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.     

紫色球杆菌视紫红质光谱特性的机器学习研究

近年来，机器学习等人工智能技术被应用于蛋白质工程，其在蛋白质结构、功能预测、催化活性等研究中具有独特优势。在未知蛋白质结构的情况下，将蛋白质序列和功能特性与机器学习相结合，基于序列-活性关系（innovative sequence-activity relationship，ISAR）算法，将蛋白质氨基酸序列数字化，用快速傅里叶变换（fast four transform，FFT）进行预处理，再进行偏最小二乘回归建模，可在数据集较少情况下拟合得到最佳模型。通过机器学习对紫色球杆菌视紫红质（gloeobacter violaceus rhodopsin，GR）的突变体蛋白质氨基酸序列与光谱最大吸收波长进行建模，获得了最佳模型。用最佳索引LEVM760106建模得到的确定系数R² 为0.944，均方误差E为11.64。用小波变换进行的预处理，其R² 虽也约为0.944，但E大于11.64，不及FFT进行的预处理。方法较好地解决了蛋白质序列与功能特性之间的数学建模问题，在蛋白质工程中可为预测更优的突变体提供支持。     

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.     

一种非正交对称条带束流位置监测器设计

介绍了一种条带束流位置监测器(BPM)的设计与仿真方法。在国家同步辐射实验室"太赫兹近场高通量材料物性测试系统"工程项目中,针对波荡器出口处真空室非正交对称性的问题,设计了矩形真空室和跑道形真空室下的两种非正交对称性条带BPM,并与传统的圆形真空室下条带BPM进行对比。基于边界元法,利用MATLAB软件分别对三种真空室下的条带BPM进行建模和仿真。仿真结果表明:相对于传统的圆形真空室下条带BPM,矩形和跑道形真空室下条带BPM灵敏度提高了30%,阻抗匹配误差相对降低了20%,束流位置拟合误差降低了80%。考虑加工精度,矩形真空室下的条带BPM更适用于该工程。     

Generating Artificial Reverberation via Genetic Algorithms for Real-Time Applications

We introduce a Virtual Studio Technology (VST) 2 audio effect plugin that performs convolution reverb using synthetic Room Impulse Responses (RIRs) generated via a Genetic Algorithm (GA). The parameters of the plugin include some of those defined under the ISO 3382-1 standard (e.g., reverberation time, early decay time, and clarity), which are used to determine the fitness values of potential RIRs so that the user has some control over the shape of the resulting RIRs. In the GA, these RIRs are initially generated via a custom Gaussian noise method, and then evolve via truncation selection, random weighted average crossover, and mutation via Gaussian multiplication in order to produce RIRs that resemble real-world, recorded ones. Binaural Room Impulse Responses (BRIRs) can also be generated by assigning two different RIRs to the left and right stereo channels. With the proposed audio effect, new RIRs that represent virtual rooms, some of which may even be impossible to replicate in the physical world, can be generated and stored. Objective evaluation of the GA shows that contradictory combinations of parameter values will produce RIRs with low fitness. Additionally, through subjective evaluation, it was determined that RIRs generated by the GA were still perceptually distinguishable from similar real-world RIRs, but the perceptual differences were reduced when longer execution times were used for generating the RIRs or the unprocessed audio signals were comprised of only speech.