Vertex operator algebras of Argyres-Douglas theories from M5-branes

We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d N=(2, 0) theory of type $J$ on a punctured sphere. We denote the AD theories as $(J^b[k],Y)$, where $J^b[k]$ and $Y$ represent an irregular and a regular singularity respectively. We restrict to the `minimal' case where $J^b[k]$ has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the W-algebra $\mathcal{W}^{k_{2d}}(J,Y)$, where $k_{2d}=-h+ \frac{b}{b+k}$ with $h$ being the dual Coxeter number of $J$. We verify this conjecture by showing that the Schur index of the AD theory is identical to the vacuum character of the corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of the Higgs branch. We also find that the Schur and Hall-Littlewood index for the AD theory can be written in a simple closed form for $b=h$. We also test the conjecture that the associated variety of such VOA is identical to the Higgs branch. The M5-brane construction of these theories and the corresponding TQFT structure of the index play a crucial role in our computations.Comment: 35 pages, 1 figure, v2: minor corrections, referenced adde

Property Tax in Urban China

This paper examines the urban housing sector of China and proposes a property tax reform. Over the past decade, housing price in urban China has been increasing dramatically because of strong demand for self-use, investment and speculation. The booming housing market, however, has brought several challenges for further development, such as housing affordability, inequality, and possible housing bubble. One strategy is to reform the current property tax system. Specifically, this paper proposes that China significantly reduces taxes in circulation but levies property tax during possession. Doing so will increase housing affordability because of lower transaction costs, reduce speculation because of higher cost of holding, stabilize fiscal system because of more sustainable tax revenues, and improve the efficiency and fairness of the property tax system because of the implementation of “ability-to-pay” and “who use who pay” principles.Property tax; China

Automated Generation of Geometric Theorems from Images of Diagrams

We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to mine basic geometric relations. Candidate propositions are generated from the retrieved information by using six strategies and geometric theorems are obtained from the candidates via algebraic computation. Experiments with a preliminary implementation illustrate the effectiveness and efficiency of the proposed approach for generating nontrivial theorems from images of diagrams. This work demonstrates the feasibility of automated discovery of profound geometric knowledge from simple image data and has potential applications in geometric knowledge management and education.Comment: 31 pages. Submitted to Annals of Mathematics and Artificial Intelligence (special issue on Geometric Reasoning

Learning Deep Representations of Appearance and Motion for Anomalous Event Detection

We present a novel unsupervised deep learning framework for anomalous event detection in complex video scenes. While most existing works merely use hand-crafted appearance and motion features, we propose Appearance and Motion DeepNet (AMDN) which utilizes deep neural networks to automatically learn feature representations. To exploit the complementary information of both appearance and motion patterns, we introduce a novel double fusion framework, combining both the benefits of traditional early fusion and late fusion strategies. Specifically, stacked denoising autoencoders are proposed to separately learn both appearance and motion features as well as a joint representation (early fusion). Based on the learned representations, multiple one-class SVM models are used to predict the anomaly scores of each input, which are then integrated with a late fusion strategy for final anomaly detection. We evaluate the proposed method on two publicly available video surveillance datasets, showing competitive performance with respect to state of the art approaches.Comment: Oral paper in BMVC 201