arXiv subjects

Shilong Huang

Publications and source records attributed to Shilong Huang.

5 recordsLinked to original sources

arXiv2026

On singular solitons of the KP equation and the Go-diagrams

It has been proven that real and regular soliton solutions of the KP equation are classified in terms of the totally nonnegative Grassmannian. It is well known that vertex operators can be used to construct soliton solutions. In this paper, we consider several regular soliton solutions and study their combinations through products of vertex operators. In general, the resulting solutions become singular. Totally nonnegative elements are parametrized by the Le-diagrams introduced by Postnikov. We show that the resulting singular solutions can be parametrized by Go-diagrams, which extend Le-diagrams and arise in the Deodhar decomposition of the Grassmannian.

nlin.SI↗

arXiv2026

Gravitational waveforms and accretion characteristics in a quantum-corrected black hole without Cauchy horizons

The use of physical phenomena in the strong-field regime has become a primarily methodology for probing quantum-corrected gravity. This paper investigates periodic orbits, gravitational waves, and accretion disk radiation for a quantum-corrected black hole without Cauchy horizons. First, by analyzing the trajectory equations of massive particles in the equatorial plane, we study the influence of the quantum parameter $\zeta$ on the stability of circular orbits. The results show that an increase in $\zeta$ leads to an outward migration of both the innermost stable circular orbit and the marginally bound orbit, accompanied by an increase in the required specific angular momentum for particle motion on these two orbits. Then, we further investigate the periodic orbit characteristics of particles and compute the associated gravitational waveforms for extreme mass-ratio inspirals. It is demonstrated that quantum corrections induce a cumulative phase shift in the gravitational wave signal, leading to significant dephasing compared to the classical Schwarzschild case. Furthermore, based on the Novikov-Thorne thin accretion disk model, we evaluate the radiation characteristics of the accretion disk around this quantum-corrected black hole. The results indicate that the introduction of the quantum parameter suppresses the radiant energy flux, effective temperature, and overall radiative efficiency of the disk. These distinctive dynamical and radiative deviations provide potential phenomenological support for distinguishing quantum-corrected geometries from classical black holes using multiple observational means in the future.

gr-qc↗

arXiv2025

Image of a quantum-corrected black hole without Cauchy horizons illuminated by a static thin accretion disk

Latest advances in effective quantum gravity propose a quantum-corrected black hole solution that avoids Cauchy horizons. This paper studies the images of this black hole when illuminated by a static thin accretion disk and explores the effect of the quantum parameter {\zeta} on its appearance. First, we investigate the influence of {\zeta} on the event horizon, photon sphere, critical impact parameter, and innermost stable circular orbit associated with the black hole. We find that all these quantities exhibit an increase with increasing {\zeta}. Meanwhile, we also use observational data from M87* and Sgr A* to impose constraints on {\zeta} and compare the results with the theoretical constraint. Our analysis reveals that the observational constraint from Sgr A* is stronger than the theoretical one. We then derive the photon trajectory equation and analyze briefly the behavior of the trajectories. A detailed analysis shows that as {\zeta} increases, the trajectories of photons undergo slight modifications when approaching the event horizon. Finally, by plotting the black hole's optical appearance under three emission models, we find that as {\zeta} increases, the quantum-corrected black hole exhibits a larger shadow, along with narrower lensed and photon rings and reduced spacing between them. Furthermore, we also implement Johnson's unbound distribution to simulate the image of the quantum-corrected black hole under large quantum parameters and reach the same conclusion. This work validates the rationality of this black hole solution through observational data, and provides its unique optical signatures that can serve as a promising avenue for probing quantum gravity effects near black holes.

gr-qc↗

arXiv2025

Non-crossing permutations for the KP solitons under the Gel'fand-Dickey reductions and the vertex operators

We give a classification of the $regular$ soliton solutions of the KP hierarchy, referred to as the $KP solitons$, under the Gel'fand-Dickey $\ell$-reductions in terms of the permutation of the symmetric group. As an example, we show that the regular soliton solutions of the (good) Boussinesq equation as the 3-reduction can have $at ~most$ one resonant soliton in addition to two sets of solitons propagating in opposite directions. We also give a systematic construction of these soliton solutions for the $\ell$-reductions using the vertex operators. In particular, we show that the $non-crossing$ permutation gives the regularity condition for the soliton solutions.

nlin.SI↗

arXiv2020

Automatic Lumbar Spinal CT Image Segmentation with a Dual Densely Connected U-Net

The clinical treatment of degenerative and developmental lumbar spinal stenosis (LSS) is different. Computed tomography (CT) is helpful in distinguishing degenerative and developmental LSS due to its advantage in imaging of osseous and calcified tissues. However, boundaries of the vertebral body, spinal canal and dural sac have low contrast and hard to identify in a CT image, so the diagnosis depends heavily on the knowledge of expert surgeons and radiologists. In this paper, we develop an automatic lumbar spinal CT image segmentation method to assist LSS diagnosis. The main contributions of this paper are the following: 1) a new lumbar spinal CT image dataset is constructed that contains 2393 axial CT images collected from 279 patients, with the ground truth of pixel-level segmentation labels; 2) a dual densely connected U-shaped neural network (DDU-Net) is used to segment the spinal canal, dural sac and vertebral body in an end-to-end manner; 3) DDU-Net is capable of segmenting tissues with large scale-variant, inconspicuous edges (e.g., spinal canal) and extremely small size (e.g., dural sac); and 4) DDU-Net is practical, requiring no image preprocessing such as contrast enhancement, registration and denoising, and the running time reaches 12 FPS. In the experiment, we achieve state-of-the-art performance on the lumbar spinal image segmentation task. We expect that the technique will increase both radiology workflow efficiency and the perceived value of radiology reports for referring clinicians and patients.

eess.IV↗