Conformal Embedding Analysis with Local Graph Modeling on the Unit Hypersphere

Author(s):  
Yun Fu ◽  
Ming Liu ◽  
Thomas S. Huang
2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Dan Xie ◽  
Wenbin Yan

Abstract We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general $$ \mathcal{N} $$ N = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.


2021 ◽  
Vol 12 (2) ◽  
pp. 1-22
Author(s):  
Jianguo Chen ◽  
Kenli Li ◽  
Keqin Li ◽  
Philip S. Yu ◽  
Zeng Zeng

Benefiting from convenient cycling and flexible parking locations, the Dockless Public Bicycle-sharing (DL-PBS) network becomes increasingly popular in many countries. However, redundant and low-utility stations waste public urban space and maintenance costs of DL-PBS vendors. In this article, we propose a Bicycle Station Dynamic Planning (BSDP) system to dynamically provide the optimal bicycle station layout for the DL-PBS network. The BSDP system contains four modules: bicycle drop-off location clustering, bicycle-station graph modeling, bicycle-station location prediction, and bicycle-station layout recommendation. In the bicycle drop-off location clustering module, candidate bicycle stations are clustered from each spatio-temporal subset of the large-scale cycling trajectory records. In the bicycle-station graph modeling module, a weighted digraph model is built based on the clustering results and inferior stations with low station revenue and utility are filtered. Then, graph models across time periods are combined to create a graph sequence model. In the bicycle-station location prediction module, the GGNN model is used to train the graph sequence data and dynamically predict bicycle stations in the next period. In the bicycle-station layout recommendation module, the predicted bicycle stations are fine-tuned according to the government urban management plan, which ensures that the recommended station layout is conducive to city management, vendor revenue, and user convenience. Experiments on actual DL-PBS networks verify the effectiveness, accuracy, and feasibility of the proposed BSDP system.


2021 ◽  
Vol 13 (3) ◽  
pp. 526
Author(s):  
Shengliang Pu ◽  
Yuanfeng Wu ◽  
Xu Sun ◽  
Xiaotong Sun

The nascent graph representation learning has shown superiority for resolving graph data. Compared to conventional convolutional neural networks, graph-based deep learning has the advantages of illustrating class boundaries and modeling feature relationships. Faced with hyperspectral image (HSI) classification, the priority problem might be how to convert hyperspectral data into irregular domains from regular grids. In this regard, we present a novel method that performs the localized graph convolutional filtering on HSIs based on spectral graph theory. First, we conducted principal component analysis (PCA) preprocessing to create localized hyperspectral data cubes with unsupervised feature reduction. These feature cubes combined with localized adjacent matrices were fed into the popular graph convolution network in a standard supervised learning paradigm. Finally, we succeeded in analyzing diversified land covers by considering local graph structure with graph convolutional filtering. Experiments on real hyperspectral datasets demonstrated that the presented method offers promising classification performance compared with other popular competitors.


2020 ◽  
pp. 1-1
Author(s):  
Alexander Jung ◽  
Yasmin Sarcheshmehpour
Keyword(s):  

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Kathryn E. Schertz ◽  
James Saxon ◽  
Carlos Cardenas-Iniguez ◽  
Luís M. A. Bettencourt ◽  
Yi Ding ◽  
...  

AbstractCrime is a costly societal issue. While many factors influence urban crime, one less-studied but potentially important factor is neighborhood greenspace. Research has shown that greenspace is often negatively associated with crime. Measuring residents’ use of greenspace, as opposed to mere physical presence, is critical to understanding this association. Here, we used cell phone mobility data to quantify local street activity and park visits in Chicago and New York City. We found that both factors were negatively associated with crime, while controlling for socio-demographic factors. Each factor explained unique variance, suggesting multiple pathways for the influence of street activity and greenspace on crime. Physical tree canopy had a smaller association with crime, and was only a significant predictor in Chicago. These findings were further supported by exploratory directed acyclic graph modeling, which found separate direct paths for both park visits and street activity to crime.


2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Mert Besken ◽  
Jan de Boer ◽  
Grégoire Mathys

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.


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