Random network coding, Subspace codes, Rank metric codes and self-duality of generalized twisted Gabidulin codes

Random network coding, Subspace codes, Rank metric codes and self-duality of generalized twisted Gabidulin codes

Speaker: Prof. Ferruh Ozbudak
Middle East Technical University

Title: Random network coding, Subspace codes, Rank metric codes and self-duality of generalized twisted Gabidulin codes

Date and time: Friday 21 July 2017, 3:00–4:00pm
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract: Subspace codes constitute the mathematical backdrop of random network coding. Optimal rank metric codes are used to construct large subspace codes. In this talk, these relations will be summarized and the criterion of being self-dual will be examined for generalized twisted Gabidulin codes (a family of optimal rank metric codes).

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Classifying bent functions by their Cayley graphs

Classifying bent functions by their Cayley graphs

Speaker: Dr Paul Leopardi
Bureau of Meteorology

Title: Classifying bent functions by their Cayley graphs

Date and time: Friday, 28 April 2017, 3:00–4:00pm
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract: Bent Boolean functions are fascinating and useful combinatorial objects, whose applications include coding theory and cryptography. The number of bent functions explodes with dimension, and various concepts of equivalence are used to classify them. In 1999 Bernasconi and Codenotti noted that the Cayley graph of a bent function is strongly regular. This talk describes the concept of extended Cayley equivalence of bent functions, discusses some connections between bent functions, designs, and codes, and explores the relationship between extended Cayley equivalence and extended affine equivalence. SageMath scripts and SageMathCloud worksheets are used to compute and display some of these relationships, for bent functions up to dimension 8.

Bio: Paul Leopardi is a computer scientist and mathematician who works to support scientific applications at the Bureau of Meteorology in Melbourne. His academic career has included stints at UNSW, the University of Sydney, ANU and the University of Newcastle. He is an honorary Fellow at the University of Melbourne. His research interests have included high performance numerical computing, computations with Cifford algebras, constructive approximation, and bioinformatics and well as combinatorics. He was enticed to study Hadamard matrices by Judy-Anne Osborn, Jennifer Serberry and Kathy Horadam, amongst others. This led to the present study.

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Fast Extraction of the backbone of projected bipartite networks

Fast Extraction of the backbone of projected bipartite networks

Speaker: Dr Jessica Liebig
RMIT University

Title: Fast Extraction of the backbone of projected bipartite networks

Date and time: Friday, 7 April 2017, 3:00–4:00pm
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract: The study of complex networks has received much attention over the past few decades, presenting a simple, yet efficient means of modelling and understanding complex systems. The majority of network science literature focuses on simple one-mode networks. In the real world, however, we often find systems that are best represented by bipartite networks that are commonly analysed by examination of their one-mode projection. One-mode projections are naturally very dense and noisy networks and hence the most relevant information may be hidden. One way to reveal hidden information is the extraction of significant edges, forming the backbone of the projection. Existing methods are computationally expensive. In this talk, I will introduce a computationally inexpensive method for extracting the backbone of projected bipartite networks. I will demonstrate that the edge weights of projections follow a Poisson binomial distribution and that finding the expected weight distribution of a random bipartite projection only requires knowledge of the bipartite degree distributions.

Bio: Jessica Liebig received her PhD in January 2017 from RMIT University. Her primary research interest lies in the area of network science and is directed toward the study of large, complex bipartite data. The work presented in her thesis examines bipartite networks with the aim of uncovering significant behaviour in real world networks.

Joint InfoSec/RMITOpt talk: Joanne Hall, Semi-Fields and Planar Functions

Joint InfoSec/RMITOpt talk: Joanne Hall, Semi-Fields and Planar Functions

On 10 March we will have our first joint Information Security/RMIT Optimisation Group talk that starts a new series of Information Security seminars. As usual, the talk will be followed by light snacks in the staff room.

 

Speaker: Dr Joanne Hall
School of Science
RMIT University

Title: Semi-Fields and Planar Functions

Date and time: Friday, 10 March 2017, 3:00-4:00pm
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract: Planar functions are a class of Perfectly Nonlinear functions which have uses in cryptography, error correcting codes, and wireless signal transmission as well as of being of theoretical interest in geometry and abstract algebra. Almost all planar functions over finite fields belong to the class of Dembowski-Ostrom polynomials.

In 2008 it was shown that Dembowski-Ostrom Planar polynomials are equivalent to commutative semi-fields [Coulter & Henderson]. The connection with semi-fields allowed us to use algebraic techniques to find several new planar functions.

Bio: Joanne is known to many of us at RMIT from the time she spent doing her PhD with Asha Rao. Her research on algebraic, combinatorial and geometric structures and their applications in cryptography, error control and data compression has been published in a variety of top ranked journals. Immediately after submitting her thesis in May, 2011, Joanne went to Europe with postdoctoral positions at the Institue of Astronomy of the Slovak Academy of Sciences and the Department of Algebra of Charles University in Prague. Joanne then spent 4 years as a lecturer in the Mathematical Sciences School at QUT, developing a university wide minor in discrete mathematics. Returning to RMIT in 2017, Joanne is looking forward to participating in the graduation parade, having missed her own PhD graduation ceremony.

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InfoSec talk: Stephen Davis, Gamification of Crime Scene Fingerprint Analysis

InfoSec talk: Stephen Davis, Gamification of Crime Scene Fingerprint Analysis

Speaker: Dr Stephen Davis
School of Science
RMIT University

Title: Gamification of Crime Scene Fingerprint Analysis

Date and time: Friday, 24 March 2017, 3:00-4:00pm
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract: Over the last decade we have investigated the possible benefits of graph representations of ridge pattern biometrics (such as fingerprints and ball prints) and vascular biometrics (such as retina and hand vein). For automatic recognition of imposter matches, and the use of dissimilarity vectors to avoid storing the actual biometric (its distances from a set of prototypes are stored instead), it has become clear that vascular biometrics benefit from graph representation far more than ridge pattern biometrics do. However, our most recent application has been in gamifying forensic fingerprint analysis. We have developed Delta Core which is a web application where players engage in the first stage (Analysis) of the ACE-V process used by law enforcement to establish the source of fingerprints left at the scene of a crime, disaster or act of terrorism. The game mechanics rely on noisy graph matching techniques to compare the performance of players to that of human experts and create an environment wherein players develop forensic skills.

Bio: Stephen is a mathematician who can be spotted teaching Calculus to hapless first-year students at RMIT University when he is not researching or designing Serious Games like Delta Core. His passion for applying mathematics first led him to work on models of infectious disease and he has first-author papers in Nature and Science contributing to the theory and practice of managing disease outbreaks. Following postdoctoral appointments abroad at the University of Antwerp, the University of Utrecht and Yale University, he returned to Melbourne in 2009 to join RMIT University. He’s currently fascinated by pattern matching problems in the forensic sciences and has collaborated with Victoria Police for the last 5 years.

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