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Researcher profile

Weiming Feng

Weiming Feng contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Data Structures and Algorithmsmath.PRastro-ph.EPDiscrete MathematicsMachine Learningmath-phmath.COmath.MPphysics.space-ph

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Published work

9 published item(s)

preprint2026arXiv

On Computing Total Variation Distance Between Mixtures of Product Distributions

We study the problem of approximating the total variation distance between two mixtures of product distributions over an $n$-dimensional discrete domain. Given two mixtures $\mathbb{P}$ and $\mathbb{Q}$ with $k_1$ and $k_2$ product distributions over $[q]^n$, respectively, we give a randomized algorithm that approximates $d_{\mathrm{TV}}\left({\mathbb{P}},{\mathbb{Q}}\right)$ within a multiplicative error of $(1\pm \varepsilon)$ in time $\mathrm{poly}((nq)^{k_1+k_2},1/\varepsilon)$. We also study the special case of mixtures of Boolean subcubes over $\{0,1\}^n$. For this class, we give a deterministic algorithm that exactly computes the total variation distance in time $\mathrm{poly}(n,2^{O(k_1+k_2)})$, and show that exact computation is $\#\mathsf{P}$-hard when $k_1+k_2=Θ(n)$.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Distribution of dust ejected from the lunar surface into the Earth-Moon system

Aims. An asymmetric dust cloud was detected around the Moon by the Lunar Dust Experiment on board the Lunar Atmosphere and Dust Environment Explorer mission. We investigate the dynamics of the grains that escape the Moon and their configuration in the Earth-Moon system. Methods. We use a plausible initial ejecta distribution and mass production rate for the ejected dust. Various forces, including the solar radiation pressure and the gravity of the Moon, Earth, and Sun, are considered in the dynamical model, and direct numerical integrations of trajectories of dust particles are performed. The final states, the average life spans, and the fraction of retrograde grains as functions of particle size are computed. The number density distribution in the Earth-Moon system is obtained through long-term simulations. Results. The average life spans depend on the size of dust particles and show a rapid increase in the size range between $1\, \mathrm{μm}$ and $10\, \mathrm{μm}$. About ${3.6\times10^{-3}\,\mathrm{kg/s}}$ ($\sim2\%$) particles ejected from the lunar surface escape the gravity of the Moon, and they form an asymmetric torus between the Earth and the Moon in the range $[10\,R_\mathrm{E},50\,R_\mathrm{E}]$, which is offset toward the direction of the Sun. A considerable number of retrograde particles occur in the Earth-Moon system.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Improved bounds for randomly colouring simple hypergraphs

We study the problem of sampling almost uniform proper $q$-colourings in $k$-uniform simple hypergraphs with maximum degree $Δ$. For any $δ> 0$, if $k \geq\frac{20(1+δ)}δ$ and $q \geq 100Δ^{\frac{2+δ}{k-4/δ-4}}$, the running time of our algorithm is $\tilde{O}(\mathrm{poly}(Δk)\cdot n^{1.01})$, where $n$ is the number of vertices. Our result requires fewer colours than previous results for general hypergraphs (Jain, Pham, and Voung, 2021; He, Sun, and Wu, 2021), and does not require $Ω(\log n)$ colours unlike the work of Frieze and Anastos (2017).

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preprint2022arXiv

Optimal mixing for two-state anti-ferromagnetic spin systems

We prove an optimal $Ω(n^{-1})$ lower bound for modified log-Sobolev (MLS) constant of the Glauber dynamics for anti-ferromagnetic two-spin systems with $n$ vertices in the tree uniqueness regime. Specifically, this optimal MLS bound holds for the following classes of two-spin systems in the tree uniqueness regime: $\bullet$ all strictly anti-ferromagnetic two-spin systems (where both edge parameters $β,γ<1$), which cover the hardcore models and the anti-ferromagnetic Ising models; $\bullet$ general anti-ferromagnetic two-spin systems on regular graphs. Consequently, an optimal $O(n\log n)$ mixing time holds for these anti-ferromagnetic two-spin systems when the uniqueness condition is satisfied. These MLS and mixing time bounds hold for any bounded or unbounded maximum degree, and the constant factors in the bounds depend only on the gap to the uniqueness threshold. We prove this by showing a boosting theorem for MLS constant for distributions satisfying certain spectral independence and marginal stability properties.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Review of research on lunar dust dynamics

Lunar dust particles are generated by hypervelocity impacts of interplanetary micron-meteoroids onto the surface of the Moon, which seriously threatens the security of explorations. Studying the lunar dust dynamics helps to understand the origin and migration mechanism of lunar dust, and to provide the theoretical guidelines for the orbital design of lunar space missions. This paper reviews previous research on the lunar dust dynamics, including the interplanetary impactor environment at the Earth-Moon system, the mass production rate, the initial mass, speed and ejecta angle distributions, the related space exploration missions, the dynamical model and spatial distribution of dust particles originating from the lunar surface in the whole Earth-Moon system.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Swendsen-Wang dynamics for the ferromagnetic Ising model with external fields

We study the sampling problem for the ferromagnetic Ising model with consistent external fields, and in particular, Swendsen-Wang dynamics on this model. We introduce a new grand model unifying two closely related models: the subgraph world and the random cluster model. Through this new viewpoint, we show: (1) polynomial mixing time bounds for Swendsen-Wang dynamics and (edge-flipping) Glauber dynamics of the random cluster model, generalising the bounds and simplifying the proofs for the no-field case by Guo and Jerrum (2018); (2) near linear mixing time for the two dynamics above if the maximum degree is bounded and all fields are (consistent and) bounded away from $1$.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

What can be sampled locally?

The local computation of Linial [FOCS&#39;87] and Naor and Stockmeyer [STOC&#39;93] concerns with the question of whether a locally definable distributed computing problem can be solved locally: for a given local CSP whether a CSP solution can be constructed by a distributed algorithm using local information. In this paper, we consider the problem of sampling a uniform CSP solution by distributed algorithms, and ask whether a locally definable joint distribution can be sampled from locally. More broadly, we consider sampling from Gibbs distributions induced by weighted local CSPs in the LOCAL model. We give two Markov chain based distributed algorithms which we believe to represent two fundamental approaches for sampling from Gibbs distributions via distributed algorithms. The first algorithm generically parallelizes the single-site sequential Markov chain by iteratively updating a random independent set of variables in parallel, and achieves an $O(Δ\log n)$ time upper bound in the LOCAL model, where $Δ$ is the maximum degree, when the Dobrushin&#39;s condition for the Gibbs distribution is satisfied. The second algorithm is a novel parallel Markov chain which proposes to update all variables simultaneously yet still guarantees to converge correctly with no bias. It surprisingly parallelizes an intrinsically sequential process: stabilizing to a joint distribution with massive local dependencies, and may achieve an optimal $O(\log n)$ time upper bound independent of the maximum degree $Δ$ under a stronger mixing condition. We also show a strong $Ω(diam)$ lower bound for sampling independent set in graphs with maximum degree $Δ\ge 6$. This lower bound holds even when every node is aware of the graph. This gives a strong separation between sampling and constructing locally checkable labelings.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Perfect sampling from spatial mixing

We introduce a new perfect sampling technique that can be applied to general Gibbs distributions and runs in linear time if the correlation decays faster than the neighborhood growth. In particular, in graphs with sub-exponential neighborhood growth like $\mathbb{Z}^d$, our algorithm achieves linear running time as long as Gibbs sampling is rapidly mixing. As concrete applications, we obtain the currently best perfect samplers for colorings and for monomer-dimer models in such graphs.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Rapid mixing from spectral independence beyond the Boolean domain

We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis Gharan [ALO20]) from the Boolean domain to general discrete domains. This property characterises distributions with limited correlations, and implies that the corresponding Glauber dynamics is rapidly mixing. As a concrete application, we show that Glauber dynamics for sampling proper $q$-colourings mixes in polynomial-time for the family of triangle-free graphs with maximum degree $Δ$ provided $q\ge (α^*+δ)Δ$ where $α^*\approx 1.763$ is the unique solution to $α^*=\exp(1/α^*)$ and $δ>0$ is any constant. This is the first efficient algorithm for sampling proper $q$-colourings in this regime with possibly unbounded $Δ$. Our main tool of establishing spectral independence is the recursive coupling by Goldberg, Martin, and Paterson [GMP05].

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