Speaker: Fran Aragon, CARMA, The University of Newcastle Co-authors: David Bailey, Jon Borwein and Peter Borwein. Title: Walking on real numbers Abstract: Motivated by the desire to visualise large mathematical data sets, especially in number theory, we offer various tools for representing floating point numbers as planar walks and for quantitatively measuring their "randomness". What to expect: some interesting ideas, many beautiful pictures (including a 108-gigapixel picture of pi), and some easy-to-understand maths. What you won't get: too many equations, difficult proofs, or any "real walking".
Speaker: Michael Barnsley, Australian National University Title: Maths Visualization & mdash; Historical Theoretical and Practical Perspectives Abstract: I will trace some key events (theorem moments and realizations about images) that have happened to me during the last thirty-plus years, that inform my current research and view of the future of computergraphical mathematics.
Speaker: Jon Borwein, CARMA, The University of Newcastle
Title: Seeing things in Mathematics
Abstract: "It is not knowledge, but the act of learning, not possession but the act of
getting there, which grants the greatest enjoyment}. When I have clarified and exhausted a
subject, then I turn away from it, in order to go into darkness again;" (Carl Friedrich
I display roughly a dozen examples where computational experimentation, computer algebra and special function theory have led to pleasing or surprising results. In the style of Ramanujan, very few proofs are given but may be found in the references.
Much of this work requires extensive symbolic, numeric and graphic computation. It makes frequent use of the new NIST Handbook of Mathematical Functions and related tools such as gfun.
My intention is to show off the interplay between symbolic, numeric and especially graphic computing while exploring the various topics in my title.
Speaker: William Cummins, Wallaby Fabrications Pty Ltd
Title: Geometric Sculptures
Sculpture images: http://www.spreaders.com.au/index_files/Page759.htm
Speaker: Peter Eades, University of Sydney Title: How to draw a graph, revisited Abstract: W. T. Tutte published a paper in 1963 entitled "How to Draw a Graph". Tutte's motivation was mathematical, and his paper can be seen as a contribution to the long tradition of geometric representations of combinatorial objects. Over the following 50 years, the motivation for creating visual representations of graphs has changed from mathematical curiosity to Visual Analytics. Current demand for Graph Drawing methods is now high, because of the potential for more human- comprehensible visual forms in industries as diverse as Biotechnology, Homeland Security, and Sensor Networks. Many new methods have been proposed, tested, implemented, and found their way into commercial tools. This paper describes two strands of this history: the force directed approach, and the planarity approach. Both approaches originate in Tutte's paper.
Speaker: Attila Egri-Nagy, University of Western Sydney Title: Viz package for the GAP computer algebra system Abstract: In computer algebra we only have a limited set of tools available for visualization. On the level of active research there are basically no ready-made solutions available. That is why in semigroup theory we had to unite our forces and start developing a new visualization package specialized for discrete mathematical structures. In this talk we summarize the design principles (instant visualization and publication quality figures) and some of the implementation techniques of the Viz package.
Speaker: Bishnu Lamichhane, CARMA, The University of Newcastle Title: Visualizing solutions of partial differential equations Duration: 15 minutes Abstract: We consider visualization of solutions of partial differential equations, where the solutions are computed by using some numerical techniques. Problems from heat conduction, elasticity and image processing are considered.
Speaker: John Maindonald, Australian National University Title: The R system - a broad umbrella for visualisation Abstract: The R system provides a coherent interface to what is now a huge range of scientific computing abilities. A ready ability to build on what is already in place has been a major reason why it has proved attractive as a development environment, now with over 4000 packages. It has particularly strong graphical abilities. This talk will focus on displays that seem particularly striking, including interfaces to Google motion charts, to Google Maps and to Google Earth.
Speaker: Sean O'Donoghue, CSIRO and Garvan Institute for Medical Research Title: Visualizing Biological Data for Research and for Outreach Abstract: Experimental methods in biological research are delivering data of rapidly increasing volume and complexity. However, many current methods and tools used to visualize and analyse these data are inadequate, and urgent improvements are needed if life scientists are to gain insight from this data deluge, rather than being overwhelmed. I will discuss a recent switch in focus away from algorithmic bioinformatics towards data visualization and usability principles, illustrating how such a focus can have significant impact. I will also discuss a recent, international community initiative I'm leading that brings visualization experts together with computational biologists, bioinformatics, graphic designers, animators, and medical illustrators, and aims to raise the global standard of bioinformatics software (http://vizbi.org/). Finally, I'll present an upcoming project designed to inspire the Australian public to engage with biomedical research (http://csironewsblog.com/2012/06/13/science-animations-take-us-on-fantastic-voyages/).
Speaker: Judy-anne Osborn, CARMA, The University of Newcastle Coauthor: Nathan Clisby Title: Visualizing maximal determinant matrices Abstract: Inspired by the famous Folding@home project (http://folding.stanford.edu/English/HomePage) which turned a scientific problem of protein-folding into a publicly accessible visual game which allowed amateurs and scientists to collaborate on solving a real scientific problem, we are working on turning a mathematical back-tracking problem into its own kind of visual game which could eventually be made accessible to the public on the web. The mathematical problem is that of finding maximal determinant binary matrices. These matrices are themselves useful in all kinds of contexts from statistical design theory to coding theory. Our implementation, still in its infancy, has the potential to be applied more broadly to other back-tracking problems. Our hope is that in making the mathematical problem into a visual one, we can develop heuristics to help understand problems which computers alone cannot solve; and share around some fun while doing it, too!
Speaker: Konrad Polthier, Freie Universität Berlin
Title: Making of "A Mathematical Picturebook"
Bio: See http://www.polthier.info/
Abstract: The demand for pictures in mathematical publications and courses is increasing, e.g. due to the enormous development of new communication devices and due to the increasing number of interested non-specialists. Nevertheless the ability to produce adequate state-of-the-art imagery is not widely available, especially not in the community of productive mathematicians.
The talk will show various visualization activities in many areas of mathematics, it will introduce several effective visualization tools, and demonstrate the effectiveness of novel visualization algorithms at the interface of pure mathematics and industrial applications.
Speaker: Malcolm Roberts, CARMA, The University of Newcastle Title: Visualisation and My Thoughts for Its Use in Education Abstract: As part of the "laptops in schools" program the open source dynamic geometry package GeoGebra was loaded onto all machines handed out. In this talk I will give a brief overview of my observations of the impact that this decision has had on the use of visualisation in our classrooms.
Speaker: Henry Segerman, University of Melbourne Title: Using Mathematica and Rhinoceros to produce 3D printed mathematical models Abstract: This workshop will be a hands-on introduction to producing physical 3D printed mathematical models using computer software. 3D printing is rapidly becoming a very affordable way to produce physical objects, for use in outreach, teaching or research. In addition to being excellent visualisation aids, physical objects go further, allowing for a tactile understanding. Depending on the interests of the participants, we will use Mathematica, the 3D design program "Rhinoceros", and/or the Python scripting interface to Rhinoceros to produce 3D files ready to be sent to a 3D printer. The workshop will be based in part on this article: http://www.ms.unimelb.edu.au/~segerman/papers/3d_printed_visualisation.pdf
Speaker: Tobias Sargeant, The Walter and Eliza Hall Institute of Medical Research, Melbourne, VIC, Australia Title: Visualising Patterns of Correlated Gene Expression in Blood Transcriptomes Affilation: The Walter and Eliza Hall Institute of Medical Research, Melbourne, VIC, Australia Abstract: We have applied minimum spanning trees to the problem of clustering and visualising gene and cell co-expression data. Cell types clustered in this manner more directly mirror biological knowledge regarding ordering of differentiation than do other clustering methods, correctly reconstructing the maturation steps of a number of lineages. Networks of genes constructed using minimum spanning trees have proven useful as a representational tool on top of which we have overlaid ontology, drug target and phenotypic information, as well as experimental data from mutant-vs-wildtype expression studies. Further, we have observed that the minimum spanning tree represents a generalization of fixed-threshold correlation-based gene expression clustering. We have made use of this observation to visualize the hierarchy of networks defined by correlation of gene expression over the full range of possible thresholds. It is clear from this visualization that a one size fits all approach to selection of a correlation threshold is impractical both at a dataset level and at an expression sub-network level. In contrast, our method determines thresholds adaptively and automatically, generating biologically meaningful networks of genes. The tools we have developed for exploring patterns correlated gene expression have provided us with new insights into the biology of gene expression in normal hematopoiesis and in acute myeloid leukemia, and we feel that their utility will continue to increase as RNA-Seq supplants microarrays as the technology of choice for the generation of large transcriptomic datasets.
Speakers: Richard Vella and Jon Drummond, The University of Newcastle Title: Modeling, Creativity, Music and Mathematics Abstract: In this talk we will refer to some intersections between mathematics and music. We will use these intersections as points of departure to discuss creativity models and their role in research practice. We begin with a discussion on the similarities between mathematics and music with respect to visualisation and other representations of data through sonification and spatialisation. In unpacking these data representations the presentation concludes with a discussion on symbolic representation, plausibility and schemas within disciplinary and interdisciplinary context.