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.     

基于无人机多光谱图像的土壤水分检测方法研究

以表层土壤为对象,探究土壤的多光谱反射率与土壤水分含量相关性,进行基于无人机多光谱图像的土壤水分含量预测模型方法的探究。选取中国农业大学通州实验站为研究区域,实地采集试验田的土壤样本100组,按照一定梯度配制土壤含水量,配成的土壤含水率为10%~50%之间,土壤含量的真实值采用土壤烘干法进行测定。多光谱相机灵巧便捷,可搭载在无人机上对土壤进行监测。将RedEdged-M型多光谱相机搭载在Phantom 3型无人机上,选择阳光充足的采集环境,实时采集土壤样本的多光谱图像,建立土壤多光谱信息与水分含量之间的模型。利用处理光谱数据的ENVI5.3软件提取土壤样本多光谱信息,以多光谱相机自带的标准白板反射率为100%,计算出土壤样本在蓝、绿、红、红边、近红外五个波段的光谱反射率。采用BP神经网络算法、支持向量机算法、偏最小二乘算法分别建立基于无人机多光谱图像的土壤水分含量的预测模型。以80组土壤样本数据作为训练集,建立基于多光谱图像的土壤水分含量预测模型。采用莱文贝格-马夸特算法对BPNN进行改进,提高了其训练速度,当网络结构为5-10-1时,训练效果最好,本文选择该网络结构;SVM采取高斯核函数,当参数为0.56时,模型效果最好。本研究采用归一化均方根误差(NRMSE)和决策系数(R 2)对三种土壤水分含量的预测模型进行定量对比。以20组土壤样本数据作为测试集,结果可知,基于BP神经网络土壤水分含量预测模型的NRMSE为0.268,R 2为0.872;基于支持向量机的土壤水分含量预测模型的NRMSE为0.298,R 2为0.821;基于偏最小二乘土壤水分含量预测模型的NRMSE为0.316,R 2为0.789。对三种模型分析可知,基于BPNN的土壤水分含量预测模型效果均较好。结果可知,土壤的光谱反射率与含水率间存在较密切的相关性,将多光谱相机搭载在无人机上可以对土壤水分含量进行有效的实时监测,对监测土壤墒情提供技术支持和理论支撑。     

基于双向循环神经网络的汉语语音识别*

当前基于深度神经网络模型中,虽然其隐含层可设置多层,对复杂问题适应能力强,但每层之间的节点连接是相互独立的,这种结构特性导致了在语音序列中无法利用上下文相关信息来提高识别效果,而传统的循环神经网络虽然做出了改进,但是只能对上文信息进行利用。针对以上问题,该文采用可以同时利用语音序列中上下文相关信息的双向循环神经网络模型与深度神经网络模型相结合,并应用于语音识别。构建具有5层隐含层的模型,其中第3层为双向循环神经网络结构,其他层采用深度神经网络结构。实验结果表明:加入了双向循环神经网络结构的模型与其他模型相比,较好地提高了识别正确率;噪声对双向循环神经网络汉语识别有重要影响,尤其是训练集和测试集附加噪声类型不同时,单一的含噪声语音的训练模型无法适应不同噪声类型的语音识别;调整神经网络模型中隐含层神经元数量后,识别正确率并不是一直随着隐含层中神经元数量的增加而增加,神经元数量数目增加到一定程度后正确率出现了降低的趋势。     

Exceptional Cycles in the Bounded Derived Categories of Quivers

An exceptional n-cycle in a Hom-finite triangulated category with Serre functor has been recently introduced by Broomhead,Pauksztello and Ploog.When n=1,it is a spherical object.We explicitly determine all the exceptional cycles in the bounded derived category D^b(kQ)of a finite quiver Q without oriented cycles.In particular,if Q is an Euclidean quiver,then the length type of exceptional cycles in D^b(kQ)is exactly the tubular type of Q;if Q is a Dynkin quiver of type E_m(m=6,7,8),or Q is a wild quiver,then there are no exceptional cycles in D^b(kQ);and if Q is a Dynkin quiver of type An or D_n,then the length of an exceptional cycle in D^b(kQ)is either h or h/2,where h is the Coxeter number of Q.     

Certain fractional calculus and integral transform results of incomplete ℵ-functions with applications

In this paper, we study certain interesting and useful properties of incomplete $\aleph$-functions. The incomplete $\aleph$-function is an extension of the $\aleph$-function. We find several useful classical integral transforms of these functions. Further, we examine the fractional calculus with the incomplete $\aleph$-functions and point out several special cases. Finally, we give the applications of incomplete $\aleph$-functions in detecting glucose supply in human blood.     

A DNA Switch for Detecting Single Nucleotide Polymorphism within a Long DNA Sequence Under Denaturing Conditions

DNA detection is usually conducted under nondenaturing conditions to favor the formation of Watson–Crick base-paring interactions. However, although such a setting is excellent for distinguishing a single-nucleotide polymorphism (SNP) within short DNA sequences (15–25 nucleotides), it does not offer a good solution to SNP detection within much longer sequences. Here we report on a new detection method capable of detecting SNP in a DNA sequence containing 35–90 nucleotides. This is achieved through incorporating into the recognition DNA sequence a previously discovered DNA molecule that forms a stable G-quadruplex in the presence of 7 molar urea, a known condition for denaturing DNA structures. The systems are configured to produce both colorimetric and fluorescent signals upon target binding.     

贝叶斯优化卷积神经网络公共场所异常声识别*

针对公共场所异常声的感知和识别问题,提出一种基于贝叶斯优化卷积神经网络的识别方法。提取声信号的Gammatone倒谱系数、倍频程功率谱、短时能量和谱质心,组合成声信号的特征图。构建卷积神经网络作为分类器,利用递增的卷积核设置和池化操作处理不同尺度的特征。基于贝叶斯优化算法优化卷积神经网络的模型参数,对包括火苗噼啪声、婴儿啼哭声、烟花燃放声、玻璃破碎声和警报声的5种公共场所异常声进行识别。该方法的识别结果与基于不同的特征提取和分类器方案得到的识别结果进行比较,结果表明该方法的识别效果优于其他特征提取和分类器方案的识别效果。最后分析了该方法在不同信噪比噪声干扰下的识别结果,验证了该方法的有效性。