## Seminars 2006

Title: | On Some Weakly Nonlinear Long Waves Models for Water Waves |

Speaker: | Professor Jean-Claude Saut |

Date: | 22 November 2006 |

Time: | 4.00pm - 5.00pm |

Venue: | Chemistry Computational Lab LT19A-B4-02 |

Abstract: | We will derive systematically and justify rigorously classes of models for the description of water waves in the regime of weakly nonlinear dispersive waves. Two situations will be considered. First, in the isotropic case, we will derive and analyse new classes of Boussinesq systems. Second, in the weakly transverse (KP) regime, we will construct weakly transverse Boussinesq systems. Those later systems will be shown to have the correct error estimate as an approximation of the Euler system with free boundary, in contrast to the KP equation which constitutes a rather poor approximation of the Euler system. |

Title: | Nuclear Magnetic Resonance in solution as a tool for structural studies
of biomolecules: overview and focus on mathematical problems of
construction of optimal NMR experiments |

Speaker: | Associate Professor Konstantin Pervushin |

Date: | 21 November 2006 |

Time: | 10.30am - 11.30am |

Venue: | NIE5-01-LT11 |

Abstract: | |

Title: | “A Synthesis of a Posteriori Error Estimation Techniques for
Conforming, Non-Conforming, Mixed and Discontinuous
Galerkin Finite Element Methods” |

Speaker: | Professor Mark Ainsworth |

Date: | 17 November 2006 |

Time: | 2.30pm - 3.30pm |

Venue: | NTU, LT2 (NS4-2-36) |

Abstract: | A posteriori error estimation for conforming, non-conforming, mixed and discontinuous finite element schemes are discussed within a single framework. By dealing with four ostensibly different schemes under the same umbrella, the same common underlying principles at work in each case are highlighted leading to a clearer understanding of the issues involved. The ideas are presented in the context of piecewise affine finite element approximation of a second-order elliptic problem. It is found that the framework leads to known a posteriori error estimators: the equilibrated residual method in the case of conforming Galerkin FEM; the estimator of Ainsworth in the case of the Crouzeix-Raviart scheme. In the remaining cases, we obtain new estimators recently derived by Ainsworth. In all cases one has computable upper bounds on the error measured in the energy norm and corresponding local lower bounds showing the efficiency of the schemes. We present numerical examples illustrating how the estimators may be used to solve a variety of physical problems efficiently. |

Title: | “PBD Closed Sets and the Existence
and Constructions of Designs” |

Speaker: | Dr Shen Hao |

Date: | 6 October 2006 |

Time: | 4.00pm - 5.00pm |

Venue: | Chemistry Computational Lab (LT19A-B4-01) |

Host: | Professor Ling San |

Abstract: | Let v be a positive integer and K be a set of positive integers, a pairwise
balanced design, denoted B (K, 1; v), is a pair (X, A) where X is a v-set and A is
a set of subsets (called blocks) such that number of points contained in any
block in an integer of K. Now let B (K) = (v: there exists a B (K, 1; v}. K is called
a PBD closed set if B(K)=K.
PBD closed sets play an important role in the study of existence and construction of combinatorial designs. In this talk, we will show how PBD closed sets can be used in the construction of various kinds of designs, including block designs, group divisible designs and resolvable designs. |

Title: | Double Circulant Codes from Two Class Association Schemes |

Speaker: | Dr Patrick Solé |

Date: | 22 September 2006 |

Title: | Order Selection in Finite Mixture Models - A Fundamental and Challenging Problem |

Speaker: | Professor Chen Jiahua |

Date: | 27 April 2006 |

Title: | Pointwise Convergence of
Harmonic Functions |

Speaker: | Dr Anders Gustavsson |

Date: | 18 April 2006 |

Time: | 11.30am |

Venue: | NIE Blk 5 Level 3 Rm 4(NIE5-03-04) |

Abstract: | The speaker will characterize those real valued functions on a compact set K in Rn, which a re pointwise limits of functions harmonic in some neighbourhood of K. He will also give a short introduction to fine topology and its role in harmonic approximation. |

Title: | CLOSED BILLIARD TRAJECTORIES CLOSED BILLIARD TRAJECTORIES |

Speaker: | Dr Fedor Duzhin |

Date: | 13 April 2006 |

Time: | 2.30pm |

Venue: | NIE Blk 5, Level 3, Rm 4(NIE5 -03 -04) |

Abstract: | Given a domain or, more generally, a Riemannian manifold with boundary, a billiard is the motion of a particle
when the field of force is absent. Trajectories of such a motion are geodesics inside the domain; and the
particle rebounds from the boundary making the angle of incidence equal the angle of reflection. The billiard
motion can happen to be a closed (or periodic) one when the billiard ball rebounds
k times and then gets to
the initial position with the same speed vector as in the beginning. The study of closed billiard trajectories is
due to George Birkhoff who in 1927 proved the following fact:
Theorem. Let D ⊂ R ² be a plane domain with a strictly convex smooth boundary and let k> 2 be an integer. Then there exists at least φ(k) billiard motions of period k inside the domain D. Here φ(k) is the Euler function, i.e., the number of integers coprime with k among 1,2,…,k-1. Periodic billiard trajectories arise in various branches of mathematics. Being defined in terms of dynamical systems, they are connected with closed geodesics, knot invariants, braids and configuration spaces, Morse theory – some of these areas are purely topological. The classical Birkhoff's problem of estimating the number of closed billiard trajectories can be naturally generalized by considering a billiard motion in a space of any dimension. The most general known statement of this kind involves an arbitrary manifold as the boundary of a billiard table: we estimate the number of closed billiard trajectories in terms of homology groups of the manifold. |

Title: | CHANGE OF BASIS IN VECTOR SPACES AND HOMOGENEOUS FACTORISATIONS OF GRAPHS |

Speaker: | Dr Lim Tian Koon |

Date: | 11 April 2006 |

Time: | 10.30am |

Venue: | NIE Blk 5, Level 3, Rm 4 (NIE5-03-04) |

Abstract: |

Title: | AUTOMATA AND ALGEBRAIC SYSTEMS AUTOMATA AND ALGEBRAIC SYSTEMS |

Speaker: | Professor Bakhadyr Khoussainov |

Date: | 30 March 2006 |

Time: | 3.30pm - 4.30pm |

Venue: | School of Biological Sciences (SBS-01n-28) |

Abstract: | In this talk, the speaker introduces the concept of algebraic systems that can be presented by finite state machines, e.g. finite automata. He gives main definitions and many examples of such systems. He also outlines some of the basic proofs. The area is relatively new and its systematic study began in the mid of 90s by the speaker and Nerode. In recent years there has been an increasing interest in the area due to the following facts. The first order theory of any automata presentable system is decidable. There are some natural characterizations of linearly ordered sets, finitely generated groups, Boolean algebras that have finite automata presentations. If time permits, he will present some of these results. The work is joint with Nerode, Nies, Stephan, and Rubin. |

Title: | TOWARDS AUTONOMOUS NAVIGATION |

Speaker: | Mr Ji Hui |

Date: | 8 March 2006 |

Time: | 10.30am - 11.30am |

Venue: | NIE Journal Room (NIE 5 om (NIE 5-03-04) |

Abstract: | Autonomous navigation in unstructured environments requires that the system can estimate its own motion and the motion of other moving objects and can extract a geometric representation of its environments, which is used to build a map and localize itself within the environment. In this talk, the speaker will describe a number of modules he has developed for visual navigation. Firstly, he will show a new approach to segmentation, motion and structure estimation from a video sequence in a feed-back loops instead of in the classical feed-forward manner. In particular, he will discuss a new constraint to estimate 3D motion by combining all available images through shape information. Also, a new fractal-based texture descriptor will be discussed. Its invariance to the changes of viewpoint and lighting makes it ideal for matching and recognizing large scene structure in autonomous navigation. Lastly, he will describe his work on visual illusions for better understanding how human perform these visual tasks, which brings up important principles and paradigms on designing and engineering visual navigation system. |

Title: | Symplectic reflection algebras and Symplectic reflection algebras and
quantum Hamiltonian reduction |

Speaker: | Dr Gan Wee Liang |

Date: | 1 March 2006 |

Time: | 1.30pm - 2.30pm |

Venue: | NIE Journal Room (NIE 5 -03 -04) |

Abstract: | Symplectic reflection algebras of wreath-product type give non-commutative deformations of the symmetric products of Kleinian singularities. The representation theory of these algebras is expected to be closely related to the geometry of Hilbert schemes of points on minimal resolutions of the Kleinian singularities. The speaker will give an overview of some recent developments. |

Title: | Classical and Quantum Function Reconstruction in Finite Fields |

Speaker: | Professor Igor Shparlinski |

Date: | 10 February 2006 |

Title: | Introduction to Public
Key Cryptography |

Speaker: | Professor Igor Shparlinski |

Date: | 8 February 2006 |

Time: | 1.30pm - 2.30pm |

Venue: | NIE 5-03-04 (Journal Room) |

Abstract: | The speaker will explain main tasks and constructions in public key cryptography. He will also outline several attacks on these constructions which can be launched if they are used carelessly. No preliminary knowledge is assumed but some familiarity with elementary algebra and number theory (such as congruences) will be helpful. This talk is intended specially for students. |

Title: | An Efficient Estimation
Procedure for Semiparametric
Models |

Speaker: | Dr Wenyang Zhang |

Date: | 1 February 2006 |

Time: | 1.30pm - 2.30pm |

Venue: | NIE 5-03-04 (Journal Room) |

Abstract: | Maximum likelihood estimation is the most powerful estimation method when the joint distribution of samples is available. Traditional parametric modelling assumes the samples come from a specific distribution family, and estimate the unknown parameters based on the samples. However, in reality, we don't know which distribution family the samples come from. Misspecification can result in biased estimator. Nonparametric modelling makes no assumptions on the model specification. However, there are more unknown stuffs to be estimated in nonparametric models, which would pay the price on the variance side. Even worse, when the dimension of the covariate is large we cannot implement the standard nonparametric modelling due to ``curse of dimensionality". A promising idea in statistical modelling is to relax the restrictions imposed on the classic parametric models to make model specification more flexible. In this talk, the speaker is going to present a hybrid model of parametric and nonparametric models. He will introduce an efficient estimation method for the proposed model. He will show that the proposed estimator of unknown constant has convergence rate of $n^{1/2}$, the estimator of unknown function enjoys oracle property. He will also show how to construct AIC, BIC and Cross-validation for the proposed model. Finally, he is going to use the proposed model together with the estimation method to analyse the infant mortality data from China |

Title: | HOMOGENEOUS CONE OPTIMIZATION HOMOGENEOUS CONE OPTIMIZATION |

Speaker: | Dr Chua Chek Beng |

Date: | 25 January 2006 |

Time: | 1.30pm - 2.30pm |

Venue: | SBS-01n-28 |

Abstract: | Homogeneous cone optimization (also known as linear optimization over homogeneous cones) is an extension of linear optimization where all linear inequality constraints are replaced by a linear conic constraint involving a homogeneous cone. While it is a large class of optimization that includes semidefinite optimization and convex quadratic optimization (and much more), homogeneous cone optimization is almost never used in practice for two reasons: 1) all homogeneous cone optimization problems can be modeled (hence solved) as semidefinite optimization problems, and 2) there is a lack of development of primal-dual algorithms for homogeneous cone optimization. In this talk, the speaker will present a few interesting practical optimization problems that can be naturally modeled by homogeneous cone optimization. This will be followed with a presentation of recent research on primal-dual algorithms for homogeneous cone optimization. |

Title: | WHY DIDN’T THE SUPERSONIC CAR FLY! |

Speaker: | Professor Oubay Hassan |

Date: | 20 January 2006 |

Time: | 11.30am - 12.30pm |

Venue: | SBS-01N-28 |

Abstract: | The lecture will describe how computer simulation has been used to design the first car to travel faster than the speed of sound – that is to travel at a supersonic speed. Following a brief history of the land speed record the technical challenges that arise in the design of aeroplanes and cars that travel at supersonic speeds will be introduced. It will be shown that computer simulation of airflow, coupled with the use of high performance computers, is now a critical technology in aerodynamic design. The talk will also provide a brief overview of this new and exciting computer simulation technology and will illustrate, by the use of video clips and computer animation and visualisation, various fields where this technology has become an integral part of the design cycle. |