arXiv subjects

Beibei Liu

Publications and source records attributed to Beibei Liu.

At least 55 records · Page 3Linked to original sources

arXiv2022

UmeTrack: Unified multi-view end-to-end hand tracking for VR

Real-time tracking of 3D hand pose in world space is a challenging problem and plays an important role in VR interaction. Existing work in this space are limited to either producing root-relative (versus world space) 3D pose or rely on multiple stages such as generating heatmaps and kinematic optimization to obtain 3D pose. Moreover, the typical VR scenario, which involves multi-view tracking from wide \ac{fov} cameras is seldom addressed by these methods. In this paper, we present a unified end-to-end differentiable framework for multi-view, multi-frame hand tracking that directly predicts 3D hand pose in world space. We demonstrate the benefits of end-to-end differentiabilty by extending our framework with downstream tasks such as jitter reduction and pinch prediction. To demonstrate the efficacy of our model, we further present a new large-scale egocentric hand pose dataset that consists of both real and synthetic data. Experiments show that our system trained on this dataset handles various challenging interactive motions, and has been successfully applied to real-time VR applications.

cs.CV↗

arXiv2022

ET White Paper: To Find the First Earth 2.0

We propose to develop a wide-field and ultra-high-precision photometric survey mission, temporarily named "Earth 2.0 (ET)". This mission is designed to measure, for the first time, the occurrence rate and the orbital distributions of Earth-sized planets. ET consists of seven 30cm telescopes, to be launched to the Earth-Sun's L2 point. Six of these are transit telescopes with a field of view of 500 square degrees. Staring in the direction that encompasses the original Kepler field for four continuous years, this monitoring will return tens of thousands of transiting planets, including the elusive Earth twins orbiting solar-type stars. The seventh telescope is a 30cm microlensing telescope that will monitor an area of 4 square degrees toward the galactic bulge. This, combined with simultaneous ground-based KMTNet observations, will measure masses for hundreds of long-period and free-floating planets. Together, the transit and the microlensing telescopes will revolutionize our understandings of terrestrial planets across a large swath of orbital distances and free space. In addition, the survey data will also facilitate studies in the fields of asteroseismology, Galactic archeology, time-domain sciences, and black holes in binaries.

astro-ph.IM↗

arXiv2022

Growth after the streaming instability: The radial distance dependence of the planetary growth

Streaming instability is hypothesized to be triggered at particular protoplanetary disk locations where the volume density of the solid particles is enriched comparable to that of the gas. A ring of planetesimals thus forms when this condition is fulfilled locally. These planetesimals collide with each other and accrete inward drifting pebbles from the outer disk to further increase masses. We investigate the growth of the planetesimals that form in a ring-belt at various disk radii. Their initial mass distributions are calculated based on the formula summarized from the streaming instability simulations. We simulate the subsequent dynamical evolution of the planetesimals with a protoplanetary disk model based either on the minimum mass solar nebula (MMSN) or on the Toomre stability criterion. For the MMSN model, both pebble accretion and planetesimal accretion are efficient at a close-in orbit of $0.3$ AU, resulting in the emergence of several super-Earth mass planets after $1$ Myr. For comparison, only the most massive planetesimals undergo substantial mass growth when they are born at $r{=}3$ AU, while the planetesimals at $r{=}30$ AU experience little or no growth. On the other hand, in the denser Toomre disk, the most massive forming planets can reach Earth mass at $t{=}1$ Myr and reach a mass between that of Neptune and that of Saturn within $3$ Myr at $30$ AU and $100$ AU. Both the pebble and planetesimal accretion rate decrease with disk radial distance. Nevertheless, planetesimal accretion is less pronounced than pebble accretion at more distant disk regions. Taken together, the planets acquire higher masses when the disk has a higher gas density, a higher pebble flux, and/or a lower Stokes number of pebbles.

astro-ph.EP↗

arXiv2022

Early Solar System instability triggered by dispersal of the gaseous disk

The Solar System's orbital structure is thought to have been sculpted by an episode of dynamical instability among the giant planets. However, the instability trigger and timing have not been clearly established. Hydrodynamical modeling has shown that while the Sun's gaseous protoplanetary disk was present the giant planets migrated into a compact orbital configuration in a chain of resonances. Here we use dynamical simulations to show that the giant planets' instability was likely triggered by the dispersal of the gaseous disk. As the disk evaporated from the inside-out, its inner edge swept successively across and dynamically perturbed each planet's orbit in turn. The associated orbital shift caused a dynamical compression of the exterior part of the system, ultimately triggering instability. The final orbits of our simulated systems match those of the Solar System for a viable range of astrophysical parameters. The giant planet instability therefore took place as the gaseous disk dissipated, constrained by astronomical observations to be a few to ten million years after the birth of the Solar System. Terrestrial planet formation would not complete until after such an early giant planet instability; the growing terrestrial planets may even have been sculpted by its perturbations, explaining the small mass of Mars relative to Earth.

astro-ph.EP↗

arXiv2022

Natural separation of two primordial planetary reservoirs in an expanding solar protoplanetary disk

Meteorites display an isotopic composition dichotomy between non-carbonaceous (NC) and carbonaceous (CC) groups, indicating that planetesimal formation in the solar protoplanetary disk occurred in two distinct reservoirs. The prevailing view is that a rapidly formed Jupiter acted as a barrier between these reservoirs. We show a fundamental inconsistency in this model: if Jupiter is an efficient blocker of drifting pebbles, then the interior NC reservoir is depleted by radial drift within a few hundred thousand years. If Jupiter lets material pass it, then the two reservoirs will be mixed. Instead, we demonstrate that the arrival of the CC pebbles in the inner disk is delayed for several million years by the viscous expansion of the protoplanetary disk. Our results support that Jupiter formed in the outer disk (>10 AU) and allowed a considerable amount of CC material to pass it and become accreted by the terrestrial planets.

astro-ph.EP↗

arXiv2022

Discrete subgroups of small critical exponent

We prove that finitely generated higher dimensional Kleinian groups with small critical exponent are always convex-cocompact. Along the way, we also prove some geometric properties for any complete pinched negatively curved manifold with critical exponent less than 1.

math.DG↗

arXiv2021

Knot Graphs and Gromov Hyperbolicity

We define a broad class of graphs that generalize the Gordian graph of knots. These knot graphs take into account unknotting operations, the concordance relation, and equivalence relations generated by knot invariants. We prove that overwhelmingly, the knot graphs are not Gromov hyperbolic, with the exception of a particular family of quotient knot graphs. We also investigate the property of homogeneity, and prove that the concordance knot graph is homogeneous. Finally, we prove that that for any $n$, there exists a knot $K$ such that the ball of radius $n$ in the Gordian graph centered at $K$ contains no connected sum of torus knots.

math.GT↗

arXiv2021

TOI-530b: A giant planet transiting an M dwarf detected by TESS

We report the discovery of TOI-530b, a transiting giant planet around an M0.5V dwarf, delivered by the Transiting Exoplanet Survey Satellite (TESS). The host star is located at a distance of $147.7\pm0.6$ pc with a radius of $R_{\ast}=0.54\pm0.03\ R_{\odot}$ and a mass of $M_{\ast}=0.53\pm0.02\ M_{\odot}$. We verify the planetary nature of the transit signals by combining ground-based multi-wavelength photometry, high resolution spectroscopy from SPIRou as well as high-angular-resolution imaging. With $V=15.4$ mag, TOI-530b is orbiting one of the faintest stars accessible by ground-based spectroscopy. Our model reveals that TOI-530b has a radius of $0.83\pm0.05\ R_{J}$ and a mass of $0.4\pm0.1\ M_{J}$ on a 6.39-d orbit. TOI-530b is the sixth transiting giant planet hosted by an M-type star, which is predicted to be infrequent according to core accretion theory, making it a valuable object to further study the formation and migration history of similar planets. We discuss the potential formation channel of such systems.

astro-ph.EP↗

arXiv2021

Four manifolds with no smooth spines

Let $W$ be a compact smooth $4$-manifold that deformation retract to a PL embedded closed surface. One can arrange the embedding to have at most one non-locally-flat point, and near the point the topology of the embedding is encoded in the singularity knot $K$. If $K$ is slice, then $W$ has a smooth spine, i.e., deformation retracts onto a smoothly embedded surface. Using the obstructions from the Heegaard Floer homology and the high-dimensional surgery theory, we show that $W$ has no smooth spines if $K$ is a knot with nonzero Arf invariant, a nontrivial L-space knot, the connected sum of nontrivial L-space knots, or an alternating knot of signature $<-4$. We also discuss examples where the interior of $W$ is negatively curved.

math.GT↗

arXiv2021

Kleinian groups via strict hyperbolization

In this paper, we construct Kleinian groups $Γ<\mathrm{Isom}(\mathbb{H}^{2n})$ from the direct product of $n$ copies of the rank 2 free group $F_2$ via strict hyperbolization. We give a description of the limit set and its topological dimension. Such construction can be generalized to other right-angled Artin groups.

math.GR↗

arXiv2021

Heegaard Floer homology and plane curves with non-cuspidal singularities

We study possible configurations of singular points occuring on general algebraic curves in $\mathbb{C}P^2$ via Floer theory. To achieve this, we describe a general formula for the $H_{1}$-action on the knot Floer complex of the knotification of a link in $S^3$, in terms of natural actions on the link Floer complex of the original link. This result may be interest on its own.

math.GT↗

arXiv2021

Fibered and strongly quasi-positive $L$-space links

Every $L$-space knot is fibered and strongly quasi-positive, but this does not hold for $L$-space links. In this paper, we use the so called H-function, which is a concordance link invariant, to introduce a subfamily of fibered strongly quasi-positive $L$-space links. Furthermore, we present an infinite family of $L$-space links which are not quasi-positive.

math.GT↗

arXiv2020

A Tale of Planet Formation: From Dust to Planets

The characterization of exoplanets and their birth protoplanetary disks has enormously advanced in the last decade. Benefitting from that, our global understanding of the planet formation processes has been substantially improved. In this review, we first summarize the cutting-edge states of the exoplanet and disk observations. We further present a comprehensive panoptic view of modern core accretion planet formation scenarios, including dust growth and radial drift, planetesimal formation by the streaming instability, core growth by planetesimal accretion and pebble accretion. We discuss the key concepts and physical processes in each growth stage and elaborate on the connections between theoretical studies and observational revelations. Finally, we point out the critical questions and future directions of planet formation studies.

astro-ph.EP↗

arXiv2020

Two-Stream Compare and Contrast Network for Vertebral Compression Fracture Diagnosis

Differentiating Vertebral Compression Fractures (VCFs) associated with trauma and osteoporosis (benign VCFs) or those caused by metastatic cancer (malignant VCFs) are critically important for treatment decisions. So far, automatic VCFs diagnosis is solved in a two-step manner, i.e. first identify VCFs and then classify it into benign or malignant. In this paper, we explore to model VCFs diagnosis as a three-class classification problem, i.e. normal vertebrae, benign VCFs, and malignant VCFs. However, VCFs recognition and classification require very different features, and both tasks are characterized by high intra-class variation and high inter-class similarity. Moreover, the dataset is extremely class-imbalanced. To address the above challenges, we propose a novel Two-Stream Compare and Contrast Network (TSCCN) for VCFs diagnosis. This network consists of two streams, a recognition stream which learns to identify VCFs through comparing and contrasting between adjacent vertebra, and a classification stream which compares and contrasts between intra-class and inter-class to learn features for fine-grained classification. The two streams are integrated via a learnable weight control module which adaptively sets their contribution. The TSCCN is evaluated on a dataset consisting of 239 VCFs patients and achieves the average sensitivity and specificity of 92.56\% and 96.29\%, respectively.

eess.IV↗

arXiv2020

Triple linking numbers and Heegaard Floer homology

We establish some new relationships between Milnor invariants and Heegaard Floer homology. This includes a formula for the Milnor triple linking number from the link Floer complex, detection results for the Whitehead link and Borromean rings, and a structural property of the $d$-invariants of surgeries on certain algebraically split links.

math.GT↗

arXiv2020

Promoted Mass Growth of Multiple, Distant Giant Planets through Pebble Accretion and Planet-Planet Collision

We propose a pebble-driven planet formation scenario to form giant planets with high multiplicity and large orbital distances in the early gas disk phase. We perform N-body simulations to investigate the growth and migration of low-mass protoplanets in the disk with inner viscously heated and outer stellar irradiated regions. The key feature of this model is that the giant planet cores grow rapidly by a combination of pebble accretion and planet-planet collisions. This consequently speeds up their gas accretion. Because of efficient growth, the planet transitions from rapid type I migration to slow type II migration early, reducing the inward migration substantially. Multiple giant planets can sequentially form in this way with increasing semimajor axes. Both mass growth and orbital retention are more pronounced when a large number of protoplanets are taken into account compared to the case of single planet growth. Eventually, a few numbers of giant planets form with orbital distances of a few to a few tens of AUs within $1.5{-}3$ Myr after the birth of the protoplanets. The resulting simulated planet populations could be linked to the substructures exhibited in disk observations as well as large orbital distance exoplanets observed in radial velocity and microlensing surveys.

astro-ph.EP↗

arXiv2020

Pebble-driven Planet Formation around Very Low-mass Stars and Brown Dwarfs

We conduct a pebble-driven planet population synthesis study to investigate the formation of planets around very low-mass stars and brown dwarfs, in the (sub)stellar mass range between $0.01 \ M_{\odot}$ and $0.1 \ M_{\odot}$. Based on the extrapolation of numerical simulations of planetesimal formation by the streaming instability, we obtain the characteristic mass of the planetesimals and the initial masses of the protoplanets (largest bodies from the planetesimal size distributions), in either the early self-gravitating phase or the later non-self-gravitating phase of the protoplanetary disk evolution. We find that the initial protoplanets form with masses that increase with host mass, orbital distance and decrease with disk age. Around late M-dwarfs of $0.1 \ M_{\odot}$, these protoplanets can grow up to Earth-mass planets by pebble accretion. However, around brown dwarfs of $0.01 \ M_{\odot}$, planets do not grow larger than Mars mass when the initial protoplanets are born early in self-gravitating disks, and their growth stalls at around $0.01$ Earth-mass when they are born late in non-self-gravitating disks. Around these low mass stars and brown dwarfs, we find no channel for gas giant planet formation because the solid cores remain too small. When the initial protoplanets form only at the water-ice line, the final planets typically have ${\gtrsim} 15\%$ water mass fraction. Alternatively, when the initial protoplanets form log-uniformly distributed over the entire protoplanetary disk, the final planets are either very water-rich (water mass fraction ${\gtrsim}15\%$) or entirely rocky (water mass fraction ${\lesssim}5\%$).

astro-ph.EP↗

arXiv2020

Pebble drift and planetesimal formation in protoplanetary discs with embedded planets

Nearly-axisymmetric gaps and rings are commonly observed in protoplanetary discs. The leading theory regarding the origin of these patterns is that they are due to dust trapping at the edges of gas gaps induced by the gravitational torques from embedded planets. If the concentration of solids at the gap edges becomes high enough, it could potentially result in planetesimal formation by the streaming instability. We test this hypothesis by performing global 1-D simulations of dust evolution and planetesimal formation in a protoplanetary disc that is perturbed by multiple planets. We explore different combinations of particle sizes, disc parameters, and planetary masses, and find that planetesimals form in all these cases. We also compare the spatial distribution of pebbles from our simulations with protoplanetary disc observations. Planets larger than one pebble isolation mass catch drifting pebbles efficiently at the edge of their gas gaps, and depending on the efficiency of planetesimal formation at the gap edges, the protoplanetary disc transforms within a few 100,000 years to either a transition disc with a large inner hole devoid of dust or to a disc with narrow bright rings. For simulations with planetary masses lower than the pebble isolation mass, the outcome is a disc with a series of weak ring patterns but no strong depletion between the rings. Lowering the pebble size artificially to 100 micrometer-sized "silt", we find that regions between planets get depleted of their pebble mass on a longer time-scale of up to 0.5 million years. These simulations also produce fewer planetesimals than in the nominal model with millimeter-sized particles and always have at least two rings of pebbles still visible after 1 Myr.

astro-ph.EP↗