Seminars

Title: Low Correlation Zone Sequences

Date: 26 Nov 2009, Thursday, 10.30am -11.30am

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr. Udaya Parampalli
Department of Computer Science
University of Melbourne

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.

About the Speaker:
Udaya Parampalli akn Parampalli Udaya obtained his doctoral degree in Electrical Engineering from Indian Institute of Technology (I.I.T), Kanpur, in 1993. From 1992 to July 1996, he worked in Industry as a Member Research Staff at Central Research Laboratory, Bharat Electronics, Bangalore. From 1997 to 2000, he was an ARC research associate at the Department of Mathematics, RMIT University, Melbourne, Australia. Since February 2000, he has been
working at the Department of Computer Science and Software Engineering, of the University of Melbourne, Australia. His research interests are in the area of coding theory, cryptography and sequences over finite fields and rings for communications and information security.

In the second half of 2008, he is a Visiting Professor in Department of Computer Science at University of Calgary, Canada.

Professional Activities: IEEE member since 1989. Actively participating Information theory society in terms of refereeing for ISITs and IT transactions since he came to Australia in 1997. Served as program committee member in various conferences and workshops in the area of sequences. Organized workshops with the support of Australian Mathematics Sciences Institute (AMSI) in the area of pairing based cryptography and sequences for communications. He is one of the experts in sequences area in information theory. He is a Guest editor for a Special Section on Sequence
Design and its Application in Communications to be published in the IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences in 2008.

He is a co-chair of Technical Program Committee of IWSDA 2007, the third International Workshop on Signal Design and Its Applications in Communications held in Chengdu, China on September 23-27, 2007.

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

Date: 11 Nov 2009, Wednesday, 3.30pm - 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Professor Antonio Leitao
Associate Professor
Department of Mathematics
Federal University of Santa Catarina
Florianopolis, Brazil

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.

About the Speaker:
Prof. A. Leitao received his Ph.D. from Goethe-Universitat, Germany in 1996. He is now
an associate professor at Federal University of St. Catarina, Brazil. Prof. Leitao's research
interests include numerical PDE, inverse problems and image processing. He has published over 30 papers and several books. So far, he has given over 40 invited talks on
various conferences.

Title: Model-Free Tests for Multiple Forecast Comparison

Date: 11 Nov 2009, Wednesday, 12pm - 1pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr Daniel Preve
School of Economics
Singapore Management University

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.

About the Speaker:
Daniel Preve was born in Stockholm, Sweden, in 1975. He studied at Stockholm and Uppsala
universities and has a PhD in statistics. He is currently a postdoctoral research fellow at Singapore Management University. His research interests include stationary and non-stationary time series econometrics, finite sample econometrics, time series forecasting and financial econometrics. More information on the speaker is available on his home page at http://smu-sg.academia.edu/DanielPreve.

Title: Robust Interactive Mesh Segmentation Using Fast Geodesic Curvature Flow

Date: 4 Nov 2009, Wednesday, 3.30pm - 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Mr Juyong Zhang
School of Computer Engineering
Nanyang Technological University

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.

About the Speaker:
Mr Juyong Zhang received his B.E. degree in Computer Science and Technology from University of Science and Technology of China (USTC), China, in 2006. He is current pursing his PhD studies at the School of Computer Engineering in Nanyang Technological University (NTU), Singapore. His research interests include geometry processing and image processing.

Title: On some applications of stochastic analysis

Date: 30 Oct 2009, Friday, 5pm - 6pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr Nicolas Privault
Associate Professor,
Department of Mathematics,
City University of Hong Kong

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.

About the Speaker:
Dr Nicolas PRIVAULT received his PhD in probability in 1994 from the University of Paris VI. He
has held a number of visiting and long term appointments in Europe, Asia, and the Americas, and
is currently an Associate Professor at City University of Hong Kong. His research interests are in
stochastic analysis, including stochastic calculus, stochastic inequalities, statistical estimation,
probabilistic methods for PDEs, and applications to finance and insurance. He has tutored over 10
PhD students and is the author of 90 refereed publications including two recent books, on
stochastic analysis and on interest rate modeling, published by Springer-Verlag and World
Scientific respectively.

Title: Random Matrix Theory: A Wireless Communications Perspective

Date: 20 Oct 2009, Tuesday, 4pm - 5pm

Venue: SPMS-MAS-03-07, EC2

Speaker:
Dr Ying-Chang LIANG
Senior Scientist
Institute for Infocomm Research
A*STAR

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.

About the Speaker:

Dr Ying-Chang Liang is presently a Senior Scientist in the Institute for Infocomm Research (I2R), Singapore. He holds adjunct associate professorship positions in Nanyang Technological University (NTU) and National University of Singapore (NUS), both in Singapore, and adjunct professorship position with University of Electronic Science & Technology of China (UESTC). He has been teaching graduate courses in NUS since 2004. From Dec 2002 to Dec 2003, Dr Liang was a visiting scholar with the Department of Electrical Engineering, Stanford University, CA, USA. His research interests include statistical signal processing, cognitive radio, dynamic spectrum access, reconfigurable signal processing for broadband communications, space-time wireless communications, wireless networking, and information theory, in which he has co-authored over 250 international journal/conference papers. He is the co-author of the book
"Wireless Broadband Networks" (Johe Wiely & Sons Inc., March 2009) and the co-author (with Z.D. Bai and Z. Fang) of the book "Spectral Theory of Large Random Matrices and its Applications in Wireless Communications and Finance Statistics" (English version, University of Science & Technology of China (USTC) Press, June 2009). Dr Liang is presently an Associate Editor of IEEE Transactions on Vehicular Technology. He was an Associate Editor of IEEE Transactions on Wireless Communications from 2002 to 2005. He has also served as a guest editor for four special issues related to cognitive radio in IEEE and other prestigious journals. He received the Best Paper Awards from IEEE VTC-Fall’1999 and IEEE PIMRC’2005, and 2007 Institute of Engineers Singapore (IES) Prestigious Engineering Achievement Award. He served as a Co-Chair for the Thematic Program on Random matrix theory and its applications in statistics and wireless communications, organized by Institute for Mathematical Sciences, National University of Singapore, 2006.

Title: Lattice DFT, quadrature and interpolation

Date: 12 Oct 2009, Monday, 4.30pm - 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr Huiyuan Li
Institute of Software,
Chinese Academy of Sciences,
Beijing, China

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.

About the Speaker:
Dr. Li received his PhD in Computational Mathematics from Shanghai University in 2002. He is now an Associate Professor at the Institute of Software, Chinese Academy of Sciences. His research interests include spectral methods, Fourier analysis and high performance computing.

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

Date: 7 Oct 2009,Wednesday, 4.30pm - 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr Wu Chunlin
Research Fellow
School of Physical and Mathematical Sciences
Nanyang Technological University

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.

About the Speaker:
Dr. Chunlin Wu got his Bachlor and Ph.D. degrees in University of Science and Technology of China in 2001 and 2006, respectively. He is now a research fellow in MAS, SPMS, NTU. Dr. Wu's research interests include computer graphics and image processing.

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

Date: 7 Oct 2009,Wednesday, 3.30pm - 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Professor Michael Hintermüller
Full professor (chair in Applied Mathematics) and MATHEON Research Professor,
Department of Mathematics,
Humboldt-University of Berlin, Germany

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.

About the Speaker:
2008 MATHEON-Research Professor and W3-Professor in Applied Mathematics, Humboldt - University of Berlin
2007 Chair in Applied Mathematics, University of Sussex
2005 START award by BMWF (Austrian Federal Ministry of Science and Research)
2004 Associate Professor, Department of Mathematics, University of Graz
2003 Visiting Associate Professor, Rice University
2000 Assistant Professor, Department of Mathematics, University of Graz
1997 Research Assistant, SFB "Optimization & Control", University of Graz

Degrees:
2003 Habilitation in Mathematics, University of Graz
1997 Dr. techn. degree, University of Linz
1994 Diploma in Technical Mathematics, University of Linz

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

Date: 22 Sep 2009,Wednesday, 4pm - 5pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Prof. Jiti Gao

Professor of Economics,

The University of Adelaide,

Australia

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.

About the Speaker:
Prof. Jiti Gao has been Professor of Economics (with Chair in Econometrics) at The University of Adelaide since January 2008. Prior to that, he was Professorial Fellow (12/2004-12/2007), Senior Lecturer (05/2002-11/2004) and Lecturer (01/2000-04/2002) at The University of Western Australia. Prof. Gao has a PhD degree in Economics (specialized in Econometrics) from Monash University, Doctoral and Master degrees in Science (specialized in Probability Theory and Mathematical Statistics) from The University of Science and Technology of China, and a Bachelor degree in Science (specialized in Applied Mathematics) from The University of Anhui, China.  His research interests lie in Econometric Theory, Financial Econometrics, Nonparametric and Semiparametric Econometrics, Panel Data and Time Series Econometrics.

Title: Nucleation of superconductors and liquid crystals

Date: 18 Sep 2009, Friday, 3.30pm - 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Professor Pan Xingbin

Zijiang Chaired Professor,

East China Normal University, China

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.

About the Speaker:
Prof. Pan received his PhD degree in 1987 from Shandong University, China. He is now the Zijiang Chaired Professor at East China Normal University. He is a very active researcher and has visited many universities and institutions in USA, Singapore and France. Prof. Pan's research interests include nonlinear partial differential equations, calculus of variations, mathematical theory of superconductivity and liquid crystals. So far, he has published nearly 65 papers.

Title: Predictive Fence Methods for Small Area Estimation

Date: 17 Sep 2009, Thursday, 4pm - 5pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Prof. Jiming Jiang
Professor of Statistics

University of California, Davis

 USA

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.

About the Speaker:
Professor Jiming Jiang received his Bachelor of Mathematics and Master of Probability and Statistics from Peking University and PhD in Statistics under Professor Peter J. Bickel from the University of California at Berkeley. He is now a Professor of Statistics at The University of California, Davis. He has wide interests in statistics and has one monograph in the prestigious Springer Series in Statistics (Linear and Generalized Linear Mixed Models and Their Applications, 2007).

Title: A Strong Direct Product Theorem for Disjointness

Date: 3 Sep 2009, Thursday, 10.30am - 11.30am

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr. Hartmut Klauck

Centre for Quantum Technologies

National University of Singapore

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.

About the Speaker:
Hartmut Klauck received a Diplom (Master’s degree) in computer science from the University of Paderborn in 1995, and a PhD in computer Science from Johann Wolfgang Goethe-Universität in 2000 (Advisor: Georg Schnitger). He was then a postdoctoral fellow at CWI (Amsterdam), spent the year 2002-2003 at the Institute for Advanced Study in Princeton, and another year as postdoc at the University of Calgary. From 2004-2008, he led a “Junior Research Group” at the University of Frankfurt before joining Singapore’s Centre for Quantum Technologies this year. His research interests include complexity theory, in particular communication complexity, and quantum computation.

Title: Blob-Based Super-Resolution Image Reconstruction

Date: 2 September 2009,Wednesday, 3.30pm - 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr. Ho Yu Tat Edward

Research Fellow

EEE/Division of Information Engineering

Nanyang Technological University

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.

About the Speaker:
Edward Ho was born in Penang, Malaysia in 1975. He received his B.Eng (Hons) degree from Nanyang Technological University, Singapore in 2000. He then went to the University of Cambridge, United Kingdom to do a short study in Partical Physics and Astronomy. He also worked as a researcher for a few years in the UK before he started his PhD study. In 2008, he obtained his PhD degree in Medical Physics and Bioengineering from University College London. Dr Ho is currently a Research Fellow at Nanyang Technological University in Singapore. He has extensive research experiences in image reconstruction, image processing, computer vision, augmented reality, numerical analysis, engineering dynamics and geometric (Clifford) algebra.

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

Date: 19 Aug 2009,Wednesday, 4pm - 5pm

Venue: SPMS-MAS-03-07, EC2

Speaker:
Professor Perumal Nithiarasu

 Civil and Computational Engineering Centre,

Swansea University,

Swansea SA2 8PP, United Kingdom

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.

About the Speaker:
Professor Perumal Nithiarasu is currently a personal chair and EPSRC advanced fellow (biomedical) at the Civil and Computational Engineering centre (C2EC), School of Engineering, Swansea University. Professor Nithiarasu obtained his BE, MTech and PhD from India and moved to Swansea University in 1996. He received his DSc from Swansea University in 2007 and became a lecturer in 2000, senior lecturer in 2004, reader in 2006 and professor in 2008. His research interests include biomedical engineering, computational fluid dynamics and numerical methods.

Title: Wavelets and Probability

Date: 19 Aug 2009,Wednesday, 4pm - 5pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Professor Alfredo J. Rios

Departamento de Matemáticas,

Universidad Simón Bolívar, Caracas,

Bolivarian Republic of Venezuela

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.

About the Speaker:
Alfredo Rios obtained his Ph.D. from Rutgers University in 2004 under the supervision of Prof. Richard Gundy.  He had held a visiting position in Lehigh University in Bethlehem Pennsylvania.  Currently, he is an assistant professor in Universidad Simón Bolívar in Caracas, Venezuela.  His mathematical interests include harmonic analysis and probability.

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

Date: 19 Aug 2009,Wednesday, 2.30pm - 3.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Prof. David A. A. Radnell

Department of Mathematics and Statistics,

American University of Sharjah,

Sharjah, United Arab Emirates

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.

About the Speaker:
David Randell obtained his Ph.D. from Rutgers University in 2003 under the supervision of Prof. Yi-Zhi Huang.  He has held research positions in the University of Michigan in Ann Arbor and the Max Plank Institute for Mathematics in Bonn Germany.  Currently, he is an assistant professor in the American University of Sharjah.  He specializes in Riemannian geometry.

Title: On a kind of nonlinear eigenvalue problem

Date: 19 Aug 2009,Wednesday, 1pm - 2pm

Venue: SPMS-MAS-03-07, EC2

Speaker:
Professor Yongqing Li

School of Mathematics and Computer Science,

Fujian Normal University,

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.

About the Speaker:
Prof. Yongqing Li is currently a professor in the School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, China. He obtained his PhD from Stockholm University in 1994. His research interests include nonlinear analysis and calculus of variations (critical point theory and its application to problems of nonlinear elliptic PDEs).

Title: Survival mixture modelling of recurrent infections

Date: 18 Aug 2009, Tuesday, 4pm - 5pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Professor Andy Lee

Chair Professor of Biostatistics

School of Public Health,

Curtin University of Technology,

Perth, Australia

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.

About the Speaker:
Professor Andy H. Lee received a BMath degree in 1982 from the University of Waterloo, Canada, a MMath degree in 1983 from the same university, and a PhD in 1988 from the Australian National University. He is currently Chair Professor of Biostatistics at the School of Public Health, Curtin University of Technology, Perth, Australia. His multidisciplinary research includes statistical computing, nutritional epidemiology and chronic disease modelling.

Title: Variational Models for Image Processing and Fast Algorithms

Date: 14 Aug 2009, Friday, 3.30pm - 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Professor Ke Chen

Centre for Mathematical Imaging Techniques,

Department of Mathematical Sciences,                  
University of Liverpool, UK 

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.

About the Speaker:
Prof Chen received his BSc in Applied Mathematics from Dalian University of Technology in 1983, MS and PhD in Numerical Analysis at Manchester and Plymouth (UK) respectively in 1987, 1990.

After 3 years' postdoctoral work at the University of Reading, he joined the University of Liverpool in 1993 as a lecturer. He is currently a professor at the University of Liverpool and the director of Research Centre for Mathematical Imaging Techniques. His areas include Numerical PDEs, Numerical Linear Algebra and various image processing applications.

Title: Primes in rapidly increasing sequences

Date: 13 Aug 2009, Thursday, 2pm - 3pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr. Stephan Baier
Department of Mathematics,
University of Bristol,
Bristol, UK

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.

About the Speaker: 
Dr. Stephan Baier obtained his Ph.D. and habilitation from the Free University of Berlin in 2000 and 2009, respectively. He has held research positions in the University of Cambridge, Harish-Chandra Research Institute in Allahabad, Alfred Renyi Institute of Mathematics in Budapest, Queen’s University in Canada and Jacobs University in Bremen, Germany.  He currently is a researcher in the University of Bristol. His mathematical interests mainly lie in analytic number theory.

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

Date: 12 Aug 2009, Wednesday, 4.30pm - 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr Hui Zhang
School of Mathematical Sciences,
Beijing Normal University,
Beijing, P.R. China

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.

About the Speaker: 
Dr. Hui Zhang received his PhD in 2001 from the Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences. He was a postdoc in Peking University from 2001-2003, and a Research Fellow of Alexan-der von Humboldt Foundation at Max-Planck Institute of Mathematical Science from 2007-2008. He is currently an Associate Professor in Beijing Normal University since 2005. His research interests are mainly in mathematical modeling of liquid crystal and fluid dynamics, and scientific computing.   

Title: Morphology of ParticlesIin Stressed Solids

Date: 12 Aug 2009, Wednesday, 3.30pm - 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr Xiaofan Li
Department of Applied Mathematics,
Illinois Institute of Technology,
Chicago, USA

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.

About the Speaker: 
Dr Xiaofan Li received his BS in Applied Mathematics at Zhejiang University in 1987, MS and PhD in Applied Mathematics at UCLA in 1993. He was a postdoc at UCSD and Ohio State University from 1994 to 1999. He joined the Department of Applied Mathematics at Illinois Institute of Technology in 1999 as an Assistant Professor and became Associate Professor in 2005. He is also the Director of Graduate Studies since 2005. His research interests include suspension of deformable particles, phase transformation in binary alloys and boundary integral methods.

Title: A Journey to the Center of the Earth

Date: 11 Aug 2009, Tuesday, 4pm - 5pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr. Ping Ma
Assistant Professor
Department of Statistics,
University of Illinois at Urbana-Champaign, USA

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.

About the Speaker: 
Prof. Ping Ma obtained his Ph.D. in Statistics from Purdue University in 2003. He then accepted a postdoctoral position at Harvard University working with Prof. Jun Liu during 2003 to 2005. He is currently an Assistant Professor at the Department of Statistics, UIUC. Prof. Ma's research has been featured in prominent media such as Science, National Geographics, Fox News.

Title: Centroidal Voronoi Tessellations and Applications to PDEs

Date: 7 Aug 2009, Friday, 3.30pm - 4.30pm

Venue: SPMS-MAS-03-07, EC2

Speaker:
Dr Qiang Du
Verne M. Willaman Professor of Mathematics and Professor of Materials Science,
Pennsylvania State University

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.

About the Speaker:
Dr. Qiang Du received his BS degree from the University of Science and Technology of China in 1983 and PhD from Carnegie-Mellon University in 1988. After first serving as a Dickerson instructor at the University of Chicago, he has held academic appointments at several universities and national labs including Michigan State, Iowa State, Carnegie Mellon, Hong Kong Science and Technology and Argonne. He is presently the Verne Willaman Professor of Mathematics and Professor of Materials Science at Penn State University. Dr. Du has published over 150 scientific papers and has been invited to speak at many research institutions and international conferences. He served as the chief scientist of the 973 project on "Large Scale Scientific Computing Research" in China from 1999 to 2004. He is now serving on editorial boards of several journals including SIAM Journal of Numerical Analysis, Discrete and Continuous Dynamic Systems, Applied Mathematics Research Exp., etc. Dr. Du received the Feng Kang prize in scientific computing in 2005, the faculty outreach and extension award at Iowa State University in 2000, the Frame faculty teaching award at Michigan State University in 1992, and the Eberly college of science medal at the Pennsylvania State University in 2006.

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

Date: 5 Aug 2009, Wednesday, 2pm - 3pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr. Patrick Solé
Director of Research,
CNRS Laboratory I3S,
Sophia Antipolis, France

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.

About the Speaker: 
 Patrick Solé  received the Ingénieur and Docteur-Ingénieur degrees both from Ecole Nationale Supérieure des Télécommunications, Paris, France, in 1984 and 1987, respectively, and the habilitation à diriger des recherches from Université de Nice-Sophia Antipolis, Sophia Antipolis, France, in 1993. He has held visiting positions in Syracuse University, Syracuse, NY, from 1987 to 1989, Macquarie University, Sydney, Australia, from 1994 to 1996, and Lille University, Lille, France, from 1999 to 2000. Since 1989, he has been a permanent member of the CNRS Laboratory I3S, Sophia Antipolis, France, and became Directeur de Recherche in 1996. His research interests include coding theory ( codes over rings, quasi-cyclic codes), interconnection networks (graph spectra, expanders), vector quantization (lattices), and cryptography (boolean functions, pseudo random sequances). Dr. Solé is the recipient (jointly with Hammons, Kumar, Calderbank, and Sloane) of the IEEE Information Theory Society Best Paper Award in 1994.

Title: Modeling of Water Waves: Theory and Simulations

Date: 3 Aug 2009, Monday, 3.30pm - 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Prof. Min Chen
Department of Mathematics,
Purdue University, USA

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.

About the Speaker: 
Min Chen received her B.S. in  1982 and  her Master's degree in Mathematics in 1985 from Beijing University. She received her Master's degree in Mechanical and Aerospace Engineering from Princeton University and then received her Ph.D. in Mathematics from Indiana University. Her advisor was Roger Temam. She is currently a professor in the Mathematics Department of Purdue University, USA. Min Chen is an applied mathematician interested in problems coming from attempts to understand, predict and control real world phenomena. Her research work ranges from innovative general purpose numerical methods to the development of schemes and computer code. She is also involved in the derivation and analysis of mathematical models for fluid flows. Min Chen is an editorial board member of Nonlinear Analysis: Theory, Method & Application and European Journal of Pure and Applied Mathematics.

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

Date: 31 Jul 2009, Friday, 11am - 12pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr. Peng Gao
Division of Mathematical Sciences,
School of Physical and Mathematical Sciences,
Nanyang Technological University

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.

About the Speaker: 
Peng Gao received his PhD from the University of Michigan in 2005 under the direction of Prof. Hugh Montgomery and Prof. Kannan Soundararajan. He spent the academic year 2005-2006 visiting the American Institute of Mathematics (AIM) in fall 2005 and the Centre de Recherches Mathematiques (CRM) at the Universite de Montreal in spring 2006. He was a postdoc at the University of Toronto working with Prof. John Friedlander from July 2006 to June 2008. He is currently a research fellow at NTU. He is interested in analytic number theory as well as functional analysis.

Title: Squares, Sums of Two Squares and Almost Squares

Date: 29 Jul 2009, Friday, 2pm - 3pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Prof. Tsz Ho Chan
Assistant Professor
Department of Mathematical Sciences
University of Memphis

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 $n^2 \alpha (\bmod 1)$.

About the Speaker: 
Prof. Tsz Ho Chan obtained his degree from the University of Michigan under the supervision of Prof. Hugh Montgomery in 2002.  Since the completion of his degree, he has worked in Case Western Reserve University and the American Institute of Mathematics.  Currently, he is an assistant professor in the Department of Mathematics in the University of Memphis.  He studies various problems in analytic number theory.

Title: Computational Surface Partial Differential Equations

Date: 24 Jul 2009, Friday, 4.30pm - 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Prof. Charles Elliott

Mathematics Institute

University of Warwick, UK

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.

About the Speaker: 
Prof. Charles Elliott received his B.S (1972), M.S (1973) and Ph.D (1976) from the University of Birmingham and University of Oxford. He is currently a Professor of Mathematics at the University of Warwick. He served as the Chair of the Department of Mathematics at the University of Sussex from 1987 to 2007. Prof. Elliott serves as the editors of several top journals in numerical analysis and scientific computing involving IMA J. Numerical Analysis.  He has made great contributions in the areas including unfitted finite element method, free boundary problems, PDE based image processing, PDEs on surfaces and geometric evolution equations.

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

Date: 24 Jul 2009, Friday, 3.30pm - 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Prof. Max Gunzburger
Francis Eppes Distinguished Professor of Mathematics
Department of Mathematics
Florida State University

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.

About the Speaker: 
Prof. Max Gunzburger received his B.S (1966), M.S.(1967) and Ph.D.(1969) in New York University. He is currently a Francis Eppes Distinguished Professor of Mathematics at Florida State University and serves as the Chair of the Department of Scientific Computing. He was the 2008 winner of the SIAM W.T. and Idalia Reid Prize in Mathematics.  Prof. Gunzburger served as the Editor-in-Chief of the SIAM Journal on Numerical Analysis from 2000-2007. He also served as the Chairman of the Board of Trustees of SIAM in 2003 and has held various positions at SIAM. His seminal research areas include flow control, finite element analysis, superconductivity and voronoi tessellations. He has also made great contributions in the areas of aerodynamics, materials, acoustics, climate change, groundwater, image processing and risk assessment.

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

Date: 15 Jul 2009, Friday, 10am – 11am

Venue: SPMS-MAS-03-06, EC1

Speaker:
Prof. Koh Hock Lye
River Engineering and Urban Drainage Research Centre
Universiti Sains Malaysia

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.

(Please click here for Figures 1 and 2)

A copy of the ppt slides for the seminar is available here.

Title: On the Generalised Hermite Constant

Date: 10 Jul 2009, Friday, 11am – 12pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr. Bertrand Meyer
Institut de mathématiques de Bordeaux,

Université de Bordeaux,

France

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

Date: 19 Jun 2009, Friday, 9.30am – 10.30am

Venue: SPMS-MAS-03-06, EC1

Speaker:
Ms Qin Yingli
PhD Candidate
Department of Statistics  
Iowa State University
Ames, USA

   
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

Date: 29 May 2009, Friday, 9am – 10am

Venue: SPMS-MAS-03-06, EC1

Speaker:
Ms Li Wen
PhD Candidate
Department of Statistics  
Iowa State University
Ames, USA

   
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

Date: 25 May 2009, Monday, 2pm – 3pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Professor Charles J. Colbourn
Professor of Computer Science and Engineering

   
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

Date: 22 May 2009, Friday, 2.30pm – 3.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Professor Alan Ling Chi Hung
Department of Computer Science  
University of Vermont
Berlington, VT, USA

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

Date: 30 Apr 2009, Thursday, 3.30pm – 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Prof. Steven W. McLaughlin
V ice Provost for International Initiatives
Ken Byers Professor
School of Electrical and Computer Engineering
Georgia Institute of Technology, USA

   
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

Date: 17 Apr 2009, Friday, 4.30pm – 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Professor Yi Mu
Centre for Computer and Information Security Research,
University of Wollongong, Australia

   
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

Date: 13 Apr 2009, Monday, 4pm – 5pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Dr. Zhu Lixing
Head and Professor,
Department of Mathematics,
Hong Kong Baptist University,

   
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

Date: 9 Apr 2009, Thursonday, 4.30pm – 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Professor Ronald Cramer
Professor, Mathematical Institute, Leiden University, The Netherlands
Head of the Cryptology and Information Security Research Group, CWI Amsterdam

   
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

Date: 3 Apr 2009, Thursday, 5.30pm – 6.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:
Mr. Ignacio Cascudo Pueyo
PhD Candidate
University of Oviedo, Spain

   
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

Date: 3 Apr 2009, Thursday, 4.30pm – 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Professor Carles Padró
Department of Applied Mathematics IV
Universitat Politecnica de Catalunya

   
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

Date: 2 Apr 2009, Thursday, 4.30pm – 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Mr. Timothy Foo
Graduate Student
Division of Mathematical Sciences
School of Physical and Mathematical Sciences

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

Date: 1 Apr 2009, Wednesday, 3.30pm – 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Mr. Zhou Jinghui
Research Fellow
Division of Mathematical Sciences
School of Physical and Mathematical Sciences

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

Date: 31 Mar 2009, Tuesday, 10.30 – 11.30am

Venue: SPMS-MAS-03-06, EC1

Speaker:

Prof. Alfred Bruckstein
Visiting Professor & Technion Ollendorf Chair in Science
Division of Mathematical Sciences
School of Physical and Mathematical Sciences

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

Date: 27 Mar 2009, Friday, 5.30pm – 6.30pm

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

Speaker:

Dr. Vassil Dimitrov
Research Fellow
Division of Mathematical Sciences
School of Physical and Mathematical Sciences

Australian National University

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

Date: 27 Mar 2009, Friday, 4.30pm – 5.30pm

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

Speaker:

Dr. Matt Henricksen
Institute for Infocomm Research (I2R)

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.

[Colloquium]
Title: Applications of Semi-definite Programming: A Tutorial

Date: 26 MarA 2009, Wednesday, 3.30pm – 4.30pm

Venue: SPMS-MAS-03-07, EC2

Speaker:

Prof. Etienne de Klerk
Department of Econometrics and Operations Research,
Faculty of Economic Sciences,
Tilburg University,
The Netherlands

Abstract: 
Semi-definite programming (SDP) is one of the most active areas in mathematical programming, due to varied applications and the availability of interior point algorithms.

In this tutorial we will review various applications of SDP, including:

- The Lovasz theta number and Shannon capacity of a graph;

- Approximation algorithms for the MAXIMUM k-CUT problem in graphs;

- Certifying positivity of a polynomial;

- The S-lemma in control theory

Materials for the talk are available here.

Title: Efficient Distributed Approximation Algorithms

Date: 26 Mar 2009, Thursday, 11am – 12pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. Gopal Pandurangan
Department of Computer Science
Purdue University

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.

[Undergraduate Lecture]
Title: Discrete Random Variables

Date: 26 Mar 2009, Thursday, 10 – 11am

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. Gopal Pandurangan
Department of Computer Science
Purdue University

Abstract:

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

Date: 25 Mar 2009, Wednesday, 3.30 – 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Mr. Chen Jie
Graduate student
Division of Mathematical Sciences
Nanyang Technological University

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 l₂ 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

Date: 25 Mar 2009, Thursday, 11am – 12pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. David Adams
Department of Physics and Astronomy
Seoul National University

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.       

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

Date: 25 Mar 2009, Wednesday, 10 – 11am

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. David Adams
Department of Physics and Astronomy
Seoul National University

Abstract:

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

Date: 20 Mar 2009, Friday, 4.30 – 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. Praveen Gauravaram
Research Fellow
Department of Mathematics
Technical University of Denmark

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)

[Colloquium]
Title: On $q$-Product Expansios of Modular Forms

Date: 19 Mar 2009, Friday, 4.30 – 5.30pm

Venue: SPMS-MAS-03-07, EC2

Speaker:

Prof.Dr. Winfried Kohnen
Professor of Mathematics
Faculty of Mathematics and Computer Sciences
University of Heidelberg

Abstract:
Modular forms are (meromorphic) functions on the complex upper half-plane that satisfy simple transformation formulas under fractional linear transformations. In particular, a modular form has a Fourier expansion in the variable $q=e^{2\pi iz}, and the Fourier coefficients often are interesting arithmetical functions. Modular forms are fundamental objects in complex analysis and number theory. What seems to be less known is that modular forms also have infinite product expansions of the form $\prod_n(1-q^n)^{c(n)}$ and the exponents $c(n)$ also often seem to carry important information on the function. For example, there is famous work by Borcherds that relates the exponents of modular forms with so called "Heegner divisors" to Fourier coefficients of modular forms of half-integral weight.

In this talk, I would like to show how these exponents can also be used to characterize those modular forms which do not have zeros or poles on the upper half-plane.

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

Date: 18 Mar 2009, Thursday, 3.30 – 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Prof. Hoang Viet Ha
Division of Mathematical Sciences
School of Physical and Mathematical Sciences

Australian National University

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

Date: 13 Mar 2009, Friday, 4.30 – 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. Luo Jinquan
Research Fellow
Division of Mathematical Sciences
School of Physical and Mathematical Sciences

Australian National University

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

Date: 12 Mar 2009, Thursday, 2.30 – 3.30pm

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

Speaker:

Dr. Markus Hegland
Centre for Mathematics and its Applications

Mathematical Sciences Institute

Australian National University

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.

[Crypto/Coding Seminar]
Title: Lightweight Cryptography from an Engineer's Perspective

Date: 6 Mar 2009, Friday, 4.30 – 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. Axel Poschmann
Research Fellow,

Division of Mathematical Sciences,

School of Physical and Mathematical Sciences,

Nanyang Technological University

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.

Date: 4 Mar 2009, Friday, 3.30 – 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. Wang Hanquan
School of Statistics and Mathematics,
Yunnan University of Finance and Economics,
China

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.

Date: 20 Feb 2009, Friday, 4.30 – 6pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

K.A. (Kees) Schouhamer Immink
Fellow, IEE, SMPTE, IEEE, and AES,
Member, Royal Netherlands Academy of Sciences,
Foreign associate, (US) National Academy of Engineering

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.

Date: 19 Feb 2009, Thursday, 2.30 – 3.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Prof. Geoffrey Whittle
Professor of Mathematics,
School of Mathematical and Computing Sciences,
Victoria University of Wellington,

New Zealand

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.

Date: 19 Feb 2009, Thursday, 10.30 – 11.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. Patrick Solé

Director of Research

CNRS, I3S

Sophia Antipolis, France

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.

Date: 18 Feb 2009, Wednesday, 3.30 – 4.30pm

Venue: SPMS-MAS-03-07, EC2

Speaker:

Dr. Zhu Liyong

Research Fellow,

Division of Mathematical Sciences,

Nanyang Technological University,

Singapore

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.

Date: 18 Feb 2009, Wednesday, 11.30am – 12.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Mr. Jeffrey Pang

Centre for Applied Mathematics,

Cornell University,

USA

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.

Date: 18 Feb 2009, Wednesday, 10 – 11am

Venue: SPMS-MAS-03-06, EC1

Speaker:

Mr. Jeffrey Pang

Centre for Applied Mathematics,

Cornell University,

USA

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.

Date: 13 Feb 2009, Friday, 3.30 – 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Prof. Dr. Christoph Schwab
Professor,
Seminar for Applied Mathematics,
ETH Zurich

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.

Date: 4:30 - 6:00pm 13 Feb 2008, Friday

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

Speaker:

Wu Hongjun

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.

Date: 12 Feb 2009, Thursday, 4.30 – 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. Gao Peng

Research Fellow,

Division of Mathematical Sciences,

Nanyang Technological University,

Singapore

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. 

Date: 11 Feb 2009, Wednesday, 3.30 – 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Prof. Zhong-Ci Shi

Institute of Computational Mathematics,

Chinese Academy of Sciences,

China

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.

Date: 11 Feb 2009, Wednesday, 11.30– 12.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. Meng Fanwen

Research Fellow,

The Logistics Institute - Asia Pacific,

National University of Singapore

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.

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. Meng Fanwen

Research Fellow,

The Logistics Institute - Asia Pacific,

National University of Singapore

Abstract:

Date: 5 Feb 2009, Thursday, 4.30 – 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. Satadal Ganguly

Postdoctoral Fellow, School of Mathematics, Tata Institute of Fundamental Research,

Mumbai, India

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.

Date: 4 Feb 2009, Wednesday, 3.30 – 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker:

Dr. Xu Jing

Research Fellow, Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University,

Singapore

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.

Date: 2 Feb 2009, Monday, 10 – 11am

Venue: SPMS-MAS-03-06, EC1

Speaker: Professor Dr. Martin Reiser

Founding Director, Institute for Media Innovation, Nanyang Technological University,

Singapore

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

Date: 21 Jan 2009, Wednesday, 3.30 – 4.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker: Dr. Hahn Jooyoung,

Research Fellow, Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University,

Singapore

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.

Date: 19 Jan 2009, Wednesday, 10 – 11am

Venue: SPMS-MAS-03-06, EC1

Speaker: Mr. Shaowei Lin

PhD Student, Department of Mathematics, University of California, Berkeley,

USA

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.

Date: 15 Jan 2009, Wednesday, 4 – 5pm

Venue: SPMS-MAS-03-06, EC1

Speaker: Dr. Stephan Baier,

Lecturer in Mathematics, School of Engineering and Science, Jacobs University,
Germany

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.

Date: 15 Jan 2009, Wednesday, 3 – 4pm

Venue: SPMS-MAS-03-07, EC2

Speaker: Prof. Qi-Man Shao,

Professor, Department of Mathematics, Hong Kong University of Science and Technology,  
Hong Kong

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

Date: 13 Jan 2009, Tuesday, 10.30 – 11.30am

Venue: SPMS-MAS-03-06, EC1

Speaker: Prof. Leonard H. Soicher,

Professor, School of Mathematical Sciences, Queen Mary, University of London,
UK

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.

Date: 07 Jan 2009, Wednesday, 4.30– 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker: Prof. Xie Ziqing,
Professor, College of Mathematics and Computer Science, Hunan Normal University,
China

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

Date: 02 Jan 2009, Friday, 2 – 3pm

Venue: SPMS-MAS-03-06, EC1

Speaker: Prof. Tang Tao,
Head and Chair Professor, Department of Mathematics, Hong Kong Baptist University,
Hong Kong

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.