arXiv subjects
Publications and source records attributed to Jingzhou Sun.
We study the Bergman embeddings of degenerating families of K\"{a}hler-Einstein manifolds of negative curvature. We show that when the central fiber has only simple normal crossing singularities, we can construct orthonormal bases so that the induced Bergman embeddings converge to the Bergman embedding of the limit space together with multi-bubbles.
We prove an explicit formula for the Bergman kernel of polarized abelian varieties. As applications, we show that if two positive line bundles represent the same first Chern class and have identical Bergman kernel functions for some tensor power, then the corresponding powers of the bundles are isomorphic. We also obtain localization results for the maxima and minima of the Bergman kernel function and establish exponential off-diagonal decay estimates.
We prove a formula for the Bergman kernel of polarized complex hyperbolic manifolds. The formula expresses the Bergman kernel as a sum over the geodesic loops in the manifold. As an application, we prove a result about the maximum and minimum of the Bergman kernel function. We also prove an estimate of the off-diagonal Bergman kernel.
We study the Bergman embeddings of degenerating families of Kähler-Einsten manifolds of negative curvature. In one special case, we show that we can construct orthonormal bases so that the induced Bergman embeddings converge to the Bergman embedding of the limit space together with bubbles.
We continue our study on the logarithmic balanced model metric initiated in our previous work. By a non-trivial refinement of the set of tools developed in our previous work, we are able to confirm partially a conjecture we made in our previous work on the asymptotic behavior of the balanced metric near infinity.
We talk about the image of the Hilbert map. We show the necessary and sufficient condition that the Hilbert map is surjective.
This is the sequel to our first paper concerning the balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. We prove the uniqueness of such an embedding. The proof relies on fine estimates of the asymptotics of a balanced embedding.
Intelligent real-time applications, such as video surveillance, demand intensive computation to extract status information from raw sensing data. This poses a substantial challenge in orchestrating computation and communication resources to provide fresh status information. In this paper, we consider a scenario where multiple energy-constrained devices served by an edge server. To extract status information, each device can either do the computation locally or offload it to the edge server. A scheduling policy is needed to determine when and where to compute for each device, taking into account communication and computation capabilities, as well as task-specific timeliness requirements. To that end, we first model the timeliness requirements as general penalty functions of Age of Information (AoI). A convex optimization problem is formulated to provide a lower bound of the minimum AoI penalty given system parameters. Using KKT conditions, we proposed a novel scheduling policy which evaluates status update priorities based on communication and computation delays and task-specific timeliness requirements. The proposed policy is applied to an object tracking application and carried out on a large video dataset. Simulation results show that our policy improves tracking accuracy compared with scheduling policies based on video content information.
We consider collaborative perception (CP) systems where a fusion center monitors various regions by multiple sources. The center has different age of information (AoI) constraints for different regions. Multi-view sensing data for a region generated by sources can be fused by the center for a reliable representation of the region. To ensure accurate perception, differences between generation time of asynchronous status updates for CP fusion should not exceed a certain threshold. An algorithm named scheduling for CP with asynchronous status updates (SCPA) is proposed to minimize the number of required channels and subject to AoI constraints with asynchronous status updates. SCPA first identifies a set of sources that can satisfy the constraints with minimum updating rates. It then chooses scheduling intervals and offsets for the sources such that the number of required channels is optimized. According to numerical results, the number of channels required by SCPA can reach only 12% more than a derived lower bound.
We consider a status information updating system where a fusion center collects the status information from a large number of sources and each of them has its own age of information (AoI) constraints. A novel grouping-based scheduler is proposed to solve this complex large-scale problem by dividing the sources into different scheduling groups. The problem is then transformed into deriving the optimal grouping scheme. A two-step grouping algorithm (TGA) is proposed: 1) Given AoI constraints, we first identify the sources with harmonic AoI constraints, then design a fast grouping method and an optimal scheduler for these sources. Under harmonic AoI constraints, each constraint is divisible by the smallest one and the sum of reciprocals of the constraints with the same value is divisible by the reciprocal of the smallest one. 2) For the other sources without such a special property, we pack the sources which can be scheduled together with minimum update rates into the same group. Simulations show the channel usage of the proposed TGA is significantly reduced as compared to a recent work and is 0.42% larger than a derived lower bound when the number of sources is large.
We investigate the problem of balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. In this paper we prove the existence of such an embedding in a model case. The strategy is by using a gradient flow in a Hilbert space; both the long-time existence and convergence at infinite time are non-trivial. The long time existence is established by choosing a perturbation of the ODE; the convergence depends on a priori bounds that uses techniques in the proof of the Tauber-Hardy-Littlewood theorem.
In up-to-date machine learning (ML) applications on cloud or edge computing platforms, batching is an important technique for providing efficient and economical services at scale. In particular, parallel computing resources on the platforms, such as graphics processing units (GPUs), have higher computational and energy efficiency with larger batch sizes. However, larger batch sizes may also result in longer response time, and thus it requires a judicious design. This paper aims to provide a dynamic batching policy that strikes a balance between efficiency and latency. The GPU-based inference service is modeled as a batch service queue with batch-size dependent processing time. Then, the design of dynamic batching is a continuous-time average-cost problem, and is formulated as a semi-Markov decision process (SMDP) with the objective of minimizing the weighted sum of average response time and average power consumption. The optimal policy is acquired by solving an associated discrete-time Markov decision process (MDP) problem with finite state approximation and "discretization". By introducing an abstract cost to reflect the impact of "tail" states, the space complexity and the time complexity of the procedure can decrease by 63.5% and 98%, respectively. Our results show that the optimal policies potentially possess a control limit structure. Numerical results also show that SMDP-based batching policies can adapt to different traffic intensities and outperform other benchmark policies. Furthermore, the proposed solution has notable flexibility in balancing power consumption and latency.
In this work, we study a status update system with a source node sending timely information to the destination through a channel with random delay. We measure the timeliness of the information stored at the receiver via the Age of Information (AoI), the time elapsed since the freshest sample stored at the receiver is generated. The goal is to design a sampling strategy that minimizes the total cost of the expected time average AoI and sampling cost in the absence of transmission delay statistics. We reformulate the total cost minimization problem as the optimization of a renewal-reward process, and propose an online sampling strategy based on the Robbins-Monro algorithm. Denote $K$ to be the number of samples we have taken. We show that, when the transmission delay is bounded, the expected time average total cost obtained by the proposed online algorithm converges to the minimum cost when $K$ goes to infinity, and the optimality gap decays with rate $\mathcal{O}\left(\ln K/K\right)$. Simulation results validate the performance of our proposed algorithm.
We study the asymptotic of the partial density function associated to holomorphic section of a postive line bundle vanishing to high orders along a fixed smooth subvariety. Assuming local torus-action-invariance, we describe the forbidden region, generalizing the result of Ross-Singer.
Given a sequence of genus $g\geq 2$ curves converging to a punctured Riemann surface with complete metric of constant Gaussian curvature $-1$. we prove that the Kodaira embedding using orthonormal basis of the Bergman space of sections of a pluri-canonical bundle also converges to the embedding of the limit space together with extra complex projective lines.
We prove the asymptotic of the logarithmic Bergman kernel. And as an application, we calculate the conditional expectation of density of zeros of Gaussian random sections of powers of a positive line bundle that vanish along a fixed smooth subvariety.
We consider a star-topology wireless network for status update where a central node collects status data from a large number of distributed machine-type terminals that share a wireless medium. The Age of Information (AoI) minimization scheduling problem is formulated by the restless multi-armed bandit. A widely-proven near-optimal solution, i.e., the Whittle's index, is derived in closed-form and the corresponding indexability is established. The index is then generalized to incorporate stochastic, periodic packet arrivals and unreliable channels. Inspired by the index scheduling policies which achieve near-optimal AoI but require heavy signaling overhead, a contention-based random access scheme, namely Index-Prioritized Random Access (IPRA), is further proposed. Based on IPRA, terminals that are not urgent to update, indicated by their indices, are barred access to the wireless medium, thus improving the access timeliness. A computer-based simulation shows that IPRA's performance is close to the optimal AoI in this setting and outperforms standard random access schemes. Also, for applications with hard AoI deadlines, we provide reliable deadline guarantee analysis. Closed-form achievable AoI stationary distributions under Bernoulli packet arrivals are derived such that AoI deadline with high reliability can be ensured by calculating the maximum number of supportable terminals and allocating system resources proportionally.
Using the techniques developed in \cite{SunSun}, we give estimations of the Bergman kernel of the punctured disk with the standard complete Poincaré metric. As an application, we improve the result of \cite{AMM} on the Bergman kernels of punctured Riemann surfaces near singularities.