**First Kyushu-UNSW Joint Workshop on the Mathematics underpinning Industry and Innovation**

Date and Time: 18th November 2016 (Friday), 11:00 - 17:30

Venue: Red Centre 4082, Kensington Campus, University of New South Wales

Organizers:

John Roberts (School of Mathematics and Statistics, University of New South Wales)

Kenji Kajiwara (Institute of Mathematics for Industry, Kyushu University)

Speakers from Kyushu:

(1) Yasuhide Fukumoto (Institute of Mathematics for Industry, Kyushu University)

Title:

**Topological ideas in magnetohydrodynamics (MHD) and its application to spectra and stability of MHD rotating flows**

Abstract:

There are a few topological invariants associated with the ideal magnetohydrodynamics (MHD), namely, dynamics of an electrically conducting fluid subject to a magnetic field. We expose the iso-magnetovortical structure lying behind these invariants. A steady flow of an ideal incompressible MHD is characterized as an extremum of the total energy (=the Hamiltonian) with respect to perturbations constrained to an iso-magnetovortical sheet. We exploit this structure to calculate the spectra and stability of MHD rotating flows.

In galaxies, stars are formed at the center of accretion disks by absorbing matters. Since the total angular momentum is conserved, the angular momentum must be transported away while the mass is absorbed to the center. The magnetorotational instability (MRI) is a desired mechanism for triggering turbulence necessary to account for outwards transport of the angular momentum. We develop a Lagrangian approach, combined with the WKB analysis, to short-wave instability of axisymmetric rotating MHD flows subjected to azimuthal magnetic field. An attempt is also made to incorporate the effect of the viscosity and the electric resistivity.

This work is a collaboration with Rong Zou.

(2) Kei Hirose (Institute of Mathematics for Industry, Kyushu University)

Title:

**MM algorithm for high-dimensional robust graphical modeling**

Abstract:

We introduce a robust sparse Gaussian graphical modeling. The robust estimation is realized by the gamma-divergence (Fujisawa and Eguchi, 2008, JMVA). The parameter estimation procedure is constructed using the Majorize-Minimization (MM) algorithm, which guarantees that the objective function monotonically decreases at each iteration.

(3) Kenji Kajiwara (Institute of Mathematics for Industry, Kyushu University)

Title:

**Integrable Deformations of Plane/Space Curves**

Abstract:

It is well-known that classical differential geometry is one of the sources of integrable systems which dates back to 19th century, as seen in the classical works of Bäcklund and Darboux on the construction of transformations of surfaces. Dynamics of space/plane curves is another interesting interface between integrable systems and differential geometry, which was initiated by the pioneering work of Hasimoto followed by Lamb in 70s. It is an intriguing problem to formulate discretized theories preserving underlying relationship with integrable systems.

In this talk, we start from some historical remarks and basic ideas of integrable systems and their discretization. We next explain how the hierarchies of integrable systems naturally arise in the context of deformation theory of plane/space curves. We then present a discrete model of vortex filaments in 3D fluid, which is a discrete analogue of the space curve deformation driven by the binormal flow described by the nonlinear Schrödinger equation.

(4) Takashi Okayasu (Faculty of Agriculture, Kyushu University)

Title:

**Measurement and Visualization of Agricultural Information by Using ICT Information**

Abstract:

Communication Technology (ICT) can be applied to improve agricultural production in terms of advancing the knowledge and techniques of farming, reducing production costs, and improving the quality of agricultural produce. Various ICT systems to support and improve agricultural practices have been developed, focusing on environmental measurement and control, plant growth and motion estimation, and farm work recording. The development of several ICT systems to support small- and medium-scale farms in Japan using affordable smart devices such as low-price microcomputers and sensors, and open-source software, and its evaluation results for their feasibility will be introduced.

(5) Trinh Khanh Duy (Institute of Mathematics for Industry, Kyushu University)

Title:

**Global asymptotic behaviours of Gaussian beta ensembles**

Abstract:

Gaussian beta ensembles, as generalizations of Gaussian Orthogonal/Unitary/Symplectic Ensembles (GOE, GUE and GSE), were initially defined in terms of joint distribution of eigenvalues. They are now realized as eigenvalues of certain random symmetric tridiagonal matrices, also called Jacobi matrices, with independent entries distributed according to specific distributions. This talk introduces recent developments in spectra statistics of the ensembles, with emphasis on a new interpretation of classical Wigner's semi-circle law.

(6) Yoshihiro Yamanishi (Medical Institute of Bioregulation, Kyushu University)

Title: Statistical machine learning for drug discovery

Abstract:

In this study, we develop a new statistical machine learning method for drug discovery based on various biomedical big data of genes, proteins, and diseases. The originality lies in the kernel-based distance learning algorithm in a framework of supervised network inference. The proposed method enables us to efficiently find drug candidate compounds for a wide range of diseases.

Speakers from UNSW:

(1) Dr Quoc Le Gia (School of Mathematics and Statistics, University of New South Wales)

Title:

**Bayesian estimations in partial differential equations with random coefficients**

Abstract:

Bayesian estimations of solutions to parametric operator equations arise in numerical uncertainty quantification of operator equations with distributed uncertain inputs, such as uncertain coefficients, uncertain domains or uncertain source terms and boundary data.

We propose and analyze deterministic multilevel approximations for Bayesian estimations of operator equations with uncertain distributed parameters, subject to additive Gaussian measurement data. The algorithms use a multilevel approach based on deterministic, higher order quasi-Monte Carlo quadrature for approximating the high-dimensional expectations, which arise in the Bayesian estimators, and a Petrov-Galerkin method for approximating the solution to the underlying partial differential equation.

This is a joint work with Josef Dick (UNSW) and Robert Gantner and Christoph Schwab (ETH)

(2) Takehito Yoshiki (School of Mathematics and Statistics, University of New South Wales)

Title:

**Quasi Monte Carlo method with higher order convergence**

Abstract:

My research area is numerical integration over the high dimensional domain. In particular, I study about Quasi Monte Carlo integration. (Not Quasi) Monte Carlo integration using N random points gives us the convergence rate of the integration error 1/N^(1/2). On the other hand, Quasi Monte Carlo integration uses a deterministic point set with cardinality N. If we choose a good quadrature point set, we can provide good convergence rate compared with Monte Carlo integration, say 1/N^C for some constant C. In this talk, we show how to choose a good point sets with my previous research results and my future research vision.

(3) Herbert Huppert (School of Mathematics and Statistics, University of New South Wales/DAMTP, University of Cambridge)

Title:

**Gravity currents: from the desk-top through gigantic umbrella clouds to Mars**

Abstract:

The presentation will describe the present understanding of gravity currents, which occur whenever fluid of one density flows mainly horizontally into fluid of a different density. The talk will explain effects associated with currents at both high and low Reynolds, and due to particle content, as well as outlining the effects of mean flows and the role of gravity currents in Carbon sequestration. Different situations will be outlined which require the solution of nonlinear governing equations, sometimes using similarity methods or numerical analysis (at least in part). Some results will be compared with experiments in the laboratory and observations in the field. A desk-top experiment will be performed that will show how easy it is to transform a stable current to an unstable one.

(4) Adelle Coster (School of Mathematics and Statistics, University of New South Wales)

Title:

**Biochemical Network Dynamics: data-driven structure and design**

Abstract:

Experimental data usually comes from a variety of sources which often measure different aspects of a system under various perturbations and using different techniques. This complicates the process of building a universal model that encompasses all the known behaviours of the system. One approach to identifying the network structure for a model is to simultaneously optimise the parameters across multiple data sets, and then iteratively adapting the model. This requires the deconstruction of experimental information into meaningful and quantitative variables and importantly the construction of representations of what the model system would produce under the different experimental conditions. The model can then be analysed explored to determine the points at which other influences and perturbations affect the system. For instance, if a particular biochemical component is knocked-down or removed, how and where does this affect the dynamics? This greatly improves the process of selecting high priority targets for, and the design of, future experiments. An example of this approach is presented for the GLUT4 translocation system in cells. GLUT4, or glucose transporter 4, is the main insulin-responsive glucose transporter in mammalian fat and muscle cells. GLUT4 dynamically cycles to and from the cell surface controlling the level of glucose uptake by the cell. I will discuss the approaches we have employed to construct data-driven mathematical models of insulin-controlled glucose transport and the benefits such models provide in disentangling complex biological behaviour.

(5) Dinh T Tran (School of Mathematics and Statistics, University of New South Wales)

Title:

**Poisson brackets of mappings obtained from lattice equations**

Abstract:

In this talk, I will present Poisson brackets of mappings obtained from quad-graph equations. The first class of mappings is a class of 4-dimensional maps which are obtained as lifts of integrable lattice equations. Their Poisson brackets can be found from two ways: Sklyanin bracket and the existence of three-leg forms. The second class of mappings is obtained as periodic reductions of lattice equations. Their Poisson brackets can be derived by using the existence of Lagrangians and the discrete analogue of Ostrogradsky transformation.