Date/Time : 27 May 2021 16:00
Venue : via Zoom
Speaker : Niangjun Chen, Singapore University of Technology and Design

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Many problems in data science and cloud computing can be cast as online optimization problems. In this talk, we study general online optimization problems with uncertainties, where the payoff or cost information is only known to the decision-maker up to some bounded uncertainty set. We develop an algorithmic framework, CRT, that can be applied to both online cost minimization problems with revenue constraints and online revenue maximization problems with inventory constraints. In both scenarios, we design online algorithms based on the CRT framework and prove their optimality in terms of competitive ratio. Furthermore, while prior works on online nonlinear optimization with inventory constraint require the revenue functions to be concave, we show that CRT-based algorithms have optimal competitive ratios in general online optimization settings with non-convex cost functions or non-concave revenue functions. We demonstrate our proposed algorithms’ practical performance via trace-driven simulations in a cloud computing application against prominent existing algorithms.

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Date/Time : 26 May 2021 15:00
Venue : via Zoom
Speaker : Wen Deng, Chinese Academy of Sciences

Join Zoom Meeting https://nus-sg.zoom.us/j/83402872988?pwd=UWxhOEFKam9oYnk1N1FqT2JCdnFzdz09 Meeting ID: 834 0287 2988 Password: 471879 We consider the stability problem of the Couette flow for the 2D Boussinesq system. Due to the presence of the buoyancy forcing, the energy of the standard Boussinesq equations could grow in time. It is the enhanced dissipation created by the linear non self-adjoint operator in the perturbation equation that makes the stability possible. In this work, we prove the nonlinear stability of the Couette flow for 2D Boussinesq system with full dissipation and with only vertical dissipation in Sobolev spaces. This is a joint work with J. Wu and P. Zhang.

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Date/Time : 21 May 2021 09:00
Venue : via Zoom
Speaker : Yudong Chen, Cornell University

Join Zoom Meeting https://nus-sg.zoom.us/j/82907817525?pwd=bU1tWlNwTXhwbC9sa3R5eDZKOVovQT09 Meeting ID: 829 0781 7525 Passcode: 752172 We consider the problems of learning discrete structures from network data under statistical settings. Popular examples include various planted and block models, Z2 synchronization and mixture models. Semidefinite programming (SDP) relaxation has emerged as a versatile and robust approach to these problems. We show that despite being a relaxation, SDP achieves the optimal Bayes error rate in terms of distance to the target solution. Moreover, SDP relaxation is provably robust under the so-called semirandom model, which frustrates many existing algorithms. Our proof involves a novel primal-dual analysis that establishes what we call the Hidden Integrality property: the SDP relaxation tightly approximates the optimal (yet unimplementable) integer program with oracle information. Joint work with Yingjie Fei (Cornell Ph.D.), who won 2nd place in INFORMS Nicholson Student Paper Competition.

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Date/Time : 20 May 2021 16:00
Venue : via Zoom
Speaker : Yuan FANG, Singapore Management University

JJoin Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Heterogeneous Information Networks (HIN) often model complex graph-structured data with multi-typed relationships between different types of objects. The heterogeneity gives rise to the rich semantics on HINs, such as different user interactions on social networks, and different functional associations between proteins on a biological network. Metagraphs, which model recurring subgraph structures on HINs, emerge as a powerful tool to capture the rich semantics. Compared to their simpler variant metapaths, metagraphs are higher-order structures with stronger expressiveness and can be regarded as nonlinear functions of metapaths. Not surprisingly, metagraphs can be used to derive effective graph representations on HINs, to enable various downstream tasks such as node classification and link prediction. The efficacy of metagraph-based representations can be demonstrated in various domains including social, cyberphysical and biological networks.

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Date/Time : 19 May 2021 15:00
Venue : via Zoom
Speaker : Yanlin Liu, Beijing Normal University

Join Zoom Meeting https://nus-sg.zoom.us/j/86563869492?pwd=MlRhL0k5VDhRbVFXTmFUVCtWZ0hsZz09 Meeting ID: 865 6386 9492 Passcode: 488917 We show that any unique global solution (here we do not require any smallness condition beforehand) to 3-D axisymmetric Navier-Stokes equations in some scaling invariant spaces must eventually become a small solution. In particular, we show that the limits of $\|\omega^\theta(t)/r\|_{L^1}$ and $\|u^\theta(t)/\sqrt r\|_{L^2}$ are all $0$ as $t$ tends to infinity. And by using this, we can refine some decay estimates for the axisymmetric solutions.

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Date/Time : 07 May 2021 09:00
Venue : via Zoom
Speaker : Weiqiang Wang, University of Virginia

Join Zoom Meeting https://nus-sg.zoom.us/j/82997442700?pwd=TzI5bGJEM2JMb1o0enFRMFlReEZLZz09 Meeting ID: 829 9744 2700 Passcode: 178346 The original quantum Schur duality (due to Jimbo) concerns about commuting actions on a tensor space of a quantum group and a Hecke algebra of type A. Several years ago, Huanchen Bao and I generalized this to a duality between a Hecke algebra of type B and an i-quantum group arising from quantum symmetric pairs. Both dualities are deeply connected to canonical basis, flag varieties, and Kazhdan-Lusztig theory of type ABC. In this talk, I will explain a new unification of both dualities, which leads to an unexpected generalization of Kazhdan-Lusztig construction. This is joint work with Yaolong Shen.

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Date/Time : 28 Apr 2021 15:00
Venue : via Zoom
Speaker : Chao Liu, Huazhong University of Science and Technology

Join Zoom Meeting https://nus-sg.zoom.us/j/81653239587?pwd=U2lCTS9qV01IejN3VDJ2eDB4dml2UT09 Meeting ID: 816 5323 9587 Password: 918779 Motivated by the astrophysical problems of star formations from molecular clouds, we make the first step on the possible behaviors of certain molecular clouds. This talk (1) establishes the diffuse boundary problem of Euler-Poisson system for describing the evolution of molecular clouds; (2) proves the local existence, uniqueness and continuation principle of the classical solution to the diffuse boundary problem; (3) proves the classical solution (without any symmetry condition) to the diffuse problem blows up at finite time if there is no the first class of global solution and the data is admissible (large scale, irregularly-shaped, expanding and rotational molecular clouds); (4) proves certain singularities can be removed from the boundary if the data is strongly admissible. This result partially answers Makino’s conjecture (1992) on the finite blowup of any tame solution without symmetries and gives the possibilities of star formations, fragmentation and possibilities of formations of shocks and physical vacuum boundary in perfect fluids with Newtonian self-gravity. This talk is based on the article arXiv:2102.11550.

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Date/Time : 27 Apr 2021 15:00
Venue : via Zoom
Speaker : Jinxin Xue, Tsinghua University

Join Zoom Meeting https://nus-sg.zoom.us/j/86384771548?pwd=RnMzcXJrcUtERmFrbHVXMUFrejVsZz09 Meeting ID: 863 8477 1548 Password: 244323 In this talk, we study the dynamics of geodesic flows in perturbed blackhole backgrounds using the techniques of Hamiltonian dynamics. The central object in our work is the blackhole shadow. It gives a normally hyperbolic invariant submanifold in the phase space and is robust under perturbations. We find a gap structure within the blackhole shadow and also use it to construct long chaotic orbit with large oscillation of angular momentum. Moreover, similar methodology applies to the event horizon of Kerr to give chaotic orbit skirting around the event horizon.

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Date/Time : 23 Apr 2021 16:00
Venue : via Zoom
Speaker : Jiange Li, Hebrew University of Jerusalem

Join Zoom Meeting Meeting ID: 872 8371 4051 Password: 226133 Abstract:  The balls into bins problem is a classical problem in probability theory that has many applications in computer science. It involves m balls and n bins. Each time, a ball is placed into a bin selected uniformly at random. We are interested in the following two-thinning variant. For each ball, after a random bin has been selected, we may choose to either accept it or place the ball into a new random bin. We are not aware of the secondary allocation before deciding whether accept the primary allocation. We show explicit strategies that can achieve nearly optimal maximum loads. Comparisons are also drawn between this two-thinning variant and the well-known two-choice variant, in which case one selects two random bins and places a ball into the less loaded bin and ties are broken arbitrarily. (This talk is based on joint work with Ohad Noy Feldheim and Ori Gurel-Gurevich.)

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