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  6. Abstract The multiple-try Metropolis method is an interesting extension of the classical Metropolis–Hastings algorithm. However, theoretical understanding about its usefulness and convergence behavior is still lacking. We here derive the exact convergence rate for the multiple-try Metropolis Independent sampler (MTM-IS) via an explicit eigen analysis. As a by-product, we prove that an naive application of the MTM-IS is less efficient than using the simpler approach of “thinned” independent Metropolis–Hastings method at the same computational cost. We further explore more variants and find it possible to design more efficient algorithms by applying MTM to part of the target distribution or creating correlated multiple trials. 
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    Free, publicly-accessible full text available August 1, 2024
  7. For heat conduction along polymer chains, a decrease in the axial thermal conductivity often occurs when the polymer structure changes from one-dimensional (1D) to three-dimensional (3D). For example, a single extended aliphatic chain (e.g., polyethylene or poly(dimethylsiloxane)) usually has a higher axial thermal conductivity than its double-chain or crystal counterparts because coupling between chains induces strong interchain anharmonic scatterings. Intuitively, for chains with an aromatic backbone, the even stronger π–π stacking, once formed between chains, should enhance thermal transport across chains and suppress the thermal conductivity along the chains. However, we show that this trend is the opposite in poly(p-phenylene) (PPP), a typical chain with an aromatic backbone. Using molecular dynamics simulations, we found that the axial thermal conductivity of PPP chains shows an anomalous dimensionality dependence where the thermal conductivity of double-chain and 3D crystal structures is higher than that of a 1D single chain. We analyzed the probability distribution of dihedral angles and found that π–π stacking between phenyl rings restricts the free rotation of phenyl rings and forms a long-range order along the chain, thus enhancing thermal transport along the chain direction. Though possessing a stronger bonding strength and stabilizing the multiple-chain structure, π–π stacking does not lead to a higher interchain thermal conductance between phenyl rings compared with that between aliphatic chains. Our simulation results on the effects of π–π stacking provide insights to engineer thermal transport in polymers at the molecular level. 
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  9. ABSTRACT

    We conduct a systematic search for quasars with periodic variations from the archival photometric data of the Zwicky Transient Facility by cross-matching with the quasar catalogues of the Sloan Digital Sky Survey and Véron-Cetty and Véron. We first select out 184 primitive periodic candidates using the generalized Lomb–Scargle periodogram and autocorrelation function and then estimate their statistical significance of periodicity based on two red-noise models, i.e. damped random walk (DRW) and single power-law (SPL) models. As such, we finally identify 106 (DRW) and 86 (SPL) candidates with the most significant periodic variations out of 143 700 quasars. We further compare DRW and SPL models using Bayes factors, which indicate a relative preference of the SPL model for our primitive sample. We thus adopt the candidates identified with SPL as the final sample and summarize its basic properties. We extend the light curves of the selected candidates by supplying other archival survey data to verify their periodicity. However, only three candidates (with 6–8 cycles of periods) meet the selection criteria. This result clearly implies that, instead of being strictly periodic, the variability must be quasi-periodic or caused by stochastic red-noise. This exerts a challenge to the existing search approaches and calls for developing new effective methods.

     
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