School of Mathematics and Statistics - Applied Seminar
https://www.maths.unsw.edu.au/category/school-seminar-series/applied-seminar
en 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 class="western" lang="en-GB" style="line-height: 100%;" xml:lang="en-GB"> </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.auDiscontinuous Galerkin Time-Stepping
https://www.maths.unsw.edu.au/seminars/2019-04/discontinuous-galerkin-time-stepping
<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">Bill McLean</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">School of Mathematics and Statistics, 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, 18/04/2019 - 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>This talk is an overview of the discontinous Galerkin (DG) method as a time-stepping procedure for classical and fractional diffusion problems. After motivating the definition of the procedure, I outline its implementation and then illustrate key properties with simple, scalar ODEs and fractional ODEs. I then describe results for classical and fractional diffusion problems in 1D, and sketch an explanation for the observed superconvergence behaviour.</p>
<div>Bill McLean is an Associate Professor in the School of Mathematics and Statistics at UNSW. His research interests centre on numerical analysis for partial differential equations, and in particular on nonlocal evolution equations.</div>
<div> </div></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>Thu, 21 Mar 2019 07:43:33 +0000z33407774906 at https://www.maths.unsw.edu.auOn Emergence in Complex Physical Systems
https://www.maths.unsw.edu.au/seminars/2019-03/emergence-complex-physical-systems
<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">Peter Cudmore</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 Melbourne</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, 28/03/2019 - 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 class="western" style="line-height: 100%;">Many problems in biology, physics and engineering involve predicting and controlling complex systems, loosely defined as interconnected system-of-systems. Such systems can exhibit a variety of interesting non-equilibrium features such as emergence and phase transitions, which result from mutual interactions between nonlinear subsystems.</p>
<p class="western" style="line-height: 100%;">Modelling these systems is a task in-and-of itself, as systems can span many physical domains and evolve of multiple time scales. Nonetheless, one wishes to analyse the geometry of these models and relate both qualitative and quantitative insights back to the physical system.</p>
<p class="western" style="line-height: 100%;">Beginning with the modelling and analysis of a coupled optomechanical systems, this talk presents some recent results concerning the existence and stability of emergent oscillations. This forms the basis for a discussion of new directions in symbolic computational techniques for complex physical systems as a means to discuss emergence more generally.</p>
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<p class="western" style="line-height: 100%;">Peter Cudmore is a Postdoctoral Research Fellow in the Systems Biology Lab at University of Melbourne where he is developing and applying multi-physics network modelling techniques to biological systems. A key focus of his research is to understand the geometry of complex systems, and how emergence can be predicted, controlled. Peter completed his B.Sc. and Ph.D. (Applied Mathematics) at the University of Queensland.</p>
<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>Wed, 27 Feb 2019 00:19:45 +0000z33407774892 at https://www.maths.unsw.edu.auUnraveling the thermohaline structure of the Southern Ocean using functional data analysis
https://www.maths.unsw.edu.au/seminars/2019-02/unraveling-thermohaline-structure-southern-ocean-using-functional-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">Gurvan Madec</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">LOCEAN-IPSL, CNRS / Université P. et M. Curie, Paris, France</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">Tue, 26/02/2019 - 3:05pm</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-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"><div>
<p style="margin: 0px 0px 14px; text-align: justify; min-height: 17px;"> </p>
<p class="western" style="margin-bottom: 0.15in;" align="justify"><span style="font-family: Times New Roman;"><span style="font-size: large;">The Southern Ocean connects the Indian, Pacific and Atlantic Oceans and provides a direct pathway to exchange mass, heat and salt across the World Ocean, therefore playing an important role in the climate system. Due to the complexity of its structure and the general inadequacy of its sampling, both in time and space, it remains a challenge to describe and visualize the three dimensional pattern of its circulation and the associated tracer distribution (temperature, salinity, oxygen or nutrients). This work contributes to the understanding of the thermohaline structure of the ocean and especially of the Southern Ocean by introducing a novel decomposition method, the Functional Principal Component Analysis applied on combined T-S vertical profiles. We first normalize hydrographic profiles by using a functional spline representation and then, the statistical method of dimension reduction and feature extraction reveals the main spatial patterns of the T-S variations. Applied to the Southern Ocean, t</span></span><span style="font-family: Times;"><span style="font-size: large;">he first two modes explain ~92% of the combined T–S variance, thus providing a surprisingly good approximation of the thermohaline properties. T</span></span><span style="font-family: Times New Roman;"><span style="font-size: large;">he vertical modes present circumpolar patterns that can be closely related to the stratification regimes that define the circumpolar fronts. Notably the Polar Front is located at the natural boundary between the region controlled by the first (thermal) mode to the north and the second (haline) mode to the south. A mapping of the fundamental zonation is provided with an estimate of the width of the water mass boundaries. As a validation of this method, the Antarctic Polar Front is investigated further in the Indian sector using the same statistical framework. We show that the Polar Front latitudinal position varies seasonally upstream of the Kerguelen Plateau. This meandering is confirmed by hydrographic data gathered by elephant seals equipped with miniaturized sensors. Finally, the potential of the method is illustrated with an application to the World ocean where the first three vertical modes explain to 93% of the combined T-S variance and are related to very robust structures of the World Ocean. </span></span></p>
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</div></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>Wed, 20 Feb 2019 05:15:46 +0000z33407774872 at https://www.maths.unsw.edu.auA Topological Theory of Oceanic Neutral Surfaces
https://www.maths.unsw.edu.au/seminars/2019-03/topological-theory-oceanic-neutral-surfaces
<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">Geoff Stanley</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">School of Mathematics and Statistics, 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, 07/03/2019 - 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 class="western"> Most of the mixing in the ocean occurs along "neutral surfaces" rather than across them, but difficulties arising from nonlinearities in the density of seawater mean neutral surfaces can only be approximated. Here, a multivalued functional relationship between the pressure, p, and the density on neutral surfaces is exploited. Single-valued branches are found for geographic regions determined by the arcs of the Reeb graph of p. The regions meet at saddles of p which are represented by internal nodes of the Reeb graph, while leaf nodes represent extrema of p. Islands and other holes in the neutral surface can create cycles in the Reeb graph, raising some interesting new challenges. This topological theory also solves an open problem from 1989: the exact geostrophic stream function (GSF) for neutral surfaces is expressed using path integrals of this multivalued function. In practice, this theory gives rise to a new class of approximately neutral surfaces, called topobaric surfaces. These possess geographic dependence like neutral density while maintaining the exactness of a GSF like orthobaric density, two of the most advanced variables used in modern oceanography. The exact GSF for topobaric surfaces can be used effectively on any approximately neutral surface.</p>
<p class="western"> </p>
<p class="western"><span style="font-size: small;">Geoffrey J. Stanley is a postdoctoral fellow in the School of Mathematics and Statistics at UNSW. Presently, his research focuses on developing theory and algorithms for neutral surfaces in the ocean. His past research interests include Southern Ocean dynamics, flow around topography, the abyssal overturning circulation, and the transition to turbulence. In Physical Oceanography, he holds a PhD from the University of Oxford and an MSc from University of Victoria, as well as a BMath in Pure and Applied Mathematics from the University of Waterloo.</span></p>
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<p class="western"> </p>
<p class="western"> </p>
<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>Wed, 20 Feb 2019 05:11:50 +0000z33407774871 at https://www.maths.unsw.edu.auUnion averaged operators with applications to proximal algorithms
https://www.maths.unsw.edu.au/seminars/2019-01/union-averaged-operators-applications-proximal-algorithms
<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">Minh N. Dao</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">CARMA, University of Newcastle</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, 31/01/2019 - 2:05pm</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">M-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 style="margin-top: 0; margin-bottom: 0;"> </p>
<p style="margin-top: 0; margin-bottom: 0;">In this paper, we introduce and study a class of structured set-valued operators, which we call union averaged nonexpansive. At each point in their domain, the value of such an operator can be expressed as a finite union of single-valued averaged nonexpansive operators. We investigate various structural properties of the class and show, in particular, that is closed under taking unions, convex combinations, and compositions, and that their fixed point iterations are locally convergent around strong fixed points. We then systematically apply our results to analyze proximal algorithms in situations, where union averaged nonexpansive operators naturally arise. In particular, we consider the problem of minimizing the sum two functions, where the first is convex and the second can be expressed as the minimum of finitely many convex functions.</p>
<p style="margin-top: 0; margin-bottom: 0;"> </p>
<p style="margin-top: 0; margin-bottom: 0;"><strong>Biography:</strong> Minh N. Dao received the Ph.D. degree in applied mathematics from the University of Toulouse, France in 2014. He was a Lecturer at Hanoi National University of Education, Vietnam from 2004 to 2010, a Lecturer and Research Assistant at National Institute of Applied Sciences (INSA) in Toulouse, France from 2013 to 2014, and a Postdoctoral Fellow at the University of British Columbia, Canada from 2014 to 2016. He is currently a Research Associate in the Priority Research Centre for Computer-Assisted Research Mathematics and its Applications (CARMA) at The University of Newcastle, Australia. His research interests include nonlinear optimization, nonsmooth analysis, iterative methods, monotone operator theory, control theory, and operations research. In 2017, he received the Annual Best Paper Award from the Journal of Global Optimization.</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 Jan 2019 05:56:37 +0000z33407774843 at https://www.maths.unsw.edu.au