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Jingzhou Sun

Publications and source records attributed to Jingzhou Sun.

25 records · Page 2Linked to original sources
arXiv2019

Optimizing Information Freshness in Broadcast Network with Unreliable Links and Random Arrivals: An Approximate Index Policy

With the rapid growth of real-time Internet of Things (IoT) applications, the need for fresh information has surged. Age of Information (AoI) is a tailor-made metric to characterize the information freshness perceived by the devices. In this paper, we investigate the problem of scheduling updates to minimize AoI in broadcast network. In this case, a central controller, e.g. a base station, collects status updates from different sources and schedules them to corresponding clients. Different from previous work, we consider both stochastic status updates and unreliable links. The problem is first modeled as an infinite horizon average constrained cost Markov decision problem (CMDP). With Lagrangian relaxation, an approximation of Whittle's index is derived and a scheduling policy is designed based on the approximate index. The results in previous work can be view as degenerate cases of the approximation index policy either with reliable links or periodic arrival constraints. Simulation results demonstrate the near-optimal performance of the proposed policy.

cs.IT↗
arXiv2017

Projective embedding of log Riemann surfaces and K-stability

Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric $ω$ with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defined by L^k is asymptotically almost balanced in a weighted sense. The proof depends on sufficiently precise understanding of the behavior of the Bergman kernel in three regions, with the most crucial one being the neck region around D. This is the first step towards understanding the algebro-geometric stability of extremal Kähler metrics with singularities.

math.DG↗
arXiv2017

Projective embedding of pairs and logarithmic K-stability

Let $\hat{L}$ be the projective completion of an ample line bundle $L$ over $D$, a smooth projective manifold. Hwang-Singer \cite{HwangS} have constructed complete CSCK metric on $\hat{L}\backslash D$. When the corresponding \kahler form is in the cohomology class of a rational divisor $A$ and when $L$ has negative CSCK metric on $D$, we show that the Kodaira embedding induced by orthonormal basis of the Bergman space of $kA$ is almost balanced. As a corollary, $(\hat{L},D,cA,0)$ is K-semistable.

math.AG↗
arXiv2011

On the Demailly-Semple jet bundles of hypersurfaces in $\CP^3$

Let $X$ be a smooth hypersurface of degree $d$ in $\CP^3$. By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle $X_3$ of $X$, the bundle $\ocal_{X_3}(1)$ is big for $d\geq 11$, and that on the fourth Demailly-Semple jet bundle $X_4$ of $X$, the bundle $\ocal_{X_4}(1)$ is big for $d\geq 10$, improving a recent result of Diverio.

math.AG↗
arXiv2011

Expected Euler characteristic of excursion sets of random holomorphic sections on complex manifolds

We prove a formula for the expected euler characteristic of excursion sets of random sections of powers of an ample bundle $(L,h)$, where $h$ is a Hermitian metric, over a Kähler manifold $(M,ω)$. We then prove that the critical radius of the Kodaira embedding $Φ_N:M\rightarrow \CP^n$ given by an orthonormal basis of $H^0(M,L^N)$ is bounded below when $N\rightarrow \infty$. This result also gives conditions about when the preceding formula is valid.

math.CV↗