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A Bivariate Zero-inflated Poisson Regression Model and application to some Dental Epidemiological data
14:10 Fri 27 Oct, 2006 :: G08 Mathematics Building University of Adelaide :: University Prof Sudhir Paul

Data in the form of paired (pre-treatment, post-treatment) counts arise in the study of the effects of several treatments after accounting for possible covariate effects. An example of such a data set comes from a dental epidemiological study in Belo Horizonte (the Belo Horizonte caries prevention study) which evaluated various programmes for reducing caries. Also, these data may show extra pairs of zeros than can be accounted for by a simpler model, such as, a bivariate Poisson regression model. In such situations we propose to use a zero-inflated bivariate Poisson regression (ZIBPR) model for the paired (pre-treatment, posttreatment) count data. We develop EM algorithm to obtain maximum likelihood estimates of the parameters of the ZIBPR model. Further, we obtain exact Fisher information matrix of the maximum likelihood estimates of the parameters of the ZIBPR model and develop a procedure for testing treatment effects. The procedure to detect treatment effects based on the ZIBPR model is compared, in terms of size, by simulations, with an earlier procedure using a zero-inflated Poisson regression (ZIPR) model of the post-treatment count with the pre-treatment count treated as a covariate. The procedure based on the ZIBPR model holds level most effectively. A further simulation study indicates good power property of the procedure based on the ZIBPR model. We then compare our analysis, of the decayed, missing and filled teeth (DMFT) index data from the caries prevention study, based on the ZIBPR model with the analysis using a zero-inflated Poisson regression model in which the pre-treatment DMFT index is taken to be a covariate
Interpolation of complex data using spatio-temporal compressive sensing
13:00 Fri 28 May, 2010 :: Santos Lecture Theatre :: A/Prof Matthew Roughan :: School of Mathematical Sciences, University of Adelaide

Many complex datasets suffer from missing data, and interpolating these missing elements is a key task in data analysis. Moreover, it is often the case that we see only a linear combination of the desired measurements, not the measurements themselves. For instance, in network management, it is easy to count the traffic on a link, but harder to measure the end-to-end flows. Additionally, typical interpolation algorithms treat either the spatial, or the temporal components of data separately, but in many real datasets have strong spatio-temporal structure that we would like to exploit in reconstructing the missing data. In this talk I will describe a novel reconstruction algorithm that exploits concepts from the growing area of compressive sensing to solve all of these problems and more. The approach works so well on Internet traffic matrices that we can obtain a reasonable reconstruction with as much as 98% of the original data missing.
Counting lattice points in polytopes and geometry
15:10 Fri 6 Aug, 2010 :: Napier G04 :: Dr Paul Norbury :: University of Melbourne

Counting lattice points in polytopes arises in many areas of pure and applied mathematics. A basic counting problem is this: how many different ways can one give change of 1 dollar into 5,10, 20 and 50 cent coins? This problem counts lattice points in a tetrahedron, and if there also must be exactly 10 coins then it counts lattice points in a triangle. The number of lattice points in polytopes can be used to measure the robustness of a computer network, or in statistics to test independence of characteristics of samples. I will describe the general structure of lattice point counts and the difficulty of calculations. I will then describe a particular lattice point count in which the structure simplifies considerably allowing one to calculate easily. I will spend a brief time at the end describing how this is related to the moduli space of Riemann surfaces.
Spectra alignment/matching for the classification of cancer and control patients
12:10 Mon 8 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr Tyman Stanford :: University of Adelaide

Proteomic time-of-flight mass spectrometry produces a spectrum based on the peptides (chains of amino acids) in each patient’s serum sample. The spectra contain data points for an x-axis (peptide weight) and a y-axis (peptide frequency/count/intensity). It is our end goal to differentiate cancer (and sub-types) and control patients using these spectra. Before we can do this, peaks in these data must be found and common peptides to different spectra must be found. The data are noisy because of biotechnological variation and calibration error; data points for different peptide weights may in fact be same peptide. An algorithm needs to be employed to find common peptides between spectra, as performing alignment ‘by hand’ is almost infeasible. We borrow methods suggested in the literature by metabolomic gas chromatography-mass spectrometry and extend the methods for our purposes. In this talk I will go over the basic tenets of what we hope to achieve and the process towards this.
World Is Fukt, or, Why our system for elections doesn't reflect the will of the people, but micro parties like it Just The Way It Is.
12:10 Mon 2 Jun, 2014 :: B.19 Ingkarni Wardli :: Casey Briggs :: University of Adelaide

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Results of elections for upper houses in Australia are notoriously difficult to predict, largely because of the quirky voting counting system used. In this seminar I will explain how the system works and why voters have low control over the outcome. I will then demonstrate using a senate calculator the sensitivity of these elections, including how small changes in votes can lead to dramatically different outcomes.
How to count Betti numbers
12:10 Fri 6 May, 2016 :: Eng & Maths EM205 :: David Baraglia :: University of Adelaide

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I will begin this talk by showing how to obtain the Betti numbers of certain smooth complex projective varieties by counting points over a finite field. For singular or non-compact varieties this motivates us to consider the "virtual Hodge numbers" encoded by the "Hodge-Deligne polynomial", a refinement of the topological Euler characteristic. I will then discuss the computation of Hodge-Deligne polynomials for certain singular character varieties (i.e. moduli spaces of flat connections).
What is the best way to count votes?
13:10 Mon 12 Sep, 2016 :: Hughes 322 :: Dr Stuart Johnson :: School of Mathematical Sciences

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Around the world there are many different ways of counting votes in elections, and even within Australia there are different methods in use in various states. Which is the best method? Even for the simplest case of electing one person in a single electorate there is no easy answer to this, in fact there is a famous result - Arrow's Theorem - which tells us that there is no perfect way of counting votes. I will describe a number of different methods along with their problems before giving a more precise statement of the theorem and outlining a proof

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