Seminar 2017

 
20 September 2017

Title : Matrix spaces as a linear algebraic analogue of graphs

Dr Youming Qiao
Centre for Quantum Software and Information
University of Technology Sydney

Time : 3.30 pm – 4.30 pm
Venue : MAS Executive Classroom 2, MAS-03-07
School of Physical and Mathematical Sciences

Abstract:
In the last few years, two research projects of mine (joint with collaborators) suggest that it is fruitful to view linear spaces of matrices as a linear algebraic analogue of graphs. In this talk I will first formally propose such an analogue, and then review how this helps in some decades-old problems from theoretical computer science and mathematics. We will see how this serves as a platform for interactions among algorithm design, combinatorics, and algebraic geometry. Finally I will mention some future directions.
Based on joint works with Gabor Ivanyos, K. V. Subrahmanyam, and Yinan Li.

Host: Dr Bei Xiaohui
Division of Mathematical Sciences, School of Physical and Mathematical Sciences

14 August 2017

Title : An Exact Spectrum Formula for the Maximum Size of Finite Length Block Codes

Dr Vincent Tan
Department of Electrical and Computer Engineering,
Department of Mathematics,
National University of Singapore (NUS)

Time : 3.00 pm – 4.00 pm
Venue : MAS Executive Classroom 2, MAS-03-07
School of Physical and Mathematical Sciences

Abstract:
An exact information spectrum- type formula for the maximum size of finite length block codes subject to a minimum pairwise distance constraint is presented. This formula can be applied to codes for a broad class of distance measures. As revealed by the formula, the largest code size is fully characterized by the information spectrum of the distance between two independent and identically distributed (i.i.d.) random codewords drawn from an optimal distribution. A new family of lower bounds to the maximal code size is thus established, and the well -known Gilbert -Varshamov (GV) lower bound is a special case of this family.
By duality, an explicit expression for the largest minimum distance of finite length block codes o f a fixed code size is also obtained. Under an arbitrary uniformly bounded symmetric distance measure, the asymptotic largest code rate (in the block length n) attainable for a sequence of (n,M,nd) - codes is given exactly by the maximum large deviation rate function of the normalized distance between two i.i.d. random codewords. The exact information spectrum- type formula also yields bounds on the second -order terms in the asymptotic expansion of the optimum finite length rate for block codes with a fixed no rmalized minimum distance.
This is joint work with Ling- Hua Chang (National Chiao Tung University, Taiwan), Carol Wang (NUS), Po -Ning Chen (NCTU, Taiwan), and Yunghsiang S. Han (Dongguan University of Technology, China). It can be found on arXiv:1706.04709.

Host: Dr Kiah Han Mao
Division of Mathematical Sciences, School of Physical and Mathematical Sciences

12 July 2017

Title : Lightweight Symmetric - Key Cryptography

Dr Guo Jian
Nanyang Technological University

Time : 10.00am – 11.00am
Venue : MAS Executive Classroom 2, MAS-03-07
School of Physical and Mathematical Sciences

Abstract:
Recent years have witnessed massive and wide deployment of IoT devices, ranging from smart cards to implanted medical devices. It is estimated that 50 billion IoT devices will be connected by year 2020. The diverse feature of IoT devices results in many special requirements to cryptographic mechanisms over traditional ones, such as low hardware area when implemented on small devices or low energy consumption when running on devices powered by limited battery. We show, by examples of concrete designs, how effective cryptographic mechanisms are still possible under these constraints without affecting the security strengths. It is also interesting to note that a single algorithm could be implemented in several ways to fit very different IoT usecase scenarios while keeping the functionality and security strength unaffected.

Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences

14 June 2017

Title : Viruses and Geometry: New Insights into Virus structure, Assembly and Evolution

Prof Reidun Twarock
Department of Mathematics
University of York, UK

Time: 11.00am to 12.00pm
Venue: MAS Executive Classroom 2, MAS-03-07
School of Physical and Mathematical Sciences

Abstract:
Viruses are remarkable examples of order at the nanoscale. The capsids of many viruses, enclosing and protecting their genomes, are organised in lattice like arrangements with overall icosahedral symmetry. Mathematical techniques from group, graph and tiling theory can therefore be used to characterise their architectures. In this talk, I will introduce our mathematical approach to the modelling of viral capsids, and demonstrate its applications in vaccine design. I will then present our Hamiltonian path approach to the modelling of genome packing in RNA viruses that underpins the discovery of an RNA-encoded assembly instruction manual in a wide range of viruses, including Picornavirusus, Hepatitis C and Hepatitis B virus. Finally, I will introduce our models of virus assembly and demonstrate how they can be used to develop implicit fitness functions that shed new light on viral evolution and anti-viral drug therapy.

Host: Assistant Professor Kelin Xia, School of Physical and Mathematical Sciences

01 June 2017  

Title:Geometric Understanding and analysis of unstructured data

Prof Zhao Hongkai
University of California, Irvine

Time: 4.50pm to 5.50pm
Venue: MAS Executive Classroom 2, MAS-03-07
School of Physical and Mathematical Sciences

Abstract:
One of the simplest and most natural ways of representing geometry and information in three and higher dimensions is using point clouds, such as scanned 3D points for shape modeling and feature vectors viewed as points embedded in high dimensions for general data analysis. Geometric understanding and analysis of point cloud data poses many challenges since they are unstructured, for which a global mesh or parametrization is difficult if not impossible to obtain in practice. Moreover, the embedding is highly non-unique due to rigid and non-rigid transformations. In this talk, I will present some of our recent work on geometric understanding and analysis of point cloud data. I will first discuss a multi-scale method for non-rigid point cloud registration based on the Laplace-Beltrami eigenmap and optimal transport. The registration is defined in distribution sense which provides both generality and flexibility. If time permits I will also discuss solving geometric partial differential equations directly on point clouds and show how it can be used to “connect the dots” to extract intrinsic geometric information for the underlying manifold.

Host: Associate Professor Chan Song Heng, School of Physical and Mathematical Sciences

2 June 2017

Title:Identities of A. I. Popov

Prof Bruce C. Berndt
Department of Mathematics
University of Illinois at Urbana-Champaign

Time: 10.30am - 11.30am
Venue: MAS Executive Classroom 2, MAS-03-07,
School of Physical and Mathematical Sciences


Host: Associate Professor Chan Song Heng, School of Physical and Mathematical Sciences

2 May 2017

Title:Open dynamical systems: ß-expansion map on an interval with a hole

Assistant Professor Nikita Agarwal
Mathematics
Indian Institute of Science Education and Research Bhopal

Time: 3pm - 4pm
Venue: MAS Executive Classroom 2, MAS-03-07,
School of Physical and Mathematical Sciences


Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences

28 April 2017

Title:Torus knots and quantum modular forms

Dr Jeremy Lovejoy
Researcher, CNRS, Université Paris Diderot - Paris 7

Time: 10.30am - 11.30am
Venue: SPMS LT 4 (SPMS-03-09)
School of Physical and Mathematical Sciences

Abstract:
In the first part of this talk I will explain how the theory of Bailey pairs leads to an explicit formula for the cyclotomic coefficients of the colored Jones polynomial of the torus knots (2,2t+1). In the second part, I will describe how this gives a kind of "analytic continuation" of a family of quantum modular forms (the generalized Kontsevich-Zagier series). If time permits, I will also discuss how formulas for the colored Jones polynomial lead to qhypergeometric and Hecke-type formulas for certain families of unified WRT invariants.

Host: Associate Professor Chan Song Heng, School of Physical and Mathematical Sciences

27 April 2017

Title: Basic Properties of the Blockchain

Dr Juan Garay
Yahoo Research

Time: 11.00am - 12.00pm
Venue: MAS Executive Classroom 2, MAS-03-07,
School of Physical and Mathematical Sciences

Abstract:
As the first decentralized cryptocurrency, Bitcoin has ignited much excitement, not only for its novel realization of a central bank-free financial instrument, but also as an alternative approach to classical distributed computing problems, such as reaching agreement distributedly in the presence of misbehaving parties, as well as to numerous other applications―contracts, reputation systems, name services, etc. The soundness and security of these applications, however, hinges on the thorough understanding of the fundamental properties of its underlying blockchain data structure, which parties (“miners”) maintain and try to extend by generating “proofs of work” (POW, aka “cryptographic puzzle”).

In this talk we formulate such fundamental properties of the blockchaincommon prefix, chain quality, chain growthand show how applications such as consensus and a robust public transaction ledger can be built ``on top'' of them, assuming the adversary’s hashing power (our analysis holds against arbitrary attacks) is strictly less than ½ and high network synchrony:

The above properties hold assuming that all parties―honest and adversarial―”wake up” and start computing at the same time, or, alternatively, that they compute on a common random string (the “genesis” block) only made available at the exact time when the protocol execution is to begin. In this talk we also consider the question of whether such a trusted setup/behavioral assumption is necessary, answering it in the negative by presenting a Bitcoin-like blockchain protocol that is provably secure without trusted setup, and, further, overcomes such lack in a scalable way―i.e., with running time independent of the number of parties [4].

A direct consequence of our construction above is that consensus can be solved directly by a blockchain protocol without trusted setup assuming an honest majority (in terms of computational power).

Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences

21 April 2017 Title: Gradient Boosting for Partially Linear Additive Models in Survival Analysis

Dr Tang Xingyu
Nanyang Technological University

Time: 9.30am – 10.30am
Venue: MAS Executive Classroom 2, MAS-03-07,
School of Physical and Mathematical Sciences

Abstract:
The partially linear additive model is a special form of additive models, which combines the strengths of linear and nonlinear models by allowing linear and nonlinear predictors to coexist. One of the most interesting questions associated with the partially linear additive model is to identify nonlinear, linear, and non-informative covariates with no such pre-specification given, and to simultaneously recover underlying component functions which indicate how each covariate affects the response.

Survival analysis is a popular topic in statistics, and the Cox’s model is one of the most commonly used models in survival analysis. Here the partially linear additive model is adapted to survival analysis, and gradient boosting approaches are applied to optimize the Cox’s log partial likelihood, with simple linear regressions and univariate penalized splines are together used as base learners. Twin boosting is incorporated as well to achieve better variable selection accuracy. Simulation studies as well as real data applications illustrate the strength of our proposed algorithms.

Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences

30 March 2017 Title: Genome-wide association studies: Applications and insights gained in Ophthalmology

Dr Zhao Wanting
Singapore Eye Research Institute

Time: 9.30am – 10.30am
Venue: MAS Executive Classroom 2, MAS-03-07,
School of Physical and Mathematical Sciences

Abstract:
Genome-wide association studies (GWAS) use high-throughput genotyping technologies to genotype and impute millions of single-nucleotide polymorphisms (SNPs) and relate them to the development of clinical and quantitative traits. Their use has been highly successful in the field of ophthalmology, and since the advent of GWAS in 2005, many genes not previously suspected of having a role in disease have been identified and the findings replicated.

In this seminar, Dr. Zhao will report findings from the large multi-ethnic meta-analysis of genomewide association studies of complex ocular diseases by the International Cataract Genetics Consortium. They identified several new loci associated with these eye diseases and replicated the association through large-scale multi-ethnic meta-analysis of GWAS. These findings provide additional candidate genes for follow-up work and may lead to uncovering of previously unknown mechanisms in ocular diseases formation.

Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences

 21 March 2017 Title: Clinical Drug Development with Statistics: A Personal Perspective

Dr Yeo Kwee Poo
Eli Lilly and Company

Time: 9.30am – 10.30am
Venue: MAS Executive Classroom 2, MAS-03-07,
School of Physical and Mathematical Sciences

Abstract:
In this talk, I want to give the audience an idea of what the work of a statistician in a pharmaceutical company might look like using my own experiences. I will give an overview of the drug development; an examples of applied statistics during early phase drug development; and discuss the desirable skill sets that help statisticians in the industry to succeed. I will conclude with some general comments that might be helpful for young statisticians considering to work in the pharmaceutical industry.

Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences

28 February 2017 Title: Parameter estimation and multilevel clustering with mixture and hierarchical models

Mr Nhat Ho
Department of Statistics
University of Michigan

Time: 10.30am – 11.30am
Venue: MAS Executive Classroom 2, MAS-03-07,
School of Physical and Mathematical Sciences

Abstract:
This talk addresses statistical inference with mixture and hierarchical models: efficiency of parameter estimation in finite mixtures, and scalable clustering of multilevel structured data. It is well-known that due to weak identifiability and singularity structures of latent variable models’ parameter space, the convergence behaviors of parameter estimation procedures for mixture models remain poorly understood. In the first part of the talk, we describe a general framework for characterizing impacts of weak identifiability and singularity structures on the convergence behaviors of the maximum likelihood estimator in finite mixture models. This allows us to resolve several open questions regarding popular models such as Gaussian and Gamma mixtures, as well as to explicate the behaviors of complex models such as mixtures of skew normal distributions.

In the second part of the talk, we address a clustering problem with multilevel structured data, with the goal of simultaneously clustering a collection of data groups and partitioning the data in each group. By exploiting optimal transport distance as a natural metric for distributions and a collection of distributions, we propose an optimization formulation that allows to discover the multilevel clustering structures in grouped data in an efficient way. We illustrate the performance of our clustering method in a number of application domains, including computer vision .
Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences

14 February 2017 Title: Net-Trim: A Layer-wise Convex Pruning of Deep Neural Networks

Dr Alireza Aghasi
Department of Mathematical Sciences
IBM TJ Watson Research Center

Time: 10.30am – 11.30am
Venue: MAS Executive Classroom 2, MAS-03-07,
School of Physical and Mathematical Sciences

Abstract:
Model reduction is a highly desirable process for deep neural networks. While large networks are theoretically capable of learning arbitrarily complex models, overfitting and model redundancy negatively affects the prediction accuracy and model variance. Net-Trim is a layer-wise convex framework to prune (sparsify) deep neural networks. The method is applicable to neural networks operating with the rectified linear unit (ReLU) as the nonlinear activation. The basic idea is to retrain the network layer by layer keeping the layer inputs and outputs close to the originally trained model, while seeking a sparse transform matrix. We present both the parallel and cascade versions of the algorithm. While the former enjoys computational distributability, the latter is capable of achieving simpler models. In both cases, we mathematically show a consistency between the retrained model and the initial trained network. We also derive the general sufficient conditions for the recovery of a sparse transform matrix. In the case of standard Gaussian training samples of dimension N being fed to a layer, and s being the maximum number of nonzero terms across all columns of the transform matrix, we show that O(s.logN) samples are enough to accurately learn the layer model.

Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences

13 February 2017 Title: Ramanujan congruences for bipartitions

Associate Professor Bernard Lishuang Lin
School of Science
Jimei University, China

Time: 10.30am – 11.30am
Venue: MAS Executive Classroom 1, MAS-03-06,
School of Physical and Mathematical Sciences



Host: Associate Professor Chan Song Heng, School of Physical and Mathematical Sciences

 23 January 2017 Title: Growth of homology torsion in finite covering

Professor Thang Le
School of Mathematics
Georgia Institute of Technology, USA

Time: 1.30pm – 2.30pm
Venue: MAS Executive Classroom 2, MAS-03-07,
School of Physical and Mathematical Sciences

Abstract:
We discuss the growth of homology torsion of finite coverings. For 3- manifolds we show that the growth rate of the homology torsion is bounded from above by the hyperbolic volume (or Gromov norm). This upper bound is conjectured to be exact.

Host: Associate Professor Andrew James Kricker, Division of Mathematical Sciences,School of Physical and Mathematical Sciences

 5 January 2017 Title: Recent Advances in the Theory of Hilbert C*-Modules over Reduced Twisted Crossed-Product C*-Algebras

Leonard Huang
Department of Mathematics
University of Colorado Boulder

Time: 2.30pm – 3.30pm
Venue: MAS Executive Classroom 1, MAS-03-06,
School of Physical and Mathematical Sciences

Abstract:
In this talk, I will discuss the main result of my PhD dissertation, which is a classification — up to isomorphism — of Hilbert C*-modules over reduced twisted crossed-product C*-algebras. This classification result generalizes an earlier one established by Ralf Meyer (Mathematisches Institut, Georg-August-Universität Göttingen) for Hilbert C*-modules over reduced crossed-product C*-algebras. I will then explain how a certain powerful Fourier- analytic technique used to construct Hilbert C*-modules over non-commutative tori — introduced by Marc Rieffel (University of California, Berkeley) and later refined by Franz Luef (Norwegian University of Science and Technology) — can be viewed as a natural example of my result.

Host: Associate Professor Wu Guohua, School of Physical and Mathematical Sciences