# Seminars 2013

Title: | The Bayesian approach to inverse problems |

Speaker: | Professor Andrew M. Stuart |

Date: | 3 December 2013 |

Time: | 4.00pm – 5.00pm |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Abstract: | Probabilistic thinking is of growing importance in many areas of mathematics. In this talk I will demonstrate the beautiful mathematical framework, coupled with practical outcomes, which results from thinking probabilistically about inverse problems. Many inverse problems in the physical sciences require the determination of an unknown field from a finite set of indirect measurements. Examples include oceanography, oil recovery, water resource management and weather forecasting. In the Bayesian approach to these problems, the unknown and the data are modelled as a jointly varying random variable, and the solution of the inverse problem is the distribution of the unknown given the data. This approach provides a natural way to provide estimates of the unknown field, together with a quantification of the uncertainty associated with the estimate. It is hence a useful practical modeling tool. However it also provides a very elegant mathematical framework for inverse problems: whilst the classical approach to inverse problems leads to ill-posedness, the Bayesian approach leads to a natural well-posedness and stability theory. I will overview this mathematical framework. |

Title: | Order of convergence of splitting schemes for both deterministic and stochastic nonlinear Schrodinger equations |

Speaker: | Assistant Professor LIU Jie |

Date: | 28 November 2013 |

Time: | 10.30am – 11.30am |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Abstract: | We first prove the second order convergence of the Strang-type splitting scheme for the nonlinear Schrodinger equation. The proof does not require commutator estimates but crucially relies on an integral representation of the scheme. It reveals the connection between Strang-type splitting and the midpoint rule. We then show that the integral representation idea can also be used to study the stochastic nonlinear Schrodinger equation with multiplicative noise of Stratonovich type. Even though the nonlinear term is not globally Lipschitz, we prove the first order convergence of a splitting scheme of it. Both schemes preserve the mass. They are very efficient because they use explicit formulas to solve the subproblems containing the nonlinear or the nonlinear plus stochastic terms. |

Title: | Implicit/Explicit Schemes for the Navier-Stokes Equations |

Speaker: | Professor Yinnian He |

Date: | 17 October 2013 |

Time: | 3.30pm – 4.30pm |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Abstract: | In this work, we present the fully discrete implicit/explicit schemes for the Navier-Stokes equations. Also, we prove the stabilities and optimal error estimates under the corresponding stability conditions, where the schemes are almost unconditionally stable and convergent for the smooth initial data u_0 in H^2, i.e., the time step size is less than or equivalent to C_0; and the schemes are almost weak unconditionally stable and convergent for the non-smooth initial data u_0 in H^1, i.e., the time step size is less than or equivalent to C_0|log h| for the mesh size 0<h<1; and the schemes are conditionally stable for the non-smooth initial data u_0 in L^2, i.e., the time step size less than or equivalent to C_0 h^2. |

Title: | Why I Care About Derivatives |

Speaker: | Dr Douglas Streeter Rolph |

Date: | 9 October 2013 |

Time: | 1.30pm – 2.30pm |

Venue: | SPMS-LT4 (03-09) |

Abstract: | Dr Streeter will be talking about the duration of a bond, which is a concrete example of a derivative of a function. And how derivative measures the sensitivity of the function to small changes in the variable. |

Title: | Modeling Rare Events in Complex Systems |

Speaker: | Associate Professor Ren Weiqing |

Date: | 26 September 2013 |

Time: | 3.30pm – 4.30pm |

Venue: | MAS Executive Classroom 2 (SPMS-MAS-03-07) |

Abstract: | Many problems arising from applied sciences can be abstractly formulated as a system that navigates over a complex energy landscape of high or infinite dimensions. Well known examples include nucleation events during phase transitions, conformational changes of bio-molecules, chemical reactions, etc. The system is confined in metastable states for long times before making transitions from one metastable state to another. The disparity of time scales makes the study of transition pathways and transition rates a very challenging task. In this talk, I will present the string method for the study of complex energy landscapes and the associated transition events. |

Title: | Why I Care About Derivatives |

Speaker: | Dr Douglas Streeter Rolph |

Date: | 18 September 2013 |

Time: | 1.30pm – 2.30pm |

Venue: | LT 23 – South Spine |

Abstract: | Dr Streeter will be talking about the duration of a bond, which is a concrete example of a derivative of a function. And how derivative measures the sensitivity of the function to a small changes in the variable. |

Title: | Why I Care About Matrices |

Speaker: | Mr Jan Hakenberg |

Date: | 5 September 2013 |

Time: | 1.30pm – 2.30pm |

Venue: | SPMS LT4 (SPMS-03-09) |

Abstract: | Matrices teach me how to rotate things. And here's what you can expect: Affine transformations, infinite products of matrices, curve subdivision and surface subdivision in matrix form, affine transformations in cimputer graphics in 2D/3D, configuration of rigid bodies in 2D/3D. |

Title: | Euclidean Functions of Computable Euclidean Domains |

Speaker: | Professor Rod Downey |

Date: | 12 September 2013 |

Time: | 4pm – 5pm |

Venue: | MAS Executive Classroom 2 (SPMS-MAS-03-07) |

Abstract: | This talk treats the security when a given random number is partially leaked to a third party. In this one of the first algorithms discussed in almost any elementary algebra course is Euclid's algorithm for computing the greatest common divisor of two integers. In a first course in abstract algebra, this idea is explained by describing both Z and Q[X] as Euclidean domains. Recall the definition of Euclidean domains: Definition: A commutative ring R is a Euclidean domain if R is an integral domain and there is a function f from R/{0} to N, the set of natural numbers, such that for any a, d in R, if d is not zero, then there exists a q in R such that either a+qd=0 or f(a+qd)<f(d). The function f is called a (finitely-valued) Euclidean function for R. |

Title: | MD Simulations for Motions of Evaporative Droplets Driven by Thermal Gradients |

Speaker: | Associate Professor Congmin Wu |

Date: | 29 August 2013 |

Time: | 3.30pm – 4.30pm |

Venue: | MAS Executive Classroom 2 (SPMS-MAS-03-07) |

Abstract: | The driving mechanism of fluid transport at nanoscale is one of the key problems on the design of micro-and nanofluidic devices. We performed molecular dynamics simulations to study the motions of evaporative droplets driven by thermal gradients along nanochannels. The effect of droplet size and the effect of the co-existent fluid temperature on the motions of droplets are investigated. The molecular dynamics simulations presented provide a series of numerical experiments to semi-quantitatively confirm the physical mechanism proposed in the continuum model and simulations (Xu and Qian 2012 Phys. Rev. E 85 061603). This is a joint work with Xinpeng Xu and Tiezheng Qian from HKUST. |

Title: | Truthful Approximations to Range Voting |

Speaker: | Professor Peter Bro Miltersen |

Date: | 20 August 2013 |

Time: | 3.00pm – 4.00pm |

Venue: | MAS Executive Classroom 1 (SPMS-MAS-03-06) |

Abstract: | We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare maximization in this setting. With m being the number of alternatives, we exhibit a randomized truthful-in-expectation ordinal mechanism implementing an outcome whose expected social welfare is at least an Omega(m^{-3/4}) fraction of the social welfare of the socially optimal alternative. On the other hand, we show that for sufficiently many agents and any truthful-in-expectation ordinal mechanism, there is a valuation profile where the mechanism achieves at most an O(m^{-{2/3}) fraction of the optimal social welfare in expectation. We get tighter bounds for the natural special case of m = 3, and in that case furthermore obtain separation results concerning the approximation ratios achievable by natural restricted classes of truthful-in-expectation mechanisms. In particular, we show that for m = 3 and a sufficiently large number of agents, the best mechanism that is ordinal as well as mixed-unilateral has an approximation ratio between 0.610 and 0.611, the best ordinal mechanism has an approximation ratio between 0.616 and 0.641, while the best mixed-unilateral mechanism has an approximation ratio bigger than 0.660. In particular, the best mixed-unilateral non-ordinal (i.e., cardinal) mechanism strictly outperforms all ordinal ones, even the non-mixed-unilateral ordinal ones. This is joint work with Aris Filos-Ratsikas. |

Title: | Estimation in Nonlinear Regression with Harris Recurrent Markov Chains |

Speaker: | Dr Degui Li |

Date: | 15 August 2013 |

Time: | 2.00pm – 3.00pm |

Venue: | MAS Executive Classroom 2 (SPMS-MAS-03-07) |

Abstract: | In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory for the proposed estimators. Our results show that the convergence rates for the estimators rely not only on the properties of the nonlinear regression function, but also on the number of regenerations for the Harris recurrent Markov chain. We also discuss the estimation of the parameter vector in a conditional volatility function and its asymptotic theory. Furthermore, we apply our results to the nonlinear regression with I(1) processes and establish an asymptotic distribution theory which is comparable to that obtained by Park and Phillips (2001). Some numerical studies are provided to illustrate the proposed approaches and results. |

Title: | Shrinkage Estimation of Nonlinear Models |

Speaker: | Dr Jiang Qian |

Date: | 7 August 2013 |

Time: | 2.00pm – 3.00pm |

Venue: | MAS Executive Classroom 2 (SPMS-MAS-03-07) |

Abstract: | Recent developments in shrinkage estimation are remarkable. Capable of shrinking some coefficients to exactly 0, the penalized approach combines continuous shrinkage with automatic variable selection. In this talk, I will discuss the methodology and application of the shrinkage estimation from the following two aspects. 1. We propose to employ the adaptive LASSO approach in threshold variable selection of smooth threshold autoregressive (STAR) model. Moreover, by penalizing the direction of the coefficient vector in this nonlinear model, the threshold variable is more accurately selected. 2. We propose a novel varying coefficient model, called principal varying coefficient model (PVCM), by characterizing the varying coefficients through linear combinations of a few principal functions. Model estimation and identification are investigated, and the better estimation efficiency is justified theoretically. Incorporating the estimation with the - penalty, variables in the linear combinations can be selected automatically and hence the estimation efficiency can be further improved. Numerical experiments suggest that the model together with the estimation method are useful even when the number of covariates is large. |

Title: | Secure key generation in the classical and quantum settings |

Speaker: | Professor Masahito Hayashi |

Date: | 16 July 2013 |

Time: | 2.00pm – 3.00pm |

Venue: | MAS Executive Classroom 1 (SPMS-MAS-03-06) |

Abstract: | This talk treats the security when a given random number is partially leaked to a third party. In this case, applications of hash functions generate secure key. We investigate what kinds of hash function are useful for this purpose. We also discuss how to evaluate the security quantitatively. In the beginning part, we discuss the classical setting. In the next part, we treat the quantum setting, which is important for quantum key distribution. |

Title: | Topological / Geometrical Methods and Data Structures for Real-World Data Analysis |

Speaker: | Associate Professor François Anton |

Date: | 26 June 2013 |

Time: | 10.30am – 11.30am |

Venue: | MAS Executive Classroom 1 (SPMS-MAS-03-06) |

Abstract: | This presentation will start by introducing interval analysis as well as continuous deformations of functions and topological spaces (homotopies). We will then present several applications of interval valued homotopies to data analysis in different fields: 3D/4D reconstruction using multi-beam echo sounder acoustic data and power and radiation emulation of hand-held devices. We will conclude this presentation with new potential applications of topological/geometric methods and data structures to data analysis. |

Title: | Factor Copula Models for Item Response Data |

Speaker: | Dr Nikoloulopoulos |

Date: | 13 June 2013 |

Time: | 4.00pm – 5.00pm |

Venue: | MAS Executive Classroom 2 (SPMS-MAS-03-07) |

Abstract: | Factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item response. The factor copula models have interpretations of latent maxima/minima (in comparison with latent means) and can lead to more probability in the joint upper and/or lower tail compared with factor models based on the discretized multivariate normal distribution (or multidimensional normal ogive model). Details on maximum likelihood estimation of parameters for the factor copula model are given, as well as analysis of the behavior of the log-likelihood. Our general methodology is illustrated with several item response data sets and it is shown that there is a substantial improvement on existing models both conceptually and in fits to data. This talk will be based on collaborative work with Harry Joe (U. of British Columbia). |

Title: | Crossing Numbers |

Speaker: | Professor Gelasio Salazar |

Date: | 6 June 2013 |

Time: | 4.00pm – 5.00pm |

Venue: | MAS Executive Classroom 1 (SPMS-MAS-03-06) |

Abstract: | In many applications of graph drawing and visualization, it is desirable to find representations (drawings) of graphs in the plane with as few as possible crossings among edges. The crossing number cr(G) of a graph G is the minimum number of edge crossings in a drawing of G in the plane. In this talk we will review the history of crossing numbers, whose origins can be traced to a question raised by Zarankiewicz while he did forced labor in a concentration camp in World War II. We will also review some of the most common crossing number variants (such as the rectilinear crossing number and the book crossing number), and their surprising connections with long standing, important open problems in other branches of mathematics, such as discrete geometry and geometric probability. |

Title: | Mitigate Delays and Unfairness in Appointment Systems |

Speaker: | Ms. Jin Qi |

Date: | 28 May 2013 |

Time: | 2.00pm – 3.00pm |

Venue: | MAS Executive Classroom 2 (SPMS-MAS-03-07) |

Abstract: | In this presentation, we discuss a general scheduling model, which is applicable in outpatient clinics to design consultation slots and operating theatres to deliver an efficient and smooth schedule. We consider a system where heterogeneous patients are sequenced and scheduled for medical care. As care times are uncertain, the aim is to mitigate the unpleasantness experienced by patients when their waiting times or delays exceed acceptable thresholds, and by doctors when they work overtime. We also address fairness concerning balance of service levels among patients. In evaluating uncertain delays, we propose the Delay Unpleasantness Measure (DUM), which takes into account the frequency and intensity of delays above a threshold. We also introduce the concept of lexicographic min-max fairness to design scheduling systems from the perspective of the worst-off participants. The performance measure we established is consistent with hospitals’ key performance indicators in providing patients service commitments. This is joint work with Professor Melvyn Sim. |

Title: | CBMF : A Clustering Approach to Binary Matrix Factorization |

Speaker: | Dr Peng Jiming |

Date: | 27 May 2013 |

Time: | 2.00pm – 3.00pm |

Venue: | MAS Executive Classroom 2 (SPMS-MAS-03-07) |

Abstract: | In general, binary matrix factorization (BMF) refers to the problem of finding a matrix product of two binary low rank matrices such that the difference between the matrix product and a given binary matrix is minimal. As an important tool in dimension reduction for high-dimensional data sets with binary attributes, BMF has been widely and successfully used in various applications. In this talk, we first introduce two new constrained BMF models (called CBMF) and discuss their relation to other dimensional reduction models such as unconstrained BMF (UBMF). Then we propose alternating update procedures for CBMF. In every iteration of the proposed procedure, we solve a specific binary linear programming (BLP) problem to update the involved matrix argument. By exploring the interrelation between the BLP subproblem and clustering, we develop both efficient deterministic and randomized approximation algorithms for CBMF. An effectitive algorithm for UBMF is also developed. We conclude the talk by presenting numerical results obtained from applying the new models and algorithms on data mining applications in bioinformatics and document clustering. |

Title: | The Hardest Math I've Ever Really Used |

Speaker: | Professor Dror Bar-Natan |

Date: | 23 May 2013 |

Time: | 10.30am – 11.30am |

Venue: | MAS Executive Classroom 1 (SPMS-MAS-03-06) |

Abstract: | What's the hardest math I've ever used in real life? Me, myself, directly - not by using a cellphone or a GPS device that somebody else designed? And in "real life" - not while studying or teaching mathematics? I use addition and subtraction daily, adding up bills or calculating change. I use percentages often, though mostly it is just "add 15 percents". I seldom use multiplication and division: when I buy in bulk, or when I need to know how many tiles I need to replace my kitchen floor. I've used powers twice in my life, doing calculations related to mortgages. I've used a tiny bit of geometry and algebra for a tiny bit of non-math-related computer graphics I've played with. And for a long time, that was all. In my talk I will tell you how recently a math topic discovered only in the 1800s made a brief and modest appearance in my non-mathematical life. There are many books devoted to that topic and a lot of active research. Yet for all I know, nobody ever needed the actual formulas for such a simple reason before. Hence we'll talk about the motion of movie cameras, and the fastest way to go from A to B subject to driving speed limits that depend on the locale, and the "happy segway principle" which is a the heart of the least action principle which in itself is at the heart of all of modern physics, and finally, about that funny discovery of Janos Bolyai's and Nikolai Ivanovich Lobachevsky's, that the famed axiom of parallels of the ancient Greeks need not actually be true. For more info, please refer to : http://www.math.toronto.edu/~drorbn/Talks/Singapore-1305/ |

Title: | Non-commutative Gaussian Elimination and Rubik’s Cube |

Speaker: | Professor Dror Bar-Natan |

Date: | 22 May 2013 |

Time: | 10.30am – 11.30am |

Venue: | SPMS-LT3 (SPMS-03-02) |

Abstract: | A simple generalization of Gaussian elimination to a non-commutative setting allows us to solve the cube and a dozen other permutation group puzzles in no effort at all. This should be a fun talk, accessible to undergraduates with some knowledge of and interest in group theory, and its applications. |

Title: | Trees and Wheels and Balloons and Hoops |

Speaker: | Professor Dror Bar-Natan |

Date: | 21 May 2013 |

Time: | 10.30am – 11.30am |

Venue: | MAS Executive Classroom 1 (SPMS-MAS-03-06) |

Abstract: | Balloons are two-dimensional spheres. Hoops are one dimensional loops. Knotted Balloons and Hoops (KBH) in 4-space behave much like the first and second fundamental groups of a topological space - hoops can be composed like in π1, balloons like in π2, and hoops "act" on balloons as π1 acts on π2. We will observe that ordinary knots and tangles in 3-space map into KBH in 4-space and become amalgams of both balloons and hoops. We give an ansatz for a tree and wheel (that is, free-Lie and cyclic word) -valued invariant ζ of KBHs in terms of the said compositions and action and we explain its relationship with finite type invariants. We speculate that ζ is a complete evaluation of the BF topological quantum field theory in 4D, though we are not sure what that means. We show that a certain "reduction and repackaging" of ζ is an "ultimate Alexander invariant" that contains the Alexander polynomial (multivariable, if you wish), has extremely good composition properties, is evaluated in a topologically meaningful way, and is least-wasteful in a computational sense. If you believe in categorification, that's a wonderful playground. |

Title: | Algebraic Coding Theory over Rings |

Speaker: | Professor Marcus Greferath |

Date: | 20 May 2013 |

Time: | 3.00pm – 4.00pm |

Venue: | MAS Executive Classroom 1 (SPMS-MAS-03-06) |

Abstract: | Ring-linear algebraic coding theory gained importance at the beginning of the previous decade, when it was discovered that certain non-linear binary codes of high quality could be understood as linear codes over the ring of integers modulo 4. This talk gives some insight into this amazingly beautiful chapter of applied algebra. We will report on a collection of results from the literature and from our own previous and current research. |

Title: | Variance Decomposition of Dividend-Price-Ratios and Long-Term Income-Oriented Asset Allocation |

Speaker: | Prof. Dr. Dietmar Hillebrand |

Date: | 9 May 2013 |

Time: | 2.00pm – 3.00pm |

Venue: | MAS Executive Classroom 2 (SPMS-MAS-03-07) |

Abstract: | Fundamental ratios of stocks like the dividend-price ratio contain information about future dividend growth or future returns. In this talk I present estimates for the german stock market: In the cross section the dividend-price ratio forecasts mainly future dividend growth, whereas in the time series it predicts future returns. Building on this, I argue that short-term volatility in equity markets can – to a degree – be ignored by long-term investors. An income-oriented asset allocation based on dividend-price ratio signals is constructed that is compared with the widely used rolling over of 10 year government bonds. |

Title: | Integral Equation Methods for Fourth Order PDEs |

Speaker: | Associate Professor Shidong Jiang |

Date: | 7 May 2013 |

Time: | 3.30pm – 4.30pm |

Venue: | MAS Executive Classroom 1 (SPMS-MAS-03-06) |

Abstract: | In this talk, we will discuss integral equation methods for solving certain boundary value problems of fourth order PDEs. In particular, we will present stable second kind integral equation (SKIE) formulations for the first Dirichlet problem of the biharmonic equation in three dimensions and the fluid problem of the modified biharmonic equation in two dimensions. A fast algorithm based on randomized matrix compressions has been constructed for the first problem and a high order discretization scheme has been developed for the second problem. Several numerical examples are provided to illustrate the performance of the overall algorithm. |

Title: | Computation of Maxwell Singular Solution by Nodal-Continuous Elements |

Speaker: | Professor Huoyuan Duan |

Date: | 3 May 2013 |

Time: | 3.30pm – 4.30pm |

Venue: | MAS Executive Classroom 1 (SPMS-MAS-03-06) |

Abstract: | In computational electromagnetism, whenever the physical domain is nonsmooth, with reentrant corners and edges, Maxwell solution may exhibit strong singularity in the vicinity of the reentrant corners and edges. Mathematically, the Maxwell solution does not belong to1()H space (A Hilbert space in which the functions as well as their gradients are square integrable), instead, it may only be in a fractional-order Hilbert space()rH, for some real number r<1. Such ( ) r H is an intermediate between 20()()LH and1()H, where 2()L is a Hilbert space of square integrable functions. In other words, the gradient of the solution is not longer square integrable. As is well-known, the finite element method of Lagrange nodal-continuous elements has been prevailing in the area of numerical solutions of partial differential equations, such as computational fluid dynamics and computational mechanics( solid mechanics and structure mechanics). Unfortunately, this finite element method was never genuinely successful in computational electromagnetism, so long as the strong singular solution exists (This is the case for nonsmooth domains, such as nonconvex polygon). Unexpectedly, until the last decade, have several theoretically and numerically successful nodal-continuous finite element methods been available. In my talk, the speaker will report a number of numerical results of the so-called L2-projection method, the original creative research of this speaker and co-authors in recent years. The idea of the L2-projection method lies in applying L2 projectors to the curl and the divergence operators (These two operators characterize the physical nature of electromagnetic phenomenon of electrical field and magnetic field). So, whatever the solution is, it is approximated in the 2L () space and even in the 1()L space (A Lebesgue integrable space ). In essence, like Dirac solution (It is not a member of 1()L space), the L2 projection method can work as well. Numerical experiments in my talk will include source problem and eigenvalue problem (in homogeneous or nonhomogeneous media). |

Title: | Nerve Cell Model and Asymptotic Expansions |

Speaker: | Associate Professor Yasushi Ishikawa |

Date: | 2 May 2013 |

Time: | 3.00pm – 4.00pm |

Venue: | MAS Executive Classroom 1 (SPMS-MAS-03-06) |

Abstract: | We construct a nerve cell model with a stochastic noise based on the simplified Hodgkin-Huxley model. In this model the noise factor consists of the jump-diffusion with a small parameter epsilon. Here the diffusion part consists of the Wiener process with variable coefficient, and the jump part consists of the compound Poisson process. We make compositions of noise processes with functions (tempered distributions). Using Malliavin calculus for jump-diffusion processes, we make an asymptotic expansion associated with this model as epsilon tends to 0. |

Title: | A Unified View of Design Optimization under Uncertainty |

Speaker: | Professor K. Ponnambalam |

Date: | 2 May 2013 |

Time: | 4.00pm - 5.00pm |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Abstract: | Many engineering design problems require optimization but must deal with uncertainty. When design variables are uncertain, for example, due to imperfections in manufacturing, robust optimization techniques such as design centering is commonly used. We have used copulas to extend these techniques for general classes of randomness. In another class of problems, decision variables are deterministic such as investments in portfolio optimization problems, but data uncertainties must be considered. Many well known stochastic programming methods can tackle these problems. In this talk I will provide a unified framework so that robust optimization methods can be applied in the latter class of problems and provide pathways to develop new methods. |

Title: | Accurate Genome-Wide Survival Analysis of Somatic Mutations in Cancer |

Speaker: | Assistant Professor Fabio Vandin |

Date: | 16 April 2013 |

Time: | 4.00pm - 5.00pm |

Venue: | MAS Executive Classroom 1, MAS-03-06 |

Abstract: | Deriving clinical utility from large genomic datasets requires the identification of statistically significant associations between genomic measurements and a clinical phenotype. An important instance of this problem is to identify genetic variants that distinguish patients with different survival time following diagnosis or treatment. The most widely used statistical test for comparing the survival time of two (or more) classes of samples is the nonparametric log-rank test. Nearly all implementations of the log-rank test rely on the asymptotic normality of the test statistic. However, this approximation gives poor results in many high-throughput genomics applications where: (i) the populations are unbalanced; i.e. the population containing a given variant is significantly smaller than the population without that variant; (ii) one tests many possible variants and is interested in those variants with very small p-values that remain significant after multi-hypothesis correction. Our contributions are: (1) We show empirically that the inaccuracy of the asymptotic approximation for the log-rank test results in a large number of false positives in cancer genomics applications due to unbalanced populations, and that among the two exact distributions (permutational and conditional) proposed in the literature, the permutational distribution provides a more accurate approximation of the true p-values. (2) We develop and analyze a novel fully polynomial time approximation scheme (FPTAS) for computing the p-value of the log-rank statistic for any range of population sizes under the exact permutational distribution. (3) We demonstrate the practicality and accuracy of our approach by testing the algorithm on somatic mutation data from The Cancer Genome Atlas (TCGA). |

Title: | Privacy Enhancing Technologies – Where Cryptology Meets Privacy |

Speaker: | Professor Bart Preneel |

Date: | 8 April 2013 |

Time: | 10.30am - 11.30am |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Abstract: | This talk discusses how the advances in technology are gradually erasing our privacy. It attempts to define privacy and debunk some widely held beliefs about privacy concepts. Next we evaluate how privacy enhancing technologies can complement an approach based on regulation. In particular, we present a few examples of data minimization that fall under the broader concept of privacy by design. We conclude by assessing the potential impact of privacy risks for society at large. |

Title: | Optimizing Organ Exchange System-Celebrating the 2012 Nobel Prize in Economics |

Speaker: | Professor Peter X. K. Song |

Date: | 13 March 2013 |

Time: | 3.30pm - 4.30pm |

Venue: | MAS Executive Classroom 1, MAS-03-06 |

Abstract: | The 2012 Nobel Prize in Economics is awarded to Alvin E. Roth and Lloyd S. Shapley for the theory of stable allocations and the practice of market design. The most influential work made by Alvin Roth was his seminal theory of matching organ donors with patients. This novel empirical study has provided and enhanced Shapley's basic theory and the application of Gale-Shapley algorithm in medical practice of organ exchanges. In this talk, I will first present an overview of Alvin Roth's classical static organ exchange system, including graphic formulation and integer programming optimization. I will then introduce our recent work on probabilistic organ exchange systems and optimal strategies of matching organs from living donors with biologically unrelated recipients. Through various microsimulation models, I will show that our new organ donation system outperforms Roth's organ donation system. |

Title: | Factors Related to Police Attendance at Crash Scene |

Speaker: | Dr Chan Siew Pang |

Date: | 4 February 2013 |

Time: | 2.00pm - 3.00pm |

Venue: | MAS Executive Classroom 2, MAS-03-07 |

Abstract: | Police attendance at a motor vehicle crash scene is important for investigating the causes, reducing the likelihood of a secondary crash, managing traffic and reducing congestion. However, the majority of the crashes in most jurisdictions are not attended by the police and very little research has been conducted to examine the factors contributing to the decision. With the help of conventional statistical analysis and classification trees, this study finds that roadway, environment, driver, vehicle and crash characteristics have significant effects on the likelihood of police attendance at a crash scene. |

Title: | Specification Testing Driven by Orthogonal Series for Nonstationary Time Series |

Speaker: | Professor Gao Jiti |

Date: | 23 January 2013 |

Time: | 4.30pm - 5.30pm |

Venue: | MAS Executive Classroom 1, MAS-03-06 |

Abstract: | This paper establishes two simple and new specification tests based on the use of an orthogonal series. The paper then establishes an asymptotic theory for each of the proposed tests. The first test is initially proposed for the case where the regression function involved is integrable and the second test is established to cover a class of non-integrable functions. The finite sample performance of the proposed tests is examined through using several simulated examples. Meanwhile, we employ the second test to check whether a commonly used linear model is appropriate for modeling the relationship between the United States consumers' consumption expenditure and disposable income over the time period of 1960-2009. Our experience shows that the proposed tests are easily implementable and also have stable sizes and good power properties even when the 'distance' between the null hypothesis and a sequence of local alternatives is asymptotically negligible. |

Title: | The arithmetic of arithmetic hyperbolic Coxeter's groups |

Speaker: | Associate Professor Marty Weissman |

Date: | 14 January 2013 |

Time: | 11.30am - 12.30pm |

Venue: | MAS Executive Classroom 1, MAS-03-06 |

Abstract: | In the 1990s, John Conway used a ternary regular tree to visualize the classical theory of binary quadratic forms. After covering some highlights of Conway's "topograph," I will introduce a more general framework of arithmetic Coxeter's groups. These yield more general "topographs" which have been used most recently by Savin and Bestvina to study binary Hermitian forms. This talk will be accessible to advanced undergraduates. |

Title: | Conformal Invariance of the Exploration Path in 2D Critical Bond Percolation in the Square Lattice |

Speaker: | Dr Phillip Yam |

Date: | 10 January 2013 |

Time: | 2.30pm - 3.30pm |

Venue: | MAS Executive Classroom 1, MAS-03-06 |

Abstract: | In this talk, I shall outline a proof of the convergence of the critical bond percolation exploration process on the square lattice to the trace of SLE6. This is an important conjecture in mathematical physics and probability. The case of critical site percolation on the hexagonal lattice was established in the seminal work of Smirnov via proving Cardys formula. However, our proof relies on a series of transformations that allow us to apply the convergence in the site percolation case on the hexagonal lattice to obtain certain estimates that is enough for us to prove the convergence in the case of bond percolation on the square lattice. |