School of Mathematics and Statistics - Applied Seminar
https://www.maths.unsw.edu.au/category/school-seminar-series/applied-seminar
enNonstandard slow-fast systems: geometry, singularities, and computation
https://www.maths.unsw.edu.au/seminars/2019-11/nonstandard-slow-fast-systems-geometry-singularities-and-computation
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Ian Lizarraga</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">University of Sydney</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Thu, 21/11/2019 - 12:05pm</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">RC-2063</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p style="text-align: justify;">Recent work on multiple-timescale dynamical systems has overwhelmingly focused on models where there is a global identification of “slow” versus “fast” variables throughout the phase space. But in many physical models, this standard assumption can be unnecessarily restrictive: for example, many chemical reaction networks have distinguished slow versus fast reactions, but each individual chemical concentration may change slowly or rapidly along a typical trajectory.<br />This talk discusses two recent developments in nonstandard slow-fast systems. The first is the use of the computational singular perturbation (CSP) method to approximate invariant slow manifolds and fast fibers. The second is the classification of contact singularities and bifurcations in terms of a natural algebraic factorisation of the vector field. We apply these algorithms and techniques to a variety of applied problems.<br /><br />Ian Lizarraga is a postdoctoral fellow working in the School of Mathematics and Statistics at the University of Sydney. He received his PhD in Applied Mathematics at Cornell University, where he studied bifurcation problems in slow-fast dynamical systems with John Guckenheimer and model reduction in coupled oscillators with Steven Strogatz.</p></div></div></section><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/applied-seminar">Applied Seminar</a></li></ul></section>Tue, 12 Nov 2019 04:06:51 +0000z33407775193 at https://www.maths.unsw.edu.auMoving Boundary Problems for Heterogeneous Media
https://www.maths.unsw.edu.au/seminars/2019-11/moving-boundary-problems-heterogeneous-media
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Emeritus Professor Colin Rogers</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">UNSW</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Thu, 14/11/2019 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">RC-M032, The Red Centre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p>The combined action of reciprocal and integral-type transformations is here used to sequentially reduce to canonical form a class of nonlinear moving boundary problems involving heterogeneity.Particular such Stefan Problems arise in the percolation of liquids through porous media in soil mechanics.</p>
<p>The areas of major research interest of the speaker are in invariance properties in nonlinear continuum mechanics, the geometry and application of applications of Backlund transformations, in particular, in modern soliton theory.<br />He is a graduate of Oxford University and was awarded a DSc by the University of Nottingham for his publications in continuum mechanics. Professor Rogers was elected a Fellow of the Australian Academy of Science In 1999 and in 2011 awarded its Hannan Medal for research in Applied and Computational Mathematics.He is a recipient of the Australian Government Centenary Medal. He has held Visiting Professorships at, inter alia, the University of Rome, the Technical University of Denmark, Georgia Institute of Technology, the University of Bologna, the University of Cambridge and the University of Montreal. He is a Life Member of Clare Hall, the University of Cambridge.</p></div></div></section><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/applied-seminar">Applied Seminar</a></li></ul></section>Tue, 29 Oct 2019 15:30:49 +0000z33407775178 at https://www.maths.unsw.edu.auST-metric methods, a new geometric view to data analysis
https://www.maths.unsw.edu.au/seminars/2019-09/st-metric-methods-new-geometric-view-data-analysis
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Ilknur Tulunay</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">UNSW School of Maths and Stats</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Thu, 12/09/2019 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">RC-4082, The Red Centre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p style="text-align: justify;">ST-metric, arising from relative entropy can be thought as the distance between two discrete curves in the unit interval. Any data set can also be viewed as a discrete curve and can be transformed into the unit interval. The first method is to define a utility function for risk averse investors as the ST-metric between the returns of risk-free and risky investments, and then to rank the performances of fund managers (Tulunay 2017). The second method is about finding factor weights in a factor model. That is an optimization problem where the objective is minimizing the distance between the benchmark and the constructed portfolio. Usually, the absolute value distance between the benchmark and the constructed portfolio at each time point is used. Ang et.al. (2018) used Tracking Error method, absolute value distance, smoothed by multiplying the standard deviation over some period. Using ST-metric between the curves of the benchmark and the portfolio as objective function gives better estimation of the factor weights than tracking error method. Furthermore, ST-metric is more sensitive to the fluctuations than absolute value (L1) and L2-distances.</p>
<p style="text-align: justify;"><span lang="en-GB" xml:lang="en-GB">Dr ILKNUR TULUNAY is awarded in her PhD, titled “Cuspidal Modules of Finite General Linear Groups” on representation of reductive algebraic groups at School of Mathematics and Statistics, USYD in 2001. After her post-doctoral fellowship, </span>JSPS (Japan Society for Promotion of Science) in 2003-2005, she worked as a financial analyst on infrastructure projects from all over the world in a private company for 8 years. She completed her 2nd master on Quantitative Finance, UTS in 2015. She is currently working as an independent researcher and as a casual academic at School of Mathematics and Statistics, UNSW and Market Department, Business School, UTS.</p>
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<p style="text-align: justify;"> </p></div></div></section><div class="field field-name-field-seminar-latex field-type-text-long field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><div class="field field-name-field-seminar-url field-type-link-field field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/applied-seminar">Applied Seminar</a></li></ul></section>Fri, 30 Aug 2019 03:13:53 +0000z33407775109 at https://www.maths.unsw.edu.au F-1 algorithm: Efficient differentiation through large steady-state problems
https://www.maths.unsw.edu.au/seminars/2019-08/%C2%A0f-1-algorithm-efficient-differentiation-through-large-steady-state-problems
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Benoît Pasquier</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">Department of Earth System Science of the University of California</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Thu, 08/08/2019 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">M032, The Red Centre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p lang="en-GB" xml:lang="en-GB"> Steady-state systems of nonlinear partial differential equations (PDEs) are common in engineering and the biogeosciences. These systems are typically controlled by parameters that can be estimated efficiently using second-order optimization algorithms. However, computing the gradient vector and Hessian matrix of a given objective function defined implicitly by the solution of large PDE systems is seldom economical.</p>
<p lang="en-GB" xml:lang="en-GB">A fast and easy-to-use algorithm is introduced for computing the gradient and Hessian of an objective function implicitly constrained by a steady-state PDE system. The algorithm, which is based on the use of hyperdual numbers, is called the F-1 algorithm, because it requires only one factorization of the constraint-equation Jacobian. Careful examination of the relationships that arise from differentiating the PDE system reveal analytical shortcuts that the F-1 algorithm leverages. Benchmarks of the F-1 algorithm against five numerical differentiation schemes are shown in the context of optimizing a global steady-state model of the marine phosphorus cycle that depends explicitly on m=6 parameters. In this context, the F-1 algorithm computes the Hessian 16 to 100 times faster than other algorithms, allowing for the entire optimization procedure to be performed 4 to 26 times faster. This is because other algorithms require O(m) to O(m²) factorizations, which suggests even greater speedups for larger problems.</p>
<p lang="en-GB" xml:lang="en-GB">A live demonstration of using the F-1 algorithm, which is implemented as a Julia package, is given.</p>
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<p lang="en-GB" xml:lang="en-GB">Benoît Pasquier is a postdoctoral researcher at the Department of Earth System Science of the University of California, Irvine, working on global marine biogeochemistry models with Prof. J. Keith Moore and Prof. François Primeau. Benoît is an alumnus of UNSW, with a MSc in Environmental Science obtained in 2010 and a PhD in Applied Mathematics obtained in 2017 under the supervision of Prof. Mark Holzer. Prior to returning to academia for his PhD, Benoît has worked as a water-treatment engineer for Suez-Environment and as a FOREX-trader assistant for Société Générale Investment Banking. Benoît also holds a MSc in Engineering from École Polytechnique and a MSc in Finance Mathematics from Paris-Dauphine University and ENSAE ParisTec</p>
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<p> </p></div></div></section><div class="field field-name-field-seminar-latex field-type-text-long field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><div class="field field-name-field-seminar-url field-type-link-field field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/applied-seminar">Applied Seminar</a></li></ul></section>Tue, 23 Jul 2019 05:59:23 +0000z33407775068 at https://www.maths.unsw.edu.auNon-negative Polynomials
https://www.maths.unsw.edu.au/seminars/2019-08/non-negative-polynomials
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even"> Abhishek Bhardwaj</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">ANU</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Thu, 29/08/2019 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">RC-4082, The Red Centre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p> Non-negative polynomials are fundamental objects of study in real algebraic geometry. Testing the non-negativity of polynomials is known to be NP hard. Because of this, one generally looks to satisfy easier certificates of non-negativity. A basic example of this is the gradient being zero, and the Hessian being positive definite.</p>
<p>In recent years more attention has been given to the Sum of Squares (SOS) certificates, and their corresponding algorithms related to semi-definite programming (SDP). </p>
<p>This talk will focus on presenting these certificates and their related SDP forms. We will consider the practicality of some popular algorithms for testing non-negativity of polynomials. Lastly, we'll present a specific application of all these topics related to Quantum Information Theory, and some recent related work.</p>
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<p>Abhishek Bhardwaj is a PhD Student at the Mathematical Sciences Institute, ANU</p>
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<p> </p></div></div></section><div class="field field-name-field-seminar-latex field-type-text-long field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><div class="field field-name-field-seminar-url field-type-link-field field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/applied-seminar">Applied Seminar</a></li></ul></section>Tue, 23 Jul 2019 05:56:28 +0000z33407775067 at https://www.maths.unsw.edu.au Chaos, Dynamics and Differential Equations
https://www.maths.unsw.edu.au/seminars/2019-07/chaos-dynamics-and-differential-equations
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Marat Akhmet</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">Middle East Technical University, Turkey,</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Thu, 18/07/2019 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">RC-M032, The Red Centre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p class="western" style="line-height: 100%;"> The talk introduces innovations in the areas of dynamical systems, chaos, and differential equations. It first shows that the classical theory of dynamical systems, pioneered by H.Poincare and developed by G. Birkhoff, can be further advanced if one extends the line of equilibria, periodic, almost periodic, recurrent, and Poisson stable motions with unpredictable points, as has been done in Marat Akhmet’s work. The dynamics is accompanied by chaotic phenomenon, labeled as Poincare chaos. This novel type of chaos is produced in quasi minimal sets and considered first of all with Poisson stable ingredients. The history of dynamical systems and differential equations (non-autonomous) is connected to mutual enrichment. This case demonstrates that the unpredictable point in special functional spaces can be an unpredictable function and, consequently, that a new type of chaos-generating oscillations are to be found in differential equations.</p>
<p class="western" style="line-height: 100%;">Marat Akhmet is a professor at the Department of Mathematics, Middle East Technical University, Turkey, and is a specialist in dynamical models and differential equations. He has published six books and more than a hundred scientific papers. In the last several years, he has been investigating dynamics of neural networks: periodic and almost periodic motions, stability, chaos and its control.</p>
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<p> </p></div></div></section><div class="field field-name-field-seminar-latex field-type-text-long field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><div class="field field-name-field-seminar-url field-type-link-field field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/applied-seminar">Applied Seminar</a></li></ul></section>Fri, 05 Jul 2019 04:26:55 +0000z33407775046 at https://www.maths.unsw.edu.auNilpotent Decomposition of Solvable Lie Algebras
https://www.maths.unsw.edu.au/seminars/2019-07/nilpotent-decomposition-solvable-lie-algebras
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Liqun Qi</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">Department of Applied Mathematics, The Hong Kong Polytechnic University</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Thu, 11/07/2019 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">M032, The Red Centre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p style="text-align: justify;">Semisimple Lie algebras have been completely classified by Cartan and Killing. The Levi theorem states that every finite dimensional Lie algebra is isomorphic to a semidirect sum of its largest solvable ideal and a semisimple Lie algebra. These focus the classification of solvable Lie algebras as one of the main challenges of Lie algebra research. One approach towards this task is to take a class of nilpotent Lie algebras and construct all extensions of these algebras to solvable ones. In this paper, we propose another approach, i.e., to decompose a solvable nonnilpotent Lie algebra to two nilpotent Lie algebras which are called the left and right nilpotent algebras of the solvable algebra. The right nilpotent algebra is the smallest ideal of the lower central series of the solvable algebra, while the left nilpotent algebra is the factor algebra of the solvable algebra and its right nilpotent algebra. We show that the solvable algebras are decomposable if its left nilpotent algebra is an Abelian algebra of dimension higher than one and its right algebra is an Abelian algebra of dimension one. We further show that all the solvable algebras are isomorphic if their left nilpotent algebras are Heisenberg algebras of fixed dimension and their right algebras are Abelian algebras of dimension one.</p>
<p style="text-align: justify;"><br /> Professor Liqun Qi received his B.S. in Computational Mathematics at Tsinghua University in 1968. his M.S, and Ph.D. degree in Computer Sciences at University of Wisconsin-Madison in 1981 and 1984 respectively. Professor Qi has taught in Tsinghua University, China, University of Wisconsin-Madison, USA, University of New South Wales, Australia, and The City University of Hong Kong. He is now a Chair Professor at Department of Applied Mathematics, The Hong Kong Polytechnic University. Professor Qi has published more than 330 research papers in international journals. He established the superlinear and quadratic convergence theory of the semismooth Newton method, and played a principal role in the development of reformulation methods in optimization. Professor Qi's research work has been cited by the researchers around the world. He was listed as one of the world's most highly cited mathematicians in the recent ten years in 2003-2010. In 2018, he is listed as one of the world's most highly cited mathematicians again. Prof. Qi is exceptionally strong in winning external grants. Since coming to Hong Kong at the end of 1999, Prof. Qi won 18 Hong Kong Research Council GRF grants in consecutive years. Professor Qi is an editor or an associate editor of ten international journals. He has chaired more than fifteen international conferences and workshops held at Australia, Italy, Hong Kong and the Mainland China. In 2005, Professor Qi pioneered the research on eigenvalues for higher order tensors, which now has applications in biomedical engineering, statistical data analysis, machine learning, spectral hypergraph theory, solid mechanics, quantum physics, etc. He has more than 120 papers on tensors, published or accepted for publication in international journals. His book ``Tensor Analysis: Spectral Theory and Special Tensors, was published by SIAM in April 2017. Another book ``Tensor Eigenvalues and Their Applications’’ was published by Springer in 2018.</p></div></div></section><div class="field field-name-field-seminar-latex field-type-text-long field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><div class="field field-name-field-seminar-url field-type-link-field field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/applied-seminar">Applied Seminar</a></li></ul></section>Mon, 17 Jun 2019 03:31:01 +0000z33407775024 at https://www.maths.unsw.edu.auAlgebro-geometric approach to Painleve VI and Schlesinger equations.
https://www.maths.unsw.edu.au/seminars/2019-06/algebro-geometric-approach-painleve-vi-and-schlesinger-equations
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Vladimir Dragovic</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">UT Dallas</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Thu, 20/06/2019 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">RC-4082, The Red Centre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p style="text-align: justify;"> </p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-size: medium;">A new method of construction of algebro-geometric solutions of Schlesinger systems is presented. For an elliptic curve represented as a ramified double covering of CP^1, a meromorphic differential is constructed with the following property: the common projection of its two zeros on the base of the covering, regarded as a function of the only moving branch point of the covering, is a solution of a Painleve VI equation. This differential provides an invariant formulation of a classical Okamoto transformation for the Painleve VI equations. A generalization of this differential to hyperelliptic curves is also constructed. The corresponding solutions of the rank two Schlesinger systems associated with elliptic and hyperelliptic curves are constructed in terms of these differentials. The initial data for the construction of the meromorphic differentials include a point in the Jacobian of the curve, under the assumption that this point has non-variable coordinates with respect to the lattice of the Jacobian while the branch points vary. This method is motivated by an observation of Hitchin, who related the Poncelet polygons to algebraic solutions of a Painleve VI equation. The research has been partially supported by the NSF grant 1444147. This presentation is based on joint works with Vasilisa Shramchenko: </span></span></p>
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<p style="text-align: justify;"><a class="western" href="https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=361289"><span style="color: #000000;"><span style="text-decoration: none;"><span style="font-size: medium;">Dragović, Vladimir</span></span></span></a><span style="color: #000000;"><span style="font-size: medium;">; </span></span><a class="western" href="https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=692453"><span style="color: #000000;"><span style="text-decoration: none;"><span style="font-size: medium;">Shramchenko, Vasilisa</span></span></span></a><span style="color: #000000;"><span style="font-size: medium;">; Algebro-geometric solutions of the Schlesinger systems and the Poncelet-type polygons in higher dimensions. </span></span><a class="western" href="https://mathscinet.ams.org/mathscinet/search/journaldoc.html?id=6356"><span style="color: #000000;"><span style="text-decoration: none;"><span style="font-size: medium;"><em>Int. Math. Res. Not. IMRN</em></span></span></span></a><span style="color: #000000;"><span style="text-decoration: none;"><span style="font-size: medium;"><a class="western" href="https://mathscinet.ams.org/mathscinet/search/publications.html?pg1=ISSI&s1=364095">2018, </a><a class="western" href="https://mathscinet.ams.org/mathscinet/search/publications.html?pg1=ISSI&s1=364095">no. 13,</a></span></span></span><span style="color: #000000;"><span style="font-size: medium;"> 4229–4259.</span></span></p>
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<p style="text-align: justify;"><span style="color: #000000;"><span style="font-size: medium;">Dragović, Vladimir; Shramchenko, Vasilisa; Algebro-Geometric Approach to an Okamoto Transformation, the Painlevé VI and Schlesinger Equations. </span></span><a class="western" href="https://mathscinet.ams.org/mathscinet/search/journaldoc.html?id=5488"><span style="color: #000000;"><span style="text-decoration: none;"><span style="font-size: medium;"><em>Ann. Henri Poincaré</em></span></span></span></a><span style="color: #000000;"><span style="text-decoration: none;"><span style="font-size: medium;"><a class="western" href="https://mathscinet.ams.org/mathscinet/search/publications.html?pg1=ISSI&s1=370771">20 </a><a class="western" href="https://mathscinet.ams.org/mathscinet/search/publications.html?pg1=ISSI&s1=370771">(2019), </a><a class="western" href="https://mathscinet.ams.org/mathscinet/search/publications.html?pg1=ISSI&s1=370771">no. 4,</a></span></span></span><span style="color: #000000;"><span style="font-size: medium;"> 1121–1148.</span></span></p>
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<p style="text-align: justify;"> </p></div></div></section><div class="field field-name-field-seminar-latex field-type-text-long field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><div class="field field-name-field-seminar-url field-type-link-field field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/applied-seminar">Applied Seminar</a></li></ul></section>Mon, 17 Jun 2019 03:26:34 +0000z33407775023 at https://www.maths.unsw.edu.auBayesian search for MH370 and spacetime dynamical methods
https://www.maths.unsw.edu.au/seminars/2019-05/bayesian-search-mh370-and-spacetime-dynamical-methods
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Péter Koltai</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">Freie Universität Berlin</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Thu, 09/05/2019 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">RC-4082</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p class="western" style="margin-bottom: 0in; line-height: 100%;"><span style="color: #000000;"><span style="font-family: Calibri;"><span style="font-size: small;"><span lang="en-GB" xml:lang="en-GB">In the first part of this talk a data-based Markov-chain model is constructed for the probabilistic evolution of marine debris from the missing Malaysian Airlines flight MH370. Based on the beaching location and time of the confirmed MH370 debris different probabilistic tools are employed to narrow down the potential crash site of the aircraft.<br /> The second part of the talk is concerned with the essential macroscopic transport behaviour of flows. It presents connections between the measure-theoretic autonomous and non-autonomous concepts by embedding the latter in an augmented space. This characterisation allows for efficient optimisation of the mixing behaviour of flows subject to an admissible set of perturbations.</span></span></span></span></p>
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<p class="western" style="margin-bottom: 0in; line-height: 100%;"><span style="color: #000000;"><span style="font-family: Calibri;"><span style="font-size: small;"><span lang="en-GB" xml:lang="en-GB">Péter Koltai is a researcher at the Freie Universität Berlin, working on data-based modelling of complex systems. In the first part of his talk, he employs different probabilistic tools to narrow down the potential crash site of the missing MH370 aircraft based on the beaching location and time of the debris found. In the second part, he introduces spatiotemporal characterisations of dominant dynamics in unsteady flows, viable for mixing optimisation.</span></span></span></span></p>
<p> </p></div></div></section><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/applied-seminar">Applied Seminar</a></li></ul></section>Thu, 02 May 2019 06:50:07 +0000z33407774953 at https://www.maths.unsw.edu.auAddressing redundancy in column generation using Benders' decomposition cuts
https://www.maths.unsw.edu.au/seminars/2019-05/addressing-redundancy-column-generation-using-benders-decomposition-cuts
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Dr Stephen J Maher</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">Zuse Institute Berlin / Lancaster University</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Thu, 16/05/2019 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">MC-032, The Red Centre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p>When solving the linear programming (LP) relaxation of a mixed-integer program (MIP) with column generation, columns might be generated that are not needed to express any integer optimal solution of the MIP. Such columns are called strongly redundant and the dual bound obtained by solving the LP relaxation is potentially stronger if these columns are not generated. We introduce a sufficient condition for strong redundancy that can be checked by solving a compact LP. Using a dual solution of this compact LP we generate classical Benders cuts for the subproblem so that the generation of strongly redundant columns can be avoided. The potential of these cuts to improve the dual bound of the column generation master problem is evaluated computationally using an implementation in the branch-price-and-cut solver GCG. While their efficacy is limited on classical problems, the cuts’ usefulness is significantly demonstrated on structured models, when a temporal decomposition can be applied.</p>
<p><span lang="en-GB" xml:lang="en-GB"><strong>Dr Stephen J Maher</strong> is an alumnus of UNSW, having completed his PhD in Mathematics in 2014. Since completing his PhD, Stephen has work in research groups at the Zuse Institute Berlin and Lancaster University. Stephen is a core member of the development team for the mixed integer programming solver SCIP, which is hosted at the Zuse Institute Berlin. As part of this role, he has investigate the use of decomposition techniques in various parts of mixed integer programming solvers. Most recently, his work has involved the development of a general framework for the classical mathematical programming technique of Benders' Decomposition. Stephen has also started an initiative to educate people about optimisation in the real world through his website <a href="http://www.optimisationintherealworld.co.uk/" target="_blank">www.optimisationintherealworld.co.uk</a>.</span></p>
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<p> </p></div></div></section><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/applied-seminar">Applied Seminar</a></li></ul></section>Sun, 07 Apr 2019 23:55:21 +0000z33407774926 at https://www.maths.unsw.edu.au