Convergence rates of the blocked Gibbs sampler with random scan in the Wasserstein metric

ABSTRACT

This paper establishes explicit estimates of convergence rates for the blocked Gibbs sampler with random scan under the Dobrushin conditions. The estimates of convergence in the Wasserstein metric are obtained by taking purely analytic approaches.     

Counting restricted orientations of random graphs

We count orientations of avoiding certain classes of oriented graphs. In particular, we study , the number of orientations of the binomial random graph in which every copy of is transitive, and , the number of orientations of containing no strongly connected copy of . We give the correct order of growth of and up to polylogarithmic factors; for orientations with no cyclic triangle, this significantly improves a result of Allen, Kohayakawa, Mota, and Parente. We also discuss the problem for a single forbidden oriented graph, and state a number of open problems and conjectures.     

Identifying aspirin polymorphs from combined DFT-based crystal structure prediction and solid-state NMR

A combined experimental and computational approach was used to distinguish between different polymorphs of the pharmaceutical drug aspirin. This method involves the use of ab initio random structure searching (AIRSS), a density functional theory (DFT)-based crystal structure prediction method for the high-accuracy prediction of polymorphic structures, with DFT calculations of nuclear magnetic resonance (NMR) parameters and solid-state NMR experiments at natural abundance. AIRSS was used to predict the crystal structures of form-I and form-II of aspirin. The root-mean-square deviation between experimental and calculated ¹H chemical shifts was used to identify form-I as the polymorph present in the experimental sample, the selection being successful despite the large similarities between the molecular environments in the crystals of the two polymorphs.     

Combinational Chemotherapy and Photothermal Therapy Using a Gold Nanorod Platform for Cancer Treatment

Multimodal approaches combined with various nanomaterials and advanced techniques have been developed for synergistic cancer treatment. Among various therapies, conventional chemotherapy (CHT) is a direct cancer treatment that can produce unintended side effects due to nonspecific action on both the tumor and normal cells; patient-friendly photothermal therapy (PTT) may be able to treat embedded tumors in vital regions with minimal invasion but does not guarantee complete removal of cancers. However, the combination of CHT-PTT may provide a promising tool for direct cancer treatment with minimal side effects. In this regard, nanostructured materials, such as gold nanorods with tuned size and surface characteristics, are key components designed to enhance the heating capacity and active or passive delivery of drugs to the tumor site. In this review, the pioneering work synergizing CHT and PTT is summarized, and the current state-of-the-art in the development of inorganic and organic nanocomposites for combinational therapy is described.     

Dynamics of scalar fields in an expanding/contracting cosmos at finite temperature

This study extends the investigation of quantum dissipative effects of a cosmological scalar field by taking into account cosmic expansion and contraction.Cheung,Drewes,Kang,and Kim calculated the effective action and quantum dissipative effects of a cosmological scalar field in a recent work,where analytical expressions for the effective potential and damping coefficient were presented using a simple scalar model with quartic interactions,and the work was conducted using Minkowski-space propagators in loop diagrams.In this work,we incorporate the Hubble expansion and contraction of the cosmic background and focus on the thermal dynamics of a scalar field in a regime where the effective potential changes slowly.Given that the Hubble parameter,H,attains a small but non-zero value,we carry out calculations to the first order in H.If we set H=0,all results match those in flat spacetime.Interestingly,we must integrate over the resonances,which in turn leads to an amplification of the effects of a non-zero H.This is an intriguing phenomenon,which cannot be uncovered in flat spacetime.The implications on particle creations in the early universe will be studied in a forthcoming study.     

蓝宝石冲击消光晶向效应的第一性原理

蓝宝石的冲击消光现象是高压领域中的研究热点.低压段(86 GPa范围内)的实验研究表明蓝宝石的冲击消光与晶向相关,但在高压段(压力范围:131255 GPa)是否也具有晶向相关性目前尚不清楚.为此,利用第一性原理方法,分别计算了八个不同晶向的蓝宝石理想晶体和含氧离子空位缺陷晶体在高压段的光吸收性质,结果发现:1)蓝宝石在高压段的冲击消光表现出明显的晶向效应,且该效应还随压力增大而增强;一步的数据分析可以看出,在冲击实验采用的波段内,a晶向的消光最弱(透明性最好),c晶向的消光最强与c晶向的消光接近,g晶向的消光要弱于s晶向的消光.鉴于此,如果在高压段开展加窗冲击波实验,建议选择a晶向或m晶向的蓝宝石作为其光学窗口.本文结果不仅有助于深入地认识蓝宝石在极端条件下的光学性质,而且对未来的实验研究有重要的参考作用.     

Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields

Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.