Classically, in saturation-based proof systems, unification has been
considered atomic. However, it is also possible to move unification to the
calculus level, turning the steps of the unification algorithm into inferences.
For calculi that rely on unification procedures returning large or even
infinite sets of unifiers, integrating unification into the calculus is an
attractive method of dovetailing unification and inference. This applies, for
example, to AC-superposition and higher-order superposition. We show that
first-order superposition remains complete when moving unification rules to the
calculus level. We discuss some of the benefits this has even for standard
first-order superposition and provide an experimental evaluation.

将统一规则移动到演算水平可提高欠定规则推理系统的完备性和效率

延迟统一的叠加

Superposition with Delayed Unification

This paper is a step-by-step tutorial for fitting a mixture distribution to
data. It merely assumes the reader has the background of calculus and linear
algebra. Other required background is briefly reviewed before explaining the
main algorithm. In explaining the main algorithm, first, fitting a mixture of
two distributions is detailed and examples of fitting two Gaussians and
Poissons, respectively for continuous and discrete cases, are introduced.
Thereafter, fitting several distributions in general case is explained and
examples of several Gaussians (Gaussian Mixture Model) and Poissons are again
provided. Model-based clustering, as one of the applications of mixture
distributions, is also introduced. Numerical simulations are also provided for
both Gaussian and Poisson examples for the sake of better clarification.

本文是一篇逐步教程，介绍如何拟合混合分布。文中介绍了混合分布拟合算法，应用的模型聚类等内容，并提供了高斯混合模型和泊松分布的示例。

将混合分布拟合到数据中：教程

Fitting A Mixture Distribution to Data: Tutorial

A thorough discussion and development of the calculus of real-valued
functions of complex-valued vectors is given using the framework of the
Wirtinger Calculus. The presented material is suitable for exposition in an
introductory Electrical Engineering graduate level course on the use of complex
gradients and complex Hessian matrices, and has been successfully used in
teaching at UC San Diego. Going beyond the commonly encountered treatments of
the first-order complex vector calculus, second-order considerations are
examined in some detail filling a gap in the pedagogic literature.

使用 Wirtinger 微积分的框架，对实值函数的复向量进行了彻底的讨论和发展。所提供的材料适用于介绍复梯度和复 Hessian 矩阵的电气工程研究生入门课程，并已成功应用于 UC 圣地亚哥的教学。除了一阶复向量微积分的常见处理方式外，还详细讨论了二阶考虑，填补了教学文献中的空白。