Orbifold Gromov-Witten Theory

In this article, we introduce the notion of good map and use it to establish Gromov-Witten theory for orbifolds.Comment: Late

Orbifold Quantum Cohomology

This is a research announcement of the theory of orbifold quantum cohomology.Comment: Revised version, adding more reference

Towards a Theory of Logarithmic GLSM Moduli Spaces

In this article, we establish foundations for a logarithmic compactification of general GLSM moduli spaces via the theory of stable log maps. We then illustrate our method via the key example of Witten's $r$-spin class. In the subsequent articles, we will push the technique to the general situation. One novelty of our theory is that such a compactification admits two virtual cycles, a usual virtual cycle and a "reduced virtual cycle". A key result of this article is that the reduced virtual cycle in the $r$-spin case equals to the r-spin virtual cycle as defined using cosection localization by Chang--Li--Li. The reduced virtual cycle has the advantage of being $\mathbb{C}^*$-equivariant for a non-trivial $\mathbb{C}^*$-action. The localization formula has a variety of applications such as computing higher genus Gromov--Witten invariants of quintic threefolds and the class of the locus of holomorphic differentials

A New Cohomology Theory for Orbifold

Motivated by orbifold string theory, we introduce orbifold cohomology group for any almost complex orbifold and orbifold Dolbeault cohomology for any complex orbifold. Then, we show that our new cohomology group satisfies Poincare duality and has a natural ring structure. Some examples of orbifold cohomology ring are computed.Comment: Correct some minor mistake

Serum cystatin C and chemerin levels in diabetic retinopathy

Peer reviewedPublisher PD

Regional surname affinity: a spatial network approach

OBJECTIVE We investigate surname affinities among areas of modern‐day China, by constructing a spatial network, and making community detection. It reports a geographical genealogy of the Chinese population that is result of population origins, historical migrations, and societal evolutions. MATERIALS AND METHODS We acquire data from the census records supplied by China's National Citizen Identity Information System, including the surname and regional information of 1.28 billion registered Chinese citizens. We propose a multilayer minimum spanning tree (MMST) to construct a spatial network based on the matrix of isonymic distances, which is often used to characterize the dissimilarity of surname structure among areas. We use the fast unfolding algorithm to detect network communities. RESULTS We obtain a 10‐layer MMST network of 362 prefecture nodes and 3,610 edges derived from the matrix of the Euclidean distances among these areas. These prefectures are divided into eight groups in the spatial network via community detection. We measure the partition by comparing the inter‐distances and intra‐distances of the communities and obtain meaningful regional ethnicity classification. DISCUSSION The visualization of the resulting communities on the map indicates that the prefectures in the same community are usually geographically adjacent. The formation of this partition is influenced by geographical factors, historic migrations, trade and economic factors, as well as isolation of culture and language. The MMST algorithm proves to be effective in geo‐genealogy and ethnicity classification for it retains essential information about surname affinity and highlights the geographical consanguinity of the population.National Natural Science Foundation of China, Grant/Award Numbers: 61773069, 71731002; National Social Science Foundation of China, Grant/Award Number: 14BSH024; Foundation of China of China Scholarships Council, Grant/Award Numbers: 201606045048, 201706040188, 201706040015; DOE, Grant/Award Number: DE-AC07-05Id14517; DTRA, Grant/Award Number: HDTRA1-14-1-0017; NSF, Grant/Award Numbers: CHE-1213217, CMMI-1125290, PHY-1505000 (61773069 - National Natural Science Foundation of China; 71731002 - National Natural Science Foundation of China; 14BSH024 - National Social Science Foundation of China; 201606045048 - Foundation of China of China Scholarships Council; 201706040188 - Foundation of China of China Scholarships Council; 201706040015 - Foundation of China of China Scholarships Council; DE-AC07-05Id14517 - DOE; HDTRA1-14-1-0017 - DTRA; CHE-1213217 - NSF; CMMI-1125290 - NSF; PHY-1505000 - NSF)Published versio