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Zhiyuan Li

Publications and source records attributed to Zhiyuan Li.

At least 289 records · Page 16Linked to original sources
arXiv2022

Implicit Bias of Gradient Descent on Reparametrized Models: On Equivalence to Mirror Descent

As part of the effort to understand implicit bias of gradient descent in overparametrized models, several results have shown how the training trajectory on the overparametrized model can be understood as mirror descent on a different objective. The main result here is a characterization of this phenomenon under a notion termed commuting parametrization, which encompasses all the previous results in this setting. It is shown that gradient flow with any commuting parametrization is equivalent to continuous mirror descent with a related Legendre function. Conversely, continuous mirror descent with any Legendre function can be viewed as gradient flow with a related commuting parametrization. The latter result relies upon Nash's embedding theorem.

cs.LG↗
arXiv2022

Very Large Array Multi-band Radio Imaging of the Triple AGN Candidate SDSS J0849+1114

Kpc-scale triple active galactic nuclei (AGNs), potential precursors of gravitationally-bound triple massive black holes (MBHs), are rarely seen objects and believed to play an important role in the evolution of MBHs and their host galaxies. In this work we present a multi-band (3.0, 6.0 10.0, and 15.0 GHz), high-resolution radio imaging of the triple AGN candidate, SDSS J0849+1114, using the Very Large Array. Two of the three nuclei (A and C) are detected at 3.0, 6.0, and 15 GHz for the first time, both exhibiting a steep spectrum over 3--15 GHz (with a spectral index $-0.90 \pm 0.05$ and $-1.03 \pm 0.04$) consistent with a synchrotron origin. Nucleus A, the strongest nucleus among the three, shows a double-sided jet, with the jet orientation changing by $\sim20^{\circ}$ between its inner 1" and the outer 5.5" (8.1 kpc) components, which may be explained as the MBH's angular momentum having been altered by merger-enhanced accretion. Nucleus C also shows a two-sided jet, with the western jet inflating into a radio lobe with an extent of 1.5" (2.2 kpc). The internal energy of the radio lobe is estimated to be $\rm 5.0 \times 10^{55}$ erg, for an equipartition magnetic field strength of $\rm \sim 160\ μG$. No significant radio emission is detected at all four frequencies for nucleus B, yielding an upper limit of 15, 15, 15, and 18 $\rm μJy\ beam^{-1}$ at 3.0, 6.0, 10.0, and 15.0 GHz, based on which we constrain the star formation rate in nucleus B to be $\lesssim 0.4~\rm M_{\odot}~yr^{-1}$.

astro-ph.GA↗
arXiv2022

Interpretability of Neural Network With Physiological Mechanisms

Deep learning continues to play as a powerful state-of-art technique that has achieved extraordinary accuracy levels in various domains of regression and classification tasks, including images, video, signal, and natural language data. The original goal of proposing the neural network model is to improve the understanding of complex human brains using a mathematical expression approach. However, recent deep learning techniques continue to lose the interpretations of its functional process by being treated mostly as a black-box approximator. To address this issue, such an AI model needs to be biological and physiological realistic to incorporate a better understanding of human-machine evolutionary intelligence. In this study, we compare neural networks and biological circuits to discover the similarities and differences from various perspective views. We further discuss the insights into how neural networks learn from data by investigating human biological behaviors and understandable justifications.

cs.NE↗
arXiv2022

Peridynamic modeling for impact failure of wet concrete considering the influence of saturation

In this paper, a modified intermediately homogenized peridynamic (IH-PD) model for analyzing impact failure of wet concrete has been presented under the configuration of ordinary state-based peridynamic theory. The meso-structural properties of concrete are linked to the macroscopic mechanical behavior in the IH-PD model, where the heterogeneity of concrete is taken into account, and the calculation cost does not increase. Simultaneously, the porosity of concrete is considered, which is implemented by deleting the bond between two material points, as well as the influence of porosity on the mechanical properties of concrete. Moreover, the effective bulk and shear modulus of cement mortar in wet concrete (saturated and unsaturated concrete) are calculated respectively. The dynamic model for wet concrete is described from three aspects: strength, dynamic increase factor, and equation of state. Validation of the proposed model is established through analyzing some benchmark tests and comparing with the corresponding experiment and other available numerical results.

math.NA↗
arXiv2022

Nonlinear optical radiation of a lithium niobate microcavity

The nonlinear optical radiation of an integrated lithium niobate microcavity is demonstrated, which has been neglected in previous studies of nonlinear photonic devices. We find that the nonlinear coupling between confined optical modes on the chip and continuum modes in free space can be greatly enhanced on the platform of integrated microcavity, with feasible relaxation of the phase-matching condition. With an infrared pump laser, we observe the vertical radiation of second-harmonic wave at the visible band, which indicates a robust phase-matching-free chip-to-free-space frequency converter and also unveils an extra energy dissipation channel for integrated devices. Such an unexpected coherent nonlinear interaction between the free-space beam and the confined mode is also validated by the different frequency generation. Furthermore, based on the phase-matching-free nature of the nonlinear radiation, we build an integrated atomic gas sensor to characterize Rb isotopes with a single telecom laser. The unveiled mechanism of nonlinear optical radiation is universal for all dielectric photonic integrated devices, and provides a simple and robust chip-to-free-space as well as visible-to-telecom interface.

physics.optics↗
arXiv2022

Unpolarized Shafarevich conjectures for hyper-Kähler varieties

Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collection of places. For K3 surfaces, such a finiteness result was proved by Y. She. For hyper-Kähler varieties, which are higher-dimensional analogs of K3 surfaces, Y. André has verified the Shafarevich conjecture for hyper-Kähler varieties of a given dimension and admitting a very ample polarization of bounded degree. In this paper, we provide a unification of both results by proving the (unpolarized) Shafarevich conjecture for hyper-Kähler varieties in a given deformation type. In a similar fashion, generalizing a result of Orr and Skorobogatov on K3 surfaces, we prove the finiteness of geometric isomorphism classes of hyper-Kähler varieties of CM type in a given deformation type defined over a number field with bounded degree. A key to our approach is a uniform Kuga--Satake map, inspired by She's work, and we study its arithmetic properties, which are of independent interest.

math.AG↗
arXiv2022

CAHA/PPAK Integral-field Spectroscopic Observations of M81 -- I. Circumnuclear ionized gas

Galactic circumnuclear environments of nearby galaxies provide unique opportunities for our understanding of the co-evolution between super-massive black holes and their host galaxies. Here we present a detailed study of ionized gas in the central kiloparsec region of M81, which hosts the closest prototype low-luminosity active galactic nucleus, based on optical integral-field spectroscopic observations taken with the CAHA 3.5m telescope. It is found that much of the circumnuclear ionized gas is concentraed within a bright core of $\sim$200 pc in extent and a surrounding spiral-like structure known as the nuclear spiral. The total mass of the ionized gas is estimated to be $\sim2\times10^5\rm~M_\odot$, which corresponds to a few percent of the cold gas mass in this region, as traced by co-spatial dust extinction features. Plausible signature of a bi-conical outflow along the disk plane is suggested by a pair of blueshifted/redshifted low-velocity features, symmetrically located at $\sim$ 120 -- 250 pc from the nucleus. The spatially-resolved line ratios of [N\,{\sc ii}]/H$α$ and [O\,{\sc iii}]/H$β$ demonstrate that much of the circumnuclear region can be classified as LINER (low-ionization nuclear emission-line region). However, substantial spatial variations in the line intensities and line ratios strongly suggest that different ionization/excitation mechanisms, rather than just a central dominant source of photoionization, are simultaneously at work to produce the observed line signatures.

astro-ph.GA↗
arXiv2022

Quenching of Massive Disk Galaxies in the IllustrisTNG Simulation

A rare population of massive disk galaxies have been found to invade the red sequence dominated by early-type galaxies. These red/quenched massive disk galaxies have recently gained great interest into their formation and origins. The usually proposed quenching mechanisms, such as bar quenching and environment quenching, seem not suitable for those bulge-less quenched disks in low-density environment. In this paper, we use the IllustrisTNG-300 simulation to investigate the formation of massive quenched central disk galaxies. It is found that these galaxies contain less gas and harbor giant supermassive black holes(SMBHs) (above $ 10^{8}M_{\odot}$) than their star forming counterparts. By tracing their formation history, we found that quenched disk galaxies formed early and preserved disk morphology for cosmological time scales. They have experienced less than one major merger on average and it is mainly mini-mergers (mass ratio $<$1/10) that contribute to the growth of their SMBHs. In the Illustris-TNG simulation the black hole feedback mode switches from thermal to kinetic feedback when the black hole mass is more massive than $\sim 10^{8}M_{\odot}$, which is more efficient to eject gas outside of the galaxy and to suppress further cooling of hot gaseous halo. We conclude that kinetic AGN feedback in massive red/quenched disk galaxy is the dominant quenching mechanism.

astro-ph.GA↗
arXiv2022

Quantum crosstalk analysis for simultaneous gate operations on superconducting qubits

Maintaining or even improving gate performance with growing numbers of parallel controlled qubits is a vital requirement for fault-tolerant quantum computing. For superconducting quantum processors, though isolated one- or two-qubit gates have been demonstrated with high-fidelity, implementing these gates in parallel commonly shows worse performance. Generally, this degradation is attributed to various crosstalks between qubits, such as quantum crosstalk due to residual inter-qubit coupling. An understanding of the exact nature of these crosstalks is critical to figuring out respective mitigation schemes and improved qubit architecture designs with low crosstalk. Here we give a theoretical analysis of quantum crosstalk impact on simultaneous gate operations in a qubit architecture, where fixed-frequency transmon qubits are coupled via a tunable bus, and sub-100-ns controlled-Z (CZ) gates can be realized by applying a baseband flux pulse on the bus. Our analysis shows that for microwave-driven single-qubit gates, the dressing from the qubit-qubit coupling can cause non-negligible cross-driving errors when qubits operate near frequency collision regions. During CZ gate operations, although unwanted near-neighbor interactions are nominally turned off, sub-MHz parasitic next-near-neighbor interactions involving spectator qubits can still exist, causing considerable leakage or control error when one operates qubit systems around these parasitic resonance points. To ensure high-fidelity simultaneous operations, there could raise a request to figure out a better way to balance the gate error from target qubit systems themselves and the error from non-participating spectator qubits. Overall, our analysis suggests that towards useful quantum processors, the qubit architecture should be examined carefully in the context of high-fidelity simultaneous gate operations in a scalable qubit lattice.

quant-ph↗
arXiv2022

CHANG-ES. XXIV. First Detection of A Radio Nuclear Ring and Potential LLAGN in NGC 5792

We report the discoveries of a nuclear ring of diameter 10$\arcsec$ ($\sim$1.5 kpc) and a potential low luminosity active galactic nucleus (LLAGN) in the radio continuum emission map of the edge-on barred spiral galaxy NGC~5792. These discoveries are based on the Continuum Halos in Nearby Galaxies - an Expanded Very Large Array (VLA) Survey, as well as subsequent VLA observations of sub-arcsecond resolution. Using a mixture of H$α$ and 24 $μ$m calibration, we disentangle the thermal and non-thermal radio emission of the nuclear region, and derive a star formation rate (SFR) of $\sim 0.4~M_{\sun}$ yr$^{-1}$. We find that the nuclear ring is dominated by non-thermal synchrotron emission. The synchrotron-based SFR is about three times of the mixture-based SFR. This result indicates that the nuclear ring underwent more intense star-forming activity in the past, and now its star formation is in the low state. The sub-arcsecond VLA images resolve six individual knots on the nuclear ring. The equipartition magnetic field strength $B_{\rm eq}$ of the knots varies from 77 to 88 $μ$G. The radio ring surrounds a point-like faint radio core of $S_{\rm 6GHz}=(16\pm4)$ $μ$Jy with polarized lobes at the center of NGC~5792, which suggests an LLAGN with an Eddington ratio $\sim10^{-5}$. This radio nuclear ring is reminiscent of the Central Molecular Zone (CMZ) of the Galaxy. Both of them consist of a nuclear ring and LLAGN.

astro-ph.GA↗
arXiv2022

Beauville-Voisin filtrations on zero cycles of moduli space of stable sheaves on K3 surfaces

The Beauville-Voisin conjecture predicts the existence of a filtration on projective hyper-Kähler manifolds opposite to the conjecture Bloch-Beilinson filtration, called the Beauivlle-Voisin filtration. Voisin has introduced a filtration on zero cycles of an arbitrary projective hyper-Kähler manifold. On moduli space of stable objects of a projective K3 surface, there are other candidates constructed by Shen-Yin-Zhao, Barros-Flapan-Marian-Silversmith and more recently by Vial from different point of views. According to the work of Vial, all of them are proved to be equivalent except Voisin's filtration. In this paper, we show that Voisin's filtration is the same as the other filtrations. As an application, we prove a conjecture in Barros-Flapan-Marian-Silversmith's paper.

math.AG↗
arXiv2022

Deligne-Beilinson cohomology of the universal K3 surface

O'Grady's generalized Franchetta conjecture (GFC) is concerned with codimension 2 algebraic cycles on universal polarized K3 surfaces. In \cite{BL17}, this conjecture has been studied in the Betti cohomology groups. Following a suggestion of Voisin, we investigate this problem in the Deligne-Beilinson (DB) cohomology groups. In this paper, we develop the theory of Deligne-Beilinson cohomology groups on separated (smooth) Deligne-Mumford stacks. Using the automorphic cohomology group and Noether-Lefschetz theory, we compute the 4-th DB-cohomology group of universal oriented polarized K3 surfaces with at worst an $A_1$-singularity and show that GFC for such family holds in DB-cohomology. In particular, this confirms O'Grady's original conjecture in DB cohomology.

math.AG↗
arXiv2022

Quantum circuit architecture search on a superconducting processor

Variational quantum algorithms (VQAs) have shown strong evidences to gain provable computational advantages for diverse fields such as finance, machine learning, and chemistry. However, the heuristic ansatz exploited in modern VQAs is incapable of balancing the tradeoff between expressivity and trainability, which may lead to the degraded performance when executed on the noisy intermediate-scale quantum (NISQ) machines. To address this issue, here we demonstrate the first proof-of-principle experiment of applying an efficient automatic ansatz design technique, i.e., quantum architecture search (QAS), to enhance VQAs on an 8-qubit superconducting quantum processor. In particular, we apply QAS to tailor the hardware-efficient ansatz towards classification tasks. Compared with the heuristic ansatze, the ansatz designed by QAS improves test accuracy from 31% to 98%. We further explain this superior performance by visualizing the loss landscape and analyzing effective parameters of all ansatze. Our work provides concrete guidance for developing variable ansatze to tackle various large-scale quantum learning problems with advantages.

quant-ph↗
arXiv2021

Evidence for A Hot Wind from High-resolution X-ray Spectroscopic Observation of the Low-luminosity Active Galactic Nucleus in NGC 7213

Super-massive black holes (SMBHs) spend most of their lifetime accreting at a rate well below the Eddington limit, manifesting themselves as low-luminosity active galactic nuclei (LLAGNs). The prevalence of a hot wind from LLAGNs is a generic prediction by theories and numerical simulations of black hole accretion and is recently becoming a crucial ingredient of AGN kinetic feedback in cosmological simulations of galaxy evolution. However, direct observational evidence for this hot wind is still scarce. In this work, we identify significant Fe XXVI Ly$α$ and Fe XXV K$α$ emission lines from high-resolution Chandra grating spectra of the LLAGN in NGC\,7213, a nearby Sa galaxy hosting a $\sim10^8\rm~M_\odot$ SMBH, confirming previous work. We find that these lines exhibit a blueshifted line-of-sight velocity of $\sim1100\rm~km s^{-1}$ and a high XXVI Ly$α$ to XXV K$α$ flux ratio implying for a $\sim16$ keV hot plasma. By confronting these spectral features with synthetic X-ray spectra based on our custom magnetohydrodynamical simulations, we find that the high-velocity, hot plasma is naturally explained by the putative hot wind driven by the hot accretion flow powering this LLAGN. Alternative plausible origins of this hot plasma, including stellar activities, AGN photoionization and the hot accretion flow itself, are quantitatively disfavored. The inferred kinetic energy and momentum carried by the wind can serve as strong feedback to the environment. We compare NGC\,7213 to M81*, in which strong evidence for a hot wind was recently presented, and discuss implications on the universality and detectability of hot winds from LLAGNs.

astro-ph.HE↗
arXiv2021

Uniqueness and stability for inverse source problem for fractional diffusion-wave equations

This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the analyticity and the new established unique continuation principle provided that the coefficients are all temporally independent. We also derive a Lipschitz stability of our inverse source problem under a suitable topology whose norm is given via the adjoint system of the fractional diffusion-wave equation.

math.AP↗
arXiv2021

An inverse problem of determining fractional orders in a fractal solute transport model

A fractal mobile-immobile (MIM in short) solute transport model in porous media is set forth, and an inverse problem of determining the fractional orders by the additional measurements at one interior point is investigated by Laplace transform. The unique existence of the solution to the forward problem is obtained based on the inverse Laplace transform, and the uniqueness of the inverse problem is proved in the real-space of Laplace transform by the maximum principle, and numerical inversions with noisy data are presented to demonstrate a numerical stability of the inverse problem.

math.NA↗
arXiv2021

Searching for Quasi-periodic Oscillations in Active Galactic Nuclei of the Chandra Deep Field South

Recent X-ray observations have revealed growing evidence of quasi-periodic oscillation (QPO) in the light curve of active galactic nuclei (AGNs), which may serve as a useful probe of black hole physics. In this work, we present a systematic search for X-ray QPOs among ~ 1000 AGNs of the Chandra Deep Field South (CDF-S) in a homogeneous fashion. Dividing the 7-Ms Chandra observations into four epochs, we search for periodic signals that are persistent throughout any of these epochs, using two independent methods: Lomb-Scargle periodogram and Gregory-Loredo Algorithm. No statistically significant periodic signal is found with either method on any of the four epochs. Our extensive simulations of source light curves suggest that this non-detection is primarily due to a moderate sensitivity of the CDF-S data in QPO detection. Using the simulation-predicted detection efficiency, we are able to provide a meaningful constraint on the intrinsic occurrence rate of persistent QPOs, < (15-20) %, provided that they share a similar power spectral density with a handful of currently known AGN QPOs. The true intrinsic occurrence rate might be significantly below this upper limit, however, given the non-detection among the CDF-S sources. Our additional search for short-lived QPOs that are only detected over a small subset of all observations results in two candidates, one in source XID 643 at a period of ~ 13273 s and the other in source XID 876 at a period of ~ 7065 s.

astro-ph.HE↗