### Organizers

The occasion of the annual Board meeting of the International Council for Industrial and Applied Mathematics (ICIAM) provides a confluence of distinguished applied mathematicians from around the world. This workshop provides a forum to exchange ideas, to review recent developments in applied mathematics, and to allow the local community of mathematical scientists to share this international perspective.

The theme of the meeting will be broad, reflecting the range of expertise of these scientists.

The workshop is hosted by the Mathematical Biosciences Institute at OSU, with additional funding provided by the Mathematics Research Institute of OSU and by the Institute for Mathematics and its Applications (University of Minnesota).

The grant from the IMA allows us to support speakers and participants from neighboring institutions in Ohio and throughout the Midwest. In particular, we would like to invite graduate students to attend.

Partial support is available for students and junior participants. We solicit contributions for a poster session.

### Accepted Speakers

Thursday, May 15, 2014 | |
---|---|

Time | Session |

07:45 AM | Shuttle to MBI |

08:00 AM 09:00 AM | Breakfast |

09:00 AM 09:30 AM | Remarks (Peter, Marty, MBI staff) |

09:30 AM 10:00 AM | Marty Golubitsky - Binocular Rivalry and Symmetry-Breaking In binocular rivalry a subject is presented with two different images --- one to each eye. Usually, the subject perceives alternation between these two images. However, in a number of binocular rivalry experiments, subjects report perceiving surprising combinations of the two presented images. Wilson has proposed a class of neuronal networks that admit multiple competing patterns. We show that symmetry-breaking in appropriately constructed Wilson-type networks predicts the surprising perceived images in the rivalry experiments. This is joint work with Casey Diekman and Yunjiao Wang. |

10:00 AM 10:30 AM | Shin'ichi Oishi |

10:30 AM 11:00 AM | Poster and Coffee Break |

11:00 AM 11:30 AM | Tomás C. Rebollo - Some remarks on the numerical approximation of turbulence models with wall laws This talk deals with the numerical approximation of Large Eddy Simulation (LES) and Projection-based Variational Multi-Scale (VMS) turbulence models by the finite element method. We consider mixed boundary conditions that combine Dirichlet and non-linear wall laws. We prove convergence to the continuous targeted models. We prove density results by finite element $C^0$ spaces, for polyhedric domains, that replace the usual ones by smooth functions. We study the uniform well-posedness with respect to the discretization parameters and the asymptotic energy balance. We finally present some numerical results for 3D benchmark flows: Cavity and Turbulent Channel flow. |

11:30 AM 12:00 PM | Daniel Thompson - Coding Sequence Density Estimation via Topological Pressure I will describe an approach to coding sequence (CDS) density estimation in genomic analysis introduced recently by myself and David Koslicki. Our approach is based on the topological pressure, which is a measure of ‘weighted information content’ adapted from ergodic theory. We use the topological pressure (with suitable training data) to give ab initio predictions of CDS density on the genomes of Mus Musculus, Rhesus Macaque and Drososphilia Melanogaster. While our method is not sufficiently precise to predict, for example, the exact locations of genes, we demonstrate that our method gives reasonable estimates for the ‘coarse scale’ problem of predicting CDS density. This is joint work with David Koslicki (Oregon State). |

12:00 PM 01:30 PM | Lunch Break |

01:30 PM 02:00 PM | Helena J. Nussenzveig Lopes |

02:00 PM 02:30 PM | Pierangelo Marcati |

02:30 PM 03:00 PM | Ian Frigaard |

03:00 PM 03:30 PM | Poster and Coffee Break |

03:30 PM 04:00 PM | Sean Bohun |

04:00 PM 04:30 PM | Jean-Paul Berrut |

04:30 PM 05:00 PM | Grégoire Allaire |

05:15 PM | Shuttle pick-up from MBI |

06:30 PM 08:00 PM | Reception/dinner at Marty and Barbara's home. Directions will be provided. |

Friday, May 16, 2014 | |
---|---|

Time | Session |

07:45 AM | Shuttle to MBI |

08:00 AM 09:00 AM | Breakfast |

09:00 AM 09:30 AM | Robert Kass |

09:30 AM 10:00 AM | Iain S. Duff - Preconditioning of Least-Squares Problems by Identifying Basic Variables We study the preconditioning of the augmented system formulation of the least squares problem $\min_x || b - A x ||^2_2$, viz. $$ \left[ \begin{array}{cc} I_m & A\\ A^T & 0 \end{array} \right] \; \left[ \begin{array}{c} r\\x \end{array} \right] = \left[ \begin{array}{c} b\\0 \end{array} \right], $$ where A is a sparse matrix of order $m imes n$ with full column rank and $r$ is the residual vector equal to $b - Ax$. We split the matrix $A$ into basic and non-basic parts so that $P A = \left[ \begin{array}{c} B\\N \end{array}\right],$ where $P$ is a permutation matrix, and we use the preconditioner $$M = \left[ \begin{array}{cc} I & 0\\ 0 & B^{-T} \end{array}\right] $$ to symmetrically precondition the system to obtain, after a simple block Gaussian elimination, the reduced symmetric quasi-definite (SQD) system $$ \begin{eqnarray*} \left[ \begin{array}{cc} I_{m-n} & N B^{-1}\\ B^{-T}N^T & -I_n \end{array} \right] \; \left[ \begin{array}{c} r_N\\ B x \end{array} \right] = \left[ \begin{array}{c} b_N\\-b_B \end{array} \right] . \end{eqnarray*} $$ We discuss the conditioning of the SQD system with some minor extensions to standard eigenanalysis, show the difficulties associated with choosing the basis matrix $B$, and discuss how sparse direct techniques can be used to choose it. We also comment on the common case where A is an incidence matrix and the basis can be chosen graphically. |

10:00 AM 10:30 AM | Pingwen Zhang |

10:30 AM 11:00 AM | Poster and Coffee Break |

11:00 AM 11:30 AM | Chang-Ock Lee |

11:30 AM 12:00 PM | Lê Hùng Sơn - Applications of the Initial value Problems in weather and nature catastrophe forecasts Many problems of weather and nature catastrophe forecasts are reduced to the Initial Value Problem (IVP) of the type:$$\begin{equation} \partial _t u = L\left( {t,x,u,\partial _{x_j } u} \right)\end{equation}$$ $$\begin{equation} u(0, x) = {u_0}(x)\end{equation}$$ where $x = (x_{1}, \ldots., x_{n}) \in \Omega \subset \mathbb{R}^n$, $t \geq 0$ is time variable, $u = u(t, x) \in C^1 $ is the unknown vector function and $L$ in (\ref{eq:1}) is a differential operator of the first order. \\ The abstracts Cauchy-Kovalevskaya theorem states that the IVP (\ref{eq:1}) and (\ref{eq:2}) is uniquely solved if the initial data ${u_0}(x)$ satisfies the supplement condition $\ell u = 0$, where $\ell$ is an elliptic differential operator and associated to the operator $L$\\ In this paper $\ell$ is defined by $$\begin{equation} \ell u:=\sum\limits_{j=1}^{3}A_j\frac{\partial u}{\partial x_j}, \end{equation}$$ where $$A_1= \begin{pmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \\ 0 & 0 & 0 \end{pmatrix}, A_2=\begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & -1 \end{pmatrix}, A_3=\begin{pmatrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{pmatrix}, \dfrac{\partial u}{\partial x_j}= \begin{pmatrix} \dfrac{\partial u_1}{\partial x_j} \\ \dfrac{\partial u_2}{\partial x_j}\\ \dfrac{\partial u_3}{\partial x_j} \end{pmatrix},$$ $u = (u_1, u_2, u_3)$ is the unknown vector function.\\ \\ $L$ are the operators of following type $$\begin{equation} Lu:=\sum_{k=1}^{3}B_k\frac{\partial u}{\partial x_k}+Cu+D \end{equation}$$ where $B_k=[b_{ij}^k]_{3 \times 3}$, $C = [c_{ij}]_{3 \times 3}$, $D=[d_1, d_2, d_3]^T$. The matrix elements are the continuously differentiable functions up to second order of the space-variables $x_1, x_2, x_3$ and continuously differentiable up to first order of the time variable $t$.\\ $\ell$ and $L$ are called an associated operator if $\ell u = 0$\ \Rightarrow \ $\ell(Lu) = 0$.\\ The general theorem for problem (\ref{eq:1}) and (\ref{eq:2}) states that if $L$ is associated with $\ell$ then the problem (\ref{eq:1}) and (\ref{eq:2}) is uniquely solvable with ${u_0}$ belongs to root space of $\ell u = 0$.\\ In his Ph.D. dissertation (2013) Le Cuong given the necessary and sufficient conditions so that the $L$ is associated to the operator $\ell$ Based on the results of Le Cuong we will use the scientific computing software Mathematica to build a program to find all $L$ operators of type (\ref{eq:4}) associated with $\ell$ of type (\ref{eq:3})\\ Therefore we can describe all differential operators $L$ so that the IVP (\ref{eq:1}) and (\ref{eq:2}) is uniquely solved.\\ Keywords: Initial Value Problem; Associated space; Interior estimate; Mathematica; 2000 MR Subject Classifications; 35B45; 35F10; 47H10 |

12:00 PM 01:00 PM | Lunch Break |

01:00 PM 01:30 PM | NOORE ZAHRA |

01:30 PM 02:00 PM | Hiroshi Kokubu - Detecting Morse Decompositions of the Global Attractor of Regulatory Networks by Time Series Data Complex network structure frequently appear in biological systems such as gene regulatory networks, circadian rhythm models, signal transduction circuits, etc. As a mathematical formulation of such biological complex network systems, Fiedler, Mochizuki and their collaborators (JDDE 2013) recently defined a class of ODEs associated with a finite directed graph called a regulatory network, and proved that its dynamics on the global attractor can in principle be faithfully monitored by information from a (potentially much) fewer number of vertices of the graph called the feedback vertex set. In this talk, I will use their theory to give a method for detecting a more detailed information on the dynamics of regulatory networks, namely the Morse decomposition of its global attractor. The main idea is to take time series data from the feedback vertex set of a regulatory network, and construct a combinatorial multi-valued map, to which we apply the so-called Conley-Morse Database method. As a test example, we study Mirsky’s mathematical model for mammalian circadian rhythm which can be represented as a regulatory network with 21 vertices. This is a joint work with B. Fielder, A. Mochizuki, G. Kurosawa, and H. Oka. |

02:00 PM 02:30 PM | Irene Fonseca - Variational Methods for Crystal Surface Instability Using the calculus of variations it is shown that important qualitative features of the equilibrium shape of a material void in a linearly elastic solid may be deduced from smoothness and convexity properties of the interfacial energy. In addition, short time existence, uniqueness, and regularity for an anisotropic surface diffusion evolution equation with curvature regularization are proved in the context of epitaxially strained two-dimensional films. This is achieved by using the $H^{-1}$-gradient flow structure of the evolution law, via De Giorgi's minimizing movements. This seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity. |

02:30 PM 03:00 PM | Michael Günther |

03:00 PM 03:30 PM | Poster and Coffee Break |

03:30 PM 04:00 PM | Weizhu Bao |

04:00 PM 04:30 PM | Peter Benner - Parametric Model Order Reduction using Bilinear Systems Model order reduction (MOR) nowadays is an important tool in simulation and control for dynamical systems arising in various engineering disciplines. Often, models of physical processes contain parameters, either describing material properties and geometry variations or arising from changing boundary conditions. For purposes of design, optimization and uncertainty quantification, it is often desirable to preserve these parameters as symbolic quantities in the reduced-order model (ROM). This allows the re-use of the ROM after changing the parameter so that the repeated computation of reduced-order models can be avoided. Significant savings in simulation times for full parameter sweeps, Monte Carlo simulations, or within optimization algorithms can be achieved this way. In this talk, we study a particular approach for computing ROMs for linear parametric systems based on interpreting the reduced-order model as a bilinear system. This open the door to employ methods designed for MOR of bilinear systems in the context of parametric MOR. We will discuss the merits and pitfalls of using this approach as well as the MOR methods that become available via this re-formulation of the MOR problem. Numerical results illustrate the performance of all the methods under consideration. |

04:30 PM 05:00 PM | Yuan Lou - ESS in Spatial Models for Evolution of Dispersal From habitat degradation and climate change to spatial spread of invasive species, dispersal plays a central role in determining how organisms cope with a changing environment. How should organisms disperse “optimally” in heterogeneous environments? I will discuss some recent development on the evolution of dispersal, focusing on finding evolutionarily stable strategies (ESS) for dispersal. |

05:00 PM | Shuttle to MBI |

06:30 PM 08:00 PM | Conference Banquet at Crowne Plaza |

Name | Affiliation | |
---|---|---|

Allaire, Gregoire | smai-president@emath.fr | Applied Mathematics, Ecole Polytechnique |

Bao, Weizhu | bao@math.nus.edu.sg | Mathematics, National University of Singapore |

Benner, Peter | benner@mpi-magdeburg.mpg.de | Computational Methods in Systems and Control, Max Planck Institute for Dynamics of Complex Technical Systems |

Berrut, Jean-Paul | jean-paul.berrut@unifr.ch | Departement de Mathematiques, Universite de Fribourg |

Bohun, Sean | sean.bohun@uoit.ca | Science, University of Ontario Institute of Technology |

Brezzi, Franco | brezzi@imati.cnr.it | Science and Technology, IUSS |

ChacÃ³n Rebollo, TomÃ¡s | chacon@us.es | Differential Equations and Numerical Analysis, University of Sevilla |

Chen, Zhiming | zmchen@lsec.cc.ac.cn | CSCM, Acadamy of Mathematics and Systems Science |

Conti, Sergio | sergio.conti@uni-bonn.de | Institute for Applied Mathematics, University of Bonn |

Crowley, James | jcrowley@siam.org | EDO, SIAM |

Cuminato, Jose | jacumina@icmc.usp.br | Applied Mathematics and Statistics, University of Sao Paulo |

Damlamian, Alain | damla@univ-paris12.fr | Dept. of Mathematics, Universite Paris Est Creteil Val de Marne |

Dawes, Adriana | dawes.33@osu.edu | Department of Mathematics / Department of Molecular Genetics, The Ohio State University |

Duff, Iain S. | iain.duff@stfc.ac.uk | SCD, Rutherford Appleton Laboratory |

Esteban, Maria J. | esteban@ceremade.dauphine.fr | CEREMADE, CNRS & University Paris-Dauphine |

Fitt, Alistair | afitt@brookes.ac.uk | Senior Management Team, Oxford Brookes University |

Fonseca, Irene | fonseca@andrew.cmu.edu | Department of Mathematical Sciences, Carnegie Mellon University |

Frigaard, Ian | frigaard@math.ubc.ca | Mechanical Engineering and Mathematics, UBC |

Gao, Xiaoshan | xgao@mmrc.iss.ac.cn | Chinese Academy of Sciences, Academy of Mathematics and Systems Science, CAS |

GÃ¼nther, Michael | guenther@math.uni-wuppertal.de | Applied Mathematics / Numerical Analysis, University of Wuppertal |

Golubitsky, Marty | mg@mbi.osu.edu | Mathematical Biosciences Institute, The Ohio State University |

Guan, Bo | guan@math.osu.edu | Mathematics, Ohio State University |

Hsu, Ting-Hao | hsu@math.ohio-state.edu | Mathematics, Ohio State University |

Iyiola, Olaniyi | samuel@kfupm.edu.sa | Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals |

Jin, Yu | yjin6@unl.edu | Mathematics, University of Nebraska-Lincoln |

Kass, Robert | kass@stat.cmu.edu | Department of Statistics, Carnegie-Mellon University |

Keyfitz, Barbara | bkeyfitz@math.ohio-state.edu | Department of Mathematics, The Ohio State University |

Kokubu, Hiroshi | kokubu@math.kyoto-u.ac.jp | Department of Mathematics, Kyoto University |

Lee, Chang-Ock | colee@kaist.edu | Mathematical Sciences, KAIST |

Lou, Yuan | lou@math.ohio-state.edu | Department of Mathematics, The Ohio State University |

Marcati, Pierangelo | pierangelo.marcati@univaq.it | Information Engineering,Computer Science and Mathematics, University of LAquila |

Marini, Donatella | donatella.marini@unipv.it | Mathematics, Pavia University |

Mitsui, Taketomo | tamitsui@mail.doshisha.ac.jp | Mathematical Science, Doshisha University |

Nussenzveig Lopes, Helena J. | hlopes@ime.unicamp.br | Mathematics, Universidade Federal do Rio de Janeiro |

Oishi, Shin'ichi | oishi@waseda.jp | Applied Mathematics, Waseda University |

Park, Chunjae | cjpark@konkuk.ac.kr | Mathematics, Konkuk University |

Phillips, Cynthia | caphill@sandia.gov | Analytics, Sandia National Laboratories |

Pipher, Jill | jpipher@math.brown.edu | math, Brown University |

Quy, Tong Dinh | son.lehung@hust.edu.vn | School of Applied Mathematics and Informatics, Hanoi University of Science and Technology |

Rousseau, Christiane | rousseac@DMS.UMontreal.CA | Mathematics and Statistics, University of Montreal |

Sloan, Ian | i.sloan@unsw.edu.au | Applied Mathematics, The University of New South Wales |

Son, Le Hung | son.lehung@hust.edu.vn | Applied Mathematics and Informatics, Hanoi University of Science and Technology |

Thompson, Daniel | thompson@math.osu.edu | Mathematics, The Ohio State University |

Xu, Xuejun | xxj@lsec.cc.ac.cn | |

Xue, Chuan | cxue@mbi.osu.edu | Mathematics, The Ohio State University |

Yan, Guiying | yangy@amss.ac.cn | |

Ying, Hao | ying.32@osu.edu | Mathematics, The Ohio State University |

ZAHRA, NOORE | noor_zahra_india@yahoo.co.in | School of Engineering and Technology, Sharda University |

Zhang, Pingwen | pzhang@pku.edu.cn | School of Mathematical Sciences, Peking University |

Model order reduction (MOR) nowadays is an important tool in simulation and control for dynamical systems arising in various engineering disciplines. Often, models of physical processes contain parameters, either describing material properties and geometry variations or arising from changing boundary conditions. For purposes of design, optimization and uncertainty quantification, it is often desirable to preserve these parameters as symbolic quantities in the reduced-order model (ROM). This allows the re-use of the ROM after changing the parameter so that the repeated computation of reduced-order models can be avoided. Significant savings in simulation times for full parameter sweeps, Monte Carlo simulations, or within optimization algorithms can be achieved this way.

In this talk, we study a particular approach for computing ROMs for linear parametric systems based on interpreting the reduced-order model as a bilinear system. This open the door to employ methods designed for MOR of bilinear systems in the context of parametric MOR. We will discuss the merits and pitfalls of using this approach as well as the MOR methods that become available via this re-formulation of the MOR problem. Numerical results illustrate the performance of all the methods under consideration.

This talk deals with the numerical approximation of Large Eddy Simulation (LES) and Projection-based Variational Multi-Scale (VMS) turbulence models by the finite element method. We consider mixed boundary conditions that combine Dirichlet and non-linear wall laws. We prove convergence to the continuous targeted models. We prove density results by finite element $C^0$ spaces, for polyhedric domains, that replace the usual ones by smooth functions. We study the uniform well-posedness with respect to the discretization parameters and the asymptotic energy balance. We finally present some numerical results for 3D benchmark flows: Cavity and Turbulent Channel flow.

Using the calculus of variations it is shown that important qualitative features of the equilibrium shape of a material void in a linearly elastic solid may be deduced from smoothness and convexity properties of the interfacial energy.

In addition, short time existence, uniqueness, and regularity for an anisotropic surface diffusion evolution equation with curvature regularization are proved in the context of epitaxially strained two-dimensional films. This is achieved by using the $H^{-1}$-gradient flow structure of the evolution law, via De Giorgi's minimizing movements. This seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity.

In binocular rivalry a subject is presented with two different images --- one to each eye. Usually, the subject perceives alternation between these two images. However, in a number of binocular rivalry experiments, subjects report perceiving surprising combinations of the two presented images. Wilson has proposed a class of neuronal networks that admit multiple competing patterns. We show that symmetry-breaking in appropriately constructed Wilson-type networks predicts the surprising perceived images in the rivalry experiments. This is joint work with Casey Diekman and Yunjiao Wang.

Complex network structure frequently appear in biological systems such as gene regulatory networks, circadian rhythm models, signal transduction circuits, etc. As a mathematical formulation of such biological complex network systems, Fiedler, Mochizuki and their collaborators (JDDE 2013) recently defined a class of ODEs associated with a finite directed graph called a regulatory network, and proved that its dynamics on the global attractor can in principle be faithfully monitored by information from a (potentially much) fewer number of vertices of the graph called the feedback vertex set.

In this talk, I will use their theory to give a method for detecting a more detailed information on the dynamics of regulatory networks, namely the Morse decomposition of its global attractor. The main idea is to take time series data from the feedback vertex set of a regulatory network, and construct a combinatorial multi-valued map, to which we apply the so-called Conley-Morse Database method. As a test example, we study Mirsky’s mathematical model for mammalian circadian rhythm which can be represented as a regulatory network with 21 vertices. This is a joint work with B. Fielder, A. Mochizuki, G. Kurosawa, and H. Oka.

From habitat degradation and climate change to spatial spread of invasive species, dispersal plays a central role in determining how organisms cope with a changing environment. How should organisms disperse “optimally” in heterogeneous environments? I will discuss some recent development on the evolution of dispersal, focusing on finding evolutionarily stable strategies (ESS) for dispersal.

I will describe an approach to coding sequence (CDS) density estimation in genomic analysis introduced recently by myself and David Koslicki. Our approach is based on the topological pressure, which is a measure of ‘weighted information content’ adapted from ergodic theory. We use the topological pressure (with suitable training data) to give ab initio predictions of CDS density on the genomes of Mus Musculus, Rhesus Macaque and Drososphilia Melanogaster. While our method is not sufficiently precise to predict, for example, the exact locations of genes, we demonstrate that our method gives reasonable estimates for the ‘coarse scale’ problem of predicting CDS density. This is joint work with David Koslicki (Oregon State).