Date/Time : 23 Sep 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Nurul Huda binti Mohammad Ramli, Universiti Brunei Darussalam

Abstract: In this talk, I will discuss the methods of kernel density estimation for the estimation of particle concentrations in Lagrangian SDE trajectory models. We consider a simple two-dimensional Lagrangian model to describe the advection-diffusion flow in a chaotic advection regime. This method is chosen because the implemented numerical method to solve its Eulerian Fokker-Planck Equation provides very accurate solutions for the particle concentration, which can be used to assess our kernel density methods from the trajectory models. Some standard techniques of bandwidth selection are briefly discussed, and then a new approach using Green’s function to construct a more accurate kernel density estimator is proposed.

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Date/Time : 22 Sep 2022 10:00
Venue : S17 #05-11 (SR5)
Speaker : Kengo Kamatani, Institute of Statistical Mathematics

Abstract:  We construct a class of non-reversible Metropolis kernels as a multivariate extension of the guided-walk kernel proposed by Gustafson 1998. The main idea of our method is to introduce a projection that maps a state space to a totally ordered group. By using Haar measure, we construct a novel Markov kernel termed Haar-mixture kernel, which is of interest in its own right. This is achieved by inducing a topological structure to the totally ordered group. Our proposed method, the Delta-guided Metropolis–Haar kernel, is constructed by using the Haar-mixture kernel as a proposal kernel. The proposed non-reversible kernel is at least 10 times better than the random-walk Metropolis kernel and Hamiltonian Monte Carlo kernel for the logistic regression and a discretely observed stochastic process in terms of effective sample size per second.

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Date/Time : 16 Sep 2022 14:00
Venue : S17 #05-12 (SR4)
Speaker : Emile Takahiro Okada, National University of Singapore

Abstract: In my talk last year I introduced new methods for computing the wavefront set of depth 0 representations using local wavefront sets. In this series of talks I will begin by briefly recalling the main results from that talk before I go on to outline new results and open questions that have come from these ideas. These will fall into roughly 3 categories: the structure theory of nilpotent orbits, new results on the wavefront set, and finally applications to Arthurs packets.

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Date/Time : 16 Sep 2022 09:00
Venue : via Zoom
Speaker : Yusheng Luo, Stony Brook University

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https://nus-sg.zoom.us/j/88075038959?pwd=cDAyUWMwMDVrd1lwZDQwdXJkbzk3QT09

Meeting ID: 880 7503 8959
Passcode: 384618

Abstract: In 1980s, D. Sullivan formulated a dictionary between discrete subgroups of PSL_2(\C), known as Kleinian groups, and rational maps of \hat \C. The Sullivan dictionary provides a conceptual framework for understanding the connections between these two branches of conformal dynamics.

Around the same time, W. Thurston’s 3-dimensional insights revolutionized the theory of Kleinian groups. He formulated the geometrization conjecture for 3-manifolds, and proved the hyperbolization theorem which implies the conjecture for a large class of 3-manifolds. The keys to the hyperbolization theorem are two bounded results for certain deformation spaces of Kleinian groups.

In 1990s, motivated by Thurston’s boundedness theorem and the Sullivan dictionary, C. McMullen conjectured that certain deformation spaces of hyperbolic rational maps are bounded.

In this talk, I will start with a survey of historical backgrounds, and discuss a general strategy of the proof of Thurston’s boundedness theorem. I will then explain how a similar strategy could work for rational maps, and discuss some recent breakthrough towards McMullen’s boundedness conjecture.

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Date/Time : 15 Sep 2022 10:00
Venue : via Zoom
Speaker : Chen Xinyun, The Chinese University of Hong Kong

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https://nus-sg.zoom.us/j/9775606531?pwd=cVZ6eTRYS3ZzVUlFNXRuSlhMVjJSUT09

Meeting ID: 977 560 6531
Passcode: 123321

Abstract:  Motivated by the emerging needs of personalized intervention in many healthcare applications, we consider a class of multi-stage decision-making problems formulated by Markov Decision Process (MDP) with unknown model parameters. To deal with the pervasive issue of small sample size in personalized intervention, we develop a novel data-pooling estimator and the corresponding reinforcement learning (RL) algorithm based on a general perturbed value iteration framework. The model-free nature of our algorithm has the built-in benefits of being robust to model-misspecification and only requiring data-sharing via aggregate statistics. We establish a theoretical performance guarantee for our algorithm and show that it achieves strictly smaller regret bound than RL algorithms that use only target data or other data-pooling estimators. Furthermore, we substantiate our theoretical development with numerical results in a specific healthcare context: post-discharge follow-up intervention to prevent unplanned readmissions. We demonstrate the empirically better performance of our algorithm over a number of competitive benchmarks using a real hospital dataset. The talk is based on a joint work with Pengyi Shi and Shanwen Pu.

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Date/Time : 14 Sep 2022 16:00
Venue : S17 #06-11 (SR6)
Speaker : Zhang Huangwei, National University of Singapore

Abstract: High-fidelity numerical simulations with detailed chemistry have played significant roles not only in revealing fundamental physicochemical processes in combustion transient, but also designing next-generation propulsion systems. In this talk, an overview of development history and the state of the art of numerical combustion will be first provided. Then the hybrid Eulerian-Lagrangian method with two-way coupling is used in our studies for modelling detonation wave dynamics in two-phase gas-droplet mixture and the numerical implementations based on the open-source CFD package OpenFOAM will be introduced. We have studied hydrogen detonation transmission in fine water sprays based on the one-dimensional and two-dimensional problems. It is found that the existence of the dispersed droplets leads to varied detonation propagation modes depending on the droplet mass loading. Meanwhile, two-phase interfacial instability occurs due to the Kelvin–Helmholtz instability, arising from the pronounced velocity difference across the spray cloud boundary. Moreover, detonative combustion based on liquid n-heptane fuel is also studied. The results show that the fuel droplet heating and evaporation considerably affect detonation propagation speed, composite structure of shock and reaction front, as well as unsteady phenomena.

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Date/Time : 14 Sep 2022 14:00
Venue : S17 #04-04 (SR3)
Speaker : Ta Duy-Hoang, ENS Lyon

Abstract: There is a large and important collection of Ramsey-type combinatorial problems, closely related to central problems in complexity theory, that can be formulated in terms of the asymptotic growth of the size of the maximum independent sets in powers of a fixed small (directed or undirected) hypergraph, also called the Shannon capacity. An important instance of this is the corner problem studied in the context of multiparty communication complexity in the Number On the Forehead (NOF) model (and other important instances are the cap set problem in additive combinatorics and the USP capacity problem in the complexity theory of matrix multiplication).

We introduce a general method for lower bounding the Shannon capacity of hypergraphs via combinatorial degenerations, a combinatorial kind of “approximation” of subgraphs that originates from the study of matrix multiplication in algebraic complexity theory (and which plays an important role there) but which we use in a novel way. This allows us to obtain the best-known lower bounds for multiple combinatorial problems, including the corner problem and its application in communication complexity.

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Date/Time : 14 Sep 2022 17:00
Venue : S17 #04-05 (SR2)
Speaker : Ammar Fathin Sabili, National University of Singapore

Abstract: We introduce and study a new computation model called an Alternating Automatic Register Machine (AARM). An AARM possesses a basic features of a conventional register machine and an alternating Turing machine, but can carry out computations using bounded automatic relations in a single step. One particular finding is that an AARM can recognize some NP-complete problems, including CNF-SAT (using a particular encoding), in logstar n + O(1) steps. Furthermore, we also show that padding the input with a polynomial-size string will recognize polynomial hierarchy in also logstar n + O(1) steps. These results illustrate the power of alternation when combined with computations involving automatic relations.

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Date/Time : 13 Sep 2022 16:00
Venue : via Zoom
Speaker : Piyush Srivastava, Tata Institute of Fundamental Research

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https://nus-sg.zoom.us/j/83199111482?pwd=L09Yd054dDNTbDBpRkNtc0tmQnk5Zz09

Meeting ID: 831 9911 1482
Passcode: 569991

Abstract: This series of lectures will survey various applications to algorithms of a collection of techniques that are broadly referred to as “geometry of polynomials”. Specific examples include:

1) Real stable polynomials and constructions of Ramanujan expanders
2) Lee-Yang theory and deterministic “approximate counting” algorithms”
3) Lorentzian or “strongly log concave” polynomials and applications to sampling

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