quantum chemical calculations. The result indicated that the interaction energies (&Delta;E) follow the order of &Delta;E(acetone + [EMIM][DEP]) &gt; &Delta;E(acetone + [MMIM][DMP]) &gt; &Delta;E(chloroform + [EMIM][DEP]) &asymp; &Delta;E(chloroform + [MMIM][DMP]), and chloroform had stronger affinity to ionic liquids than acetone