## Seminars 2008

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

Speaker: | Professor Ju Lili |

Date: | 17 December 2008 |

Time: | 4.30pm - 5.30pm |

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

Abstract: | Centroidal Voronoi Tesssellations (CVTs) are special Voronoi tessellations whose generators are also the centers of mass (centroids) of the Voronoi regions with respect to a given density function and CVT-based methodologies have been proven to be very useful in many diverse applications in science and engineering. In the context of image processing and its simplest form, CVT-based algorithms reduce to the well-known k-means clustering and are easy to implement. In this talk, we discuss an edge-weighted centroidal Voronoi Tessellation (EWCVT) model for image segmentation and some efficient algorithms for its construction. Our EWCVT model can overcome some deficiencies possessed by the basic CVT model; in particular, the new model combines the image intensity information together with the length of cluster boundaries, and can handle very sophisticated situations. We demonstrate through extensive examples the efficiency, effectiveness, robustness, and flexibility of the proposed method. |

Title: | Modeling and Simulation of Multiphase Complex Fluids Using An Energetic Variational Phase Field Model Two-fluid Flows |

Speaker: | Professor Jie Shen |

Date: | 10 December 2008 |

Time: | 10.00am - 11.00am |

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

Abstract: | I shall present an energetic variational phase field model for multiphase incompressible flows which leads to a set of coupled nonlinear system consisting of a phase equation and the Navier-Stokes equations. I shall present efficient and accurate numerical schemes for solving this coupled nonlinear system, and show ample numerical results (drop formation and pitching-off, bubble rising in a polymeric fluid, defect motion in a liquid crystal flow etc.) which not only demonstrate the effectiveness of the numerical schemes, but also validate the flexibility and robustness of the phase-field model. |

Title: | An Immersed Interface Method for Solving Viscous Incompressible Two-fluid Flows |

Speaker: | Dr Tan Zhijun |

Date: | 3 December 2008 |

Time: | 4.30pm - 5.30pm |

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

Abstract: | In this talk, we present an immersed interface method for solving viscous incompressible two-fluid flows. The method combines the augmented immersed interface method with front tracking representation of the interface on a uniform Cartesian grid. The immersed interface is represented by a number of Lagrangian control points, and the augmented strategy is to decouple the jump conditions of the fluid variables through two augmented variables. In the proposed method, the augmented interface variables are determined by solving a small system of equations by the LU method or GMRES iterative method. The forces, the augmented variables and their derivatives along the interface, which are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, are interpolated using cubic splines. The fluid equations are discretized on a staggered Cartesian grid by a second order finite difference method. The numerical results show that the overall scheme is second order accurate |

Title: | Ideal Hierarchical Secret Sharing Schemes |

Speaker: | Dr Carles Padro |

Date: | 14 November 2008 |

Time: | 4.00pm - 5.00pm |

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

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 |

Speaker: | Professor Lei Hou |

Date: | 13 November 2008 |

Time: | 3.00pm - 4.00pm |

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

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 |

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

Speaker: | Professor Lian Heng |

Date: | 5 November 2008 |

Time: | 4.30pm - 5.30pm |

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

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. |

Title: | Billiards and the Modular Group |

Speaker: | Professor Eichard Evan Schwartz |

Date: | 5 November 2008 |

Time: | 10.00am - 11.00am |

Venue: | SPMS-MAS-03-06 (EC1) |

Abstract: | Outer Billiards is a simple dynamical system based on a convex shape in the plane. B.H. Neumann introduced this system in the 1950s and then J. Moser popularized it in the 1970s as a toy model for celestial mechanics. All along, one of the central questions has been: Does there exist an outer billiards system with an unbounded orbit? In my talk, I will discuss my (positive) solution to the Moser-Nuemann problem. My solution relates outer billards to such topics as the modular group and self-similar tilings. I'll illustrate the talk with an extensive computer demo. |

Title: | Norms on quantum states and quantum data hiding |

Speaker: | Professor Andreas Winter |

Date: | 31 October 2008 |

Time: | 4.00pm - 5.00pm |

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

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] |

Title: | Mixed multiscale finite element methods using limited global |

Speaker: | Professor Yalchin Efendiev |

Date: | 29 October 2008 |

Time: | 4.30pm - 5.30pm |

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

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. |

Title: | Testing the hypothesis that a large-dimensional variance-covariance matrix is equal to a given matrix |

Speaker: | Professor Bai Zhidong |

Date: | 28 October 2008 |

Time: | 2.00pm - 3.00pm |

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

Abstract: | In this talk, I am giving examples to show that statistics developed based on classical limiting theorems fails to work for large dimensional data and we have to seek new approaches to solve the problem for large dimensional data analysis. In this talk, I shall introduce a method based on Random Matrix Theory to modify the classical approach so that it works well for large dimensional data analysis. |

Title: | Galois Rings and Pseudo Random sequences |

Speaker: | Dr Patrick Solé |

Date: | 24 October 2008 |

Time: | 4.00pm - 5.00pm |

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

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). |

Title: | How to buy a Subgraph: Topics in Algorithmic Game Theory |

Speaker: | Dr Edith Elkind |

Date: | 21 October 2008 |

Time: | 2.00pm - 3.00pm |

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

Abstract: |

Title: | Cryptographic Hashing at Crossroads |

Speaker: | Josef Pieprzyk |

Date: | 17 October 2008 |

Time: | 4.00pm - 5.00pm |

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

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 |

Speaker: | Wang Xinli |

Date: | 17 October 2008 |

Time: | 10.30am - 11.30am |

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

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. |

Title: | Variational Image Segmentation Using Multilayer Implicit Curve |

Speaker: | Ginmo J. CHUNG |

Date: | 15 October 2008 |

Time: | 4.30pm - 5.30pm |

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

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. |

Title: | Some properties of Quasi-Twisted Codes |

Speaker: | Jia Yan |

Date: | 10 October 2008 |

Time: | 4.00pm - 5.00pm |

Venue: | SPMS-MAS-03-08 |

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. |

Title: | Variational Methods on Image Processing |

Speaker: | Dr Lin He |

Date: | 8 October 2008 |

Time: | 9.00am - 10.00am |

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

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. |

Title: | Grassmannian spaces & Codes and Division Algebras |

Speaker: | Jean Creignou |

Date: | 3 October 2008 |

Time: | 4.00pm - 5.00pm |

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. |

Title: | Linear Programming Bounds |

Speaker: | Jean Creignou, Mathematical Institute of Bordeaux (France) |

Date: | 30 September 2008 |

Time: | 10.00am - 11.00am |

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. |

Title: | An Invitation to Algebraic Design Theory |

Speaker: | Dr Feng Tao |

Date: | 26 September 2008 |

Time: | 4.00pm - 5.00pm |

Venue: | MAS-03-08 |

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. |

Title: | Fermat Quotients |

Speaker: | Igor Shparlinski |

Date: | 19 September 2008 |

Time: | 4.00pm - 5.00pm |

Venue: | MAS-03-08 |

Title: | Non-Degrading Erasure-Tolerant Information Authentication With An Application to Multicast Stream Authentication Over Lossy Channels |

Speaker: | Professor Yvo Desmedt |

Date: | 19 September 2008 |

Time: | 2.00pm - 3.00pm |

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. |

Title: | Integrals |

Speaker: | Dr Zhang Yongmin |

Date: | 19 September 2008 |

Time: | 11.00am - 12.00pm |

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

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. |

Title: | American Option Pricing Models and Obstacle Problems |

Speaker: | Dr Zhang Yongmin |

Date: | 19 September 2008 |

Time: | 9.30am - 10.30am |

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

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. |

Title: | A combinatorial problem arising from short Weil numbers |

Speaker: | Ka Hin Leung |

Date: | 12 September 2008 |

Time: | 10.00am - 11.00am |

Venue: | NUS, S16 Level 3, CRB |

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. |

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

Speaker: | Dr Mike Kaminski |

Date: | 2 August, 29 August and 12 September 2008 |

Time: | 4.00pm - 5.30pm |

Venue: | SPMS-MAS-03-08 |

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. |

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

Speaker: | Professor Yvo Desmedt |

Date: | 5 September 2008 |

Time: | 4.00pm - 5.00pm |

Venue: | SPMS-MAS-03-08 |

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. |

Title: | Hydrodynamic Instability Theory : from small disturbances to turbulence. |

Speaker: | Professor Philip Hall |

Date: | 5 September 2008 |

Time: | 3.00pm - 4.00pm |

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

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. |

Title: | On Hecke Eigenvalues at Piatetski-Shapiro Primes |

Speaker: | Liangyi Zhao |

Date: | 3 September 2008 |

Time: | 4.00pm - 5.00pm |

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

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. |

Title: | Nonexistence of Hadamard difference sets in 8x8x9 |

Speaker: | Bernhard Schmidt and Tao Feng |

Date: | 29 August 2008 |

Time: | 10.00am - 11.00am |

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

Abstract: | The search for Hadamard difference sets in 8x8x9 has attracted a lot of attention as it was considered the most promising place to look for counterexamples to Lander’s conjecture. We will show that, unfortunately, no such difference set exists. We have improved upon a previous method, and now our proof in computer free. |

Title: | An introduction to algebraic number theory |

Speaker: | Professor Tian Ye |

Date: | 19 August 2008 |

Time: | 9.30am - 10.30am |

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

Abstract: | Via studying the Diophantine equation Y^2-5=X^3, we introduce some important concepts in algebraic number theory, such as ideals, fractional ideals, ideal class groups, and unit group. |

Title: | Some constructions of optimal constant-weight codes |

Speaker: | Dau Son Hoang |

Date: | 15 August 2008 |

Time: | 3.00pm - 5.00pm |

Venue: | SPMS-MAS-03-08 |

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. |

Title: | Hadamard difference sets and Lander's conjecture |

Speaker: | Associate Professor Bernhard Schmidt |

Date: | 14 August 2008 |

Time: | 4.00pm - 5.00pm |

Venue: | SPMS-MAS-Executive Classroom 1 (Level 3) |

Abstract: | An interesting case to look for counterexamples to Lander's conjecture is Hadamard difference sets in abelian groups of order 576 whose Sylow 3-subgroup is cyclic. We present a method to settle this case, and go through the details for one example. Unfortunately, no counterexample seems to arise. |

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

Speaker: | Dr Gao Peng |

Date: | 13 August 2008 |

Time: | 2.00pm - 3.00pm |

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

Abstract: | The Density Conjecture of Katz and Sarnak associates a classical compact group to each reasonable family of L-functions. Under the assumption of the Generalized Riemann Hypothesis, Rubinstein computed the n-level density of low-lying zeros for the family of quadratic Dirichlet L-functions in the case that the Fourier transform ˆ P f(u) of any test function f is supported in the region n j=1 uj < 1 and showed that the result agrees with the Density Conjecture. In this talk, I will explain my result which improves Rubinstein’s result on computing the n-level density for the Fourier transform ˆf(u) being supported in the region Pn j=1 uj < 2 |

Title: | Intelligent information processing systems |

Speaker: | Professor Zhu Xiaoyan |

Date: | 8 August 2008 |

Time: | 10.30am– 11.30am |

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

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. |

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

Speaker: | Professor Chjan Lim |

Date: | 7 August 2008 |

Time: | 2.00pm - 3.00pm |

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

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. |

Title: | Eigenvalues of Large Dimensional Random Matrices |

Speaker: | Professor Jack W. Silverstein |

Date: | 29 July 2008 |

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

Title: | Computability, Definability, and Metamathematics |

Speaker: | Professor Theodore Slaman |

Date: | 28 July 2008 |

Time: | 4.00pm - 5.00pm |

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

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. |

Title: | Bayesian Language Models with Pitman-Yor Processes |

Speaker: | Dr Christophe Tartary |

Date: | 25 July 2008 |

Time: | 3.30pm - 4.30pm |

Venue: | SPMS-MAS-03-06 |

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. |

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

Speaker: | Dr Violet R. Syrotiuk |

Date: | 18 June 2008 |

Time: | 4.00pm - 5.00pm |

Venue: | SS2-01-17, TR100 |

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. |

Title: | Externalities in Algorithmic Game Theory |

Speaker: | Mr Ning Chen |

Date: | 9 June 2008 |

Time: | 10.00am - 11.00pm |

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

Abstract: | 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. |

Title: | Intelligent Transport Systems: Emerging Trends and the IBM Experience |

Speaker: | Dr Laura Wynter |

Date: | 2 May 2008 |

Time: | 3.30pm - 4.30pm |

Venue: | NIE Blk 5 Level 1 – TR45 |

Abstract: | Traffic congestion is a problem worldwide, resulting from demand exceeding capacity, and will only get worse. Demand can be managed through pricing to a point, but growing cities will still require more capacity. In dense urban areas, traditional construction of new capacity is prohibitively expensive, and often impossible. This has lead to a recent shift in thinking, from hardware-oriented solutions to software integration and technological innovations. Multimodal, real-time Transport Information Management can deliver more capacity from the existing network, delaying or obviating the need for massive infrastructure investments. Better information can increase customer satisfaction and ridership of public transit systems, effecting modal shift. Technological innovations can make the difference between failing and high-performing transport systems. We present an overview of the work that IBM is doing in Intelligent Transport Systems and focus on a recent pilot project with the Singapore LTA to use science and innovation to improve traffic management |

Title: | A Talk on Set Theory |

Speaker: | Dr Noam Greenberg |

Date: | 25 April 2008 |

Time: | 2.30pm - 5.30pm |

Venue: | NIE Journal room (Block 5, 03-04) |

Abstract: | Dr. Noam Greenberg is now visiting me, and he will give a 2-3 hours talk on fundamentals of forcing, a powerful tool in modern set theory, which was introduced by Cohen in 1963 to prove that the Continuum Hypothesis is independent of ZFC, and that the Axiom of Choice is independent of ZF. All of you are welcome to this talk. |

Title: | Skew-Cyclic codes |

Speaker: | Jia Yan |

Date: | 25 April 2008 |

Venue: | NIE Blk 5 Level 1 – TR45 |

Abstract: | The authors generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since there are much more skew-cyclic codes, this new class of codes allows to systematically search for codes with good properties. The authors give many examples of codes which improve the previously best known linear codes. |

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

Speaker: | Markus Grassl |

Date: | 21 April 2008 |

Time: | 2.00pm - 3.00pm |

Venue: | NIE Blk 5 Level 1 – TR45 |

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. To add more structure to the resulting codes, we extend the framework of stabilizer codes to the union of stabilizer codes. This allows to construct non-additive codes from any stabilizer code. In terms of the underlying classical block codes, codewords are replaced by cosets.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. This is joint work with Martin Roetteler. |

Title: | Minicourse in Algorithmic Game Theory (Auctions) |

Speaker: | Dr Edith Elkind |

Date: | 8 April 2008 |

Time: | 10.30am-12.30pm |

Venue: | TR 43 at NIE Block 5, Level 1 (NIE5-01-TR43), 1 Nanyang Walk |

Abstract: | Classical auction formats: English auction, Dutch auction, first and second price auctions. Strategic bidding and revenue equivalence. Revelation principle. Optimal auctions. Combinatorial auctions: communication complexity, hardness results, algorithms for special types of valuations. Procurement auctions. |

Title: | Minicourse in Algorithmic Game Theory (Matrix games) |

Speaker: | Dr Edith Elkind |

Date: | 8 April 2008 |

Time: | 5.30pm - 7.30pm |

Venue: | TR 43 at NIE Block 5, Level 1 (NIE5-01-TR43), 1 Nanyang Walk |

Abstract: | Solution concepts: dominant strategies, elimination of dominated strategies, Nash equilibria. Computational complexity of these solution concepts. Games with large numbers of players: graphical games, symmetric games, congestion games. |

Title: | Sequences with good correlation properties |

Speaker: | Professor K.T. Arasu |

Date: | 2 April 2008 |

Time: | 5.15pm - 6.15pm |

Venue: | NIE Journal Room (NIE5-03-04) |

Title: | Stream ciphers, and the distinguishing attacks |

Speaker: | Dr Lu Yi |

Date: | 1 April 2008 |

Time: | 10.30am - 11.30am |

Venue: | NIE Journal Room |

Title: | Mean Values of Cubic Character Sums |

Speaker: | Dr Stephan Baier |

Date: | 20 March 2008 |

Time: | 2.30pm - 3.30pm |

Venue: | NIE Blk 5 Level 1 – TR45 |

Abstract: | 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. |

Title: | Amalgams and representations |

Speaker: | Professor A. A. Ivanov |

Date: | 18 March 2008 |

Time: | 4.15pm |

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

Title: | Non Vanishing of L functions |

Speaker: | Jeff Hoffstein |

Date: | 14 March 2008 |

Time: | 10.00am - 11.30am |

Venue: | NIE Blk 7 Level 1 – TR53 |

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. |

Title: | Public Key Crypto Systems and NTRU |

Speaker: | Jeff Hoffstein |

Date: | 12 March 2008 |

Time: | 10.00am - 11.30am |

Venue: | NIE Blk 7 Level 1 – TR53 |

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. |

Title: | 25 years of quantum groups: from definition to classification |

Speaker: | Alexander Stolin |

Date: | 7 March 2008 |

Time: | 10.30am - 11.30am |

Venue: | NIE Block 5, Level 1 (NIE5-01-TR45) |

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. |

Title: | Pairing friendly elliptic curves and fields. |

Speaker: | Professor Igor Shparlinski |

Date: | 3 March 2008 |

Time: | 6.00pm - 7.00pm |

Venue: | NIE Journal Room |

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. |

Title: | Feebly trapdoor functions |

Speaker: | Edward A. Hirsch; S.I.Nikolenko |

Date: | 1 February 2008 |

Time: | 4.00pm - 5.00pm |

Venue: | NIE5-01-TR44 |

Abstract: | One-way functions are the basic primitive of private-key cryptography. However, no provably one-way functions (the ones that can be computed more than polynomially faster than inverted) are known. A natural question is to construct a function that would be at least a little bit (provably!) harder to compute than to invert (call it feebly secure one-way function). Alain Hiltgen (1992) answered this question affirmatively by constructing a function that can be computed by n+O(1)-size circuits but can be inverted only by 2n-size circuits. However, similar constructions of other cryptographic primitives remained unknown. Trapdoor functions are the basic primitive of public-key cryptography. In this work we construct a family of feebly secure trapdoor functions. This is joint work with Sergey Nikolenko. |

Title: | Fast family of Stream Ciphers: TPY |

Speaker: | Professor Jennifer Seberry |

Date: | 15 January 2008 |

Time: | 11.00am - 12.00pm |

Venue: | NIE Journal Room, NIE5-03-04 |

Abstract: | We use software rolling arrays to make a new very fast stream cipher family. This is joint work with Eli Biham |

Title: | Lecture Series on Cryptography (Lecture III) |

Speaker: | Professor C. Pandu Rangan |

Date: | 11 January 2008 |

Time: | 3pm - 5pm |

Venue: | NIE1 01-09 |

Host: | - |

Abstract: | Reliable and secure message transmissions are one of the most fundamental problems in cryptology and more specifically in Multiparty computations. We plan to give a comprehensive overview of this area starting from the taxonomy of various models and settings in which this problem is studied and discuss various subtle aspects of the problem under various settings. We continue the series of the talks with efficient protocols under different settings for this problem. Some of the major results that will be discussed in this series are • Lower bounds and protocols for optimal message transmission in undirected networks ( CRYPTO 2004 paper) • Characterizations for directed graphs for secure message transmission ( PODC 2003) • Optimal protocols tolerating Byzantine adversaries (Indocrypt 2006) • Optimal protocols tolerating mobile adversaries ( ACISP 2007, DISC 2007, PODC 2007) We present all the results in a tutorial style explaining in detail every aspect of the protocol. We need some basics from coding theory and they will also be discussed just in time fashion. No prerequisite is assumed except a bit of mathematical maturity and a bit of enthusiasm and open mind! |

Title: | Lecture Series on Cryptography (Lecture II) |

Speaker: | Professor C. Pandu Rangan |

Date: | 9 January 2008 |

Time: | 10:30am - 12:30pm |

Venue: | NIE1 01-09 |

Host: | - |

Abstract: | Reliable and secure message transmissions are one of the most fundamental problems in cryptology and more specifically in Multiparty computations. We plan to give a comprehensive overview of this area starting from the taxonomy of various models and settings in which this problem is studied and discuss various subtle aspects of the problem under various settings. We continue the series of the talks with efficient protocols under different settings for this problem. Some of the major results that will be discussed in this series are • Lower bounds and protocols for optimal message transmission in undirected networks ( CRYPTO 2004 paper) • Characterizations for directed graphs for secure message transmission ( PODC 2003) • Optimal protocols tolerating Byzantine adversaries (Indocrypt 2006) • Optimal protocols tolerating mobile adversaries ( ACISP 2007, DISC 2007, PODC 2007) We present all the results in a tutorial style explaining in detail every aspect of the protocol. We need some basics from coding theory and they will also be discussed just in time fashion. No prerequisite is assumed except a bit of mathematical maturity and a bit of enthusiasm and open mind! |

Title: | Lecture Series on Cryptography (Lecture I) |

Speaker: | Professor C. Pandu Rangan |

Date: | 8 January 2008 |

Time: | 1pm - 3pm |

Venue: | NIE Journal Room, NIE5-03-04 |

Host: | - |

Abstract: | Reliable and secure message transmissions are one of the most fundamental problems in cryptology and more specifically in Multiparty computations. We plan to give a comprehensive overview of this area starting from the taxonomy of various models and settings in which this problem is studied and discuss various subtle aspects of the problem under various settings. We continue the series of the talks with efficient protocols under different settings for this problem. Some of the major results that will be discussed in this series are • Lower bounds and protocols for optimal message transmission in undirected networks ( CRYPTO 2004 paper) • Characterizations for directed graphs for secure message transmission ( PODC 2003) • Optimal protocols tolerating Byzantine adversaries (Indocrypt 2006) • Optimal protocols tolerating mobile adversaries ( ACISP 2007, DISC 2007, PODC 2007) We present all the results in a tutorial style explaining in detail every aspect of the protocol. We need some basics from coding theory and they will also be discussed just in time fashion. No prerequisite is assumed except a bit of mathematical maturity and a bit of enthusiasm and open mind! |