Browsing by Author "Gao, Xin"
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- Dimensional oxidation and modular completion of non-geometric type IIB actionGao, Xin; Shukla, Pramod (Springer, 2015-05-05)Utilizing a setup of type IIB superstring theory compactified on an orientifold of T-6/(Z(2) x Z(2)), we propose a modular invariant dimensional oxidation of the four-dimensional scalar potential. In the oxidized ten-dimensional supergravity action, the standard NS-NS and RR three form fluxes (H-, F-) as well as the non-geometric fluxes (Q-, P-) are found to nicely rearrange themselves to form generalized flux-combinations. As an application towards moduli stabilization, using the same S-duality invariant scalar potential, we examine the recently proposed No-Go theorem [1] about creating a mass-hierarchy between universal-axion and the dilaton relevant for axionic-inflation. Considering a two-field dynamics of universal axion and dilator while assuming the other moduli/axions being stabilized, we find a part of the No-Go arguments to be quite robust even with the inclusion of non-geometric (Q-, P-) fluxes.
- Extending the geometry of heterotic spectral cover constructionsAnderson, Lara B.; Gao, Xin; Karkheiran, Mohsen (2020-07)In this work we extend the well-known spectral cover construction first developed by Friedman, Morgan, and Witten to describe more general vector bundles on elliptically fibered Calabi-Yau geometries. In particular, we consider the case in which the Calabi-Yau fibration is not in Weierstrass form, but can rather contain fibral divisors or multiple sections (i.e. a higher rank Mordell-Weil group). In these cases, general vector bundles defined over such Calabi-Yau manifolds cannot be described by ordinary spectral data. To accomplish this we employ well established tools from the mathematics literature of Fourier-Mukai functors. We also generalize existing tools for explicitly computing Fourier-Mukai transforms of stable bundles on elliptic Calabi-Yau manifolds. As an example of these new tools we produce novel examples of chirality changing small instanton transitions. The goal of this work is to provide a geometric formalism that can substantially increase the understood regimes of heterotic/F-theory duality. (C) 2020 The Authors. Published by Elsevier B.V.
- Fibrations in CICY threefoldsAnderson, Lara B.; Gao, Xin; Gray, James A.; Lee, Seung-Joo (Springer, 2017-10-11)In this work we systematically enumerate genus one fibrations in the class of 7; 890 Calabi-Yau manifolds defined as complete intersections in products of projective spaces, the so-called CICY threefolds. This survey is independent of the description of the manifolds and improves upon past approaches that probed only a particular algebraic form of the threefolds (i.e. searches for "obvious" genus one fibrations as in [1, 2]). We also study K3-fibrations and nested fibration structures. That is, K3 fibrations with potentially many distinct elliptic fibrations. To accomplish this survey a number of new geometric tools are developed including a determination of the full topology of all CICY threefolds, including triple intersection numbers. In 2; 946 cases this involves finding a new "favorable" description of the manifold in which all divisors descend from a simple ambient space. Our results consist of a survey of obvious fibrations for all CICY threefolds and a complete classification of all genus one fibrations for 4; 957 "Kahler favorable" CICYs whose Kahler cones descend from a simple ambient space. Within the CICY dataset, we find 139; 597 obvious genus one fibrations, 30; 974 obvious K3 fibrations and 208; 987 nested combinations. For the Kahler favorable geometries we find a complete classification of 377; 559 genus one fibrations. For one manifold with Hodge numbers (19; 19) we find an explicit description of an in finite number of distinct genus-one fibrations extending previous results for this particular geometry that have appeared in the literature. The data associated to this scan is available here [3].
- Multiple fibrations in Calabi-Yau geometry and string dualitiesAnderson, Lara B.; Gao, Xin; Gray, James A.; Lee, Seung-Joo (Springer, 2016-10-19)In this work we explore the physics associated to Calabi-Yau (CY) n-folds that can be described as a fibration in more than one way. Beginning with F-theory vacua in various dimensions, we consider limits/dualities with M-theory, type IIA, and heterotic string theories. Our results include many M-/F-theory correspondences in which distinct F-theory vacua - associated to different elliptic fibrations of the same CY n-fold - give rise to the same M-theory limit in one dimension lower. Examples include 5-dimensional correspondences between 6-dimensional theories with Abelian, non-Abelian and superconformal structure, as well as examples of higher rank Mordell-Weil geometries. In addition, in the context of heterotic/F-theory duality, we investigate the role played by multiple K3- and elliptic fibrations in known and novel string dualities in 8-, 6- and 4-dimensional theories. Here we systematically summarize nested fibration structures and comment on the roles they play in T-duality, mirror symmetry, and 4-dimensional compactifications of F-theory with G-flux. This investigation of duality structures is made possible by geometric tools developed in a companion paper [1].
- Tools for CICYs in F-theoryAnderson, Lara B.; Gao, Xin; Gray, James A.; Lee, Seung-Joo (Springer, 2016-11-02)We provide a set of tools for analyzing the geometry of elliptically fibered Calabi-Yau manifolds, starting with a description of the total space rather than with a Weierstrass model or a specified type of fi ber/base. Such an approach to the subject of F-theory compactification makes certain geometric properties, which are usually hidden, manifest. Specifically, we review how to isolate genus-one fi brations in such geometries and then describe how to find their sections explicitly. This includes a full parameterization of the Mordell-Weil group where non-trivial. We then describe how to analyze the associated Weierstrass models, Jacobians and resolved geometries. We illustrate our discussion with concrete examples which are complete intersections in products of projective spaces (CICYs). The examples presented include cases exhibiting non-abelian symmetries and higher rank Mordell-Weil group. We also make some comments on non-flat fi brations in this context. In a companion paper [1] to this one, these results will be used to analyze the consequences for string dualities of the ubiquity of multiple fi brations in known constructions of Calabi-Yau manifolds.
- Tumour heterogeneity revealed by unsupervised decomposition of dynamic contrast-enhanced magnetic resonance imaging is associated with underlying gene expression patterns and poor survival in breast cancer patientsFan, Ming; Xia, Pingping; Liu, Bin; Zhang, Lin; Wang, Yue; Gao, Xin; Li, Lihua (2019-10-17)Background Heterogeneity is a common finding within tumours. We evaluated the imaging features of tumours based on the decomposition of tumoural dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data to identify their prognostic value for breast cancer survival and to explore their biological importance. Methods Imaging features (n = 14), such as texture, histogram distribution and morphological features, were extracted to determine their associations with recurrence-free survival (RFS) in patients in the training cohort (n = 61) from The Cancer Imaging Archive (TCIA). The prognostic value of the features was evaluated in an independent dataset of 173 patients (i.e. the reproducibility cohort) from the TCIA I-SPY 1 TRIAL dataset. Radiogenomic analysis was performed in an additional cohort, the radiogenomic cohort (n = 87), using DCE-MRI from TCGA-BRCA and corresponding gene expression data from The Cancer Genome Atlas (TCGA). The MRI tumour area was decomposed by convex analysis of mixtures (CAM), resulting in 3 components that represent plasma input, fast-flow kinetics and slow-flow kinetics. The prognostic MRI features were associated with the gene expression module in which the pathway was analysed. Furthermore, a multigene signature for each prognostic imaging feature was built, and the prognostic value for RFS and overall survival (OS) was confirmed in an additional cohort from TCGA. Results Three image features (i.e. the maximum probability from the precontrast MR series, the median value from the second postcontrast series and the overall tumour volume) were independently correlated with RFS (p values of 0.0018, 0.0036 and 0.0032, respectively). The maximum probability feature from the fast-flow kinetics subregion was also significantly associated with RFS and OS in the reproducibility cohort. Additionally, this feature had a high correlation with the gene expression module (r = 0.59), and the pathway analysis showed that Ras signalling, a breast cancer-related pathway, was significantly enriched (corrected p value = 0.0044). Gene signatures (n = 43) associated with the maximum probability feature were assessed for associations with RFS (p = 0.035) and OS (p = 0.027) in an independent dataset containing 1010 gene expression samples. Among the 43 gene signatures, Ras signalling was also significantly enriched. Conclusions Dynamic pattern deconvolution revealed that tumour heterogeneity was associated with poor survival and cancer-related pathways in breast cancer.