The Happer's puzzle degeneracies and Yangian

We find operators distinguishing the degenerate states for the Hamiltonian $H= x(K+{1/2})S_z +{\bf K}\cdot {\bf S}$ at $x=\pm 1$ that was given by Happer et al$^{[1,2]}$ to interpret the curious degeneracies of the Zeeman effect for condensed vapor of $^{87}$Rb. The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of $Y(sl(2))$.Comment: 8 pages, Latex fil

Soft Methodology for Cost-and-error Sensitive Classification

Many real-world data mining applications need varying cost for different types of classification errors and thus call for cost-sensitive classification algorithms. Existing algorithms for cost-sensitive classification are successful in terms of minimizing the cost, but can result in a high error rate as the trade-off. The high error rate holds back the practical use of those algorithms. In this paper, we propose a novel cost-sensitive classification methodology that takes both the cost and the error rate into account. The methodology, called soft cost-sensitive classification, is established from a multicriteria optimization problem of the cost and the error rate, and can be viewed as regularizing cost-sensitive classification with the error rate. The simple methodology allows immediate improvements of existing cost-sensitive classification algorithms. Experiments on the benchmark and the real-world data sets show that our proposed methodology indeed achieves lower test error rates and similar (sometimes lower) test costs than existing cost-sensitive classification algorithms. We also demonstrate that the methodology can be extended for considering the weighted error rate instead of the original error rate. This extension is useful for tackling unbalanced classification problems.Comment: A shorter version appeared in KDD '1

Tropical Geometry of Phylogenetic Tree Space: A Statistical Perspective

Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. As data objects, they are characterized by the challenges associated with "big data," as well as the complication that their discrete geometric structure results in a non-Euclidean phylogenetic tree space, which poses computational and statistical limitations. We propose and study a novel framework to study sets of phylogenetic trees based on tropical geometry. In particular, we focus on characterizing our framework for statistical analyses of evolutionary biological processes represented by phylogenetic trees. Our setting exhibits analytic, geometric, and topological properties that are desirable for theoretical studies in probability and statistics, as well as increased computational efficiency over the current state-of-the-art. We demonstrate our approach on seasonal influenza data.Comment: 28 pages, 5 figures, 1 tabl

Combining Local Appearance and Holistic View: Dual-Source Deep Neural Networks for Human Pose Estimation

We propose a new learning-based method for estimating 2D human pose from a single image, using Dual-Source Deep Convolutional Neural Networks (DS-CNN). Recently, many methods have been developed to estimate human pose by using pose priors that are estimated from physiologically inspired graphical models or learned from a holistic perspective. In this paper, we propose to integrate both the local (body) part appearance and the holistic view of each local part for more accurate human pose estimation. Specifically, the proposed DS-CNN takes a set of image patches (category-independent object proposals for training and multi-scale sliding windows for testing) as the input and then learns the appearance of each local part by considering their holistic views in the full body. Using DS-CNN, we achieve both joint detection, which determines whether an image patch contains a body joint, and joint localization, which finds the exact location of the joint in the image patch. Finally, we develop an algorithm to combine these joint detection/localization results from all the image patches for estimating the human pose. The experimental results show the effectiveness of the proposed method by comparing to the state-of-the-art human-pose estimation methods based on pose priors that are estimated from physiologically inspired graphical models or learned from a holistic perspective.Comment: CVPR 201