Browsing by Author "Gu, Wei"

Now showing 1 - 9 of 9
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    Anomaly Detection in Data-Driven Coherency Identification Using Cumulant Tensor
    Sun, Bo; Xu, Yijun; Wang, Qinling; Lu, Shuai; Yu, Ruizhi; Gu, Wei; Mili, Lamine M. (IEEE, 2023-12-04)
    As a model reduction tool, coherency identification has been extensively investigated by power researchers using various model-driven and data-driven approaches. Model-driven approaches typically lose their accuracy due to linear assumptions and parameter uncertainties, while data-driven approaches inevitably suffer from bad data issues. To overcome these weaknesses, we propose a data-driven cumulant tensor-based approach that can identify coherent generators and detect anomalies simultaneously. More specifically, it converts the angular velocities of generators into a fourth-order cumulant tensor that can be decomposed to reflect the coherent generators. Also, using co-kurtosis in the cumulant tensor, anomalies can be detected as well. The simulations reveal its excellent performance.
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    A Data-Driven Koopman Approach for Power System Nonlinear Dynamic Observability Analysis
    Xu, Yijun; Wang, Qinling; Mili, Lamine M.; Zheng, Zongsheng; Gu, Wei; Lu, Shuai; Wu, Zhi (IEEE, 2023-08-15)
    A prerequisite to dynamic state estimation of a stochastic nonlinear dynamic model of a power system is its observability analysis. However, due to the model nonlinearity, the traditional methods either suffer from a poor estimation accuracy if a linear approximation is performed or yield an extremely complicated procedure if the Lie-derivative method is applied to a large-scale power system. To address these weaknesses, we propose a new data-driven Koopman-based observability method by revealing the link that exists between the Koopman operator and the Lie-derivative in the Koopman canonical coordinates. This enables the proposed data-driven method not only to be fully derivative-free, which alleviates its implementation complexity but also overcomes the model nonlinearity and inaccuracy of the system. Furthermore, as an important byproduct, the proposed observability analysis scheme provides a valuable guide for the selection of the observables of the Koopman operator, which is a major difficulty for the application of this operator. Finally, we demonstrate the excellent performance of the proposed method on several IEEE standard test systems.
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    Gauged Linear Sigma Model and Mirror Symmetry
    Gu, Wei (Virginia Tech, 2019-07-02)
    This thesis is devoted to the study of gauged linear sigma models (GLSMs) and mirror symmetry. The first chapter of this thesis aims to introduce some basics of GLSMs and mirror symmetry. The second chapter contains the author's contributions to new exact results for GLSMs obtained by applying supersymmetric localization. The first part of that chapter concerns supermanifolds. We use supersymmetric localization to show that A-twisted GLSM correlation functions for certain supermanifolds are equivalent to corresponding Atwisted GLSM correlation functions for hypersurfaces. The second part of that chapter defines associated Cartan theories for non-abelian GLSMs by studying partition functions as well as elliptic genera. The third part of that chapter focuses on N=(0,2) GLSMs. For those deformed from N=(2,2) GLSMs, we consider A/2-twisted theories and formulate the genuszero correlation functions in terms of Jeffrey-Kirwan-Grothendieck residues on Coulomb branches, which generalize the Jeffrey-Kirwan residue prescription relevant for the N=(2,2) locus. We reproduce known results for abelian GLSMs, and can systematically calculate more examples with new formulas that render the quantum sheaf cohomology relations and other properties manifest. We also include unpublished results for counting deformation parameters. The third chapter is about mirror symmetry. In the first part of the third chapter, we propose an extension of the Hori-Vafa mirrror construction [25] from abelian (2,2) GLSMs they considered to non-abelian (2,2) GLSMs with connected gauge groups, a potential solution to an old problem. We formally show that topological correlation functions of B-twisted mirror LGs match those of A-twisted gauge theories. In this thesis, we study two examples, Grassmannians and two-step flag manifolds, verifying in each case that the mirror correctly reproduces details ranging from the number of vacua and correlations functions to quantum cohomology relations. In the last part of the third chapter, we propose an extension of the Hori-Vafa construction [25] of (2,2) GLSM mirrors to (0,2) theories obtained from (2,2) theories by special tangent bundle deformations. Our ansatz can systematically produce the (0,2) mirrors of toric varieties and the results are consistent with existing examples which were produced by laborious guesswork. The last chapter briefly discusses some directions that the author would like to pursue in the future.
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    Localization of twisted N=(0,2) gauged linear sigma models in two dimensions
    Closset, Cyril; Gu, Wei; Jia, Bei; Sharpe, Eric R. (Springer, 2016-03-14)
    We study two-dimensional N=(0, 2) supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider N=(0, 2) theories with an R-symmetry, which can always be defined on curved space by a pseudo-topological twist while preserving one of the two supercharges of flat space. For GLSMs which are deformations of N=(0, 2) GILSMs and retain a Coulomb branch, we consider the A/2-twist and compute the genus-zero correlation functions of certain pseudo-chiral operators, which generalize the simplest twisted chiral ring operators away from the N=(0, 2) locus. These correlation functions can be written in terms of a certain residue operation on the Coulomb branch, generalizing the Jeffrey-Kirwan residue prescription relevant for the N=(0, 2) locus. For abelian GLSMs, we reproduce existing results with new formulas that render the quantum sheaf cohomology relations and other properties manifest. For non-abelian GLSMs, our methods lead to new results. As an example, we briefly discuss the quantum sheaf cohomology of the C rassmannian manifold.
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    A proposal for (0,2) mirrors of toric varieties
    Gu, Wei; Sharpe, Eric R. (Springer, 2017-11-20)
    In this paper we propose (0,2) mirrors for general Fano toric varieties with special tangent bundle deformations, corresponding to subsets of toric deformations. Our mirrors are of the form of (B/2-twisted) (0,2) Landau-Ginzburg models, matching Hori-Vafa mirrors on the (2,2) locus. We compare our predictions to (0,2) mirrors obtained by Chen et al. for certain examples of toric varieties, and find that they match. We also briefly outline conjectures for analogous results for hypersurfaces in Fano toric varieties. Our methods utilize results from supersymmetric localization, which allows us to incidentally gain occasional further insights into GLSM-based (2,2) mirror constructions. For example, we explicitly verify that closed string correlation functions of the original A-twisted GLSM match those of the mirror B-twisted Landau-Ginzburg model, as well as (0,2) deformations thereof.
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    Quantum cohomology from mixed Higgs-Coulomb phases
    Gu, Wei; Melnikov, Ilarion V.; Sharpe, Eric (2024-02-01)
    We generalize Coulomb-branch-based gauged linear sigma model (GLSM)–computations of quantum cohomology rings of Fano spaces. Typically such computations have focused on GLSMs without superpotential, for which the low energy limit of the GLSM is a pure Coulomb branch, and quantum cohomology is determined by the critical locus of a twisted one-loop effective superpotential. We extend these results to cases for which the low energy limit of the GLSM includes both Coulomb and Higgs branches, where the latter is a Landau-Ginzburg orbifold. We describe the state spaces and products of corresponding operators in detail, comparing a geometric phase description, where the operator product ring is quantum cohomology, to the description in terms of Coulomb and Higgs branch states. As a concrete test of our methods, we compare to existing mathematics results for quantum cohomology rings of hypersurfaces in projective spaces.
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    Quantum K theory of partial flag manifolds
    Mihalcea, Constantin; Sharpe, Eric; Gu, Wei; Zhang, Hao; Xu, Weihong; Zou, Hao (Elsevier, 2024-04)
    In this paper we use three-dimensional gauged linear sigma models to make physical predictions for Whitney-type presentations of equivariant quantum K theory rings of partial flag manifolds, as quantum products of universal subbundles and various ratios, extending previous work for Grassmannians. Physically, these arise as OPEs of Wilson lines for certain Chern-Simons levels. We also include a simplified method for computing Chern-Simons levels pertinent to standard quantum K theory.
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    Quantum K Whitney relations for partial flag varieties
    Gu, Wei; Mihalcea, Leonardo C.; Sharpe, Eric; Xu, Weihong; Zhang, Hao; Zou, Hao (2023-10-05)
    In a recent paper, we stated conjectural presentations for the equivariant quantum K ring of partial flag varieties, motivated by physics considerations. In this companion paper, we analyze these presentations mathematically. We prove that if the conjectured relations hold, then they must form a complete set of relations. Our main result is a proof of the conjectured presentation in the case of the incidence varieties. We also show that if a quantum K divisor axiom holds (as conjectured by Buch and Mihalcea), then the conjectured presentation also holds for the complete flag variety.
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    Sirt1 coordinates with ERα to regulate autophagy and adiposity
    Tao, Zhipeng; Shi, Limin; Parke, Jane; Zheng, Louise; Gu, Wei; Dong, X. Charlie; Liu, Dongmin; Wang, Zongwei; Olumi, Aria F.; Cheng, Zhiyong (2021-03-15)
    Sex difference in adiposity has long been recognized but the mechanism remains incompletely understood. Previous studies suggested that adiposity was regulated by autophagy in response to energy status change. Here, we show that the energy sensor Sirt1 mediates sex difference in adiposity by regulating autophagy and adipogenesis in partnership with estrogen receptor α (ERα). Autophagy and adipogenesis were suppressed by Sirt1 activation or overexpression, which was associated with reduced sex difference in adiposity. Mechanistically, Sirt1 deacetylated and activated AKT and STAT3, resulting in suppression of autophagy and adipogenesis via mTOR-ULK1 and p55 cascades. ERα induced Sirt1 expression and inhibited autophagy in adipocytes, while silencing Sirt1 reversed the effects of ERα on autophagy and promoted adipogenesis. Moreover, Sirt1 deacetylated ERα, which constituted a positive feedback loop in the regulation of autophagy and adiposity. Our results revealed a new mechanism of Sirt1 regulating autophagy in adipocytes and shed light on sex difference in adiposity.