DiriNet:An Estimation Network for Spectral Response Function and Point Spread Function

Hyper-and multi-spectral image fusion is an important technology to produce hyper-spectral and hyper-resolution images,which always depends on the spectral response function andthe point spread function.However,few works have been payed on the estimation of the two degra-dation functions.To learn the two functions from image pairs to be fused,we propose a Dirichletnetwork,where both functions are properly constrained.Specifically,the spatial response function isconstrained with positivity,while the Dirichlet distribution along with a total variation is imposedon the point spread function.To the best of our knowledge,the neural network and the Dirichlet regularization are exclusively investigated,for the first time,to estimate the degradation functions.Both image degradation and fusion experiments demonstrate the effectiveness and superiority of theproposed Dirichlet network.

Prediction of impurity spectrum function by deep learning algorithm

By using the numerical renormalization group(NRG)method,we construct a large dataset with about one million spectral functions of the Anderson quantum impurity model.The dataset contains the density of states(DOS)of the host material,the strength of Coulomb interaction between on-site electrons(U),and the hybridization between the host material and the impurity site(Γ).The continued DOS and spectral functions are stored with Chebyshev coefficients and wavelet functions,respectively.From this dataset,we build seven different machine learning networks to predict the spectral function from the input data,DOS,U,andΓ.Three different evaluation indexes,mean absolute error(MAE),relative error(RE)and root mean square error(RMSE),are used to analyze the prediction abilities of different network models.Detailed analysis shows that,for the two kinds of widely used recurrent neural networks(RNNs),gate recurrent unit(GRU)has better performance than the long short term memory(LSTM)network.A combination of bidirectional GRU(BiGRU)and GRU has the best performance among GRU,BiGRU,LSTM,and BiLSTM.The MAE peak of BiGRU+GRU reaches 0.00037.We have also tested a one-dimensional convolutional neural network(1DCNN)with 20 hidden layers and a residual neural network(ResNet),we find that the 1DCNN has almost the same performance of the BiGRU+GRU network for the original dataset,while the robustness testing seems to be a little weak than BiGRU+GRU when we test all these models on two other independent datasets.The ResNet has the worst performance among all the seven network models.The datasets presented in this paper,including the large data set of the spectral function of Anderson quantum impurity model,are openly available at https://doi.org/10.57760/sciencedb.j00113.00192.

Additive Maps Between Standard Operator Algebras Compressing Certain Spectral Functions

We characterize the surjective additive maps compressing the spectral function Δ（·） between standard operator algebras acting on complex Banach spaces, where Δ（·） stands for any one of nine spectral functions σ（·）, σl（·）, σr（·）,σl（·） ∩ σr（·）, δσ（·）, ησ（·）, σap（·）, σs（·）, and σap（·） ∩ σs（·）.

Walsh Spectral Characteristics and the Auto-Correlation Function Characteristics of Forming Orthomorphic Permutations of Multi-Output Functions

Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.

Functional Spectral Analysis of Paleoclimatic Evolution in Lanzhou Area over the Last 15 ka

In this paper, we make use of the functional spectral analysis to infer the periodicity of paleoclimate in the Hongzuisi section since about 15 ka. Through combined analysis of organic carbon isotope and CaCO\-3 content, the law of paleoclimatic evolution of the Hongzuisi section is obtained. There were climatic changes from 10 ka to about 0.1 ka over the last 15 ka. Among these cycles, the cycle of several ka is most remarkable. The result indicates that functional spectral analysis is helpful for paleoclimatic study, which can provide useful information about paleoclimatic reconstruction and future forecast.

Quark-antiquark scattering phase shift and meson spectral function in pion superfluid

We study the quark-antiquark scattering phase shift and meson spectral function in the pion superfluid described by the Nambu-Jona-Lasinio model. Meson mixing in the pion superfluid dramatically changes the full scattering phase shift and significantly broadens the spectral function of some collective modes.

Second-Order Correlation Function for Asymmetric-to-Symmetric Transitions due to Spectrally Indistinguishable Biexciton Cascade Emission

We report the observed photon bunching statistics of biexciton cascade emission at zero time delay in single quantum dots by second-order correlation function g（2） （T） measurements under continuous wave excitation. It is found that the bunching phenomenon is independent of the biexciton binding energy when it varies from 0.59 meV to nearly zero. The photon bunching takes place when the exeiton photon is not spectrally distinguishable from the biexciton photon, and either of them can trigger the %tart＇ in a Hanbury-Brown and Twiss setup. However, if the exciton energy is spectrally distinguishable from the biexciton, the photon statistics will become asymmetric and a cross-bunching lineshape can be obtained. The theoretical calculations based on a model of three-level rate-equation analysis are consistent with the result of g（2）（τ） correlation function measurements.

Generalized Invertibility of Operators through Spectral Sets

If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses considering the subspace determined by the range of the spectral projection associated with an operator and a spectral set containing the point 0. We compare the cases, 0 is a simple pole of the resolvent function, 0 is a pole of order n of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.

大气湍流下部分相干涡旋光束经粗糙目标回波特性

利用广义Huygens-Fresnel原理和随机高斯粗糙面模型,研究部分相干高斯-谢尔模型涡旋光束的回波特性,通过特殊积分推导出部分相干涡旋光束经随机粗糙面散射后到达接收端的交叉谱密度函数和光强解析式,并进行仿真分析。结果表明:随着拓扑荷数、束腰半径和相干长度的增加,光强自相关函数曲线下降的越来越陡峭;在强湍流环境下,自相关函数衰减越来越严重;内尺度会影响光强自相关函数,并且随着内尺度的增大而衰减严重,外尺度对其影响作用不大;随着粗糙目标相干长度的增大,光强自相关函数的半峰宽值逐渐趋增大。

基于非负矩阵分解的函数型聚类算法改进与比较

非负函数型数据可以不等间隔观测,在理论和实践中应用广泛,对其进行聚类可以更好地探索客观规律。文章利用位置积分变换将函数型数据转化为高维向量,再通过非负矩阵分解(NMF)将其转化为低维向量,以此构建函数型聚类算法。针对基于NMF的函数型谱聚类算法,给出了确定聚类个数K的两种方法:一种是根据Laplacian矩阵的特征值确定K;另一种是构建新评价指标,通过搜索确定K。数值实验结果显示:基于位置积分变换和NMF的函数型聚类算法有效,对函数结构要求宽松,但需限制函数取值为正;NMF的秩可通过cophenetic相关系数确定,建议取较小的值,以剔除类的冗余特征。在确定谱聚类的聚类个数K时,建议对降维后的数据进行标准化处理,以缩小样本间的距离变化范围;聚类个数变点图直观有效,再结合特征值差分法确定K很有参考价值,建议阈值取[0.05,0.08];根据吻合度与相似比确定K的方法有效且简单易懂。

多级冗余强干扰下医用三维力传感器数据的自动挖掘方法

针对医用三维力传感器容易受电磁场等外部环境的影响,产生大量相似特征数据,导致其输出紊乱信号,降低传感器控制精度和测量速度的问题,提出一种多级冗余强干扰下三维力传感器数据挖掘方法。根据角度标定理论采集三维力传感器冗余数据;引入相似度指数函数计算冗余因子,获取三维力传感器冗余数据活跃度,完成数据冗余分类;通过差值去噪算法高性能过滤三维力传感器冗余数据;利用谱聚类算法构建拉普拉斯矩阵,剔除冗余数据,实现三维力传感器数据自动挖掘。仿真结果表明,所提方法在多级冗余强干扰下的三维力传感器控制精度为96.54%,测量速度为0.61 ms,能量消耗为0.26 kcal。由此证明,所提方法的控制精度高、测量速度快、传输效果优,能够满足机器人辅助手术过程中的力反馈控制需求。

Er掺杂PbF_(2)晶体的局域团簇结构与光谱性能研究

本文采用Bridgman法成功生长了一系列Er∶PbF_(2)晶体。利用基于密度泛函理论的第一性原理计算详细研究了Er^(3+)在PbF_(2)晶体中的团簇效应。首次获得了Er∶PbF_(2)晶体的上转换发光特性(发光强度、颜色变化)与团簇结构之间的关系。研究发现,随着Er^(3+)浓度增加,团簇从单聚体向高阶构型演化,Er^(3+)离子之间的距离先减小后增大,这使得上转换发光中的红色发射强度先增大后减小,红绿发光比也在Er^(3+)浓度高于6.5%(摩尔分数)后逐渐减小,即发光颜色可以从红色调整为黄绿色。该研究证明了稀土离子团簇的结构演化可以调控Er∶PbF_(2)的光谱特性,为多色发光材料的设计提供一种新方法。

基于多特征核的高光谱遥感影像分类方法

支持向量机(SVM)的核函数选取是制约其分类性能的重要因素,而当前的核函数大多以光谱距离作为构核元素,而忽略了光谱角度这一光谱特征。文章提出一种均衡化光谱距离与光谱角多特征组合核(ESAD)的SVM分类器,对2003年意大利帕维亚大学的ROSIS高光谱数据作分类处理,并对影像的分类精度作评价分析。实验结果表明:ESAD核SVM整体分类精度相较于光谱距离核SVM和光谱角核SVM分别提升8.88%和11.03%,分类精度理想,一定程度上抑制了“同谱异物”现象。

Symmetric Functions and <i>q</i>-Products with an Application to Theoretical Physics

The main purpose of this paper is to show that the Poincaré q-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown that the q-series elliptic genera can be expressed in terms of q-analogs of the classical special functions, specially the equivalence between the spectral Patterson-Selberg and the Ruelle functions. The main result of this manuscript is to show that this representation can be used in theoretical physics and we analyze them in terms of the Patterson-Selberg spectral function R (s).

平滑注意力与谱上采样细化的非等距三维点云模型对应关系计算

为了解决非等距3维点云模型对应关系计算易受模型大尺度形变影响而导致对应失真、准确率低且平滑性差的问题,该文提出一种结合平滑注意力与谱上采样细化的非等距3维点云模型对应关系计算新方法。首先,利用点所在表面的几何特征信息设计平滑注意力机制与平滑感知模块,提高特征对大尺度形变区域非刚性变换的感知能力;其次,将深度函数映射模块与平滑正则化约束相结合,提升函数映射计算结果的平滑性;最后,在谱上采样细化模块中,以多分辨率重建的方式得到最终的逐点映射结果。实验结果表明,与已有算法相比,本算法在FAUST、SCAPE和SMAL数据集上构建的对应关系测地误差最小,处理大尺度形变模型时,能够提升逐点映射的平滑性和全局准确率。

基于直接概率积分法的列车-轨道-桥梁系统随机分析

由于施工和制造误差使得铁路工程结构参数不可避免地具有不确定性,同时作为系统主要自激励的轨道不平顺亦具有明显的随机性和时变性,因此,探明不确定因子对列车和轨道-桥梁结构动态性能的影响非常重要。为了高效地完成列车-轨道-桥梁系统随机性能分析,建立列车-轨道-桥梁空间振动分析模型,采用轨道不平顺概率模型和谱表达-随机函数的方式在有限随机变量空间中实现轨道不平顺随机过程的高效模拟。引入概率密度积分方程和直接概率积分法发展了列车-轨道-桥梁系统随机动力方程和相应的计算求解策略。基于MATLAB实现了列车-轨道-桥梁随机振动的直接概率积分法分析程序,计算了全概率不平顺激励和参数随机条件下车-轨-桥系统振动响应的均值、标准差和时变的概率密度信息。研究结果表明:与概率密度演化分析方法相比,直接概率积分法可较好地反映行车过程中系统响应的概率密度特征,然而其在系统响应随机后处理时更为高效,其效率可提高1~2个数量级。此外,考虑轨道不平顺全概率激励更能准确地反映行车过程系统响应的概率特征,平均概率谱可能使得计算结果偏于保守;行车速度对于列车和桥梁动态行为的影响是显著的,随着行车速度的增加系统响应的范围逐渐变大。研究结果进一步拓展了列车-轨道-桥梁随机系统的分析方法,可以高效地用于系统状态评估和设计优化。

考虑频响函数混叠误差的阻尼比识别效果研究

通过实测频响函数识别阻尼比时,识别准确性受到频谱混叠现象的影响,因此建立了考虑频响函数混叠误差的阻尼比识别有效性判断方法.首先,根据傅里叶变换原理进行理论推导,证明了采样频率不足时频响函数会发生混叠现象;然后,根据频响函数混叠原理和模态叠加原理,建立了多自由度结构的基准频响混叠误差拟合公式,进而给出考虑频响函数混叠误差的阻尼比识别结果有效性判断的步骤.通过对两自由度理论频响函数模型设置不同的等效柔度比和固有频率比,表明其对两阶模态计算频响混叠误差有显著影响;通过对比四层框架结构基准模型的响应在设置不同采样频率时对阻尼比的识别结果,验证了所提方法的可行性.

基于密度泛函理论的灭蝇胺分子的表面增强拉曼光谱特性

灭蝇胺是一种白色结晶粉末状的应用于各种瓜果类、茄果类、豆类及多种叶菜类农业生产中的昆虫杀虫剂,广泛应用农业生产等领域。灭蝇胺的大量使用对生态环境有极强的破坏性,危害人类身体健康。因此,对蔬菜农业生产过程中的灭蝇胺农药残留的快速检测技术的需求十分迫切。表面增强拉曼光谱技术(SERS)具有高灵敏度、高准确度以及样品准备简单等优点,已经成为农药残留检测领域的热点研究技术;密度泛函理论(DFT)可用于分子结构与性质的理论模拟及拉曼光谱的计算。基于密度泛函理论对引入金纳米团簇基底灭蝇胺分子的表面增强拉曼光谱进行计算,采用Multiwfn软件结合VMD软件探究了灭蝇胺分子表面静电势分布,基于B3LYP/6-31++G(d,p)基组对结合4个Au原子团簇形成的灭蝇胺—金纳米团簇复合物采用B3LYP方法,对灭蝇胺分子中与Au纳米团簇可能配位的原子使用6-31++G(d,p)基组,Au原子团簇使用LANL2DZ赝式基组,进行灭蝇胺—金纳米团簇复合物的结构优化与表面增强拉曼光谱计算,获得灭蝇胺分子的拉曼散射光谱和灭蝇胺分子与Au 4聚体吸附的表面增强拉曼光谱,并进行特征峰指认和比较。由分子静电势分布可知,Au纳米团簇可能与灭蝇胺分子中的N_(1)、N_(3)和N 5原子位置处形成配位,与C_(6)H_(10)N_(6)分子形成C_(6)H_(10)N_(6)-4Au纳米团簇化合物。计算对比分析了N_(1)、N_(3)和N_(5)原子配位形成的C_(6)H_(10)N_(6)-4Au的拉曼光谱,由于Au原子团簇的侵入,Au原子团簇与N 1、N 3和N 5配位形成的C_(6)H_(10)N_(6)-4Au分子Raman光谱特征峰最大增强分别达到4.0倍、1.4倍和3.2倍,且Raman谱峰出现了选择增强,并且谱峰位置发生一定程度的红移或者蓝移。研究结果为SERS技术用于蔬菜表面农药残留的快速检测奠定了理论基础。

基于改进EMD方法与11/2谱的DEMON谱提取方法

噪声的包络调制检测(Detection of Envelope Modulation on Noise,DEMON)谱分析技术已被广泛应用于特征提取领域,但经典DEMON谱提取中高频信号频段的选取会影响DEMON谱的提取效果。针对这一问题,文中首先运用经验模态分解(Empirical Mode Decomposition,EMD)方法获得一系列固有模态函数(Intrinsic Mode Function,IMF),依据各阶模态函数与原信号的相关程度,筛选出更具代表性的几阶固有模态函数进行解调,再对解调的结果运用11/2维谱分析方法进行谱分析以抑制高斯噪声,通过这种方法获得的DEMON谱信噪比优于传统方法。实测湖试数据分析结果表明,该改进方法可以有效地进行特征提取,结果优于经典DEMON谱分析方法;该改进方法具有一定的实用性,有利于进行后续目标分类识别。

几种常用水声信号的特性研究

水声信号是水下导航定位通信的主要信息载体,对其特性进行研究尤为重要。水声常用信号主要有连续波信号、线性调频信号和双曲线调频信号,研究了这三种常用信号的时域、频域以及功率谱波形,对它们的模糊函数、模糊度、模糊函数ξ=0和τ=0截面进行了计算,研究了这三种信号的自相关函数及小波时频分析,研究结果表明实验结果与理论值符合较好。