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Generalized Stokes parameters of random electromagnetic vortex

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where ρ l ≡ (ρlx , ρly ) is the position vector at the z plane, k is the wave number related to the wave length λ by k = 2π/λ, and ψ (ρ , s ) represents the random part of the complex phase of a spherical wave due to the turbulence, and can be written as [18] exp ψ ∗ (ρ 1 , s 1 ) + ψ(ρ 2 , s 2 ) 1 ∼ = exp − 2 (s 1 − s 2 )2 + (s 1 − s 2 )(ρ 1 − ρ 2 ) ρ0 + (ρ 1 − ρ 2 )2 where
J. Li ( ) School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China e-mail: sculijh@ C. Ding Department of Physics, Luoyang Normal College, Luoyang 471022, China B. Lü Institute of Laser Physics and Chemistry, Sichuan University, Chengdu 610064, China e-mail: baidalu0@
246
J. Li et al.来自2 Theoretical formulation The cross-spectral density matrix of random electromagnetic beams at the source plane z = 0 is expressed as [15] W (s 1 , s 2 , 0, ω) =
ABCD optical systems, as well as through uniaxial crystals were investigated [1–5, 10–13]. Setälä et al. analyzed the Stokes parameters in Young’s two-pinhole interference experiment and pointed out that the electromagnetic degree of coherence is a measure of the visibility of the intensity fringes and the modulation contrasts of the three polarization Stokes parameters [6, 7]. The experimental determination of the generalized Stokes parameters was reported by Kanseri et al. [8, 9]. All the above studies are limited to the random electromagnetic vortex-free beams. Recently, Gbur and Tyson analyzed the propagation of scalar vortex beams such as Laguerre–Gaussian beams through weak-to-strong atmospheric turbulence and topological charge conservation by using multiple phase screen simulation, and showed that the topological charge could be used as an information carrier in optical communications [14]. Thus, an interesting question arises: what will happen for the generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence? The purpose of the present paper is to study the changes in the generalized Stokes parameters of random electromagnetic vortex beams through atmospheric turbulence. In Sect. 2 the analytical expressions for the generalized Stokes parameters of random electromagnetic Gaussian Schell-model (GSM) vortex beams propagating through atmospheric turbulence are derived. Changes in the on-axis and transverse spectral Stokes parameters of random electromagnetic GSM vortex beams in atmospheric turbulence and comparison with those of random electromagnetic GSM vortex-free beams are illustrated by numerical calculation examples in Sect. 3. Section 4 concludes the main results obtained in this paper.
J. Li · C. Ding · B. Lü
Received: 8 June 2010 / Revised version: 20 August 2010 / Published online: 20 November 2010 © Springer-Verlag 2010
Abstract By using the extended Huygens–Fresnel principle, the analytical expressions for the generalized Stokes parameters of random electromagnetic Gaussian Schell-model (GSM) vortex beams propagating through atmospheric turbulence are derived, and used to study the changes in spectral Stokes parameters of random electromagnetic GSM vortex beams in atmospheric turbulence and to compare the results of random electromagnetic GSM vortex-free beams. The influence of atmospheric turbulence on the spectral Stokes parameters is analyzed. The validity of our results is interpreted physically.
Appl Phys B (2011) 103: 245–255 DOI 10.1007/s00340-010-4289-y
Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence
1 Introduction The Stokes parameters have been generalized recently from one-point quantities to two-point counterparts by Korotkova and Wolf [1]. The generalized Stokes parameters have attracted much attention because they contain information about both the polarization and the coherence properties of the beam [1–9]. The propagation properties of random electromagnetic beams and their generalized Stokes parameters in free space, through atmospheric turbulence and
↔
beams propagating through atmospheric turbulence are given by Wij (ρ 1 , ρ 2 , z) = k 2πz
2
d 2 ρ1
d 2 ρ2 Wij (s 1 , s 2 , 0)
Wxx (s 1 , s 2 , 0, ω) Wxy (s 1 , s 2 , 0, ω) , Wyx (s 1 , s 2 , 0, ω) Wyy (s 1 , s 2 , 0, ω) (1)
× exp −
ik (ρ − s 1 )2 − (ρ 2 − s 2 )2 2L 1 (5)
× exp ψ ∗ (ρ 1 , s 1 ) + ψ(ρ 2 , s 2 ) ,

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高斯随机过程超参数

高斯随机过程超参数

高斯随机过程超参数
高斯过程（Gaussian Processes）是概率论和数理统计中随机过程的一种，是多元高斯分布的扩展，被应用于机器学习、信号处理等领域。

在高斯过程中，超参数是指控制模型复杂性和行为的参数，这些参数在模型训练过程中需要进行优化。

高斯过程的超参数通常包括特征长度尺度（characteristic length-scale）和噪声水平（noise level）等。

特征长度
尺度用于控制高斯过程的平滑程度，而噪声水平则用于控制模型对数据的拟合程度。

在贝叶斯优化框架中，高斯过程的超参数可以通过最大化边缘似然函数（marginal likelihood function）来进行估计。

边缘似然函数是将超参数
与数据联系起来的关键，通过最大化该函数可以找到最优的超参数值，从而使得高斯过程模型能够最好地拟合给定的数据。

常用的核函数包括平方指数核（squared exponential kernel）和马顿核（Matern kernel）。

平方指数核的超参数包括特征长度尺度和噪声水平，而马顿核则还包括一个额外的超参数，用于控制核函数的形状。

总的来说，高斯过程的超参数对于模型的性能至关重要，需要通过优化算法进行仔细调整，以获得最佳的预测和泛化性能。

以上内容仅供参考，如需更专业的解释，建议咨询统计学或机器学习领域的专家，或查阅相关领域的专业书籍和文献。

高斯朴素贝叶斯训练集精确度的英语

高斯朴素贝叶斯训练集精确度的英语

高斯朴素贝叶斯训练集精确度的英语Gaussian Naive Bayes (GNB) is a popular machine learning algorithm used for classification tasks. It is particularly well-suited for text classification, spam filtering, and recommendation systems. However, like any other machine learning algorithm, GNB's performance heavily relies on the quality of the training data. In this essay, we will delve into the factors that affect the training set accuracy of Gaussian Naive Bayes and explore potential solutions to improve its performance.One of the key factors that influence the training set accuracy of GNB is the quality and quantity of the training data. In order for the algorithm to make accurate predictions, it needs to be trained on a diverse and representative dataset. If the training set is too small or biased, the model may not generalize well to new, unseen data. This can result in low training set accuracy and poor performance in real-world applications. Therefore, it is crucial to ensure that the training data is comprehensive and well-balanced across different classes.Another factor that can impact the training set accuracy of GNB is the presence of irrelevant or noisy features in the dataset. When the input features contain irrelevant information or noise, it can hinder the algorithm's ability to identify meaningful patterns and make accurate predictions. To address this issue, feature selection and feature engineering techniques can be employed to filter out irrelevant features and enhance the discriminative power of the model. Byselecting the most informative features and transforming them appropriately, we can improve the training set accuracy of GNB.Furthermore, the assumption of feature independence in Gaussian Naive Bayes can also affect its training set accuracy. Although the 'naive' assumption of feature independence simplifies the model and makes it computationally efficient, it may not hold true in real-world datasets where features are often correlated. When features are not independent, it can lead to biased probability estimates and suboptimal performance. To mitigate this issue, techniques such as feature extraction and dimensionality reduction can be employed to decorrelate the input features and improve the training set accuracy of GNB.In addition to the aforementioned factors, the choice of hyperparameters and model tuning can also impact the training set accuracy of GNB. Hyperparameters such as the smoothing parameter (alpha) and the covariance type in the Gaussian distribution can significantly influence the model's performance. Therefore, it is important to carefully tune these hyperparameters through cross-validation andgrid search to optimize the training set accuracy of GNB. By selecting the appropriate hyperparameters, we can ensure that the model is well-calibrated and achieves high accuracy on the training set.Despite the challenges and limitations associated with GNB, there are several strategies that can be employed to improve its training set accuracy. By curating a high-quality training dataset, performing feature selection and engineering, addressing feature independence assumptions, and tuning model hyperparameters, we can enhance the performance of GNB and achieve higher training set accuracy. Furthermore, it is important to continuously evaluate and validate the model on unseen data to ensure that it generalizes well and performs robustly in real-world scenarios. By addressing these factors and adopting best practices in model training and evaluation, we can maximize the training set accuracy of Gaussian Naive Bayes and unleash its full potential in various applications.。

最大熵与转换规则相结合识别中文名词短语

最大熵与转换规则相结合识别中文名词短语

摘 要 ：本文针 对统 计 方法 和规 则方 法各 自的特 点 ， 出基 于最大 熵方 法和转 换规 则 方法相 结合 的 中文基 本 名词 短语 识 提 别算 法 ，该 算 法是在 一 定词 性标 注 的基础 上 实现 的 。在 训练 和测 试 两个阶段 中 ，均先 采 用最 大熵 方法识 别基 本 名词短 语 ，然 后将 已具有一 定精 度 的识 别结 果作 为初 始 标注 结果运 用于转 换规 则 方法 中。 实验表 明 ，该 方法具 有 一定 的可行 性 。
计算 机 光盘软 件 与应 用
２ １ 年 第 ３期 ０１ Ｃ ｍ ｕ ｅ ＤＳ ｆｗ ｒ ｎ ｐ ｌｃ ｔｏ ｓ ｏ ｐ ｔ ｒＣ ｏ ｔ ａ ｅａ ｄＡ ｐ ａ ｎ ｉ ｉ 信息技术应用研 究
最大熵与转换规则相结合识别中文名词短语
卢朝 华 ，蒙皓兵 （ 商丘科技职业 学院，河 南商丘 ４ ６０ ７ ００）
Ｐ （ ａｔ ｆｓ ｅ ｃ）ａ ｇ ｒ ｒ ｇｔｅｔａｎｎ ｈ ｓ ｎ ｈ ｐ ｌ ａｉｎｐ ａｅｍａ ｉ ｍ ｎｒｐ ｐ ｒ ａｈ ｉ ｆ ｓ ａ ｐｉｄｔ ｈ ＯＳｐ ｒｓｏ ｐ ｅｈｔｇ ｅ． ｉ ｈ ｒｉｉｇｐ ａｅａ ｄｔｅａ ｐｉ ｔ ｈ ｓ， ｘｍｕ ｅ ｔ ｙａ ｐｏ ｃ ｓ ｉ ｔ ｐ ｌ ｏｔ ｅ Ｄｕ ｎ ｃ ｏ ｏ ｒ ｅ
Ａｂｓｒ ｃ ： ｉｉｉｇ ｆ ａｕ ｅ ｅｓａｉｔ ｐ ｏ ｃ ｎ ｈ ｅ ｕａ ｉｎ ａ ｒ ａ ｈ，ｎＣｈｎｅｅｎｏ ｎ ｐ ｒ ｓ ｎｔ ｉａｉｎ ａｇ ｒｔ ｔ ａ ｔＵｔｌ ｎ ｅ ｔ ｒ ｓｏｆ ｈ ｔ ｔ ｉ ａ ｐｒ ａ ｈ ａ ｄｔ ｅｒ ｇ ｌｔｏ ｐｐ ｏ ｃ ａ ｉ ｓ ｕ ｈ ａ ｅｉ ｚ ｔ ｓｃ ｄｅ ｉ ｃ ｔｏ ｌｏ ｉｈｍ ｆ
关键 词 ：基本 名词短 语 ；短 语识 别 ；最 大熵 ；转换 规 则
太阳非线性无力磁场的边界积分表示公式

太阳非线性无力磁场的边界积分表示公式


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