Date | Information |
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14 November 2018 | Title : Spectral Methods and Mathematical Modelling in Rarefied Gas Dynamics Assistant Professor Zhenning Cai Date : 14 November 2018 (Wednesday) Time: 3.30pm – 4.30pm Abstract By the Hermite expansion of the distribution function, we introduce a Petrov-Galerkin spectral method for the spatially homogeneous Boltzmann equation with inverse-power-law models. A practical algorithm is proposed to evaluate the coefficients in the spectral method with high accuracy. By introducing Burnett basis functions, which are essentially equivalent to Hermite basis functions, we can further reduce the computational cost using the sparsity of the coefficients. Based on the spectral methods, we generalize the idea of the BGK or Shakhov approximation of the collision model, and build a sequence of new computationally affordable collision models. These models are applied to the spatially inhomogenenous Boltzmann equation for rarefied flows in high nonequilibrium. The results show good agreement with reference solutions computed with stochastic methods. Host : Associate Professor Wang Li-Lian Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

26 October 2018 | Title: Nested Picard Iterative Integrators for the Dirac equation in the nonrelativistic limit Assistant Professor Yongyong Cai Date: 26 October 2018 (Friday) Time: 2.30pm - 3.30pm Abstract: We present the construction and analysis of uniformly accurate nested Picard iterative integrators (NPI) for the Dirac equation in the nonrelativistic limit involving a dimensionless parameter inversely proportional to the speed of light. To overcome the difficulty induced by the rapid temporal oscillation, we present the construction of several NPI methods which are uniformly first-, second- and third-order convergent in time. The NPI method can be extended to arbitrary higher order in time with optimal and uniform accuracy. The implementation of the second order NPI method will be demonstrated and analyzed. Host: Assistant Professor Xia Kelin Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

26 October 2018 | Title: Levenshtein's Deletion Codes and Weyl Groups Associate Professor Manubu Hagiwara Date: 26 October 2018 (Friday) Time: 2.00pm - 3.00pm Abstract: Since Levenshtein found VT codes were single deletion error-correcting codes in 1960's, deletion codes have been attracting coding theorists. In this talk, deletions and insertions are defined from a view point of Weyl groups, in particular, minuscule representation theory. Host: Associate Professor Frédérique Oggier Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

5 September 2018 | Title: The National Supercomputer Center in Jinan and its Current and Near-Future Projects Dr GUO Meng Date: 5 September 2018 (Wednesday) Time: 9.30am – 10.30am Abstract : Established more than seven years ago, National Supercomputing Center in Jinan is a leading center for supercomputing in resource deployment and applications development. In this seminar, we will review our current and near-future resources including the next generation Shenway supercomputer developed mostly in China. We will also review the latest applications projects. With this seminar, we explore the potentials of collaborating with Singapore in general and Nanyang Technological University in particular for exploiting the power of supercomputing for science, engineering as well as commerce. The Center’s Deputy Director Mr. PAN Jing-Shan will also present at the seminar. Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

30 August 2018 | Title: Restricted Linear Congruences and Their Applications Prof Venkatesh Srinivasan Date: 30 August 2018 (Thursday) Time: 4.00pm - 5.00pm Abstract: In this talk, we will consider two natural restrictions on the solutions of linear congruences. Firstly, we give explicit formulas for the number of solutions of weighted linear congruences in which each coordinate satisfies a gcd condition. We discuss applications of this result to universal hashing and to cryptography. Secondly, we also give explicit formulas for the number of solutions of unweighted linear congruences with distinct coordinates. As a consequence, we derive Sloan's formula for the number of codewords in the Varshamov-Tenengolts code and an explicit formula for the number of codewords in the same code with fixed Hamming weight. Our main tools are Ramanujan sums and discrete Fourier transform of arithmetic functions. It is a joint work with Khodakhast Bibak and Bruce Kapron from the University of Victoria, Canada. Host: Associate Professor Wang Huaxiong Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

21 August 2018 | Title: Machine Learning for Determining the Computing and Physics Parameters in Multiscale Modeling of Platelets Prof Yuefan Deng Date: 21 August 2018 (Tuesday) Time: 3.30pm – 4.30pm Abstract: Multiscale Modeling (MSM) is a method that describes particle properties or behaviours on one scale by models from different scales. For modeling platelet dynamics, we propose a MSM involving a particle-based multiscale model employing dissipative particle dynamics (DPD) and coarse-grained molecular dynamics (CGMD) methods characterizing flowing platelets in blood plasma. The DPD models shear blood flow at mesoscopic scale and the CGMD handles microstructure of individual platelet at microscopic scale. The ideal computing scenario is that we perform necessary and sufficient computations for given desirable physiological accuracies at the lowest computational cost, i.e., speediest completion. To achieve such goals, we must address two different classes of issues. The first is the correct selection of parameters in the microscopic platelet models. Usually, these parameters are determined either by first-principle calculations that are time-consuming or by corroborating with in-situ experiments that are also difficult or by the combination of the two methods. Through a primitive version of machine learning, we determine the parameters for the Morse potential and Hooke’s law governing the interactions at molecular levels. The second is the determination of the modeling parameters such as spatial and temporal discretization. We developed, also through machine learning, a novel state-driven adaptive time stepping algorithm which intelligently adapts time step-sizes to underlying biophysical phenomena at various spatial scales. Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

17 August 2018 | Title: Parallel Markov Chain Monte Carlo Methods and Their Applications Prof Yuefan Deng Date: 17 August 2018 (Friday) Time: 3.00pm – 4.00pm Abstract: We introduce a parallel scheme for simulated annealing, a widely used Markov Chain Monte Carlo (MCMC) method for optimization. Our method is constructed and analysed under the classical framework of MCMC. The benchmark function for optimization is used for validation and verification of the parallel scheme. The experiment results, along with the proof based on statistical theory, provide us with insights into the mechanics of the parallelization of simulated annealing for high parallel efficiency or scalability for large parallel computers. Many applications will benefit or are enabled by such 100x to 1000x speedup in processing. One of them is that of Ride-sharing for mitigating vehicular traffic congestions. Ride-sharing problem can generally be formulated into an optimization problem, where a fast and reliable algorithm is needed to solve its matching and routing issue. We discuss the formation of the problems and its solution methodologies. Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

17 August 2018 | Title: Graph Theory and its Applications for Discovering Optimal Network Topologies Prof Yuefan Deng Date: 17 August 2018 (Friday) Time: 2.00pm – 3.00pm Abstract: Graph theory has found more and more applications one of which is used to optimize the network topologies. We form clusters by connecting 32 computing nodes using several network topologies including the mainstream tori, hypercubes, fairly symmetrical regular graphs, and minimal mean-path-length regular graphs. We examine the performances of these clusters by using various standard benchmarking packages including Ping-pong, FFTE, Graph500, the collective functions in MPI, as well as NPB benchmarks. We found strong correlations between the clusters’ performances and the network topologies. For a cluster as small as 32 nodes, we observe multifold performance enhancements, depending on the needs of communication of the benchmarking packages, by using network topologies of the optimal graphs compared to the mainstream graphs. It is striking to reclaim the enhanced performance by merely adjusting the network topologies of the same computing hardware. Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

23 July 2018 | Title: Mathematical Analysis and Numerical Methods for an Underground Oil Recovery Model Prof Ying Wang Date: 23 July 2018 (Monday) Time: 10.30am – 11.30am Abstract: In this talk, I will discuss an underground oil recovery model which includes a third-order mixed derivatives term resulting from the dynamic effects in the pressure difference between the two phases. Analytic study on the computational domain reduction will be provided. A variety of numerical examples in both one and two space dimensions will be given. They show that the solutions may have many different saturation profiles depending on the initial conditions, diffusion parameter, and the third-order mixed derivatives parameter. The results are consistent with the study of traveling wave solutions and their bifurcation diagrams. Host: Assistant Professor Kelin Xia Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

17 July 2018 | Title: On eigenvalues of graphs Prof Jongyook Park Date:17 July 2018 (Tuesday) Time: 2.00pm – 3.00pm Abstract: In this talk, we introduce association schemes and a generalization of distance-regular graphs. We will study eigenvalues of graphs to classify a certain class of association schemes. This talk is designed to be accessible. Host: Dr Gary Greaves Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

28 June 2018 | Title: A 2-stage Adaptive Design to Evaluate the Intra-subject Variability of Glucodynamic Parameters Dr Yeo Kwee Poo Date: 28 June 2018 (Thursday) Time: 9.30am – 10.30am Abstract: n typical clinical trials the design is fixed and the statistician does not analyze the data until the study is terminated. Often the size of the trial is powered based on the assumptions about the effect size that cannot be verified until the actual trial has commenced. An adaptive design allows the study team to modify the sample size for the trial based on interim results. Although adaptive design is not new, most publications in the literature discussed mainly on the inference of mean. In this talk, we propose a 2-stage procedure to analyze variance based on conditional probability. We will also discuss how the overall Type I error is preserved. Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

18 June 2018 | Title : Mathematical Modeling for HIV-1 Viral Capsid Structure and Assembly Professor Jiangguo James Liu Date:18 June 2018 (Monday) Time: 10.00am – 11.00am Abstract: Human immunodeficiency virus type 1 (HIV-1) is a retrovirus that causes acquired immunodeficiency syndrome (AIDS), a condition in humans in which the immune system fails progressively. Understanding the structure and assembly of the HIV-1 virus will help find cures for AIDS. In this talk, we discuss mathematical models for characterizing the structure and formation of HIV-1 conical capsid. Particularly, we focus on three aspects: (1) generating vectors for the lattice structure of the conical shell; (2) curvature concentrations on the narrow end of the cone; (3) dynamical system models for the nucleation stage of the conical capsid. Comparison of modeling results with biological experimental data will be presented. This talk is based on the joint work with Farrah Sadre-Marandi at Ohio State University (USA), Chaoping Chen and Simon Tavener at Colorado State University, Yuewu Liu and Xiufen Zou at Wuhan University (China) . Host : Assistant Professor Kelin Xia Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

18 May 2018 | Title : Modeling, Analysis, & Augmented Strategy for Free Boundary/Moving Interface Problems Professor Zhilin Li Date:18 May 2018 (Friday) Time: 3.00pm – 4.00pm Abstract: Free boundary/moving interface problems are challenging both theoretically and numerically. In this general talk, I will introduce some application examples and corresponding differential equations models. The applications include Stefan problems of unstable crystal growth, drop spreading, and multi-phase flows. Then I will give a brief review of numerical methods for solving those challenging problems, particularly Cartesian grid methods such as Peskin's Immersed Boundary (IB) method, the Immersed Interface Method (IIM), and recent research on augmented approach. There are several motivations or advantages using the augmented approach. It can be applied to decouple problems, to have accurate discretizations for complicated problems; and utilize fast solvers. We will present some new applications of the augmented approach including multi-scale interface problems and new ADI (alternating directional implicit) methods. Host: Assistant professor Kelin Xia & Associate Professor Li-Lian Wang Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

11 May 2018 | Title : A New and Robust Approach to Construct Energy Stable Schemes for Gradient Flows Professor Jie Shen Time: 3.30pm – 4.30pm Abstract:
We present in this talk the scalar auxiliary variable (SAV) approach and the multiple scalar auxiliary variables (MSAV) approach, to deal with nonlinear terms in a large class of gradient flows. The technique is not restricted to specific forms of the nonlinear part of the free energy, it leads to linear and unconditionally energy stable second-order (or higher-order with weak stability conditions) schemes which only require solving decoupled linear equations with constant coefficients. Hence, these schemes are extremely efficient as well as accurate.
We apply the SAV approach to deal with several challenging applications which cannot be easily handled by existing approaches, and present convincing numerical results to show that the new schemes are not only much more efficient and easy to implement, but also can better capture the physical properties in these models.
We shall also present a convergence and error analysis under mild assumptions on the nonlinear free energy.
Host: Associate Professor Wang Li-Lian
Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

7 May 2018 | Title : Modeling and Inference of Local St ationarity Professor Tailen Hsing Time : 2.00pm - 3.00pm Venue: TR + 2 (SPMS-03-06) School of Physical and Mathematical Sciences Abstract: Stationarity is a common assumption in spatial statistics. The justification is often that stationarity is a reasonable approximation to the true state of dependence if we focus on spatial data "locally." In this talk, we first review various known approaches for modeling nonstationary spatial data. We then examine a particular notion of local stationarity in more detail. To illustrate, we will focus on the multi-fractional Brownian motion, for which a thorough analysis could be conducted assuming data are observed on a regular grid. Finally, extensions to more general settings that relate to Matheron's intrinsic random functions will be briefly discussed. Host: Prof Pan Guangming Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

6 April 2018 | Titl e : Coding for DNA Based Storage: Counting Profile Vectors Dr Kiah Han Mao
Time : 9.30am – 10.30am
Venue : MAS Executive Classroom 1 #03-06, School of Physical and Mathematical Sciences
Abstract:
We consider the problem of storing and retrieving information from synthetic DNA media. We introduce the DNA storage channel and model the read process through the use of profile vectors. Using de Bruijn graphs and Ehrhart theory for rational polytopes, we first provide an asymptotic analysis of the number of profile vectors. We then provide exact values and lower bounds on the number of profile vectors for finite values of alphabet size $q$, read length $l$, and word length $n$. Consequently, we demonstrate that for $q\ge 2$ and $n \le q^{l/2−1}$, the number of profile vectors is at least $q^{kn}$ with $k$ very close to one. Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

27 February 2018 | Title : Why spectral methods are preferred in PDE eigenvalue computations in some cases?
Professor Zhimin Zhang
Time : 3.30pm – 4.30pm
Venue : MAS Executive Classroom 1 #03-06, School of Physical and Mathematical Sciences Abstract:
When approximating PDE eigenvalue problems by numerical methods such as finite difference and finite element, it is common knowledge that only a small portion of numerical eigenvalues are reliable. As a comparison, spectral methods may perform extremely well in some situation, especially for 1-D problems. In addition, we demonstrate that spectral methods can outperform traditional methods and the state-of-the-art method in 2-D problems even with singularities. Host: Associate Professor Wang Li-Lian
Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

16 January 2018 | Title : Limit theorems for the realised covariation of a bivariate Brownian semistationary process
Dr Andrea Granelli
Time : 11.00am – 12.00pm
Venue : MAS Executive Classroom 1 #03-06, School of Physical and Mathematical Sciences Abstract:
Within the realm of stochastic processes that fail to be a semimartingale, the recent literature has devoted particular attention to the Brownian semistationary process, a process that has originally been used in the context of turbulence modelling, but has subsequently been employed as a price process in energy markets. This talk presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of the results lies in the fact that we derive the suitable asymptotic theory both in a multivariate setting and outside the classical semimartingale framework. The proofs rely heavily on recent developments in Malliavin calculus. This talk is based on joint work with Dr. Almut Veraart, reader in Statistics at Imperial College London. Host: Dr Pun Chi Seng Patrick Division of Mathematical Sciences, School of Physical and Mathematical Sciences |