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Bao Wang

Publications and source records attributed to Bao Wang.

At least 37 records · Page 2Linked to original sources
arXiv2025

A possible periodic RM evolution in the repeating FRB 20220529

Fast radio bursts (FRBs) are mysterious millisecond-duration radio transients of extragalactic origin. Some of them repeat, while others apparently do not. Investigations of periodic activity in repeating FRB have been conducted to probe their origins. While periodicity in the burst rate has been reported, studies of periodicities in other properties, such as dispersion measure (DM) and rotation measure (RM), are sparse. FRB~20220529 was monitored by the Five-hundred-meter Aperture Spherical radio Telescope (FAST) for nearly three years, providing an opportunity to investigate periodicity in its observed properties. Here we report a possible period of $\sim 200$ days in the RM evolution, with a significance of {4.1 $σ$} estimated via the Lomb-Scargle algorithm and {3.1 $σ$} with the phase-folding method. Periodicity in the burst rate was also investigated. It may indicate that the FRB progenitor is in a binary system, which is consistent with the significant RM increase and prompt recovery of this FRB on a week-timescale. Other scenarios, such as a system with an intermediate-mass black hole, are also explored.

astro-ph.HE↗
arXiv2025

Learning Decentralized Swarms Using Rotation Equivariant Graph Neural Networks

The orchestration of agents to optimize a collective objective without centralized control is challenging yet crucial for applications such as controlling autonomous fleets, and surveillance and reconnaissance using sensor networks. Decentralized controller design has been inspired by self-organization found in nature, with a prominent source of inspiration being flocking; however, decentralized controllers struggle to maintain flock cohesion. The graph neural network (GNN) architecture has emerged as an indispensable machine learning tool for developing decentralized controllers capable of maintaining flock cohesion, but they fail to exploit the symmetries present in flocking dynamics, hindering their generalizability. We enforce rotation equivariance and translation invariance symmetries in decentralized flocking GNN controllers and achieve comparable flocking control with 70% less training data and 75% fewer trainable weights than existing GNN controllers without these symmetries enforced. We also show that our symmetry-aware controller generalizes better than existing GNN controllers. Code and animations are available at http://github.com/Utah-Math-Data-Science/Equivariant-Decentralized-Controllers.

cs.RO↗
arXiv2024

Generalized pentagram maps via Q-nets and refactorization mappings

We introduce a family of generalizations of the pentagram maps related to $Q$-nets. A specific example is considered, and we find the map can be treated as a refactorization mapping in the Poisson-Lie group of pseudo-difference operators. This method was firstly proposed by Izosimov, and we generalize it to fit our needs. Using this description, we obtain the corresponding Lax form with a spectral parameter and invariant Poisson brackets. Finally, we consider the reduction to $B$-nets and the discrete BKP equation, offering a geometric explanation for the discrete-time Toda equation of BKP type proposed by Hirota.

nlin.SI↗
arXiv2024

Learning to Control the Smoothness of Graph Convolutional Network Features

The pioneering work of Oono and Suzuki [ICLR, 2020] and Cai and Wang [arXiv:2006.13318] initializes the analysis of the smoothness of graph convolutional network (GCN) features. Their results reveal an intricate empirical correlation between node classification accuracy and the ratio of smooth to non-smooth feature components. However, the optimal ratio that favors node classification is unknown, and the non-smooth features of deep GCN with ReLU or leaky ReLU activation function diminish. In this paper, we propose a new strategy to let GCN learn node features with a desired smoothness -- adapting to data and tasks -- to enhance node classification. Our approach has three key steps: (1) We establish a geometric relationship between the input and output of ReLU or leaky ReLU. (2) Building on our geometric insights, we augment the message-passing process of graph convolutional layers (GCLs) with a learnable term to modulate the smoothness of node features with computational efficiency. (3) We investigate the achievable ratio between smooth and non-smooth feature components for GCNs with the augmented message-passing scheme. Our extensive numerical results show that the augmented message-passing schemes significantly improve node classification for GCN and some related models.

cs.LG↗
arXiv2024

Towards Practical Overlay Networks for Decentralized Federated Learning

Decentralized federated learning (DFL) uses peer-to-peer communication to avoid the single point of failure problem in federated learning and has been considered an attractive solution for machine learning tasks on distributed devices. We provide the first solution to a fundamental network problem of DFL: what overlay network should DFL use to achieve fast training of highly accurate models, low communication, and decentralized construction and maintenance? Overlay topologies of DFL have been investigated, but no existing DFL topology includes decentralized protocols for network construction and topology maintenance. Without these protocols, DFL cannot run in practice. This work presents an overlay network, called FedLay, which provides fast training and low communication cost for practical DFL. FedLay is the first solution for constructing near-random regular topologies in a decentralized manner and maintaining the topologies under node joins and failures. Experiments based on prototype implementation and simulations show that FedLay achieves the fastest model convergence and highest accuracy on real datasets compared to existing DFL solutions while incurring small communication costs and being resilient to node joins and failures.

cs.DC↗
arXiv2024

The Dispersion Relation of Massive Photons in Plasma: A Comment on "Bounding the Photon Mass with Ultrawide Bandwidth Pulsar Timing Data and Dedispersed Pulses of Fast Radio Bursts"

The dispersion measures of fast radio bursts have been identified as a powerful tool for testing the zero-mass hypothesis of the photon. The classical approach treats the massive photon-induced and plasma-induced time delays as two separate phenomena. Recently, Wang et al. (2024) suggested that the joint influence of the nonzero photon mass and plasma effects should be considered, and proposed a revised time delay for massive photons propagating in a plasma medium, denoted as $Δt'_{m_γ} \propto ν^{-4}$, which departures from the classical dispersion relation ($\propto ν^{-2}$). Here we discuss the derivation presented by Wang et al. (2024) and show that the classical dispersion relation remains valid based on Proca equations.

astro-ph.HE↗
arXiv2024

Deep Learning with Data Privacy via Residual Perturbation

Protecting data privacy in deep learning (DL) is of crucial importance. Several celebrated privacy notions have been established and used for privacy-preserving DL. However, many existing mechanisms achieve privacy at the cost of significant utility degradation and computational overhead. In this paper, we propose a stochastic differential equation-based residual perturbation for privacy-preserving DL, which injects Gaussian noise into each residual mapping of ResNets. Theoretically, we prove that residual perturbation guarantees differential privacy (DP) and reduces the generalization gap of DL. Empirically, we show that residual perturbation is computationally efficient and outperforms the state-of-the-art differentially private stochastic gradient descent (DPSGD) in utility maintenance without sacrificing membership privacy.

cs.LG↗
arXiv2024

Probing Cosmic Background Dynamics with a Cosmological-model-independent Method

The Hubble constant $H_0$ tension has emerged as the most serious crisis in modern cosmology, potentially indicating that the $Λ$CDM model may not describe our universe accurately. In this paper, we establish a new, cosmological-model-independent method to study the cosmic background dynamics. Using the latest Pantheon+ Type Ia supernova (SN Ia) sample and the model-independent SN Ia sample (P+1690), we derive values for the luminosity distance, the Hubble parameter, and the deceleration parameter at five different redshift points ranging from 0.12 to 0.52. Our analysis shows that results obtained from the Pantheon+ sample align with the predictions of the $Λ$CDM model within 2$σ$ confidence level (CL), while those obtained from the P+1690 sample exhibit deviations of about $2\sim3σ$ CL. Furthermore, we explore the equation of state (EoS) of dark energy and find that while the EoS values from the Pantheon+ sample remain consistent with $-1$ within 2$σ$ CL, the P+1690 sample does not conform to this standard. These findings remain unchanged after the inclusion of the Hubble parameter measurements in our analysis. Our results indicate that the $Λ$CDM model remains compatible with the Pantheon+ SN Ia and the Hubble parameter measurements at 2$σ$ CL.

astro-ph.CO↗
arXiv2024

Experimental Study on Deuterium-Deuterium Thermonuclear Fusion with Interface Confinement

Nuclear fusion is recognized as the energy of the future, and huge efforts and capitals have been put into the research of controlled nuclear fusion in the past decades. The most challenging thing for controlled nuclear fusion is to generate and keep a super high temperature. Here, a sonication system, combining with micro-scale fluid control techniques, was built to generate cavitation within a limited region. As bubbles being rapidly compressed, high temperature plasma generated interior leads to particle emissions, where a Cs2LiYCl6: Ce3+ (CLYC) scintillator was used to collect the emission events. The pulse shape discrimination methods applied on captured signals revealed that only gamma ray events were observed in sonication with normal water as excepted, while obvious separation of neutron and gamma ray events was surprisingly identified in sonication with deuterated water. This result suggested that neutrons were emitted from the sonicated deuterated water, i.e. deuterium-deuterium thermonuclear fusion was initiated. This study provides an alternative and feasible approach to achieve controllable nuclear fusion and makes great sense for future researches on the application of fusion energy.

nucl-ex↗
arXiv2024

Cosmology-independent Photon Mass Limits from Localized Fast Radio Bursts by using Artificial Neural Networks

A hypothetical photon mass, $m_γ$, can produce a frequency-dependent vacuum dispersion of light, which leads to an additional time delay between photons with different frequencies when they propagate through a fixed distance. The dispersion measure--redshift measurements of fast radio bursts (FRBs) have been widely used to constrain the rest mass of the photon. However, all current studies analyzed the effect of the frequency-dependent dispersion for massive photons in the standard $Λ$CDM cosmological context. In order to alleviate the circularity problem induced by the presumption of a specific cosmological model based on the fundamental postulate of the masslessness of photons, here we employ a new model-independent smoothing technique, Artificial Neural Network (ANN), to reconstruct the Hubble parameter $H(z)$ function from 34 cosmic-chronometer measurements. By combining observations of 32 well-localized FRBs and the $H(z)$ function reconstructed by ANN, we obtain an upper limit of $m_γ \le 3.5 \times 10^{-51}\;\rm{kg}$, or equivalently $m_γ \le 2.0 \times 10^{-15}\;\rm{eV/c^2}$ ($m_γ \le 6.5 \times 10^{-51}\;\rm{kg}$, or equivalently $m_γ \le 3.6 \times 10^{-15}\;\rm{eV/c^2}$) at the $1σ$ ($2σ$) confidence level. This is the first cosmology-independent photon mass limit derived from extragalactic sources.

astro-ph.CO↗
arXiv2024

Observations favor the redshift-evolutionary $L_X$-$L_{UV}$ relation of quasars from copula

We compare, with data from the quasars, the Hubble parameter measurements, and the Pantheon+ type Ia supernova, three different relations between X-ray luminosity ($L_X$) and ultraviolet luminosity ($L_{UV}$) of quasars. These three relations consist of the standard and two redshift-evolutionary $L_X$-$L_{UV}$ relations which are constructed respectively by considering a redshift dependent correction to the luminosities of quasars and using the statistical tool called copula. By employing the PAge approximation for a cosmological-model-independent description of the cosmic background evolution and dividing the quasar data into the low-redshift and high-redshift parts, we find that the constraints on the PAge parameters from the low-redshift and high-redshift data, which are obtained with the redshift-evolutionary relations, are consistent with each other, while they are not when the standard relation is considered. If the data are used to constrain the coefficients of the relations and the PAge parameters simultaneously, then the observations support the redshift-evolutionary relations at more than $3σ$. The Akaike and Bayes information criteria indicate that there is strong evidence against the standard relation and mild evidence against the redshift-evolutionary relation constructed by considering a redshift dependent correction to the luminosities of quasars. This suggests that the redshift-evolutionary $L_X$-$L_{UV}$ relation of quasars constructed from copula is favored by the observations.

astro-ph.CO↗
arXiv2023

The Hubble Tension Survey: A Statistical Analysis of the 2012-2022 Measurements

In order to investigate the potential Hubble tension, we compile a catalogue of 216 measurements of the Hubble--Lemaître constant $H_0$ between 2012 and 2022, which includes 109 model-independent measurements and 107 $Λ$CDM model-based measurements. Statistical analyses of these measurements show that the deviations of the results with respect to the average $H_0$ are far larger than expected from their error bars if they follow a Gaussian distribution. We find that $xσ$ deviation is indeed equivalent in a Gaussian distribution to $x_{\rm eq}σ$ deviation in the frequency of values, where $x_{\rm eq}=0.72x^{0.88}$. Hence, a tension of 5$σ$, estimated between the Cepheid-calibrated type Ia supernovae and cosmic microwave background (CMB) data, is indeed a 3$σ$ tension in equivalent terms of a Gaussian distribution of frequencies. However, this recalibration should be independent of the data whose tension we want to test. If we adopt the previous analysis of data of 1976-2019, the equivalent tension is reduced to $2.25σ$. Covariance terms due to correlations of measurements do not significantly change the results. Nonetheless, the separation of the data into two blocks with $H_0<71$ and $H_0\ge 71$ km s$^{-1}$ Mpc$^{-1}$ finds compatibility with a Gaussian distribution for each of them without removing any outlier. These statistical results indicate that the underestimation of error bars for $H_0$ remains prevalent over the past decade, dominated by systematic errors in the methodologies of CMB and local distance ladder analyses.

astro-ph.CO↗
arXiv2023

On non-commutative leapfrog map

We investigate the integrability of the non-commutative leapfrog map in this paper. Firstly, we derive the explicit formula for the non-commutative leapfrog map and corresponding discrete zero-curvature equation by employing the concept of non-commutative cross-ratio. Then we revisit this discrete map, as well as its continuous limit, from the perspective of non-commutative Laurent bi-orthogonal polynomials. Finally, the Poisson structure for this discrete non-commutative map is formulated with the help of a non-commutative network. We aim to enhance our understanding of the integrability properties of the non-commutative leapfrog map and its related mathematical structures through these analysis and constructions.

math-ph↗
arXiv2023

Revisiting constraints on the photon rest mass with cosmological fast radio bursts

Fast radio bursts (FRBs) have been suggested as an excellent celestial laboratory for testing the zero-mass hypothesis of the photon. In this work, we use the dispersion measure (DM)--redshift measurements of 23 localized FRBs to revisit the photon rest mass $m_γ$. As an improvement over previous studies, here we take into account the more realistic probability distributions of DMs contributed by the FRB host galaxy and intergalactic medium (IGM) from the IllustrisTNG simulation. To better account for the systematic uncertainty induced by the choices of priors of cosmological parameters, we also combine the FRB data with the cosmic microwave background data, the baryon acoustic oscillation data, and type Ia supernova data to constrain the cosmological parameters and $m_γ$ simultaneously. We derive a new upper limit of $m_γ\le3.8\times 10^{-51}\;\rm{kg}$, or equivalently $m_γ\le2.1 \times 10^{-15} \, \rm{eV/c^2}$ ($m_γ \le 7.2 \times 10^{-51} \, \rm{kg}$, or equivalently $m_γ\le4.0 \times 10^{-15} \, \rm{eV/c^2}$) at $1σ$ ($2σ$) confidence level. Meanwhile, our analysis can also lead to a reasonable estimation for the IGM baryon fraction $f_{\rm IGM}=0.873^{+0.061}_{-0.050}$. With the number increment of localized FRBs, the constraints on both $m_γ$ and $f_{\rm IGM}$ will be further improved. A caveat of constraining $m_γ$ within the context of the standard $Λ$CDM cosmological model is also discussed.

astro-ph.HE↗
arXiv2023

Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum

This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. We use the convex $\ell_1$ and the nonconvex $\ell_1-\ell_2$ functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods.

math.OC↗
arXiv2023

Learning POD of Complex Dynamics Using Heavy-ball Neural ODEs

Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning algorithms enable learning POD-based dynamics from data and making accurate and fast predictions of dynamical systems. In this paper, we leverage the recently proposed heavy-ball neural ODEs (HBNODEs) [Xia et al. NeurIPS, 2021] for learning data-driven reduced-order models (ROMs) in the POD context, in particular, for learning dynamics of time-varying coefficients generated by the POD analysis on training snapshots generated from solving full order models. HBNODE enjoys several practical advantages for learning POD-based ROMs with theoretical guarantees, including 1) HBNODE can learn long-term dependencies effectively from sequential observations and 2) HBNODE is computationally efficient in both training and testing. We compare HBNODE with other popular ROMs on several complex dynamical systems, including the von Kármán Street flow, the Kurganov-Petrova-Popov equation, and the one-dimensional Euler equations for fluids modeling.

cs.LG↗
arXiv2023

An 8.0\% Determination of the Baryon Fraction in the Intergalactic Medium from Localized Fast Radio Bursts

The dispersion measure (DM)--redshift relation of fast radio bursts (FRBs) has been proposed as a potential new tool for probing intergalactic medium (IGM) and for studying cosmology. However, the poor knowledge of the baryon fraction in the IGM ($f_{\mathrm{IGM}}$) and its degeneracy with cosmological parameters impose restrictions on the cosmological applications of FRBs. Furthermore, DMs contributed by the IGM ($\mathrm{DM_{IGM}}$) and host galaxy ($\mathrm{DM_{host}}$), important cosmological quantities, cannot be exactly extracted from observations, which would bring uncontrolled systematic uncertainties in FRB cosmology. In this work, we use seventeen localized FRBs to constrain $f_{\mathrm{IGM}}$ and its possible redshift evolution. Other cosmological probes such as type Ia supernovae, baryon acoustic oscillations, and cosmic microwave background radiation are combined to break parameter degeneracy. Taking into account the probability distributions of $\mathrm{DM_{IGM}}$ and $\mathrm{DM_{host}}$ derived from the the IllustrisTNG simulation, we obtain a robust measurement of $f_{\mathrm{IGM}}=0.927\pm0.075$, representing a precision of 8.0\%. We find that there is no strong evidence for the redshift dependence of $f_{\mathrm{IGM}}$ at the current observational data level. The rapid progress in localizing FRBs will significantly improve the constraints on $f_{\mathrm{IGM}}$.

astro-ph.CO↗