Abstracts
Title: Morse functions, fold maps, and geometric and constructive studies ofhigher dimensional closed differentiable manifolds
Speaker : Naoki Kitazawa (Institute of Mathematics for Industry, KyushuUniversity)
Abstract : This talk introduces essential mathematical theory in this project. We
introduce Morse functions and fold maps, higher dimensional variants ofMorse functions. About applications of these tools to geometry of manifolds,
we introduce backgrounds, history, and studies of the speaker, mainly,
construction of explicit fold maps and various information of higherdimensional manifolds admitting these maps. We will also present dreams
for applications to higher dimensional data analysis, visualizations etc..
Title: Quick Survey of Reeb Spaces in Topology and Visualization
Speaker : Osamu Saeki (Institute of Mathematics for Industry, Kyushu University)
Abstract : Given a map between topological spaces, we have the associated
Reeb space, which is the space of all the connected components of thefibers. In this talk, the speaker will survey the studies of Reeb spaces
themselves together with those researches which use Reeb spaces asimportant tools, both in topology and in visualization, as far as thespeaker knows.
Title
Speaker: Applying Reeb Graphs and Reeb Spaces: Daisuke Sakurai(Research Institute for Information Technology,KyushuUniversity)
Abstract : The Reeb graph of a function represents the connectivity of the inverse
images.
The computational geometry community generalized this to the Reeb spaceof a mapping.
This talk gives a concise review around the speaker, who studies visual
data analysis, on how they can be used for understanding data.
In fact, the Reeb graph and Reeb space play a role in visual data analysis
in the researchers' pursuit for efficiently exploring features in dataof interest.
The study of adapting these concepts partly emerged in the context ofunderstanding contours in volumetric data such as computational
tomography where the Reeb graph and space give an overview of objects inthe volume.
The speaker discusses a few examplary applications and how mathematics
on homology may be adapted for data analysis.

Title: Visual analysis of geospatial multivariate data for investigating
radioactive deposition processes
Speaker : Shigeo Takahashi (University of Aizu)
Abstract : This talk presents our application study for investigating radioactive
deposition processes through visual analysis of geospatial multivariate
data. The Fukushima Daiichi Nuclear Power Plant (FDNPP) accident in 2011
raised awareness of the importance of radioactive deposition processes,
especially for proposing aerosol measures against possible air pollution.
However, identifying the types of deposition processes often results indifficult tasks due to complicated terrains around the FDNPP. Therefore,
we developed an approach for interactively investigating thecorrespondence of the geospatial positions to the air dose rate along with
relevant attributes. Our idea is to compose a set of scatterplots forpairwise attributes, onto which we project terrain surfaces to findspecific patterns of such ttributes. We applied our approach to the visual
analysis of air dose distribution data around FDNPP after the accident andclearly distinguished contamination areas derived from different
deposition processes. This is joint work with Japan Atomic Energy Agency
and Kyushu University.
TitleSpeaker: Modeling Pareto sets of multiobjective optimization problems: Naoki Hamada (K Lab Inc.）

Abstract : In industry, multi-objective optimization is often used to simultaneously
optimize multiple conflicting objective functions, such as performance andcost. The solution set that achieves the optimal trade-off between objectivefunctions is called the Pareto set, and finding it leads to the developmentof new products. The Pareto set is known to generically be a stratified setof dimension m-1, where m is the number of objective functions. In practicalproblems, the number of variables to be optimized ranges from tens tohundreds, and the number of objectives is 2 to 7, so the Pareto set is a
stratified set of dimension 1 to 6, embedded in a Euclidean space ofdimension tens to hundreds. If the intrinsic dimension is less than 4, thensome dimensionality reduction method can be used to model the Pareto set

without losing the essential features of the data. However, when theintrinsic dimension is 4 or more, there is no established method to model
the Pareto set without losing the intrinsic features. This talk will
introduce a modeling method using the Bézier simplex, which was recently
developed by the speakers, and describe the challenges of modeling solution
sets for multi-objective optimization.

Title
Speaker: An Efficient Triangulation for Extruded Spatiotemporal Prism Meshes: Akito Fujii （ Graduate School and Faculty of Information Science andElectrical Engineering, Kyushu University）

Abstract : It is common to run simulations on a spatial mesh with an associated(spatial) triangulation. We consider the problem of re-triangulating
space-time mesh that conforms to the pre-defined spatial triangulation.
Today the general dimensionality, and especially 4D, has become relevantfor online (aka in-situ) analysis. As the analysis is especially importantfor visualizing big data from scientific computation, providing aspatiotemporal triangulation equipped with the very fine temporal
resolution thanks to in-situ opens the door to a reconsideration of
spatiotemporal analysis and computational geometry algorithms. This
presentation introduces a fast and easy combinatorial triangulation for
an arbitrary sub-complex of the space-time. We assume a static spatialtriangulation, which is still common in today's simulations, including
atmospheric simulations. We extrude the spatiotemporal triangulation
along the time axis, which gives us a prism mesh, and apply re-triangulation
to get the spatiotemporal triangulation. The algorithm is memory efficient,works for arbitrary dimension, is parameter free, inserts no additionalvertex and is easy to parallelize even for distributed memory machines.