Shotgun reconstruction in the hypercube

Mossel and Ross raised the question of when a random coloring of a graph can be reconstructed from local information, namely, the colorings (with multiplicity) of balls of given radius. In this article, we are concerned with random 2-colorings of the vertices of the -dimensional hypercube, or equivalently random Boolean functions. In the worst case, balls of diameter are required to reconstruct. However, the situation for random colorings is dramatically different: we show that almost every 2-coloring can be reconstructed from the multiset of colorings of balls of radius 2. Furthermore, we show that for , almost every -coloring can be reconstructed from the multiset of colorings of 1-balls.     

化学法改性煤沥青脱除苯并芘的研究

在管式反应器中采用苯甲酸、聚乙二醇、固体古马隆树脂（S）、液体古马隆树脂（L）为添加剂来降低煤沥青中有害物质苯并芘的含量，以期使得煤沥青可绿色化应用。采用紫外-可见分光光度计分析煤沥青中苯并芘含量。考察了反应温度、反应时间、添加剂添加量、催化剂等工艺条件对添加剂脱除煤沥青中苯并芘的影响。结果表明，不同工艺条件能降低煤沥青中苯并芘的含量。在优化条件下，不同添加剂对苯并芘脱除率由高到低依次为：液体古马隆树脂、聚乙二醇、苯甲酸和固体古马隆树脂。分析其反应机理，这与催化剂的酸性相关，发生亲电取代反应。结果表明，液体古马隆树脂（L）在催化剂存在下对煤沥青中苯并芘脱除率可达73.0%，显示了良好的应用前景。     

Evaluation of Charged Defect Energy in Two-Dimensional Semiconductors for Nanoelectronics: The WLZ Extrapolation Method

Defects play a central role in controlling the electronic properties of two-dimensional (2D) materials and realizing the industrialization of 2D electronics. However, the evaluation of charged defects in 2D materials within first-principles calculation is very challenging and has triggered a recent development of the WLZ (Wang, Li, Zhang) extrapolation method. This method lays the foundation of the theoretical evaluation of energies of charged defects in 2D materials within the first-principles framework. Herein, the vital role of defects for advancing 2D electronics is discussed, followed by an introduction of the fundamentals of the WLZ extrapolation method. The ionization energies (IEs) obtained by this method for defects in various 2D semiconductors are then reviewed and summarized. Finally, the unique defect physics in 2D dimensions including the dielectric environment effects, defect ionization process, and carrier transport mechanism captured with the WLZ extrapolation method are presented. As an efficient and reasonable evaluation of charged defects in 2D materials for nanoelectronics and other emerging applications, this work can be of benefit to the community.     

Stochastic sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations

This paper presents a new sensitivity analysis method for coupled acoustic–structural systems subjected to non-stationary random excitations. The integral of the response power spectrum density (PSD) of the coupled system is taken as the objective function. The thickness of each structural element is used as a design variable. A time-domain algorithm integrating the pseudo excitation method (PEM), direct differentiation method (DDM) and high precision direct (HPD) integration method is proposed for the sensitivity analysis of the objective function with respect to design variables. Firstly, the PEM is adopted to transform the sensitivity analysis under non-stationary random excitations into the sensitivity analysis under pseudo transient excitations. Then, the sensitivity analysis equation of the coupled system under pseudo transient excitations is derived based on the DDM. Moreover, the HPD integration method is used to efficiently solve the sensitivity analysis equation under pseudo transient excitations in a reduced-order modal space. Numerical examples are presented to demonstrate the validity of the proposed method.     

Phase transitions in graphs on orientable surfaces

Let be the orientable surface of genus and denote by the class of all graphs on vertex set with edges embeddable on . We prove that the component structure of a graph chosen uniformly at random from features two phase transitions. The first phase transition mirrors the classical phase transition in the Erd?s‐Rényi random graph chosen uniformly at random from all graphs with vertex set and edges. It takes place at , when the giant component emerges. The second phase transition occurs at , when the giant component covers almost all vertices of the graph. This kind of phenomenon is strikingly different from and has only been observed for graphs on surfaces.     

The chromatic number of random Borsuk graphs

We study a model of random graph where vertices are n i.i.d. uniform random points on the unit sphere S^d in , and a pair of vertices is connected if the Euclidean distance between them is at least 2??. We are interested in the chromatic number of this graph as n tends to infinity. It is not too hard to see that if ?>0 is small and fixed, then the chromatic number is d+2 with high probability. We show that this holds even if ?→0 slowly enough. We quantify the rate at which ? can tend to zero and still have the same chromatic number. The proof depends on combining topological methods (namely the Lyusternik–Schnirelman–Borsuk theorem) with geometric probability arguments. The rate we obtain is best possible, up to a constant factor—if ?→0 faster than this, we show that the graph is (d+1)‐colorable with high probability.25     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

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.