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Siyao Liu

Publications and source records attributed to Siyao Liu.

27 records · Page 2Linked to original sources
arXiv2023

The J-twist D_J of the Dirac operator and the Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary

In [22], the authors proved a Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator on 3-dimensional and 4-dimensional almost product Riemannian spin manifold with boundary. In this paper, we develop the Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator on a 6-dimensional almost product Riemannian spin manifold with boundary.

math.DG↗
arXiv2023

Geometric structures in $Sol_3$

In this paper, we conclude the geometric structures in $Sol_3$ with the Levi-Civita connection and the semi-symmetric non-metric connection. We discuss two special cases to study the geometric structures in $Sol_3$ with the semi-symmetric non-metric connection, namely $\widehat{P}=a(X_3)\partial_3$ and $\widehat{P}=b(X_3)\partial_1$, also get relatively complete conclusions respectively. As a special case, we investigate the geometric structures in $Sol_3$ with the Levi-Civita connection.

math.DG↗
arXiv2022

Geometric structures of Morris-Thorne wormhole metric with the semi-symmetric non-metric connections

Spacetime is a 4-dimensional connected Lorentzian manifold. In this paper, we extend the Levi-Civita connection in the definition of spacetime to the semi-symmetric non-metric connection and conclude geometric structures admitted by the metric (1.1) with the semi-symmetric non-metric connections. Obviously, Morris-Thorne spacetime is Ricci generalized pseudosymmetry, Ricci generalized projectively pseudosymmetry, and has conformal 2-forms that are recurrent, etc. It also is an Einstein manifold of level 2 and 3-quasi-Einstein manifold.

math.DG↗
arXiv2022

Pairwise Nonlinear Dependence Analysis of Genomic Data

In The Cancer Genome Atlas (TCGA) data set, there are many interesting nonlinear dependencies between pairs of genes that reveal important relationships and subtypes of cancer. Such genomic data analysis requires a rapid, powerful and interpretable detection process, especially in a high-dimensional environment. We study the nonlinear patterns among the expression of pairs of genes from TCGA using a powerful tool called Binary Expansion Testing. We find many nonlinear patterns, some of which are driven by known cancer subtypes, some of which are novel.

stat.AP↗
arXiv2022

Algebraic Schouten Solitons of Three-Dimensional Lorentzian Lie Groups

In [10], Wears defined and studied algebraic T-solitons. In this paper, we give the definition of algebraic Schouten solitons as a special T-soliton and classify algebraic Schouten solitons associated to Levi-Civita connections, canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure.

math.DG↗
arXiv2022

Affine connections on singular multiply warped products and singular twisted products

In this paper, we generalize the results in [Y. Wang: Affine connections on singular warped products. Int. J. Geom. Methods Mod. Phys. 18(5), 2150076, (2021).] to singular multiply warped products and singular twisted products. We study singular multiply warped products and singular twisted products and their curvature with the semi-symmetric metric connection and the semi-symmetric non-metric connection. We also discuss Koszul forms associated with the almost product structure and their curvature of singular multiply warped products and singular twisted products. Finally, several examples are presented to demonstrate the theoretical results.

math.DG↗
arXiv2022

The perturbation of the de Rham Hodge Operator and the Kastler-Kalau-Walze type theorem for manifolds with boundary

In this paper, we give Lichnerowicz type formulas for the perturbation of the de Rham Hodge operator. We prove the Kastler-Kalau-Walze type theorems for the perturbation of the de Rham Hodge operator on 4-dimensional and 6-dimensional compact manifolds with (resp.without) boundary. Some concrete examples of the perturbation of the de Rham Hodge operator are provided for our main theorems.

math.DG↗
arXiv2019

Reinforcement learning for bandwidth estimation and congestion control in real-time communications

Bandwidth estimation and congestion control for real-time communications (i.e., audio and video conferencing) remains a difficult problem, despite many years of research. Achieving high quality of experience (QoE) for end users requires continual updates due to changing network architectures and technologies. In this paper, we apply reinforcement learning for the first time to the problem of real-time communications (RTC), where we seek to optimize user-perceived quality. We present initial proof-of-concept results, where we learn an agent to control sending rate in an RTC system, evaluating using both network simulation and real Internet video calls. We discuss the challenges we observed, particularly in designing realistic reward functions that reflect QoE, and in bridging the gap between the training environment and real-world networks.

cs.NI↗