This article gives an introduction to arithmetic motivic integration in the context of p-adic integrals that arise in representation theory. A special case of the fundamental lemma is interpreted as an identity of Chow motives.

<p style='text-indent:20px;'>We present an iterative method for solving the convex constraint nonlinear equation problem. The incorporates projection strategy by Solodov and Svaiter with hybrid Liu-Storey Conjugate descent Yang et al. unconstrained optimization proposed does not require Jacobian information, nor it to store any matrix at each iteration. Thus, has potential solve large-sca...

A two-dimensional visual device for description of the dispersion of a multivariate data set in any dimension is the scale curve, a depth-based method introduced by Liu (1990) and treated in detail by Liu, Parelius and Singh (1999). It offers an appealing alternative to covariance matrix methods and even provides an attractive new tool in the univariate case. To support applications such as uni...

The latent tree structure learned by the algorithm by [1] is shown in Figure 1. The blue nodes are hidden nodes and the red nodes are observed. Note how integrating out some of these hidden nodes could lead to very large cliques. Thus it is not surprising why both our spectral method and EM perform better than Chow Liu. The Chow Liu Tree is shown in Figure 1. Note how it is forced to pick some ...

Chow and Liu introduced the notion of tree dependence to approximate a kth order probability distribution. More recently, Wong and Wang proposed a different product approximation. The aim of this paper is to show that the tree dependence approximation suggested by Chow and Liu can be derived by minimizing an upper bound of the Bayes error rate under certain assumptions. It is also shown that th...

Liu [Liu Rui, Coexistence of multifarious exact nonlinear wave solutions for generalized b-equation, Inter. J. Bifurcation and Chaos, 20, pp. 3193-3208, 2010] investigated the coexistence of multifarious exact traveling wave solutions of the generalized b-equation, and also presented three conjectures and two questions. In this note, by using the method of complete discrimination system for pol...

A review of the genus Pteranabropsis Gorochov is presented. Five new species are described, namely Pteranabropsis tenchongensis Wang, Liu, Li sp. nov., Pteranabropsis infuscatus Wang, Liu, Li sp. nov., Pteranabropsis karnyi Wang, Liu, Li sp. nov., Pteranabropsis parallelus Wang, Liu, Li sp. nov. and Pteranabropsis tibenensis Wang, Liu, Li sp. nov.. A key to the species of Pteranabropsis is prov...