## Seminars 2009

Title: | Duality of function spaces: Results, methods and applications |

Speaker: | Professor Alexander V. ABANIN |

Date: | 9 December 2009 |

Time: | 10.30am - 11.30am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | As it is well known, in the theory of distributions and its applications, the Paley-Wiener-Schwarts theorem plays a significant role. This theorem establishes a duality, via Fourier-Laplace transformation, between the family of all distributions with compact support and the certain space of entire functions of exponential type. We give an overview of some recent results devoted to the duality problem for wide classes of ultradistributions and analytic functionals and show how these results help us to solve some problems concerning convolution equations and Whitney's extension theorems. Also, it will pose some prospects and problems for further development of duality type theorems and their applications. |

Title: | Nonlinear Absorbing Boundary Conditions for Some Time-dependent PDEs on Unbounded Domains |

Speaker: | Dr Zhang Jiwei |

Date: | 2 December 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Many physical phenomena are modeled by the time-dependent PDEs on unbounded domain such as semilinear parabolic equations with blow-up solution, nonlinear Schr\”odinger equation and so on. This talk will emphasize the numerical solution of this kind of nonlinear PDEs on unbounded spatial domain. The focus of the presentation is on the derivation of absorbing boundary conditions for one-dimensional and two-dimensional domains, which can be extended to high-dimensions. |

Title: | Low Correlation Zone Sequences |

Speaker: | Dr Udaya Parampalli |

Date: | 26 November 2009 |

Time: | 10.30am - 11.30am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Low correlation zone (LCZ) sequences were introduced to address a specific requirement of a generalized quasisynchronous code-division multiple access (QS-CDMA) communication system. In this talk, I will introduce the problem of low correlation zone sequence design and present basic schemes using Interleaving techniques. The low correlation zone requirement presents new challenges in the area of bounds involving family size and low correlation parameters. I will talk about some of the results on limitations arises from the bounds. There have been several papers dealing with the construction methods involving finite fields, finite rings and several combinatorial objects such as Hadamard matrices. The talk will include key constructions and a brief survey some recent results in the area. |

Title: | The Piecewise Constant Level Set Method with Probability Density Basis |

Speaker: | Professor Li Hongwei |

Date: | 25 November 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | In the Piecewise Constant Level Set Method, the basis (characteristic) functions are polynomials of order $O(N-1)$, where $N$ is the number of phases under consideration. Instead, we propose probability density like functions, which are piecewise polynomials of order two, as the basis. This new basis functions lead to several advantages. The relationship between the new PCLSM and the Zach's method (for Potts model) is to be revealed. Furthermore, we combine the new PCLSM with Zach's method, which results in a very efficient algorithm for the Potts model. Numerical tests will be provided to validate the efficiency. |

Title: | A regularization method based on level-sets for the problem of crack detection from electrical measurements |

Speaker: | Professor Antonio Leitao |

Date: | 11 November 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | We investigate regularization methods for solving the problem of crack detection in bounded planar domains from electrical measurements on the boundary. Based on the level-set approach in [1] and on the regularization strategy in [2], we propose a Tikhonov method for stabilizing the inverse problem. Convergence and stability results for the Tikhonov method are proven. An iterative method of level-set type is derived from the optimality conditions for the Tikhonov functional, and a relation between this method and the iterated Tikhonov method is established. |

Title: | Model-Free Tests for Multiple Forecast Comparison |

Speaker: | Dr Daniel Preve |

Date: | 11 November 2009 |

Time: | 12.00pm - 1.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | This paper describes a simple multivariate version of the Diebold-Mariano test (Diebold & Mariano 1995, DM) for equal predictive accuracy (EPA). Under the null hypothesis of EPA of two or more nonnested forecasting procedures, the proposed Wald-type test statistic has an asymptotic chi-squared distribution. The test statistic is shown to be invariant with respect to the ordering of the forecasting procedures for a wide range of variance-covariance matrix estimators. To explore whether the behavior of the test in small to large-sized samples can be improved, we also show that the finite-sample correction of Harvey, Leybourne & Newbold (1997, HLN) for the DM test extends to our multivariate setting. Additional higher-order corrections are also developed for further potential improvement. Monte Carlo simulations indicate that the proposed test has reasonable size properties in large samples but tends to be oversized in moderate samples. Furthermore, the finite-sample correction of the test succeeds in correcting the size of the test, but only partially. For size-adjusted tests, power is increasing in the sample size, as expected. It is speculated that further finite-sample improvements can be achieved using bootstrap critical values. |

Title: | Robust Interactive Mesh Segmentation Using Fast Geodesic Curvature Flow |

Speaker: | Mr Juyong Zhang |

Date: | 4 November 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | I will present a paper which considers the problem of interactively finding the cutting contour to extract components from a given mesh. Inspired by discretized geodesic curvature flow, we propose a geodesic curvature flow based framework to overcome all these problems. Since in many cases, the meaningful cutting contour on 3D mesh is locally shortest in the sense of some weighted curve length, the geodesic curvature flow is the ideal tool for our problem. It evolves the initial cutting contour to the nearby local minimum. We should mention that the previous numerical scheme, discretized geodesic curvature flow (dGCF), is too slow and has not been applied to mesh segmentation. With a careful observation to dGCF, we devise a fast computation scheme called fast geodesic curvature flow (FGCF), which only needs to solve a less-size and easier problem. Together with the GPU implementation, the FGCF can be solved in a fast manner. Initial cutting contour is generated by a variant of random walks algorithm, which is very fast and gives reasonable cutting result with little user input. We also provide a local editing tool for the user to locally adjust the contour when the current result is not fully satisfactory. Experiment results on the benchmark mesh segmentation data set show that our proposed framework is robust to user input and capable of producing good results reflecting user intention, geometric features and human shape perception. |

Title: | On some applications of stochastic analysis |

Speaker: | Dr Nicolas Privault |

Date: | 30 October 2009 |

Time: | 5.00pm - 6.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Stochastic analysis is a branch of infinite-dimensional analysis that relies on a combined use of analytic and probabilistic tools and has been the object of a rapid development in recent decades. In particular, it has been successfully applied to solve numerous problems related to PDEs, functional inequalities, mathematical finance and extensions of stochastic calculus. In this talk, we will introduce the basic tools of stochastic analysis which consist in a gradient and divergence operator defined on a probability space. And we will also present some of their applications to sensitivity analysis, statistical estimation and stochastic inequalities. |

Title: | Random Matrix Theory: A Wireless Communications Perspective |

Speaker: | Dr Ying-Chang LIANG |

Date: | 20 October 2009 |

Time: | 4.00pm - 5.00pm |

Venue: | SPMS-MAS-03-07, EC2 |

Abstract: | Random matrix theory (RMT) has become an important mathematical foundation for solving many engineering problems. In this talk, we will focus on the applications of RMT in wireless communications. An overview on the random matrix channels in wireless communications will be given first, including multiuser communications, multi-antenna communications and spectrum sensing in cognitive radios. Then, some recent results on applying RMT into each of these areas will be given. |

Title: | Lattice DFT, quadrature and interpolation |

Speaker: | Dr Huiyuan Li |

Date: | 12 October 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | In this talk, a discrete Fourier transform (DFT) associated with lattice tiling is first developed, which leads naturally to trigonometric quadrature and trigonometric interpolation based on the equally spaced points. All three quantities - discrete Fourier transform, quadrature and interpolation are important tools in numerous applications and form an integrated part of the discrete Fourier analysis. We then apply the result to the fundamental domains of several concrete lattices in the plane, providing explicit formulas and detailed analysis. By restricting two functions that are invariant under certain reflection groups, the results can be transformed to results on a triangle that makes up the fundamental domain, which define analogues of cosine and sine functions on the triangle. In particular, a Lagrange interpolation on the triangle is shown to satisfy an explicit compact formula and the Lebesgue constant of the interpolation is shown to be in the order of $\mathcal{O}(\logn)^nd$. We finally define generalized Chebyshev olynomials from those generalized cosine and sine functions respectively and develop the discrete analysis of these algebraic polynomials. We will also touch on the study of common zeros of the generalized Chebyshev polynomials and Gaussian quadrature, a topic that does not seem to have been studied systematically before. |

Title: | Augmented Lagrangian method for ROF, vectorial TV and high order models |

Speaker: | Dr Wu Chunlin |

Date: | 7 October 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | In image restoration such as deblurring and denoising, the ROF, vectorial TV and high order models have been demonstrated to be very successful. However, as they are nonlinear and non-differential, these models are difficult to be efficiently solved by traditional methods such as gradient descent. In this talk, I will present augmented Lagrangian method applied to these models, which dramatically improve the computational efficiency. In our approach, the objective function of each iteration is separated into two sub-problems which can be solved via FFT or a closed form solution. Our method produces much better restoration results in a comparable cpu cost than some Matlab built-in functions. |

Title: | Level set based shape and topology optimization with applications to imaging science |

Speaker: | Professor Michael Hintermüller |

Date: | 7 October 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | After a brief motivation by applied problems in mathematical imaging, the basic tools of shape sensitivity analysis and shape optimization are discussed and their connection to descent algorithms in a level set framework is highlighted. Besides first order (or negative shape gradient) methods, second order techniques (or Newton-like methods) will be introduced. The resulting methodology is then applied to image segmentation problems. In a second part of the talk, the concept of topological sensitivities is introduced and used in addition to the shape calculus to exemplarily solve imaging problems in electrical impedance tomography (EIT). If time permits, this talk shall end with an “exact relaxation” technique to solve binary valued problems in imaging. |

Title: | Statistical Testing for Independence in a Large Panel of Time Series |

Speaker: | Professor Jiti Gao |

Date: | 22 September 2009 |

Time: | 4.00pm - 5.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | In this paper, we propose a new diagnostic test for residual cross- section independence in a nonparametric panel data model. The proposed nonparametric cross-section dependence (CD) test is a nonparametric counterpart of an existing parametric CD test proposed in Pesaren (2004) for the parametric case. We establish an asymptotic distribution of the proposed test statistic under the null hypothesis. As in the parametric case, the proposed test has an asymptotically normal distribution. We then analyze the power function of the proposed test under an alternative hypothesis that involves a nonlinear multi-factor model. We also provide several numerical examples. The small sample studies show that the nonparametric CD test associated with an asymptotic critical value works well numerically in each individual case. An empirical analysis of a set of CPI data in Australian capital cities is given to examine the applicability of the proposed nonparametric CD test. |

Title: | Nucleation of superconductors and liquid crystals |

Speaker: | Professor Pan Xingbin |

Date: | 18 September 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | We will review some of the recent progresses on the mathematical theory of nucleation phenomena of superconductivity and of liquid crystals. We will also discuss the effects of domain geometry and physical parameters to the phase transitions, with emphasis on the analogies between superconductors and liquid crystals. |

Title: | Predictive Fence Methods for Small Area Estimation |

Speaker: | Professor Jiming Jiang |

Date: | 17 September 2009 |

Time: | 4.00pm - 5.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | The fence method is a recently developed strategy for model selection. The idea is to construct a statistical fence to isolate a subgroup of what are called correct models. Once the fence is constructed, the optimal model is selected from those within the fence according to a criterion which can incorporate quantities of practical interest. One advantage of the fence is its flexibility in choosing the measure of lack of fit to address problem of practical interest. In this talk, we show how to derive predictive measures of lack-of-fit to address the main interest in small area estimation, which is estimation of small area means. Simulation results show that the predictive measure makes a significant difference compared with the information criteria and non-predictive fence in situations where a true model does not exist among the candidate models. This is joint work with Thuan Nguyen of Oregon Health and Science University, and Sunil Rao of Case Western Reserve University. |

Title: | A Strong Direct Product Theorem for Disjointness |

Speaker: | Dr Hartmut Klauck |

Date: | 3 September 2009 |

Time: | 10.30am - 11.30am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | A strong direct product theorem says that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then the overall success probability will be exponentially small in k. We establish such a theorem for the randomized communication complexity of the Disjointness problem. This main result also implies a new lower bound for Disjointness in restricted 3-player protocols, and optimal communication-space tradeoffs for Boolean matrix product. Our main result uses a new lower bound method in communication complexity based on linear programming duality, and employs a so-called Intersection Sampling Lemma that generalizes a result by Razborov. |

Title: | Blob-Based Super-Resolution Image Reconstruction |

Speaker: | Dr Ho Yu Tat Edward |

Date: | 2 September 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | A novel approach for super-resolution image reconstruction by incorporating blob-based basis functions to further improve the quality of the reconstruction has been proposed. Blob-based basis functions, which are more commonly known as blobs were derived using a generalization of Kaiser-Bessel basis functions by Lewitt. These spatially localized and rotationally symmetric basis functions have made them very attractive for iterative image reconstruction from projection datasets. In fact, they are equally attractive for super-resolution image reconstruction from multiple low-resolution image datasets. We incorporate the blob-based basis functions into iterative super-resolution image reconstruction and show how they can be used to stabilize the iterative reconstruction at higher numbers of iteration. We also show experimentally that the basis functions are effective in suppressing random image noise and without the need of using a separate prior to regularize the reconstruction. For excessively noisy low-resolution images, we preprocess the datasets before they are used for the super-resolution reconstruction. By incorporating blob-based basis functions into the super-resolution reconstruction framework, we thus guarantee that they can improve the quality of a reconstructed image and save computational time. |

Title: | Patient-specific modelling of cardiovascular and respiratory flow problems-challenges |

Speaker: | Professor Perumal Nithiarasu |

Date: | 19 August 2009 |

Time: | 4.00pm - 5.00pm |

Venue: | SPMS-MAS-03-07, EC2 |

Abstract: | The main challenges of patient-specific fluid dynamics studies are in the translational aspects. Many research groups all over the world are carrying out research in this area but no consistent effort is made in identifying the problems relevant to translational aspects. The translational element consists of two difficulties. They are (i) Technological issues and (ii) Implementation issues. Technological issues are associated with the accuracy and difficulties associated with automating the technology. The implementation issues include the general skepticism and general lack of strong interdisciplinary understanding. This lecture will discuss both aspects in detail. |

Title: | Wavelets and Probability |

Speaker: | Professor Alfredo J. Rios |

Date: | 19 August 2009 |

Time: | 4.00pm - 5.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | The purpose of this talk is to present some connections between the theory of probability and the study of some wavelet series. The list of topics include the study of sets of convergence of wavelet series, the representation problem, tilings of the n-dimensional Euclidean space and Haar-type multivariate series with respect to dilation matrices. |

Title: | Sewing of Riemann surfaces and the fiber structure of Teichmueller space |

Speaker: | Professor David A. A. Radnell |

Date: | 19 August 2009 |

Time: | 2.30pm - 3.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Riemann surfaces with parametrized boundaries can be sewn together using the parametrizations to identify boundary points. The moduli space of these surfaces and the sewing operation are fundamental to two-dimensional conformal field theory. Teichmueller theory is the natural way to solve the complex analytic questions that arise. Moreover, the sewing operation has been applied to give new results in classical Teichmueller theory. A fiber structure and new holomorphic local coordinates for the infinite-dimensional Teichmueller space of bordered Riemann surfaces have been obtained. A brief overview of Teichmueller theory and the relation to conformal field theory will also be given. This is joint work with Eric Schippers. |

Title: | On a kind of nonlinear eigenvalue problem |

Speaker: | Professor Yongqing Li |

Date: | 19 August 2009 |

Time: | 1.00pm - 2.00pm |

Venue: | SPMS-MAS-03-07, EC2 |

Abstract: | By using of critical point theory, we deal with a kind nonlinear eigenvalue problem : $$\left\{\begin{array}{l} -\triangle u-\lambda u= f(x,u)\ \ x\in\Omega\subset \mathbb{R}^N, \\u=0 \ q\hbox{on}\ \partial\Omega \\\int_\Omega|\nabla u|^2-\lambda\int u^2=\alpha \end{array}\right.$$ and obtain some multiple and sign-changing solutions. |

Title: | Survival mixture modelling of recurrent infections |

Speaker: | Professor Andy Lee |

Date: | 18 August 2009 |

Time: | 4.00pm - 5.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Recurrent infections data are commonly encountered in biomedical applications, where the recurrent events are characterised by an acute phase followed by a stable phase after the index episode. Two-component survival mixture models, in both proportional hazards and accelerated failure time settings, are presented as a flexible method of analysing such data. To account for the inherent clustering and dependency of the recurrent observations, random effects are incorporated within the conditional hazard function. Assuming a Weibull or log-logistic baseline hazard in both mixture components of the survival mixture model, an EM algorithm is developed for the residual maximum quasi-likelihood estimation of fixed effect and variance components parameters. Application to model recurrent urinary tract infections for elderly women is illustrated, where significant individual variations are evident at both acute and stable phases. The survival mixture methodology developed enable practitioners to identify pertinent risk factors affecting the recurrent times and to draw valid conclusions inferred from these clustered and heterogeneous survival data. |

Title: | Variational Models for Image Processing and Fast Algorithms |

Speaker: | Professor Ke Chen |

Date: | 14 August 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | In recent years, the interdisciplinary field of imaging science has been experiencing an explosive growth in research activities including more models being developed, more publications generated, and above all wider applications attempted. In this talk I shall first give an overview of the various imaging work carried out in our Liverpool group, some with collaborations with UCLA (T F Chan), CUHK (R H Chan) and Bergen/NTU (X C Tai) and several colleagues from other departments in Liverpool. Then I shall focus the recent work on a working multilevel algorithm for the total variation model of combined denoising and deblurring of images. Although the model by Osher et al is nearly 20 years old, no working nonlinear multilevel algorithms have worked before (for a general blurring kernel). The new work generalizes a multilevel denoising approach based on subspace optimization. This is joint work with R H Chan. |

Title: | Primes in rapidly increasing sequences |

Speaker: | Dr Stephan Baier |

Date: | 13 August 2009 |

Time: | 2.00pm - 3.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | We are investigating various questions related to primes in rapidly increasing sequences. Our starting point will be the old but unresolved conjecture that the polynomial n^2+1 represents infinitely many primes. Methods that come into play in our investigations are mean value theorems for Dirichlet polynomials, the zero detection method and exponential sum estimates. |

Title: | Steady States Of The Fokker-Planck Models Of The Liquid Crystals |

Speaker: | Dr Hui Zhang |

Date: | 12 August 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Here, we will investigate the steady states of the Fokker-Planck model of liquid crystals. Generally, the full model will ¯rst be presented. Then focusing on the micro model, we will show the isotropic and nematic phases besides the pase transition phenomena. Moreover, there are multiple stable steady states with time dependence for the weak shear °ow. Lastly, we will give some open problems. |

Title: | Morphology of ParticlesIin Stressed Solids |

Speaker: | Dr Xiaofan Li |

Date: | 12 August 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Numerous structural materials are produced through solid state diffusional transformations. We discuss the modeling, the numerical methods and some numerical results in the diffusional evolution of microstructures in elastically stressed binary alloys. Equilibrium and growth shapes of a single precipitate embedded coherently in an infinite matrix are obtained for different materials and misfit strains. |

Title: | A Journey to the Center of the Earth |

Speaker: | Dr Ping Ma |

Date: | 11 August 2009 |

Time: | 4.00pm - 5.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | At a depth of ~2890 km, the core-mantle boundary (CMB) separates turbulent flow of liquid metals in the outer core from slowly convecting, highly viscous mantle silicates. The CMB marks the most dramatic change in dynamic processes and material properties in our planet, and accurate images of the structure at or near the CMB over large areas are crucially important for our understanding of present day geodynamical processes and the thermo-chemical structure and history of the mantle and mantle-core system. In addition to mapping the CMB, we need to know if other structures exist directly above or below it, what they look like, and what they mean (in terms of physical and chemical material properties and geodynamical processes). Detection, imaging, (multi-scale) characterization, and understanding of structure (e.g., interfaces) in this remote region have been and are likely to remain a frontier in cross-disciplinary geophysics research. I will discuss the statistical problems and challenges in imaging the CMB through generalized Radon transform. |

Title: | Centroidal Voronoi Tessellations and Applications to PDEs |

Speaker: | Dr Qiang Du |

Date: | 7 August 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-07, EC2 |

Abstract: | Centroidal Voronoi Tessellation has become a useful tool in many applications ranging from image and data analysis to physics and biology. In this talk, we first introduce the concept of centroidal voronoi tessellations and then discuss the relevant mathematical theory and related applications. We focus, in particular, on drawing connections with various issues in the numerical solution of PDEs. |

Title: | Pustyl'nikov's Criterion For The Riemann Hypothesis: A Blowout And Three Patches |

Speaker: | Dr Patrick Solé |

Date: | 5 August 2009 |

Time: | 2.00pm - 3.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | The criterion in the title attaches to every zero of Riemann zeta function in the critical strip but not on the critical line an operator with eigenvalue $-1$. It is shown here that the sufficient part of this criterion is wrong by deriving a contradiction. The argument involves results of Wong and Li on the asymptotics of solutions of second order difference equations. Three alternative criteria are derived. |

Title: | Modeling of Water Waves: Theory and Simulations |

Speaker: | Professor Min Chen |

Date: | 3 August 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | In this talk, I will start with an introduction on various water wave models and an overview of their application ranges and their limitations. Recent theoretical results on three-dimensional wave patterns will then be presented. Numerical experiments on three-dimensional waves, including experiments related to wave patterns, tsunami simulations and solitary wave interactions, will also be demonstrated. |

Title: | Some Results on $l^p$ Norms of Weighted Mean Matrices |

Speaker: | Dr Peng Gao |

Date: | 31 July 2009 |

Time: | 11.00am - 12.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Let $l^p$ ($p>1$) be the Banach space of all complex sequences ${\bf a}=(a_n)_{n \geq 1}$. The celebrated Hardy's inequality asserts that for any ${\bf a} \in l^p$, \begin{equation*}\label{eq:1} \sum^{\infty}_{n=1}\Big{|}\frac {1}{n}\sum^n_{k=1}a_k\Big{|}^p \leq \Big(\frac {p}{p-1} \Big)^p\sum^\infty_{k=1}|a_k|^p.\end{equation*}. In terms of matrix operators, Hardy's inequality says that the Ces\'aro matrix operator $C=(c_{n,k})$, given by $c_{n,k}=1/n , k\leq n$ and $0$ otherwise, is bounded on {\it $l^p$} and has norm $\leq p/(p-1)$. One is then led to the study of operator norms of general matrices. In this talk, I will present some results concerning the bounds for the $l^p$ norms of weighted mean matrices. Some applications and related results will also be discussed. |

Title: | Squares, Sums of Two Squares and Almost Squares |

Speaker: | Professor Tsz Ho Chan |

Date: | 29 July 2009 |

Time: | 2.00pm - 3.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Squares are integers of the form n = a^2. Sums of two squares are integers of the form n = a^2 + b^2. Almost squares are integers of the form n = a b where a and b are close to each other. In this talk, we will discuss the following question: what are the nearest squares, sums of two squares and almost squares to any given positive real number? It turns out to be related to uniform distribution of $n^2 \alpha (\bmod 1)$. |

Title: | Computational Surface Partial Differential Equations |

Speaker: | Professor Charles Elliott |

Date: | 24 July 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Evolutionary PDEs on stationary and moving surfaces appear in many applications such as the diffusion of surfactants on fluid interfaces, surface pattern formation on growing domains, segmentation on curved surfaces and phase separation on biomembranes and dissolving alloy surfaces. In this talk I discuss three numerical approaches based on: (I) Surface Finite Elements and Triangulated Surfaces, (II) Level Set Method and Implicit Surface PDEs and (III) Phase Field Approaches and Diffuse Surfaces. |

Title: | A Nonlocal Vector Calculus with Application to Nonlocal Boundary Value Problems |

Speaker: | Professor Max Gunzburger |

Date: | 24 July 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | We develop a calculus for nonlocal operators that mimic Gauss' theorem and the Green's identities of classical vector calculus. The operators we treat do not involve derivatives. We then apply the nonlocal calculus to define variational formulations of nonlocal "boundary" value problems that mimic the Dirichlet and Neumann problems for second-order scalar elliptic partial differential equations. For the nonlocal variational problems, we show how one can derive existence and uniqueness results and also how, under appropriate limits, they reduce to their classical analogs. Although we do not report on this in this talk, the results are easily extended to vector elliptic equations, and in particular, to the peridynamics model for materials. |

Title: | Playing the Market is Fun: Modeling Derivatives Prices by DOLPHIN |

Speaker: | Professor Koh Hock Lye |

Date: | 15 July 2009 |

Time: | 10.00am - 11.00am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | The Black Scholes (BS) models for pricing derivatives have become a standard tool for evaluating options and derivatives for the past several decades. The recent global financial tsunami and the US subprime crisis have, however, raised questions regarding the role of these models in financial chaos and cast doubt concerning the reliability of the BS models. The BS model is essentially a diffusion model that mimics many similar models used extensively in physics and ecology. Hence, insights and experience gained in these drift-diffusion-reaction models used in ecology to simulate ecosystem dynamics and stability are useful in developing innovative approaches to the classic BS models. The connection between mathematics, ecosystem concepts and economics is indeed strong, although not immediately apparent. This seminar hopefully will promote collaborative research among the relevant fields. The author has developed a set of pricing models codenamed DOLPHIN to evaluate asset and derivative prices, improving upon the framework of the BS models. DOLPHIN is used for example to analyze and explain the performance of the Kuala Lumpur Composite Index KLCI and Public Aggressive Growth Fund PAGF for the period between June 2006 and September 2008 (Figures 1 and 2), a period characterized by initial high growth for the first 18 months, followed by a subsequent sharp decline for the remaining 9 months. |

Title: | On the Generalised Hermite Constant |

Speaker: | Dr Bertrand Meyer |

Date: | 10 July 2009 |

Time: | 11.00am - 12.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | In traditional geometry of numbers, the Hermite constant accounts for the highest density of sphere packings associated with lattices in a given dimension. We shall show how a characterisation of this constant extends to a broader context that includes number theory and representation theory ingredients. We shall also present some explicit computations or methods to get the value of these constants. |

Title: | A Two Sample Test for Ultra High Dimensional Data with Applications to Gene Sets Testing |

Speaker: | Ms Qin Yingli |

Date: | 19 June 2009 |

Time: | 9.30am - 10.30am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | We proposed a two sample test for means of high dimensional data when the data dimension p is much larger than the sample size n, the so-called “large p small n” situation. The test does not require any explicit condition on the relationship between the data dimension and sample size. This offers more flexibility than other existing methods in analyzing high dimensional data. An important application of the proposed test is in testing significance for sets of genes in genetic studies. We will demonstrate empirically the usage of the proposed test on a biological data set. |

Title: | Memory Indicators And Their Incorporation Into Dynamic Models |

Speaker: | Ms Li Wen |

Date: | 29 May 2009 |

Time: | 9.00am - 10.00am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Data collected over time exhibit some type of memory structure, such as a short or long term memory. Two commonly used indicators of memory are the Hurst exponent and the self-similarity index. We investigate the relationship between the Hurst exponent and the self-similarity index and show that the two are connected for some time series such as fractional Brownian motion. We also employ windowing techniques to study the over-time behavior of the memory structure in a subset of the S&P500 series. Further, we incorporate the memory indicators into dynamical models. In particular, and due to their popularity in terms of use, we look at two continuous-timed dynamical systems – the Log Ornstein-Uhlenbeck (LogOU) and the Cox-Ingersoll-Ross (CIR) models and investigate how to extend them. We will also explore the memory structures underlying these two models and discuss how to estimate the memory indicators and other model parameters simultaneously in the two model systems within a Bayesian framework. |

Title: | Covering Arrays and Perfect Hash Families |

Speaker: | Professor Charles J. Colbourn |

Date: | 25 May 2009 |

Time: | 2.00pm - 3.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | A covering array on an alphabet of size v is an N by k array with each cell containing an entry from the alphabet. It has strength t if, whenever you choose t columns, and choose one of the v alphabet symbols for each column, there is at least one row of the array in which we find the prescribed symbols in the chosen columns. These combinatorial arrays have arisen in testing computer hardware and software, and generally in locating faults that result from component interactions. The explicit construction of covering arrays with “few” rows for given t, k, and v is a challenging problem. In this talk, we describe a strategy that employs the structure of the finite fields in two ways. First a covering array is constructed directly using the algebra of the field. Then a related object, a perfect hash family, is constructed from the field and used to inflate the number of columns of the covering array. We use this construction to explore a number of questions about the structure of arrays arising from the finite fields. |

Title: | The Spectrum of $N_2$ Resolvable Latin Squares |

Speaker: | Professor Alan Ling Chi Hung |

Date: | 22 May 2009 |

Time: | 2.30pm - 3.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | An $N_2$ resolvable Latin squares is a latin square with no $2 \times 2$ subsquares that also has an orthogonal mate. In this talk, I show that $N_2$ resolvable latin squares exist for all orders $n$ with $n \neq 2,4,6,8$. This is a joint work with J.H. Dinitz and A. Wolfe. |

Title: | The art of puncturing an LDPC code: reliability and security |

Speaker: | Professor Steven W. McLaughlin |

Date: | 30 April 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | In this talk, we show how a low density parity check code can be used for both reliability and (physical layer) security in a communication system. Careful use of puncturing shows that not only does an LDPC code have a universality property for reliability, but it can also be used as a very effective tool for hiding information against a passive eavesdropper. This tutorial talk will highlight both older and more recent work in LDPC codes. |

Title: | Asymmetric Group Key Agreement |

Speaker: | Professor Yi Mu |

Date: | 17 April 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | A group key agreement (GKA) protocol allows a set of users to establish a common secret via open networks. Observing that a major goal of GKAs for most applications is to establish a confidential channel among group members, we revisit the group key agreement definition and distinguish the conventional symmetric group key agreement from asymmetric group key agreement (ASGKA) protocols. Instead of a common secret key, only a shared encryption key is negotiated in an ASGKA protocol. This encryption key is accessible to attackers and corresponds to different decryption keys, each of which is only computable by one group member. We propose a generic construction of one-round ASGKAs based on a new primitive referred to as aggregatable signature-based broadcast (ASBB), in which the public key can be simultaneously used to verify signatures and encrypt messages while any signature can be used to decrypt cipher texts under this public key. Using bilinear pairings, we realize an efficient ASBB scheme equipped with useful properties. Following the generic construction, we instantiate a one-round ASGKA protocol tightly reduced to the decision Bilinear Diffie-Hellman Exponentiation (BDHE) assumption in the standard model. |

Title: | On Distribution Weighted Partial Least Squares With Diverging Number of Highly Correlated Predictors |

Speaker: | Dr Zhu Lixing |

Date: | 13 April 2009 |

Time: | 4.00pm - 5.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Because highly correlated data arise from many scientific fields, in this talk we investigate parameter estimation in a semi-parametric regression model with diverging number of predictors that are highly correlated. To this end, we first develop a distribution weighted least squares estimator (DWLSE) that can recover directions in central subspace (CS), then use DWLSE as a seed vector and project it onto a Krylov space by partial least squares to avoid computing the inversion of the covariance of predictors. Thus, such a distribution weighted partial least squares (DWPLS) can handle the cases with high-dimensional and highly corrected predictors. Furthermore, we suggest an iterative algorithm for obtaining a better initial value before implementing PLS. We also propose a BIC type criterion to estimate the dimension of the Krylov space in the PLS procedure. Illustrative examples by a real data set and comprehensive simulations demonstrate that the method is robust to non-ellipticity, and works well even in “small n, large p" problems. |

Title: | Approaches to Black-Box Secret Sharing from Algebraic Number Theory |

Speaker: | Professor Ronald Cramer |

Date: | 9 April 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | A black-box secret sharing scheme (BBSSS) for a given access structure works in exactly the same way over any finite Abelian group, as it only requires black-box access to group operations and to random group elements. In particular, there is no dependence on e.g. the structure of the group or its order. The expansion factor of a BBSSS is the length of a vector of shares (the number of group elements in it) divided by the number of players n. At CRYPTO 2002 Cramer and Fehr proposed a threshold BBSSS with an asymptotically minimal expansion factor THETA(log n). This dramatically improved the previous solution by Desmedt and Frankel from the late 1980s, which had expansion THETA(n). At CRYPTO 2005, Cramer, Fehr and Stam further improved the results, achieving an expansion factor that is absolutely minimal up to an additive term of at most 2, which is an improvement by a constant additive factor. All these results rely on orders in number fields that admit a large enough finite subsets of elements with appropriate number theoretical properties. In this talk we survey these and some related results. |

Title: | Asymptotically good secret sharing with strong multiplication over any finite field |

Speaker: | Mr. Ignacio Cascudo Pueyo |

Date: | 3 April 2009 |

Time: | 5.30pm - 6.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | This talk deals with the connection between efficient secure multi-party computation (MPC) and dedicated, i.e. “MPC-friendly” linear secret sharing schemes (LSSS). We resolve a problem left open in the work of Chen and Cramer from CRYPTO 2006 on a class of MPC-friendly LSSS based on algebraic geometry that enable efficient secure MPC over fixed finite fields. We show that for {\em every finite field} $\mathbb{F}_q$, there exists an infinite family of explicit LSSS over $\mathbb{F}_q$ that is asymptotically good in the following sense. First, the schemes are “ideal”: each share consists of a single $\mathbb{F}_q$-element. Second, the schemes have $t$-strong multiplication on n players, where the relative corruption tolerance (3t)/(n-1) tends to a constant when n tends to infinity. Previously, such results were only shown to hold over $\mathbb{F}_q$ with $q\geq 49$ a square. |

Title: | Algebraic Manipulation Detection Codes |

Speaker: | Professor Carles Padró |

Date: | 3 April 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | We consider an abstract device $\Sigma(\G)$ that can store a single element $x$ from a fixed, publicly known finite group $\G$. An adversary can not obtain any information on the value stored in $\Sigma(\G)$, but he can manipulate the stored data by adding some value $\delta\in \G$ of his choice. This value can depend only on the adversary's \emph{a priori\/} knowledge of $x$. This is actually an abstraction of several scenarios in cryptography as, for instance, one-time-pad encryption, linear secret sharing and secure computation, secure information dispersal and secure message transmission. We introduce the notion of an {\em algebraic manipulation detection} (AMD) code. By using such a code, a source value $s$ from a given set ${\cal S}$ can be probabilistically encoded as an element of the group $\G$. If the encoding of a source is stored in $\Sigma(\G)$, then manipulation of the stored value will be detectable except with a small error probability. This is guaranteed even if the adversary has full a priori knowledge of the source value. No secret keys are required. Read access to $\Sigma(\G)$ suffices for detection, and, in the absence of manipulation, for decoding. Several results in the literature about robust secret sharing schemes provide optimal or almost optimal AMD codes, but these results only apply to a quite limited parameter setting, where the error probability is dictated by the length of the source. We survey here these results and we discuss more recent results providing AMD codes which are close to optimal for a much more relaxed setting of the parameters. |

Title: | On The Bouniakowsky Conjecture And The Roots Of Polynomials To Prime Moduli |

Speaker: | Mr. Timothy Foo |

Date: | 2 April 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | This talk relates the conjecture that an irreducible polynomial with integer coefficients represents infinitely many primes, to the way roots of a polynomial to prime moduli, suitably normalized, are located in the unit interval (0,1). The conjecture is known as the Bouniakowsky conjecture and a more general form is Schinzel's Hypothesis H. Various theorems are known in regards to the roots of polynomials to integer moduli. Equidistribution has been proven for quadratic polynomials to prime moduli by Duke, Friedlander, Iwaniec, and Toth, and for any irreducible polynomial to integer moduli by Hooley. |

Title: | Pricing of Two-Asset Options Under Exponential L\'{e}vy Model |

Speaker: | Mr. Zhou Jinghui |

Date: | 1 April 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | This talk presents a finite element method for a partial integro-differential equation (PIDE) to price two-asset options with underlying price processes modeled as an exponential L\'{e}vy process. We provide a variational formulation in a weighted Sobolev space, and establish existence and uniqueness of the FEM-based solution. Then we discuss the localization of the infinite domain problem to a finite domain, and an explicit-implicit time-discretization of the PIDE in the domain, where the space-discretization is done through a standard continuous finite element method, and provide a localization error estimate from infinite domain to finite domain and a discretization error estimate for the numerical solution of the localized problem where two assets are assumed to have uncorrelated jumps. Numerical experiments for normal jump diffusion model, double exponential jump diffusion model and Variance Gamma model are performed with smooth and nonsmooth initial conditions. |

Title: | Digital Geometry For Image-Based Metrology |

Speaker: | Professor Alfred Bruckstein |

Date: | 31 March 2009 |

Time: | 10.30am - 11.30am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Several interesting problems in digital geometry arise due to the need to perform various types of accurate geometric measurements on objects and shapes that underwent sampling or discretization on a pixel-grid via some imaging device. High accuracy boundary reconstruction and length measurement, digital straight lines and linear separability on the grid, digital disks and precise location of shapes will be discussed. The problem of designing planar shapes that enable high-precision location and registration leads to some very challenging problems in discrete geometry, and are also very important in designing VLSI mask registration fiducials used in producing silicon chips. |

Title: | On Some Easy and Not-So-Easy Problems |

Speaker: | Dr Vassil Dimitrov |

Date: | 27 March 2009 |

Time: | 5.30pm - 6.30pm |

Venue: | SPMS-MAS-03-08, Seminar Room |

Abstract: | Multiplication of two integers is a problem that has been almost exhaustively analyzed by computer scientists and mathematicians. In the 50-ies, Kolmogoroff made a conjecture that any multiplication algorithm should have a quadratic complexity. The discovery of Karatsuba multiplication in 1963 disproved this conjecture in a rather simple manner. However, there are still unknown features associated with this simple computational problem, even in the case when one of the multiplicands is unknown. Since modern public key cryptography uses very large multipliers, it seems important to know certain nontrivial upper bounds. For example, given any 150-bit integer, x, how many additions are sufficient to implement multiplication by x if one uses binary additions and shifts only? What would be the role of the subtractions? What are the worst cases? In this talk we shall try to address some of these issues and point out various potential applications. |

Title: | Reviving the Dragon |

Speaker: | Dr Matt Henricksen |

Date: | 27 March 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-08, Seminar Room |

Abstract: | The recent eSTREAM competition recommended eight stream ciphers out of a submitted set of 34 candidates, based on various criteria. Four were chosen because they yield extremely high throughput in software. The Dragon cipher, while it was one of the finalists in the competition, did not make the final cut because of some speed and security issues. This talk is a case study of the issues with the Dragon cipher, from many perspectives, including implementation on the Intel platform, linear cryptanalysis and cache timing attacks, all of which are pivotal in stream cipher design today. |

Title: | Efficient Distributed Approximation Algorithms |

Speaker: | Dr Gopal Pandurangan |

Date: | 26 March 2009 |

Time: | 11.00am - 12.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Distributed approximation algorithms tradeoff optimality of the solution for the amount of resources consumed by the distributed algorithm. With the advent of resource-constrained networks such as sensor and peer-to-peer networks it is critical to design efficient distributed algorithms for network optimization problems that have low communication and time complexity even possibly at the cost of a reduced quality of solution. This talk will present recent results on the design and analysis of efficient distributed approximation algorithms for fundamental network optimization problems including the minimum spanning tree (MST), the minimum Steiner tree and related problems, and the shortest paths problem. I will focus on a simple scheme called the Nearest Neighbor Tree (NNT) scheme and show how it leads to the first efficient distributed logarithmic-approximation algorithm for MST in arbitrary networks. Significantly, our result also shows that there can be an exponential time gap between exact and approximate distributed MST computation. Another consequence of our result is that an approximate MST in unit-disk graphs (which are popular models of wireless networks) and in random weighted networks (which can model power-law networks such as the Internet and peer-to-peer networks) can be found in almost optimal time in a simple and local fashion. I will then briefly discuss a uniform approach to designing distributed approximation algorithms using probabilistic tree embeddings. This approach leads to the first-known time-optimal distributed logarithmic-approximation algorithms for many fundamental problems including the generalized Steiner forest and the shortest paths problem. It also leads to an improved leader election algorithm in synchronous networks that is both time optimal and almost message optimal, thus partially answering an important open problem raised by David Peleg in 1990. I will conclude with a discussion on our recent results on designing energy-efficient distributed algorithms for wireless networks. Our results initiate a distributed algorithmic theory that uses energy complexity as a new performance measure to analyze distributed algorithms. |

Title: | Discrete Random Variables [Undergraduate Lecture] |

Speaker: | Dr Gopal Pandurangan |

Date: | 26 March 2009 |

Time: | 10.00am - 11.00am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | This lecture will cover the basics of discrete probability and discrete random variables with examples. Fundamental concepts of expectation and independence will be introduced and discussed. |

Title: | Centroidal Voronoi Tessellation-based Three Dimensional Superconvergent Gradient Recovery[Graduate Seminar] |

Speaker: | Mr. Chen Jie |

Date: | 25 March 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Finite element superconvergence phenomenon based on Centroidal Voronoi Tessellation in 3D is introduced in this talk. A modified SPR method is raised to overcome the influence of slivers, which will not appear in 2D case, in CVT mesh. The laplacian operator with Dirichlet boundary condition is considered. The gradient recovered from the linear finite element solutions has an O(h^(1+α) )(α>0.5) superconvergence in l_{2} norm at nodes of CVT mesh, for an arbitrary 3D bounded domain. Numerical examples to demonstrate the superconvergence property and the well performance of modified SPR method are contained. |

Title: | Discrete Version of Atiyah - Singer Index Theory from Lattice Gauge Theory |

Speaker: | Dr David Adams |

Date: | 25 March 2009 |

Time: | 11.00am - 12.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | The Atiyah-Singer index theorem relates analytic and topological data associated with certain types of partial differential equations (PDEs). It is one of the deepest and most celebrated results in modern mathematics, and is also of major importance in quantum gauge field theories of theoretical particle physics for understanding topological phenomena of these theories. Recent developments in the lattice formulation of quantum gauge theories provide a framework and tools for developing a discrete version of Atiyah-Singer index theory. I will describe my research program on this topic, discussing what has already been achieved and the challenges that remain. The challenges involve capturing topological data in the discrete setting and dealing with additional spurious solutions of the discretized PDE. The latter is of independent interest in connection with numerical approaches to solving PDEs. |

Title: | The Spectral Theorem for Self-Adjoint Linear Operators [Undergraduate Lecture] |

Speaker: | Dr David Adams |

Date: | 25 March 2009 |

Time: | 10.00am - 11.00am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | I will prove the Spectral Theorem for self-adjoint linear operators, which states that all such operators admit an orthonormal basis of eigenvectors. This is equivalent to the statement that every Hermitian matrix can be diagonalized by a unitary transformation. |

Title: | On Randomizing Hash Functions to Strengthen the Security of Digital Signatures |

Speaker: | Dr Praveen Gauravaram |

Date: | 20 March 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Halevi and Krawczyk proposed a message randomization algorithm called RMX as a front-end tool to the hash-then-sign digital signature schemes such as DSS and RSA in order to free their reliance on the collision resistance property of the hash functions. They have shown that to forge a RMX-hash-then-sign signature scheme, one has to solve a cryptanalytical task which is related to finding second preimages for the hash function. In this article, we will show how to use Dean’s method of finding expandable messages for finding a second preimage in the Merkle-Damgard hash function to existentially forge a signature scheme based on a t-bit RMX-hash function which uses the Davies-Meyer compression functions (e.g., MD4, MD5, SHA family) in $2^{t/2}$ chosen messages plus $2^{t/2+1}$ off-line operations of the compression function and similar amount of memory. This forgery attack also works on the signature schemes that use Davies-Meyer schemes and a variant of RMX published by NIST in its Draft Special Publication (SP) 800-106. We discuss some important applications of our attack. (Paper will appear in Eurocrypt2009) |

Title: | High-Dimensional Finite elements for Elliptic Problems with Multiple Scales |

Speaker: | Professor Hoang Viet Ha |

Date: | 18 March 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Abstract Elliptic homogenization problems in a domain Ω ∈ Rd with n + 1 separate scales are reduced to elliptic problems in dimension (n + 1)d. These one-scale problems are discretized by a sparse tensor product ?nite element method (FEM). We prove that this sparse FEM has accuracy, work, and memory requirements comparable to those in a standard FEM for single-scale problems in Ω, while it gives numerical approximations of the correct homogenized limit as well as of all ?rst-order correctors, throughout the physical domain with performance independent of the physical problem’s scale parameters. |

Title: | Applications of Exponential Sums: An Overview |

Speaker: | Dr Luo Jinquan |

Date: | 13 March 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Exponential sums over finite fields are fundamental and important objects in number theory and arithmetic geometry for studying the number of solutions to the equations over finite fields. For several decades, a series of profound results on the estimation of the absolute values to the exponential sums have been found by the methods in number theory and arithmetic geometry. In practice, exponential sums have important applications in coding and cryptography. For example, in CDMA communication system we need to find sequences which have low auto and cross correlation values. It is equivalent to find a series of exponential sums which have small absolute values. In coding theory, exponential sums are used for estimating the minimum distances of linear codes. Moreover, the weight distribution of the cyclic codes can be obtained if the associated exponential sums are evaluated explicitly. In this talk, we will provide some examples to show how the exponential sums are employed in studying the properties of cyclic codes, constant composition codes, sequences, authentication codes and curves. |

Title: | Sparse Approximations of the Stochastic Chemical master Equation |

Speaker: | Dr Markus Hegland |

Date: | 12 March 2009 |

Time: | 2.30pm - 3.30pm |

Venue: | SPMS-MAS-03-08, Seminar Room |

Abstract: | Chemical reactions are stochastic processes. While in many applications the kinetic rate equations provide an adequate model for the dynamics of the expected concentrations, this is not the case when the numbers of molecules involved in the reactions are small. The situation occurs in many molecular biological processes including signalling and gene regulation. In order to understand the effect of the "reaction noise", one needes stochastic models. The chemical master equation is a continuous time discrete state Markov model which describes how the probabilities of the states evolve over time due to the chemical reactions. The states are vetors of integers. Instead of the concentrations of the kinetic rate equations here, the copy numbers of the chemical spcies form the components of the states. Their values are typically zero and a few hundred. The state space grows exponentially with the number of different chemical species and, as the probability of each state is recorded, one faces the "curse of dimensionality". This is one reason why essentially all computational approaches in this area use stochastic simulation methods. In this talk, I will discuss methods to determine solutions of the chemical master equations numerically. The approach we adopt uses a variant of the sparse grid technique based on state space aggregation, which is a finite volume type approach. The approximation order can be controlled by a method introduced by Per Loetstedt and his collaborators which uses a piecewise polynomial approximation combined with aggregation. A new bound for the approximation error using this aproach will be given. The sparse grid method will be illustrated for a very simple model of a signalling cascade. I will report on some work of an ANU student who was able to solve the master equation for a simple signalling cascade with 100 proteins species. |

Title: | Lightweight Cryptography from an Engineer's Perspective |

Speaker: | Dr Axel Poschmann |

Date: | 6 March 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | A widely shared view is that ubiquitous computing is the next paradigm in information technology. It ?ts that currently 98.8% of all manufactured microprocessors are employed in embedded applications and only 0.2% in traditional computers. The mass deployment of pervasive devices promises many bene?ts such as lower logistic costs, higher process granularity, optimized supply-chains, or location based services among others. On the other hand, many foreseen applications are security sensitive, such as wireless sensor networks for military, ?nancial or automotive applications. Furthermore privacy issues will arise in many pervasive applications. An aggravating factor is that pervasive devices are usually not deployed in a controlled but rather in a hostile environment, i.e. an adversary has physical access to or control over the devices. This adds the whole ?eld of physical attacks to the potential attack scenarios. Pervasiveness implies mass deployment which in turn implies harsh cost constraints on the used technology. For ASICs (application specific integrated circuits) this means in particular that power, energy, and area requirements (in terms of Gate equivalents, GE) must be kept to a minimum. We will also show that Moore's Law will not relax these constraints but further increase the demand for lightweight solutions. This talk gives an overview of lightweight cryptography. It covers lightweight block ciphers and lightweight hashing. We start with the design of DESL, a slightly modified lightweight variant of the Data Encryption Standard (DES). Then we look at PRESENT, which is the most compact block cipher for hardware implementations. Subsequently we use PRESENT as the basic building block for lightweight hash functions. Finally this talk is concluded and pointer for open research problems are provided. |

Title: | Numerical Simulation on Vortex Dynamics of Bose-Einstein Condensates |

Speaker: | Dr Wang Hanquan |

Date: | 4 Mar 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Recently, vortex dynamics of Bose-Einstein condensates (BEC) are one of most interesting subjects in Physics. At extremely low temperature, Bose-Einstein condensates can be modelled by the famous Gross-Pitavskii equation(GPE) or coupled Gross-Pitavskii equations (GPEs). We propose a new time-splitting spectral method for the GPE (or GPEs) and study the vortex dynamics of rotating one-component BEC, rotating two-component BEC and spin-1 BEC at a very low temperature. This new numerical method is explicit, unconditionally stable, time reversible, time transverse invariant, and of spectral accuracy in space and second-order accuracy in time. Moreover, it conserves the position density in the discretized level. How to design such a method, detailed numerical study on the efficiency of the method and application of the method to study vortex dynamics will be presented. |

Title: | Knuth's Balancing of Codewords |

Date: | 20 February 2009 |

Time: | 4.30pm - 6pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | In 1986, Don Knuth published a very simple algorithm for constructing sets of bipolar codewords with equal numbers of '1's and '-1's, called balanced codes. Knuth's algorithm is, since look-up tables are absent, very well suited for use with large codewords. The redundancy of Knuth's balanced codes is a factor of two larger than that of a code comprising the full set of balanced codewords. In our lecture we will present results of our attempts to improve the performance of Knuth's balanced codes. |

Title: | What is a matroid? |

Speaker: | Professor Geoffrey Whittle |

Date: | 19 February 2009 |

Time: | 2.30pm - 3.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Matroids abstract the properties of a finite set of vectors in a vector space. They were introduced by Whitney when he was trying to prove what was then the four colour conjecture. He noticed that a lot of theorems in graph theory were strikingly similar to theorems in linear algebra and he sought the connection. As well as arising in graphs and vector spaces, matroids have applications in combinatorial optimization, coding theory, model theory and possibly even number theory. I would argue that, in their way, matroids are as fundamental as groups or topological spaces. This talk is an introduction to the area. I assume no prior knowledge of matroids. The focus will be to develop intuition for the topic. |

Title: | Codes and Modular forms: a dictionary |

Speaker: | Dr Patrick Solé |

Date: | 19 February 2009 |

Time: | 10.30am - 11.30am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Since the 70's there are isomorphisms between ring of polynomial invariants of certain finite groups and certain rings of modular forms. These rings of polynomial invariants contain the weight enumerators of self dual codes. The theta series of unimodular lattices are amongst these modular forms. We survey known results on Jacobi and Siegel modular forms, and give recent results on modular forms for special levels. |

Title: | Phase field model of variational curve/surface smoothing and its finite element approximations |

Speaker: | Dr Zhu Liyong |

Date: | 18 February 2021 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-07, EC2 |

Abstract: | In this talk, we present a novel phase field model for variational curve/ surface smoothing. Its Euler-Lagrange equation and weak variational form are all linear, which enables various simple numerical algorithms with solid mathematical foundation be employed to solve efficiently the phase field model. Here, the finite element method is used to solve the proposed phase field model, and the related error estimates are presented. Further, a new weighted phase field method with preserving features of curve/ surface is proposed. Various numerical examples of curve smoothing in two dimensional cases demonstrate the efficiency, effectiveness and robustness of the proposed numerical algorithms. |

Title: | On Rank and the Solution of Linear Systems |

Speaker: | Mr. Jeffrey Pang |

Date: | 18 February 2009 |

Time: | 11.30pm - 12.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | This talk will be about the rank of a matrix, and how it affects the solutions of linear systems in different applied problems. We will not assume any prior knowledge of linear algebra. |

Title: | Computation of Critical Points, and Generic Continuity of Semi-Algebraic Set-Valued Maps |

Speaker: | Mr. Jeffrey Pang |

Date: | 18 February 2009 |

Time: | 10.00am - 11.00am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | This talk will be on two distinct projects I am currently working on. In the first part, we describe an algorithm to compute the "mountain pass" between two given points: a connecting path along which the maximum value is minimized. We describe an algorithm that maintains lower bounds on the optimal value by keeping the two points in separate level set components. This algorithm converges, even in the nonsmooth case, and converges superlinearly locally in the smooth finite-dimensional case. Applications include computational chemistry and partial differential equations. In the second part (independent of the first part), I will illustrate how recent methods in set-valued and variational analysis of semi-algebraic functions are helping us further our understanding in practical nonsmooth problems in optimization and control. We then present a new result on the structured discontinuity of semi-algebraic set-valued maps and its applications. |

Title: | Sparse Tensor Approximation of Elliptic sPDEs |

Speaker: | Professor Dr Christoph Schwab |

Date: | 13 February 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | We consider the Finite Element Solution of second order elliptic problems in a physical domain D ⊂ Rd with spatially inhomogeneous random coefficients. We present convergence rates and complexity estimates for deterministic, sparse Galerkin semidiscretization in the probability domain of the random solution. It is parametrized in polynomials of the ?rst M Karh´unen-Lo`eve (KL) variables of the input data [TS06]. Two cases are distinguished: (i) Exponential decay of the input’s KL expansion based on [TS] and (ii) algebraic decay of the input’s KL expansion. In (i), a “polynomial chaos” type Galerkin discretization is shown to yield spectral convergence rates in terms of NΩ, the number of deterministic elliptic problems to be solved. In (ii), approximation rates in terms of NΩ are higher than rates obtained for Monte-Carlo. Finally, in (iii) ongoing work [BS, ABS08, CDS09] on the total complexity vs. accuracy of (adaptive) tensor Galerkin discretizations in both, stochastic as well as in the deterministic domain D will be addressed. Sufficient conditions on the joint pdf’s of the random ?eld input to ensure better complexity than with (Quasi) Monte Carlo in the probability domain and with Galerkin discretization in D will be identi?ed and implementational issues will be addressed. |

Title: | Hash Function JH |

Speaker: | Wu Hongjun |

Date: | 13 February 2009 |

Time: | 4.30pm - 6.00pm |

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

Abstract: | The hash function used in cryptography compresses an arbitrary message to a message digest with fixed length. A secure hash function ensures that it is computational infeasible to find two different messages with the same message digest. In this seminar, we give an introduction to hash function design, then we introduce the new hash function JH. JH uses a new and extremely simple hash structure. With such structure, a hash function can be easily constructed from a bijective function. The bijective function in JH combines the best features of AES and Serpent, which are the top two block ciphers in the NIST AES competition. For the bijective function used in JH, the substitution- permutation network (SPN) is used to achieve diffusion and confusion. Two 4-bit-to-4-bit Sboxes are used for confusion, and each round constant bit selects which Sbox is used. A simple Maximum Distance Separable (MDS) code is applied to an eight-dimensional 1024-bit array to achieve efficient diffusion (in the i-th round, the MDS code is applied along the (i mod 8)-th dimension). Note that AES applies an MDS code to a two-dimensional 128-bit array. The bijective function in JH can be efficiently implemented in software with the bit-slice approach which is the best feature of Serpent. JH is strong in security. The simple structure and components of JH allows its security being analyzed easily. The 35.5-round compression function involves 9216 Sboxes, and a differential path involves more than 600 active Sboxes. The large number of active Sboxes ensures that JH is strong against differential attack. JH is efficient on many platforms ranging from hardware to software. The simple components and identical round functions (except for different round constants) allows efficient hardware implementation. The bit-slice implementation of JH gives efficient software performance. The hash speed of JH is about 16.8 cycles/byte on the Core 2 microprocessor running 64-bit operating system, and about 21.3 cycles/byte on the Core 2 microprocessor running 32-bit operating system. |

Title: | The Second Moment of Dirichlet Twists of Hecke L-Functions |

Speaker: | Dr Gao Peng |

Date: | 12 February 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | This is an introduction to the vision and mission of the newly formed Institute of Media Innovation. The different programs for PhD research and Seed Funding are introduced and explained. |

Title: | Cascadic Multigrid Methods |

Speaker: | Professor Zhong-Ci Shi |

Date: | 11 February 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Multigrid method is supposed to be one of the most efficient methods for solving large scale linear system of N unknowns with O(N) computational complexity. There are mainly two types of multigrids: W-cycle that uses two corrections in each cycle, and V-cycle that uses only one correction per cycle. Recently (1996--) there appears a new type of multigrids, the so-called Cascadic Multigrid which uses NO correction at all, but only a number of iterations on each level of grids. So it can be viewed as a one-way multigrid. We have established a general framework of the cascadic multigrid method and given a detailed convergence analysis of this new method in conjunction with its applications for the finite element approximation of the second as well as the fourth order elliptic partial differential equation. Meanwhile, we have proposed a new technique on the determination of iteration numbers on each level which can greatly reduce the computational costs in the whole process. |

Title: | Eigenvalues and Eigenvectors |

Speaker: | Dr Meng Fanwen |

Date: | 11 February 2009 |

Time: | 11.30am - 12.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | In this lecture, we will study the concepts of eigenvalues and eigenvectors. We also study the method to find eigenvalus and eigenvectors of a given square matirx. In addition, we will discuss an application of eigenvalues and eigenvectors in this lecture. |

Title: | Lagrangian-dual Functions and Generalized Equations of Optimization Problems |

Speaker: | Dr Meng Fanwen |

Date: | 11 February 2009 |

Time: | 10.00am - 11.00am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | In this talk, we discuss the Lagragian-dual problem of a class of convex optimization problem. We first study the semismoothness of the Lagrangian-dual function. This property is then used to investigate the second-order properties of the Moreau envelope of the dual function. We show that the Lagrangian-dual function and the gradient of the Moreau envelope are piecewise smooth and semismooth, respectively, for certain instances of the optimization problem. Further, we study the semismoothness of solutions to generalized equations over cone reducible nonpolyhedral convex sets, which is closely related to a class of optimization problems with cone constraints. In addition, we show that a locally Lipschitz homeomorphism function is semismooth at a given point if and only if its inverse function is semismooth at its image point. |

Title: | Determining Modular Forms on $SL_2(\mathbb{Z})$ by Central Values of Convolution $L$-Functions |

Speaker: | Dr Satadal Ganguly |

Date: | 5 February 2009 |

Time: | 4.30pm - 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | We show that a cuspidal normalized Hecke eigenform $g$ of level one and even weight is uniquely determined by the central values of the family of Rankin-Selberg $L$-functions $L(s, f\otimes g)$, where $f$ runs over the Hecke basis of the space of cusp forms of level one and weight $k$ with $k$ varying over an infinite set of even integers. This is a joint work with J. Hoffstein and J. Sengupta. |

Title: | Acceleration Methods for Total Variation-Based Image Denoising and Deblurring |

Speaker: | Dr Xu Jing |

Date: | 4 February 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | We focus on deblurring and denoising problems. For a given blur, we apply a fixed point method to solve the total variation-based image restoration problem. A new algorithm for the discretized system is presented. Convergence of outer iteration is efficiently improved by adding a linear term on both sides of the system of nonlinear equations. In inner iteration, an algebraic multigrid (AMG) method is applied to solve the linearized systems of equations. We adopt the Krylov subspace method to accelerate the outer nonlinear iteration. For the blur is unknown, we combine our algorithm for a given blur operator with an alternating minimization implicit iterative scheme to deal with blind deconvolution problem, recover the image and identify the point spread function(PSF). The only assumption needed is to satisfy the practical physical sense. This is a joint work with Professor Qianshun Chang and Weicheng Wang. |

Title: | Overview of the Institute for Media Innovation |

Speaker: | Professor Dr Martin Reiser |

Date: | 2 February 2009 |

Time: | 10.00am - 11.00am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | This is an introduction to the vision and mission of the newly formed Institute of Media Innovation. The different programs for PhD research and Seed Funding are introduced and explained. |

Title: | Geometric ATttraction-Driven Flow For Image Segmentation And Boundary Detection |

Speaker: | Dr Hahn Jooyoung |

Date: | 21 January 2009 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Noble forces in image segmentation based on active contours models are proposed for capturing objects in the image. Contemplating the common functionality of forces in previous active contours models, we propose the geometric attraction-driven flow (GADF), the binary edge function, and the binary balloon forces to detect objects in difficult cases such as varying illumination and complex shapes. The orientation of GADF is orthogonally aligned with the boundary of object and has the opposite direction across the boundary. It prevents the leakage on the weak edge. To reduce the interference from other forces, we design the binary edge function using the property of orientation in GADF. We also design the binary balloon force based on the four-color theorem. Combining with initial dual level set functions, the proposed model captures holes in objects and multiple junctions from different colors. The result does not depend on positions of initial contours. |

Title: | Polynomial Relations among Principal Minors of a 4x4-Matrix |

Speaker: | Mr Shaowei Lin |

Date: | 19 January 2009 |

Time: | 10.00am - 11.00am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Let P_n be the prime ideal of all polynomial relations among the principal minors of an n x n matrix. Related to the Principal Minor Assignment Problem formulated by Holtz and Schneider is the problem of finding a finite set of generators for P_n. While this elimination-type problem is in theory solvable by Groebner bases techniques, it is computationally expensive even for the case n=4. For instance, hyperdeterminantal relations among the principal minors of a symmetric 4 x 4 matrix were discovered by Holtz and Sturmfels. In this talk, we will show how to find generators in the general 4 x 4 case by considering products of the matrix entries called cycles. These cycles also allow us to prove that the image of the principal minor map is closed for all n. We will describe a group action on the principal minors that leave P_n invariant, and discuss the representation theoretic consequences. |

Title: | A Refinement of the Lang-Trotter Conjecture |

Speaker: | Dr Stephan Baier |

Date: | 15 January 2009 |

Time: | 4.00pm - 5.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Let $E$ be an elliptic curve defined over the rational numbers and $r$ a fixed integer. Using a probabilistic model, Lang and Trotter conjectured an asymptotic formula for the number of primes up to $x$ which have Frobenius trace equal to $r$. This conjecture works well for $r$'s that are small compared to $\sqrt{x}$. However it cannot hold for all $r$'s in the interval $|r| \le 2\sqrt{x}$ with a uniform bound for the error term, because an estimate of this kind would contradict the Chebotarev density theorem as well as the Sato-Tate conjecture. In my talk, I will present a refinement of the Lang-Trotter conjecture that conjecturally holds for arbitrary integers $r$ in the interval $|r|\le 2\sqrt{x}$, with a uniform error term. This is joint work with Nathan Jones. |

Title: | How Good Are Studentized Statistics? |

Speaker: | Professor Qi-Man Shao |

Date: | 15 January 2009 |

Time: | 3.00pm - 4.00pm |

Venue: | SPMS-MAS-03-07, EC2 |

Abstract: | Studentized statistics are commonly used in statistical inference since non-studentized statistics usually involve some unknown nuisance parameters. Suppose that a non-studentized and the studentized statistic have the same asymptotic limiting distribution. To use the limiting distribution in statistical inference, it is necessary to study the error of approximation. For a non-studentized statistic, one may adopt some limit theorems in probability to study the absolute error via Berry-Esseen type bounds or the relative error through a large deviation type result. It is well understood that moment conditions are necessary for these limit theorems. Many efforts have been put to obtain similar results for the studentized statistic under similar moment conditions. In this talk, we shall show that many studentized statistics preserve much better properties than the non-studentized statistics and that many limit theorems remain true for the studentized statistics under much weaker moment conditions than those necessary for the non-studentized statistics. For instance, a large deviation result holds for Student’s t-statistic without any moment condition and an exceptional non-uniform Berry-Essen bound is achievable under finite third moments. Our focus will be on the Student t-statistic, Hotelling’s T 2 statistic, the largest eigenvalue of sample correlation matrices and the Wald t-ratio statistic in unit root test. Some related topics will also be discussed. |

Title: | Block Intersection Polynomials and their Applications to Graphs and Block Designs |

Speaker: | Professor Leonard H. Soicher |

Date: | 13 January 2009 |

Time: | 10.30am – 11.30am |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | Certain integer linear equations involving binomial coefficients arise naturally in both the studies of edgeregular graphs and t-designs, and the non-negative integer solution vectors to these equations provide information about these graphs and designs. One method of studying these equations (from both a practical and theoretical point of view) uses the block intersection polynomials introduced by Peter Cameron and the speaker. In this talk, I shall define block intersection polynomials, briefly discuss their theory, and then give new applications of these polynomials to the studies of graphs and block designs. I shall discuss a new method of bounding the size of a clique in an edge-regular graph with given parameters and a new method for studying the possibility of a graph with given vertex-degree sequence being an induced subgraph of a strongly regular graph with given parameters. I shall also discuss results about the intersection sizes of pairs of blocks in a t-design with given parameters. |

Title: | Two New Numerical Methods for Solving Semi-linear Elliptic Equations |

Speaker: | Professor Xie Ziqing |

Date: | 7 January 2009 |

Time: | 4.30pm – 5.30pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | A so-called accelerated search extension method is proposed for solving semi-linear elliptic equations with multiple solutions. For semi-linear elliptic equations with unique solution, based on a series of new extrapolation expressions, a new extrapolation cascadic multigrid method is suggested. The numerical experiments verify the efficiency of our approaches. |

Title: | An Edge-Weighted Centroidal Voronoi Tessellation Model For Image Segmentation |

Speaker: | Professor Tang Tao |

Date: | 2 January 2009 |

Time: | 2.00pm - 3.00pm |

Venue: | SPMS-MAS-03-06, EC1 |

Abstract: | In this talk, we present an adaptive moving grid strategy for partial differential equations in two-space and three-space dimensions. The algorithm automatically adjusts the size of the finite elements in the physical domain to resolve the relevant scales in multi-scale physical systems while minimizing computational costs. Some subtle issues in the moving mesh scheme, in particular the solution interpolation from the old mesh to the new mesh and the choice of monitor functions will be addressed. Since the mesh redistribution procedure normally requires solving large size matrix equations (arising from discretizing the Euler-Lagrange equations or a minimization problem), we will describe a procedure to decouple the matrix equation to a much simpler block-tridiagonal type which can be solved by multi-grid methods efficiently. To demonstrate the performance of the proposed moving mesh strategy, the algorithm is implemented in moving finite element computations for multiphase flows and dendritic growth simulations. Numerical results on two-dimensional and three-dimensional simulations will be presented. |