Title: Curvature Domain Diffusion Equation and Mesh/ Image Smoothing

Date: 10 Dec 2008, Wednesday, 4.30 – 5.30pm

Venue: SPMS-MAS-03-06, EC1

Speaker: Prof. Yang Xunnian,
Associate Professor, Department of Mathematics, Zhejiang University, China
Research Fellow, Division of Mathematical Sciences, Nanyang Technological University, Singapore

Abstract:
This talk consists of four parts. Firstly, I will briefly introduce some backgrounds on discrete differential geometry, graph based Laplacian and the challenge for surface smoothing. Secondly, I will introduce the idea of curvature domain diffusion equation (CDE) and the solution to this new nonlinear equation. Thirdly, depending on the proposed CDE and its solution, normal based surface smoothing algorithm is presented. Lastly, normal based image smoothing technique is also given based on CDE.

Title: On Higher Order Convergence of the Integration Error Using quasi-Monte Carlo Rules

Date: 28 Nov 2008, Friday, 4 pm – 5 pm

Venue: SPMS-MAS-03-06, EC1

Speaker: Dr. Josef Dick
Vice Chancellor Fellow,
School of Mathematics and Statistics,
University of New South Wales, Sydney

Abstract:
A quasi-Monte Carlo rule approximates the integral of a function over the unit cube [0, 1]s using the average of function values at quadrature points x0,..., xN−1. It has been shown that there are quadrature points based on digital nets and sequences such that the integration error achieves a convergence of order N−α(log N)αs, where α ≥ 1 can be arbitrarily large for sufficiently smooth integrands. This result uses the behavior of the Walsh coefficients of smooth func¬tions. For example, if f has continuous partial mixed derivatives up to order α ≥ 1, then the question is: what can we say about the decay of its Walsh coefficients? The answer to this question will yield a criterion on the generating matrices of digital nets and sequences via the integration error. Finally, we show how we can explicitly construct generating matrices of digital nets which satisfy this criterion, hence yielding explicit constructions of quadrature points such that the integration error converges with order N−α(log N)αs .

About the Speaker:
Josef Dick received his PhD in 2004 under the supervision of Prof. I. Sloan. Currently he is a Vice-Chancellor Fellow at the School of Mathematics and Statistics at UNSW, Sydney, Australia. His research is in quasi-Monte Carlo methods for numerical integration, discrepancy theory and information based complexity. He is a recipient of the Information-based-complexity Young Researcher Award 2004, the Journal of Complexity Best Paper Award 2005 and was plenary speaker at the Monte Carlo and quasi-Monte Carlo conference in 2008.

Title: Lattice-Based Digital Signatures and NTRUSign

Time: 27 November 2008 (Thursday), 11 am – 12 pm

Venue: MAS-03-07, EC2

Speaker: Professor Jeffrey Hoffstein, Professor of Mathematics, Brown University, USA Co-VP of Research and Founder, NTRU Cryptosystems, USA

Abstract:
I'll start from the beginning, with the definition of a lattice and the concept of a digital signature. I'll explain how lattices are an attractive source of efficient digital signature schemes and how the use of some special lattices arising in the NTRU cryptosystem can make matters even better. Unfortunately, lattice-based digital signatures are also vulnerable to some very interesting attacks.

I'll explain these attacks and also describe some hopefully successful defenses.

Speaker Biography
Jeff is a co-inventor of the NTRU public key cryptographic system, co- founder of NTRU cryptosystems and a Professor of Mathematics at Brown University. He holds six patents, has published over fifty papers on the subjects of number theory, automorphic forms and cryptography, and is the recipient of numerous National Science Foundation grants. Jeff has held academic positions at the University of Rochester, IAS and Göttingen University in Germany. He holds a B.A. from Cornell University and a Ph.D. from MIT

Title: Multi-Parameter Fourier Analysis

Time: 26 November 2008 (Wednesday), 11.30 am – 12.30 pm

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

Speaker: Professor Jill Pipher
Professor of Mathematics, Brown University, USA
Director of Research and Founder,
NTRU Cryptosystems, USA

Abstract:
Classical harmonic analysis, of the Calder´on-Zygmund school, was originally driven by the desire to answer some questions about trigonometric series and to develop a calculus for the study of elliptic differential operators. The theory evolved into a study of broadly defined singular integral (and maximal) operators in Rn which have fundamental connec¬tions to operators arising in complex analysis and in linear and nonlinear partial differential equations. The basic operators are defined by kernels which are invariant under translations and a one parameter family of dilations, x → ρx,ρ > 0. In the multiparameter theory, one considers a different generalization to n dimensions in which the operators in question re¬spect a multiparameter family of dilations, for example x → (ρ1x, ρ2x, ..., ρnx),ρi > 0. Once again, there are connections to the theory of (multiple) Fourier series and to PDE. The talk is an introduction to and overview of some aspects of this theory.

Speaker Biography:
Jill Pipher is Professor of Mathematics, Chair of the Department 2005-2008. She received her Ph.D. from UCLA in 1985, and came to Brown as an Associate Professor in 1990 from the University of Chicago. Her research interests include Fourier analysis, partial differential equations, and cryptography. She has published papers in each of these areas of mathematics, and jointly holds three patents for the NTRU encryption and digital signature algorithms. Her undergraduate textbook, An Introduction to Mathematical Cryptography, jointly authored with Brown colleagues J. Hoffstein and J. Silverman, was recently published by Springer Undergraduate Textbooks in Mathematics. Her awards include an NSF Postdoctoral Fellowship, Presidential Young Investigator Award, Mathematical Sciences Research Institute Fellowship, and an Alfred P. Sloan Foundation Fellowship. Her research in Analysis has been continuously supported by NSF grants. She was recently invited to give the Coxeter Lectures in Mathematics at the Fields Institute, Toronto. She is a co-founder of Ntru Cryptosystems, Inc.

Title: Jet Schemes of Some Matrix-Related Varieties

Time: 26 November 2008 (Wednesday), 10 am – 11 am

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

Speaker: Professor Bharath Al Sethuraman, Professor, Department of Mathematics, California State University, Northridge, USA

Abstract:
We discuss an open problem in commuting matrices and describe how jet schemes of some matrix-related varieties arise naturally in this setting. Jet schemes are the analogues for algebraic varieties of the notion of tangent (and higher order) bundles from differential geometry. We describe some results on the irreducibility of jet schemes of determinantal varieties and jet schemes of the commuting matrix pairs scheme, and also describe some combinatorial results on shellability of simplicial complexes attached to one of these jet schemes.

Speaker Biography:
Prof. B.A. Sethuraman received his B.Tech in engineering from the Indian Institute of Technology, Chennai, and his Ph.D in Mathematics from the University of California San Diego. His research interests are in algebra and algebraic geometry, particularly division algebras and matrix-related varieties, and applications of algebra to wireless communication. He has worked with engineers to help develop algebraic techniques for space-time coding that have proved to be quite versatile.

Status: - Cancelled -

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

Time: 24 November 2008 (Monday), 2 pm – 3 pm

Speaker: Dr David Adams, Research Professor, Department of Physics and Astronomy, Seoul National University, South Korea

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

Abstract:
The Atiyah - Singer index theorem in its various versions is one of the deepest and most celebrated results in modern mathematics. It is also of major importance in quantum gauge field theories of theoretical
particle physics for understanding the chiral anomalies 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 mathematical goal is to extend index theory from its present “smooth” setting to a more general “rough” setting where only an approximate smoothness condition is required. This goal also has strong motivation from physics since it can be used to solve a major
unresolved problem in the lattice formulation of chiral gauge theories: showing that anomaly cancellation is working correctly in these theories.

Speaker Biography
David Adams studied Mathematics and Physics to Masters level at Aarhus University (Denmark) and went on to gain a PhD in the School of Mathematics, University of Dublin (Trinity College) in 1997. He then had postdoctoral stints at Adelaide U. (Australia), Duke U. (USA), Leiden U. (Netherlands), and Florida International U. (USA) before joining Seoul National University (Korea) as a research professor in 2006. Currently he also has a visiting appointment in Taiwan at the National Center for Theoretical Sciences at National Taiwan University. He has previously won two competitive postdoctoral fellowships: an ARC Fellowship from the Australian Research Council and a Marie Curie Individual Fellowship from the European Commission. He has given plenary talks at major international conferences. His publications include 3 single-author articles in Physical Review Letters, and his best-known publication currently has 90+ citations.

Title: On Multiple Level-Set Regularization Methods for Inverse Problems

Time: 26 November 2008 (Wednesday), 4.30-5.30 pm

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

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

Abstract:
We analyze a multiple level-set method for solving inverse problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional based on TV-$H^1$ penalization.

Biography of Speaker:

1. 1993 - 1996 : PhD. in Mathematics at the Goethe-Universit”at (Frankfurt am Main, Germany)
2. 1997 - 2007 : Adjunct professor, Department of Mathematics, Federal Univ. of St. Catarina (Florianopolis, Brazil)
3. Aug 2000 - Mar 2001 : Postdoctoral Position, Institut f"ur Industriemathematik, Kepler Universitat (Linz, Austria)
4. Apr 2003 - Mar 2004 : Postdoctoral Position, RICAM, Austrian Academy of Sciences (Linz, Austria)
5. 2007- Present : Associate professor, Department of Mathematics, Federal Univ. of St. Catarina (Florianopolis, Brazil)
6. Jan 2009 - Jul 2010 : Postdoctoral Position, Humboldt Research Fellowship for Experienced Researchers, (Frankfurt/M and Stuttgart, Germany)

Title: Maximal Orders in Space-Time Coding.

Time: 21 Nov 2008, Friday 4 - 5pm

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

Speaker: Prof. B.A. Sethuraman

Abstract:
We present an introduction to the use of maximal orders in space-time coding, based on the work of Lahtonen's group, and then describe how to construct maximal orders in quaternion algebras of minimal discriminant over the Eisenstein field $\mathbb{Q}(\sqrt{-3}$.
This is joint work with Patrick Morandi and Fr\'ed\'erique Oggier.

About the SPEAKER:
Prof. B.A. Sethuraman received his B.Tech in engineering from the Indian Institute of Technology, Chennai, and the Ph.D in mathematics from University of California San Diego.  His research interests are in algebra and algebraic geometry, particularly division algebras and matrix-related varieties, and applications of algebra to wireless communication.  He has worked with engineers to help develop algebraic techniques for space-time coding that have proved to be quite versatile.

TITLE: Golay, Heisenberg and Weyl

TIME: 20 November 2008, Thursday 3:30 - 4:30 pm

VENUE: MAS-03-06 (Executive Classroom 1)

SPEAKER: Professor A. Robert Calderbank, Princeton University

ABSTRACT:
Sixty years ago, efforts by Marcel Golay to improve the sensitivity of far infrared spectrometry led to the discovery of pairs of complementary sequences. We will describe how these sequences are finding new application in active sensing, where the challenge is how to see faster, to see more finely where necessary, and to see with greater sensitivity, by being more discriminating about how we look.

About the SPEAKER:
A. Robert Calderbank is a professor of Electrical Engineering, Mathematics and Applied and Computational Mathematics at Princeton University. He received a BSc degree from University of Warwick in 1975, an Master's degree from University of Oxford in 1976, England, and a PhD degree from the California Institute of Technology, all in mathematics.
He became a member of the technical staff at Bell Labs in 1980. Over the next 23 years, he rose through the ranks, eventually becoming vice president for research and Internet and network systems at AT&T Labs.
He joined Princeton University in 2003.

He has made numerous contributions to the fields of coding and information theory, including the discovery of space-time coding.
Widely recognized by the professional engineering community for his contributions to data communications and storage, he is the recipient of several awards from the Institute for Electrical and Electronics Engineers, including the IEEE Information Theory Prize Paper Award twice. He earned AT&T's highest technical honor in 2000 when he was appointed an AT&T Fellow. He was elected to the US National Academy of Engineering in 2005.

Title: A Nonlinear Structure Tensor with Diffusivity Matrix Composed of Image Gradient

Time: 19 November 2008 (Wednesday), 4.30 pm – 5.30 pm

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

Speaker: Dr. Hahn Jooyoung, Research Fellow, NTU

Abstract:
We propose a nonlinear partial differential equation (PDE) for regularizing a tensor which contains the first derivative information of an image, such as strength of edges and a direction of the gradient of the image. Unlike a typical diffsivity matrix which consists of derivatives of a tensor data, we propose a diffsivity matrix which consists of the tensor data itself, i.e., derivatives of an image. This allows directional smoothing for the tensor along edges which are not in the tensor but in the image. That is, a tensor in the proposed PDE is diffused fast along edges of an image but slowly across them. Since we have a regularized tensor which properly represents the first derivative information of an image, the tensor is useful to improve the quality of image denoising, image enhancement, corner detection, and ramp preserving denoising. We also prove the uniqueness and existence of solution to the proposed PDE.

Title: On the difference between the thresholds in secret sharing schemes over constant size fields

Time: 19 Nov 2008, Wednesday 1030 - 1130am

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

Speaker: Ignacio Cascudo

Abstract:
Linear secret sharing schemes are cryptographic protocols used to split the knowledge of a secret (an element of a finite field) among a number of players. This is done in such a way that any subset of players bigger than certain threshold can reconstruct the secret using the joint information they own, but for a set of players with size up to certain threshold, any element of the finite field is equally likely to be the secret. In 2006 Chen and Cramer proposed a scheme using algebraic curves, that allows to have as many players as we want, while keeping the size of the field fixed and sending only one field element to each player. In their scheme the gap between the thresholds is in principle two times the genus of the curve.
We show several ways to decrease this difference between the thresholds by appropriately selecting the parameters of the scheme. On the other hand we give some results and limitations on the minimum amount of information that the players have to receive if we want to achieve certain thresholds (joint work with H.Chen, R.Cramer, C.Xing).

Title: Privacy-Preserving Density Estimation based Clustering in Distributed Environment

Time: 18 Nov 2008, Tuesday 4 - 5pm

Venue: SPMS-MAS-03-06, EC 1

Speaker: Chunhua SU

Abstract:
The rapid growth of the Internet provides people with
tremendous opportunities for data collection, knowledge discovery and
cooperative computation.
However, it also brings the problem of sensitive information leakage.
Both individuals and enterprises may suffer from the massive data
collection and
the information retrieval by distrusted parties. In this paper we
study the privacy issue of clustering algorithms, which are the
classic algorithms for data mining. We propose a distributed data
clustering scheme using the random data perturbation (RDP) technique,
which has been widely used for preserving the privacy of individual
records in statistical databases. Our scheme applies linear
transformation to Gaussian distribution perturbed data and solves the
security problem of distributed kernel density estimation which
assumed a mediate party to help in the computation. We also show that
our scheme is more secure against the random matrix-based filtering
attack which is based on analysis of the distribution of the
eigenvalues.


About the SPEAKER:
Chunhua Su received the B.S. degree for Beijing Electronic and Science
Institute in 2003 and recieved his M.S. from Faculty of Engineering,
Kyushu University in 2006. He is currently working toward the PhD.
degree in the Graduate School of Information Science and Electrical
Engineering, Kyushu University. His current research interests are in
privacy-preserving data mining and secure multi-party computation

Title: Computing in the Dark Using Algebraic Geometry

Time: 17 November 2008 (Monday), 10 am – 12 pm

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:
Cryptology provides mathematical techniques for digital security in a malicious environment. Encryptions and digital signatures protect legitimate parties against eavesdropping and tampering by malicious outsiders, i.e. uni-lateral security. Secure computation focuses instead on multi-lateral security, i.e. secure cooperation among mutually distrusting parties or parties with conflicting interests. Potential applications are myriad, and include privacy protection, negotiations, and simulation of an incorruptible mediator. A fundamental theorem  from the 1980s say in essence that “all multi-lateral security problems solvable with a trusted host are securely solvable without.”

In 2000, it was proved by Cramer, Damgaard and Maurer that secure computation can be realized from mathematical devices called linear secret sharing schemes with (strong) multiplication. In 2006, it was shown by Chen and Cramer that such devices can be constructed using algebraic function fields. Using in addition the celebrated theorem that the Drinfeld-Vladuts bound can be attained by algebraic function fields, they showed how to perform secure computation with improved efficiency. This is the first non-trivial connection between secure computation and algebraic geometry.  

The talk consists of two parts:
Part I: Secret Sharing
Part II: Secure Multi-Party Computation

Speaker Biography:
Ronald Cramer is a Professor (Chair in Cryptology) at the Mathematical Institute, Leiden University. He is the founder and head of the Cryptology Research Group at CWI Amsterdam, the national research centre for mathematics and computer science in the Netherlands. Prior to his return to the Netherlands in 2004, he held research positions at ETH Zurich and University of Aarhus (1997-2004). His research interests include mathematical cryptology, especially interactions with number theory, geometry and combinatorics, as well as all aspects of theoretical cryptology.

Title: Sense and Respond Systems

Time: 12-14 November 2008 (Wednesday - Friday), 10.30 am – 12 pm

Venue: SPMS-MAS-03-06, EC 1

Speaker: Professor K Mani Chandy, Simon Ramo Professor of Computer Science, California Institute of Technology, USA

Abstract:
This is a sequence of three talks to explore research collaboration opportunities between NTU and other organizations in Singapore and research groups at Caltech. Therefore, these talks will be interactive with the aim of identifying the research topics in which groups in Singapore are interested and not interested, and then planning initial steps in cooperation. A sense and respond system responds to changing conditions in the environment. Conditions of interest may be natural threats such as hurricanes, flooding, and pandemics; human threats such as different forms of criminal or terrorist acts such as exploding improvised radiation-generating “dirty bombs”; smart-environment sensory information such as the best way to drive to work given varying traffic congestion; and opportunities such as commodity or stock trading opportunities given stock, blogs and news information. This talk is an introduction to sense and respond systems. The aim of the talk is to suggest that there is a common methodology, a common architecture and a common theory that forms the foundations of all sense and respond systems. The focus of the talk is on data acquisition, fusion of data to obtain intelligence and then responding based on the intelligence. This initial talk sets the framework. The following two talks discuss some of the theory and implementations into more detail.

Title: Ideal Hierarchical Secret Sharing Schemes

Time: 14 Nov 2008, Friday, 4 - 5pm

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

Speaker: Dr Carles Padro

Abstract:
We consider secret sharing schemes in which the participants are totally ordered in a hierarchy. If a participant in a qualified set is substituted by a higher participant, the resulting subset must be qualified as well. We investigate ideal hierarchical secret sharing schemes and we completely characterize their access structures. This is done by using the connection between ideal multipartite secret sharing schemes and discrete polymatroids that was introduced in our paper in Eurocrypt 2007.

Title: A Computational Study on the Non-Newtonian Impact Problem

Time: 13 November 2008, Thursday, 3 – 4 pm

Venue: MAS-03-06 (Executive Classroom 2)

Speaker: Professor Lei Hou, Professor, Department of Mathematics,
Shanghai University, China

Abstract:
Many materials perform the non-Newtonian property in the micron-scale rheometry test. In this paper, an application of non-Newtonian rate type property, such as impact hardening and share thinning behaviour, is discussed and I hope to shied further light on the mathematical and virtual test methods in the auto-crash safety analysis. Life is always too weak to protect from the non-recover solid metal (phase1) impact, we are deepening our knowledge of soft material recover protection (phase2), known as the passive safety concept. The accurate mathematical prediction would supply ultimate research tool for the passive safety analysis in such scale.

Speaker Biography
1989 – 1998 : M.Sc, PhD and Post-Doc in Computational Physics and Applied Math., United Kingdom;
1998 – 2005 : Research Fellow and PhD Supervisor in finite element modeling and nonlinear analysis on the engineering and industrial mathematical problems (EPSRC, ARUP projects), United Kingdom;
2005 – Present : Professor, Mathematics Department, Shanghai University NNSF, Shanghai Pu-Jiang & ARUP projects), China.

Title: A review of hidden Markov models and Markov random fields with recent applications in vision problems

Time: 5 November 2008, 1630-1730

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

Speaker: Prof. Lian Heng

Seminar Abstract:
In this talk, I will introduce the hidden Markov models (HMM) originally applied to natural language processing (NLP) and review the extension of HMM to the two dimensional case, the hidden Markov random fields, which has direct applications in image denoising, image segmention, etc. Along the way, connections to anisotropic diffusion and PDE methods will be explained. I will give a selected review of some recent applications of these models, including human identification using gait, dimensionality reduction, field of experts and man-made structure detection. These applications demonstrate the wide applicability of the random fields framework.

For the latest information of the seminar, you can check it in our website
http://www1.spms.ntu.edu.sg/~image

Time: 31 Oct 2008, Friday 4 - 5pm

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

Speaker: Prof. Andreas Winter

Abstract:
Every sufficiently rich set of measurements on a fixed quantum system defines a statistical norm on the states of that system via the optimal bias that can be achieved in distinguishing the states using measurements from that set (assuming equal priors). The Holevo-Helstrom theorem says that for the set of all measurements this norm is the trace norm. For finite dimension any norm is lower and upper bounded by constant (though dimension dependent) multiples of the trace norm, so we set ourselves the task of computing or bounding the best possible "constants of domination" for the norms corresponding to various restricted sets of measurements, thereby determining the worst case and best case performance of these sets relative to the set of all measurements.
Apart from some specific examples, our most important contribution is the analysis of the multipartite setting with any measurement allowed that can be implemented by local operations and classical communication (LOCC). This is an important case because of the phenomenon of "data hiding": even two orthogonal states can be almost indistinguishable under LOCC. In the case of two parties, we show that the lower domination constant is of the same order as that of a tensor product of local uniformly random POVMs. This answers in the affirmative an open question about the (near-)optimality of bipartite data hiding: The bias that can be achieved by LOCC in discriminating two orthogonal states of a d x d bipartite system is Omega(1/d), which is known to be tight.
[Based on joint work with S Wehner and W Matthews, arXiv:0810.2327]

About the Speaker:
Andreas Winter received his PhD from the Department of Mathematics, University of Bielefeld (Germany) in 1999. He has been with the University of Bristol since 2001, first as a postdoc in the Department of Computer Science, since 2003 as Lecturer with the Department of Mathematics, and finally as Professor for the Physics of Information since 2006. Since 2007 he is a visiting research professor at the National University of Singapore. His research interests include quantum information, complexity theory and discrete mathematics.

Title: Mixed multiscale finite element methods using limited global

Time: 29 October 2008, 1630-1730

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

Speaker: Prof. Yalchin Efendiev, Texas A&M University
information and applications 

Seminar Abstract :
In this talk, I will describe mixed multiscale finite element methods for solving elliptic equations with oscillatory coefficients and applications to flows in heterogeneous porous media. The use of limited global information is needed to capture non-local features of the solutions. These features cannot typically be captured via local multiscale basis functions. We will talk about the generalization of mixed MsFEMs to stochastic equations. Finally, the applications to multi-phase flow/transport and nonuniform coarsening mechanisms will be discussed.  
For the latest information of the seminar, you can check it in our website
http://www1.spms.ntu.edu.sg/~image

Title: Testing the hypothesis that a large-dimensional variance-covariance matrix is equal to a given matrix by Prof. Bai Zhidong

Date: 28 Oct 08 (Tues) 2-3pm

Venue: SPMS-MAS-03-06, EC1

Abstract: See attached

Title: Galois Rings and Pseudo Random sequences

Date: 24 Oct 2008 Friday 4 - 5pm

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

Speaker: Dr. Patrick Solé

Abstract:
We survey our joint work with Dimitrii Zinoviev on Pseudo random sequences generation by use of weighted degree trace codes over Galois rings. Applications range from cryptography (ML sequences over rings) to signal processing (PAPR reduction in OFDM communication systems).

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: Cryptographic Hashing at Crossroads

Time: 17 Oct 2008 Friday 4 - 5 pm

Venue: MAS-03-06 (Executive Class Room 1)

Speaker: Josef Pieprzyk

ABSTRACT: This is a review of the state of the art in cryptographic hashing. In particular, we first introduce basic definitions, properties and structures of cryptographic hashing. Next, we examine basic solutions of cryptographic hashing using block ciphers. Overview of custom-designed hashing follows. We next discuss solutions derived from intractable problems. Finally, we describe the requirements and expectations of the NIST call for SHA-3.

TITLE: The curve of centers of a finite points set

TIME: 17 Oct 2008 Friday 1030 - 1130 am

VENUE: MAS-03-06 (Executive Class Room 1)

SPEAKER: Wang Xinli

ABSTRACT: The talk is about a curve of centers of a finite points set.
A curve \mu_r of a certain points set embodies many symmetric properties of the points set. From this curve of \mu_r, we could speculate the original points set. What's more, it's possible to speculate the whole curve \mu from finitely many points located on this curve, and then to know the original set. The curve is related to the detection of symmetry of a points set as well as symmetrization.

About the SPEAKER:
Wang xinli had her Bachelor of Science in NCUT (North China University of Technology)(2002-2006), she is currently pursuing her PhD in NTU since August 2008 under the supervision of Prof. Chee Yeow Meng and Prof. Sinai Robins

Date: 15 Oct 08, (Wed)
Time: 1630-1730

Title : Variational Image Segmentation Using Multilayer Implicit Curve

Time : 15 October 2008, 1630-1730

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

Speaker : Ginmo J. CHUNG, Hokkaido University, Japan.
Evolution Approach

Seminar Abstract :
Recently variational image processing has become popular thanks to its strong mathematical theory and existence of state-of-the-art numerical methods for solving PDEs. In this talk, we present a piecewise constant image segmentation model based on a new implicit curve evolution technique in variational framework. In our approach, we use multiple level sets of the evolving level set function to represent the boundaries among objects. Our proposed model can be viewed as an extension of the piecewise constant Chan-Vese segmentation model by combining their model with multilayer level set approach. This new approach can be applied for images with known topology and nested structure. e.g. MR brain images. By construction our approach is more efficient way of partitioning images. We show how we can apply the multilayer segmentation model to 3D MR brain data sets. We also discuss different choices of regularization in order to keep the level set function more regular.

For the latest information of the seminar, you can check it in our website
http://www1.spms.ntu.edu.sg/~image

Abstract:
The class of quasi-twisted codes are known to contain lots of good codes. By employing Discrete Fourier Transform(DFT) and Generalized Discrete Fourier Transform(GDFT), the algebraic structure of quasi-cyclic(QC) codes have been carefully studied. Unfortunately, very little known on the algebraic structure of quasi-twisted(QT) codes or explicit constructions, especially the repeated root case. In this paper, the spectral technique has been generalized to study the algebraic structure of QT codes. With the growing interest in generator construction of QT codes, explicit construction formula is derived in this paper, which is another direction to study the construction of QT codes. It has been shown that some best-known linear codes can also be obtained by the formula.

References:
[1]S. Ling and P. Sol´e, "On the algebraic structure of quasi-cyclic codes I: Finite Fields," IEEE Trans. Inform. Theory, vol.47, pp.2751-2760, 2001.
[2]S. Ling and P. Sol´e, "On the algebraic structure of quasi-cyclic codes II: chain rings," Designs, Codes and Cryptography 30. pp.113-130, 2003.
[3]S. Ling and P. Sol´e, "On the algebraic structure of quasi-cyclic codes III: generator theory," IEEE Trans. Inform. Theory, vol.51, pp. 2692-2700, 2005.
[4]S. Ling, H. Niederreiter, and P. Sol´e,"On the Algebraic Structure of Quasi-cyclic Codes IV: Repeated Roots," Designs, Codes and Cryptography 38, no. 3, pp.337-361, 2006.

About the Speaker:
Jia Yan obtained a Bachelor Degree in Mathematics from Shanghai Jiao Tong University, China. She is currently pursuing PhD studies on "Algebraic Methods of Coding Theory" at Division of Mathematical Science, Nanyang Technology University, Singapore.

Date: 8 Oct 2008, Wed
Time: 9 am to 10 am

Title : Variational Methods on Image Processing

Speaker: Dr. Lin He

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

Seminar Abstract :
Image processing is a very broad are which can be roughly divided into three major categories: image compression, image enhancement and restoration, and measurement extraction. Variational method, a method arisen from Physics, Statistics and so on, is to find the extremum of an integral involving a function and its derivatives. For more than a decade, applying variational methods on image processing has been quite popular. And the literature over there covers more or less part of or all of the following: developing new models, theoretical analysis on mathematical models, developing fast computational algorithms and applying mathematical algorithms on different applications.
My talk will review existing models emerged from different applications I have worked on (such as noise removal, deblurring, segmentation, image inpainting, MR image reconstruction), to generalize a mathematical framework and to develop new models and fast numerical algorithms combining ideas from other fields.

About the Speaker :
Lin He received her B.A., Ph.D. from the department of Mathematics at the Peking University, China and University of California in Los Angeles, U.S.A in 2001 and 2006 respectively. After a one and a half year post-doctoral research at Radon Institute for Computational and Applied Mathematics (RICAM) in Linz, Austria, she currently works as a research and development engineer for Luminescent Technologies, Inc. in Palo Alto, California. She works on inverse problems with variational PDEs, particularly applications on image processing problems. She also works on level set methods and its applications.

Title: Grassmannian spaces & Codes and Division Algebras

Speaker: Jean Creignou

Venue: SPMS-MAS-03-08

Abstract: This talk is divided in two distinct parts.
The first part deals with codes in Grassmannian spaces.
After a short introduction on codes in Grassmannian spaces, we will present a method to construct infinite families of optimal (regarding the so-called chordal distance) codes in Grassmannian spaces.

The second part of the talk concerns codes and division algebras.
We will explain briefly how division algebras are related to wireless communication. Then we will discuss about the construction of division algebras which fulfills constrains related wireless communications.

About the Speaker:
Jean Creignou is pursuing PhD studies on "Codes for wireless multi-antennas communication" at the mathematical institute of Bordeaux
(France) and will defend his thesis in November 2008.
His scientific interests include cryptography, information security, error correcting codes and discrete mathematics. He obtained a Master Degree in Mathematics from the university of Rennes and a Master Degree in Cryptography and Information Security from the university of Bordeaux.

Title: An Analogue of the Gallai-Edmonds Structure Theorem for Nonzero Roots of the Matching Polynomial

Speaker: Ku Cheng Yeaw (NUS)

Venue: SPMS-MAS-03-6, Executive Classroom 1

Abstract
Classical Matching Theory is mostly concerned with zero roots of the matching polynomial of graphs. We prove an analogue of the celebrated Gallai-Edmonds Structure Theorem for nonzero roots. Consequently, we show that the matching polynomial of a vertex transitive graph has simple roots, thus disproving a conjecture of Mohar. This is a joint work with William Chen.

Attachment: See attached

Date: 30 Sept 08, Tues
Time: 3pm to 4 pm

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

Title: On pebble automata over infinite alphabets

Speaker: Mr Tony Tan, Israel Institute of Technology

Seminar Abstract :
In this talk we continue the study of pebble automata over infinite alphabets introduced by F. Neven, T. Schwentick and V. Vianu [1,2]. In essence, pebble automata (PA) are finite state automata with a finite number of pebbles. The pebbles are placed on the input word in the stack discipline: first in last out, to mark the input symbols. One pebble can only mark one symbol. The last pebble placed serves as the header. The automata can perform equality tests among symbols marked by the pebbles. As studied in [1,2], PA languages have desirable closure properties; but undesirable in terms of application: the emptiness problem in general is undecidable.

In this talk we present the boundary of the subclass of PA languages of which the emptiness problem is decidable. We also establish the hierarchy of PA languages based on the number of pebbles. A few of our results settle problems left open in [1,2]. Some of the proof of techniques may be of general interest. For example, the proof of the undecidability of the emptiness problem of strong 2 pebble PA is by reduction from Hilbert's tenth problem.

Reference :
[1] F. Neven, T. Schwentick, V. Vianu. Towards regular languages over infinite alphabets.  In the proceedings of 26th International Symposium on Mathematical Foundations of Computer Science 2001, LNCS 2136.

[2] F. Neven, T. Schwentick, V. Vianu. Finite state machines for strings over infinite alphabets. ACM Transactions on Computational Logic 5 (2004),  3: 403-435.


About the Speaker :
Mr Tony Tan is currently pursuing his PhD study and expected to graduate in 2009 in Technion - Israel Institute of Technology. His research interest is mainly on automata and formal languages, finite model theory (in particular, 0-1 law and satisfiability problem in finite model) and computational geometry (in particular, object approximation and deformation). He obtained his B.Comp and M.Sc. in 2003 and 2005, respectively, both in the School of Computing, National University of Singapore.

Seminar Abstract:
This talk presents a method to obtain bounds for codes in Coding Theory. We first give a rough idea of the linear programming method. Then we show how to use this method to get analytical and numerical bounds using our recent results on unitary matrices as an example.

Title: An Invitation to Algebraic Design Theory

Venue: MAS-03-08

Speaker: Dr. Feng Tao

Abstract:  In this talk, I will give a brief introduction to algebraic design theory. I will explain the basic concepts and definitions, and the tools that are used to study them: chracter theory, algebraic number theory as well as group rings. I will laso mention some conjectures we are now interested in, e.g., the Multiplier conjecture and Lander's conjecture.

Bio: Tao Feng obtained his B. Sc.from Beijing Institute of Technology in 2003, and his Ph.D. from Peking University in 2008. He is currently a research fellow at NTU

Date: 19 Sep 08 Friday Time: 4:00pm - 5:00pm

Title:  Fermat Quotients

Venue: MAS-03-08

Speaker: Igor Shparlinski

Abstract: See attached

Venue: MAS-03-08

Abstract:
The concept of erasure-tolerant information authentication was recently introduced to study an unconditionally secure setting where it is allowed to loose a limited number of message letters during transmission. Even if a part of the message is lost, the verifier will still be able to check the authenticity of some or all of the received message letters.  In general, there might be some letters whose authenticity cannot be verified although they have arrived at the recipient's side. These letters will be discarded.

We consider a special case when the verifier can always check the authenticity of all received message letters.  This property is desirable since no data will be lost due to the verifier's inability to verify its authenticity (i.e., the scheme does not introduce additional degradation of the quality of the received information). We provide necessary and sufficient conditions for a set system based erasure-tolerant authentication scheme to be non-degrading. We also discuss efficient implementations and propose a provably secure stream authentication scheme that makes use of erasure-tolerant authentication codes.

This is based on joint work with Goce Jakimoski and was presented at CT-RSA 2007.

SHORT BIO: Yvo Desmedt received his Ph.D. (Summa cum Laude) from the University of Leuven, Belgium (1984).  He is presently the BT Chair of Information Security at University College London, UK. He is also a courtesy professor at Florida State University. His interests include cryptography, network security and computer security. He was program chair of ICITS 2007, co-program chair of CANS 2005, program chair of PKC 2003, the 2002 ACM Workshop on Scientific Aspects of Cyber Terrorism and Crypto '94. He is editor-in-chief of the IET Information Security, editor of the Journal of Computer Security, of Information Processing Letters and of Advances in Mathematics of Communications.
He has given invited lectures at several conferences and workshop in 5 different continents. He has authored over 150 refereed papers. He has
135 entries on DBLP.

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

Seminar Title : Integrals

Seminar Abstract :
We will study some basic properties of definite integrals and mean value theorem. We will prove fundamental theorem of calculus which links indefinite integrals to definite integrals. Methods of integration will be discussed together with examples.

About the Speaker :
Dr Zhang Yongmin is a lead research analyst in Capital Market Research Group of Washington Mutual. His area is in fixed income and mortgage analysis. Before he joined this group, he was an assistant professor at State University of New York where he did research in turbulent flow and American options with more than twenty publications. He has also taught numerous courses in Applied Mathematics and Statistics. Prior to this appointment, he was a research scientist at SUNY Research Foundation. He was a co-principle investigator for various grants from US Department of Energy. He holds his Ph.D. in Applied Mathematics from University of Chicago.

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

Seminar Title: American Option Pricing Models and Obstacle Problems

Seminar Abstract :
We first give a brief overview of American option pricing models and numerical methods. We treat American option models as a special class of obstacle problems. Finite element formulation is introduced together with error analysis of numerical solutions. Some interesting properties about sensitivity of the option price to the payoff function are proved. We also give a criterion for the convergence of numerical free boundaries (optimal exercise boundaries) under mesh refinement. Some future research plans will be discussed.

About the Speaker :
Dr Zhang Yongmin is a lead research analyst in Capital Market Research Group of Washington Mutual. His area is in fixed income and mortgage analysis. Before he joined this group, he was an assistant professor at State University of New York where he did research in turbulent flow and American options with more than twenty publications. He has also taught numerous courses in Applied Mathematics and Statistics. Prior to this appointment, he was a research scientist at SUNY Research Foundation. He was a co-principle investigator for various grants from US Department of Energy. He holds his Ph.D. in Applied Mathematics from University of Chicago.

Abstract:
A Weil number is called short if it can be represented as the sum of a small number of roots of unity. Kedlaya has shown that short, nontrivial Weil numbers in Q(\zeta_p) cannot exist under some condition. It is conjectured that short Weil numbers in Q(\zeta_p) still cannot exist under much weaker conditions. A proof of this conjecture would be very useful for the theory of multipliers of difference sets. In this talk, we study short Weil numbers of a specific form which give rise to an intriguing combinatorial problem. It turns out that a celebrated addition theorem of Kneser's yields useful insights.

Venue: SPMS-MAS-03-08

Seminar Title: From algorithms for polynomial multiplication to error-correcting codes and back

Speaker: Dr. Mike Kaminski

BIOGRAPHY: Dr. Mike Kaminski is currently visiting our division. Website: http://www.cs.technion.ac.il/people/kaminski/

ABSTRACT: This is a series of three lectures, each between one and one and a half hour,
intended to show a very tight relationship between algorithms for multiplication of polynomials
over finite fields and error-correcting codes.

Tutorial 1: Algorithms for polynomial multiplication.

This is a general introduction to polynomial multiplication that does not require any
background (neither in Computability, nor in Mathematics). I have already taught this
material in my first MAS720 lecture.

Tutorial 2: From algorithms for polynomial multiplication to error-correcting codes – a lower bound.

In this tutorial I will show how algorithms for polynomial multiplication can be transformed
into error-correcting codes. I will teach all necessary Math background (that is not deep,
but acquaintance with regular matrix representation of field extensions would help).

Tutorial 3: From Goppa codes to algorithms for polynomial multiplication – an upper bound.

In this tutorial I will show how Goppa codes transform into algorithms for polynomial
multiplication (the D.V. & G.V. Chudnovsky algorithm). Math background required is basics
of Algebraic Function Fields (up to the Riemann-Roch theorem) needed for understanding
Goppa codes.

Venue: SPMS-MAS-03-08

Title: Revisiting the Karnin, Greene and Hellman Bounds for Secrets Sharing

Speaker: Prof. Yvo Desmedt

Abstract:
Secret sharing plays an important role in modern cryptography. In a t- out-of-n threshold scheme, n parties receive shares of a secret such that any t
+1 can
reconstruct the secret, but t cannot. When the probability distribution corresponding to these t shares is independent of the secret, the threshold scheme is called perfect. To satisfy this requirement the size of each share must be at least the size of the secret. If we have equality, we call the scheme "ideal".

Karnin, Greene and Hellman (1983) gave several bounds concerning the maximal number of participants (i.e., the maximal n) in ideal threshold sharing schemes.  We revisit and update the Karnin, Greene, and Hellman bounds, providing optimal bounds on the number of participants in ideal linear threshold secret sharing schemes for various finite fields. We construct these bounds using the same tools that Karnin, Greene, and Hellman introduced in their seminal paper.  We provide optimal bounds for the maximal number of players for a t-out-of-n ideal linear threshold scheme when t=3, for all possible finite fields.  These bounds are very similar to the Bush bounds on MDS codes.  We then generalize this observation.

Seminar Abstract :
A review of hydrodynamic stability theory for fluid flows of practical importance is given. Particular attention is given to the stability of shear flows relevant to aerodynamics. Strongly nonlinear theories are used to determine the stream-wise vortex component of the flow. The latter component plays the crucial role in the preparation of the flow to admit small-scale disturbances which ultimately lead to the onset of turbulence. A new criterion for the onset of transition is derived.

Abstract: This is joint work with Stephan Baier.  Mean-values of arithmetic functions are very often well-understood unless the averaging is taken over a sparse set of natural numbers.  The arithmetic function of interest in this talk is λ(n), the normalized n-th Fourier coefficient of a holomorphic cusp form for the full modular group, and the sparse set consists of Piatetski-Shapiro primes (defined below).  We show that there exists some constant C>0 depending on the cusp form and for every fixed c with 1 < c < 8/7, the mean value of λ(p) is << exp(-C (\log N)1/2 ) as p runs over all (Piatetski-Shapiro) primes of the form [nc] with for some natural number n ≤ N.  I will discuss the history and motivation of the relevant topics, give a rough idea of the proof and some possible future directions of this problem.

Date: 15th Aug 08, Fri
Time: 3 - 5pm

Seminar Title: Some constructions of optimal constant-weight codes

Abstract: In this presentation, I will introduce a couple of new constructions for optimal nonbinary constant-weight codes. These constructions show that 1) A_q(q, 4, 3) = q(q - 1)(q - 2)/6 for all q > 2, and 2) with q and w are given, A_q(n, 2w - 1, w) = (q - 1)n/w, for all sufficiently large n satisfying w|(q - 1)n. Here the notation A_q(n, d, w) refers to the maximal size of a q-ary code of length n, distance d, and constant-weight w.

Speaker: Dau Son Hoang

Biography: Dau Son Hoang got his Bachelor's degree in Applied Mathematics and Informatics in 2006, from the College of Science, Vietnam National University, Hanoi, and his Master's degree in Coding Theory in 2008, from the School of Physical and Mathematical Sciences, NTU. His research interests include coding theory, discrete mathematics and their applications.

Venue: Executive Classroom 1, MAS-03-06

Title:  n-level density of the low-lying zeros of quadratic Dirichlet L-functions

Speaker: Dr. Gao Peng, NTU

Abstract: See Attached

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

Seminar Title : Intelligent information processing systems

Seminar Abstract: An important issue that we encounter today is how to make effective use of the enormous amount of data. These data we can get via internet are from various ways such as various database, electronic articles, academia literatures, technical experimental results, etc. How to automatically and effectively extract, integrate and make use of information embedded in such heterogeneous unstructured data is a challenging task. Two systems, ONBIRES and QUANTA, will be introduced in the talk.

ONBIRES (ONtology-based BIological Relation Extraction System) is designed to perform the tasks: automatic relation extraction from literature, knowledge management such as biological interaction network visualization and query answer, providing hypothesis prediction information for new biological concepts discovery, and even information for knowledge inference.

QUANTA (QUestion Answering Tavern) is a prototype system of question answering, which is designed for natural language search. Currently, search engines, such as Google, all push the task of data mining back to users. The process of a web search is an interactive process repeating what’s illustrated below: the user has to analyze pages to find the information needed and, often, requires better keywords to repeat the search. We think the next generation search engine should be able to provide direct answers. Such a system is possible as demonstrated in our QUANTA system.


About the Speaker : ZHU Xiaoyan, Professor, Deputy Head of state key lab of intelligent technology and systems, Tsinghua University. She got her bachelor degree at University of Science and Technology Beijing in 1982, master degree at Kobe University in 1987 and Ph. D. degree at Nagoya Institute of Technology, Japan in 1990. She is teaching at Tsinghua University since 1993. Her research interests include pattern recognition, neural network, machine learning, natural language processing and bioinformatics.

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

Title : Computational Math/Physics on Desktops can now resolve hard open problems in Planetary Atmospheres

Abstract : Several open problems regarding super-rotation of Venus atmosphere and the structure and persistence of Jupiter’s Great Red Spot (14000 km across) – in particular the high velocity of 100 m/s in its circumferential band of 3000 km width as observed by Voyagers 1 and 2 – were partially resolved using advanced Monte-Carlo simulations on Desktops of the author’s recent unified statistical theory of shallow water flows on a rotating sphere.

This talk will emphasize some open mathematical problems connected with the existence of constrained minimizers for the Lagrangian of the flow and their relation to the minimizers of the free energy of the statistical theory. Collaborations include T. Andersen, S.M. Assad, Xueru Ding, J. Nebus, R.S. Mavi, and Junping Shi and research over the past 4 years funded by US ARO and DOE.

About the Speaker : Prof Chjan Lim has been a Full Professor at Rensselaer Polytechnic University since 2002. He was appointed as a Visiting Professor at National University of Singapore during parts of 2000 to 2001. He has been invited to give talks on several occasions at ICIAM Zurich, GAMM Berlin, IUTAM  Moscow, Como, Italy. He won the Silver Medal at the Malaysian Math Olympiad 1977.  He graduated with a B.S.E from Princeton University in 1982 and holds a M.Sc and PhD in Applied Math from Brown University. He obtained his Postdoc from University of Michigan Ann Arbor and IMA, University of Minnesota.

Venue: Executive Classroom 1, MAS-03-06

Title:  Eigenvalues of Large Dimensional Random Matrices

Speaker: Prof Jack W. Silverstein, North Carolina State University, USA

Abstract: See Attached

Venue : Executive Classroom 1, MAS-03-06

Seminar Title :  Computability, Definability, and Metamathematics

Seminar Abstract :
There is a natural hierarchy of mathematical objects going from finite, to infinite, to analytic, and finally to the horizon of the very large. Within each context there is also a hierarchy of properties of the objects there and methodologies used to study them.  Part of the role of Mathematical Logic is to make sense of this structure, classify, and calibrate it.  Then one can ask and answer interesting questions, such as  measuring to what extent phenomena in the large are reflected within the small, both theoretically and practically.  One can also ask whether the explanation given is inevitable.

We will give a survey of results in the subject, with more focus on concrete examples than on generalities.

About the Speaker :
Professor Theodore Slaman, University of California Berkeley,  is best known for his work in Recursion Theory and recently for applying recursion and set theoretic methods to the study of randomness.

Slaman received his PhD in 1981 from Harvard University under the supervision of Gerald Sacks.  He spent his early career at the University of Chicago and then moved to the University of California, Berkeley in 1996, where he is now a Distinguished Professor of Mathematics.  He is the recipient of a National Science Foundation Presidential Young Investigator Award, a Japan Society for the Promotion of Science Fellowship, and a Alexander von Humboldt Research Award. 

Slaman is a frequent visitor to Singapore and currently holds a three-year Distinguished Visiting Professorship at NUS.

Venue: SPMS-MAS-03-06

Title: Secret Sharing: a Taxonomy of Data Distribution Protocols

Abstract: With the expansion of communication networks, it became obvious to ask for the existence of protocols to distribute information amongst several participants in order to overcome the requirement of having a member storing all secret parameters of a construction. However, to achieve this goal, security has to be provided. Secret sharing was designed to facilitate the distributed storage of a secret in an unreliable environment. Since its introduction by Blakley and Shamir in 1979, this primitive has been playing important roles in group-oriented cryptography. In this talk, we will present a taxonomy of the main constructions and properties for secret sharing techniques. This presentation is mainly dedicated to research students.

About the speaker: Christophe Tartary obtained a PhD in Computer Science from Macquarie University, Australia (2007). He is currently a research fellow in the Division of Mathematical Sciences at Nanyang Technological University (Singapore) and in the Institute for Theoretical Computer Science at Tsinghua University (Beijing, P. R. China). His research interests include multicast security, multiparty computation, secret sharing and coding theory. web: http://www1.spms.ntu.edu.sg/~ctartary

Venue : MAS-03-06, Executive Classroom 1

Seminar Title : Bayesian Language Models with Pitman-Yor Processes

Abstract : We study Bayesian models of natural languages achieving state-of-the-art performance. The models are based upon two ideas.
First, languages have power law statistical behaviour with a few very common events and very many rare events; we model this with a class of nonparametric Bayesian models called Pitman-Yor processes. Second, language models are very large and language data sparse, thus smoothing (or sharing of information) across the models is essential to the success of the models; we use the concept of hierarchical Bayesian modelling to achieve smoothing. Put together, our hierarchical Pitman-Yor language model succeeds in achieving state-of-the-art performance. We show that interpolated Kneser-Ney (one of the best and most well-known smoothing techniques) can be interpreted as an approximation to the hierarchical Pitman-Yor language model. We also show that an extension of our model can address the issue of domain adaptation in a principled Bayesian fashion.

About the Speaker :
Teh Yee Whye became a lecturer (equivalent to assistant professor) at Gatsby Computational Neuroscience Unit, UCL, United Kingdom in 2007. He received his PhD from the University of Toronto in 2003 under the tutelage of Geoffrey Hinton. He was a postdoc at the University of California, Berkeley working with Michael Jordan, and at the National University of Singapore working with Wee Sun Lee, where he received a Lee Kwan Yew Postdoctoral Fellowship. He is interested in Bayesian and probabilistic approaches to machine learning, and applications in information retrieval, natural language processing, computer vision, and computational biology.

Venue: SS2-01-17, TR100

Title: Network FRESCO: A Framework for Experimental Screening, Control, and Optimization

Seminar Abstract: FRESCO is an interdisciplinary project driven by the challenging long-standing problem of optimizing performance of wireless networks under changing operating conditions. A new experimental design called a locating array is introduced to efficiently identify significant factors and low-order interactions of factors when the number of factors is massive.  Profile-driven regression is a new hybrid regression methodology to address the issues in non-linear modelling through the use of profiling. The methodology is applied to derive models from a stochastic simulation of a mobile ad hoc network. Novel self-tuning techniques are developed to decide when and what localized measurements are needed in the network to drive the real-time statistical monitoring, model evolution, and adaptive control to optimize network performance as conditions change.

About the Speaker: Violet R. Syrotiuk earned her Ph.D. in Computer Science from the University of Waterloo (Canada) in 1992. She joined Arizona State University in 2002 and is currently an Associate Professor of Computer Science and Engineering. Dr. Syrotiuk's research has been supported by the U.S. National Science Foundation, Los Alamos National Laboratory,  Defence Science and Technology Organisation (Australia), Architecture Technology Corp., Raytheon Co., and General Dynamics.  She serves on the Editorial Board of Computer Networks and the International Journal of Communication Systems, and on the Technical Program Committee of several major conferences including Mobicom, Mobihoc, and Infocom. Her research interests include medium access control (MAC) and higher layer protocols for multi-hop wireless networks.

VENUE : Block N2, Level 4, Section A, Room no. 2

SEMINAR TITLE : Externalities in Algorithmic Game Theory

SEMINAR EXTRACT : In recent years, there has been a great deal of interests in research at the boundaries between algorithms, game theory and economics. This is because many important artifacts, such as the Internet and the web, are deeply affected by cooperation and competition among parties with different economic interests, and logarithms and protocols, e.g. for routing, resource allocation and electronic commerce, need to be rethought in light of these economic effects.

We consider one particular effect, externalities (or network effects), that links the value of a good to a consumer to the set of other consumers having that good. We will review recent studies on externalities in different areas (including mechanism design, viral marketing and social networks, online dating systems, and envy-free pricing) in algorithmic game theory, and discuss directions for future study.

ABOUT THE SPEAKER : Ning Chen is a Ph.D. candidate in the department of Computer Science & Engineering at the University of Washington, Seattle. He obtained his B.S and M.S. degree both from Fudan University, Shanghai, 2001 and 2004. His research interests include Algorithmic Game Theory, Computational Economics, and Algorithmic and Economic aspects of the Internet.

Title: Coset Stabilized Quantum Codes: New quantum codes from Goethals and Preparata codes

Lecturer: Markus Grassl (Institute for Quantum Optics and Quantum Information Austrian Academia of Sciences Innsbruck, Austria).

Venue: NIE Blk 5 Level 1 – TR45

Seminar Abstract :
Most of the quantum error-correcting codes (QECCs) are based on the stabilizer formalism which relates quantum codes to certain additive codes over GF(4). However, it is known that non-additive QECCs can have a higher dimension compared to additive QECCs with the same length and minimum distance. The most prominent example is the code
((5,6,2)) of Rains et al. More recently, some improved one-error-correcting codes of length 9 and 10 have been found. All these codes can be described as codeword stabilized (CWS) quantum codes.
The class of CWS QECCs is very rich, it includes e.g. all stabilizer codes. The prize we have to pay for this generality is that with increasing length it is getting more difficult to find good codes.

Based on the classical non-linear binary Goethals and Preparata codes, we obtain a new family of non-additive quantum codes with parameters ((2^m,2^{2^m-5m+1},8)). The dimension of these codes is eight times higher than the dimension of the best known additive quantum codes of equal length and minimum distance.

Title: Sequences with good correlation properties
Speaker: Professor K.T. Arasu Wright State University)
Venue: NIE Journal Room (NIE5-03-04)

Abstract: See Attached

Venue: NIE Blk 5 Level 1 – TR45

Title: Mean Values of Cubic Character Sums

Speaker:
Dr. Stephan Baier completed his Ph.D. at the Free University in Berlin, Germany. He has held postdoctoral position in Harish-Chandra Research Institute, the University of Cambridge and Queen’s University in Canada. His research area is in analytic number theory. Currently, he is working as a lecturer in Jacobs University in Bremen.

Seminar:
This is joint work with Matthew Young. Our main result is the following: There exist infinitely many primitive Dirichlet characters $\chi$ of order 3 such that $L(s,\chi)$ does not vanish at the central point, i.e. $L(1/2,\chi)\not=0$. More precisely, the number of such characters with conductor $\le Q$ is $\gg Q^{4/5}$. This result will be deduced from a new asymptotic estimate for the average of $L(1/2,\chi)$ and a new bound for the first moment of $L(1/2,\chi)$ for cubic characters $\chi$. As tools we use the approximate functional equation and certain recursive estimates on cubic character sums.

Venue: NIE Journal Room (NIE, blk. 5 lev. 3)

Title: Amalgams and representations

Speaker: Prof. A.A.Ivanov, Imperial College (London)

Abstract: See Attached

Venue: NIE Blk 7 Level 1 – TR53

Title: Non Vanishing of L functions

Speaker:
Jeff Hoffstein does research in number theory, automorphic forms and multiple Dirichlet series. In 1996 he, Jill Pipher, Joe Silverman created the NTRU public key cryptosystem and founded the company NTRU.

Abstract :
It is well known that given an elliptic curve, whose L-series has a positive sign in its functional equation, there must exist a quadratic twist of the L-series that does not vanish at the center of the critical strip. Suppose one is given two such elliptic curves. Must there exist a quadratic twist such that both L-series simultaneously do not vanish at the center of the critical strip? I'll show that the answer to this question is yes.

Venue: NIE Blk 7 Level 1 – TR53

Title : Public Key Crypto Systems and NTRU

Speaker:
Jeff Hoffstein does research in number theory, automorphic forms and multiple Dirichlet series. In 1996 he, Jill Pipher, Joe Silverman created the NTRU public key cryptosystem and founded the company NTRU.

Abstract :
I'll describe a public key cryptosystem called NTRU. Depending on how one wants to look at it, NTRU is based on convolution rings of polynomials, or on lattices over the integers. It differs from other public key cryptosystems in that the fundamental hard problem it is based on is the difficulty of finding short vectors in lattices of high dimension. It is not based on integer factorization, as in RSA, or the discrete logarithm problem, as in Diffie-Hellman and elliptic curve based cryptosystems. As a result, it is considerably faster and more efficient, and better suited for low powered devices such as cell phones. I will assume no previous knowledge of cryptography or lattices, and the lecture should be entirely self contained.

Abstract: Quantum groups appeared aproximately 25 years ago as a tool
to solve the so-called Yang-Baxter equation. They appeared in form of basic examples and these examples wererelated to simple complex finite dimensional Lie algebras, polynomial Lie algebras, and loop algebras

In the talk I will explain the notion of quantum group and its classical limit, Lie bialgebra.Surprisingly, it turned out to be possible to classify quantum groups,which have  simple complex finite dimensional Lie algebras and
polynomial Lie algebras as the classical limit. 

Venue: NIE Journal Room

Title: Pairing friendly elliptic curves and fields.

Speaker: Professor Igor Shparlinski

Abstract: We present some theoretic and heuristic estimates for the number of elliptic curves with low embedding which is essential for their applicability in pairing based cryptography. We also give estimates for the number of fields over which such curves may exist. The main ideas behind the proofs will be explained as well. Finally, we give a heuristic analysis of the so-called MNT algorithm and show that it produces a rather "thin" sequence of curves.

About the Speaker: Professo