Workshop on data science and related mathematics in Wakkanai
- Dates:
- 2024 Aug 25th - 26th.
- Venue:
- Ikueikan University, Wakkanai, Hokkaido.
- 新館(Shinkan) 4F 1401.
Venue
Ikueikan University, Wakkanai, Hokkaido.
(育英館大学 (稚内)).
新館4階.
Schedule (Tentative)
2024 Aug 25th(Sun)
- 13:00--
-
Yasuaki HIRAOKA (Kyoto University)
-
Irreducible decomposition of a certain class of multi-parameter persistence modules
-
- 14:00--
-
Hiroyuki OCHIAI (Kyushu University)
-
Linear algebraic approach to commutative ladder of size 2 times 3.
-
Motivated by the examples presented in Hiraoka's talk, we will use an operation to construct an irreducible component from one or more irreducible components with smaller parameters, and we will provide an interpretation of Hiraoka's examples. The tool used is a base-field-free aspect of linear algebra.
- 15:00--
-
Patrice KOEHL (U.C. Davis)
-
A physicist's view on partial 3D shape comparison
-
Scientists have access to a wide range of digital sensors that allow them to report at multiple time and length scales on the subjects of their studies.
Finding efficient algorithms to describe and compare the shapes included in those reports has become a central problem in data science.
Those algorithms have gained from developments in computational geometry and in machine learning.
In this talk I will present another source of support to further improve those algorithms.
Using techniques from statistical physics, I show that we can define a possibly partial correspondence between 3D shapes,
with a cost associated with this correspondence that serves as a measure of the similarity of the shapes.
I will illustrate the effectiveness of this approach on synthetic data as well as on real anatomical data.
This is joint work with Dr Henri Orland, IPHT, CEA, Saclay, France.
- 16:00--
-
Herbert EDELSBRUNNER (Institute of Science and Technology Austria)
-
Merge Trees of Periodic Filtrations.
-
2024 Aug 26th (Mon)
- 10:00--
-
Naomichi NAKAJIMA (Shibaura Institute of Technology)
-
Dually flat geometry of plane curves and maximum likelihood estimation
-
The notion of a dually flat structure was introduced by Amari for studying statistical inference, informatics, machine learning and so on. Prior to Amari’s work, Efron gave pioneering insights into the extrinsic geometry of a one parameter curved exponential family in a two dimensional exponential family. In this talk, we study dually flat geometry of plane curves. In particular, new ingredients are the e/m-envelopes or the e/m-caustics, which arise when we replace the distance-squared function in Euclidean geometry with the Bregman divergence in dually flat geometry. Our approach also describes catastrophe phenomena in the root selection problem of maximum likelihood estimation.
- 11:00--
-
Kaito KAYO (Hokkaido Univ.)
-
Quasi-Codazzi structure and affine differential geometry
-
Nakajima-Ohmoto introduced the quasi-Hessian structure as the Hessian structure with degenerate metric.
In this study, we introduce the quasi-Codazzi structure which is a lager concept than the Hessian structure.
Moreover, we describe a relationship with the affin differential geometry.
-
Lunch
- 13:00--
-
Takahiro KAJISA (Hokkaido Univeristy)
-
Study on the hypersurfacial concentration phenomena of Gibbs samplers
-
In a high-dimensional probability space, we sometimes encounter phenomena that go against our intuition. One is the spherical concentration which states that the i.i.d standard gaussian samples become localized on the scaled sphere as the dimensions of the distributions increase. In this talk, I show a generalization of such a pathology; the data points sampled not independently, but identically from the Gibbs distribution concentrate around the energy hypersurface induced by a certain Hamiltonian. The concentration phenomenon is also known as ``the equivalence of ensembles'' in the context of statistical mechanics, and a key lemma is proven in my recent paper https://doi.org/10.1142/S0129055X24500211. This presentation is based on it and my successive works (to be published).
- 14:00--
-
Olympio HACQUARD (Kyoto University)
-
Topologically penalized regression for data on manifolds
-
We tackle a regression problem on a compact manifold \(M\). To take advantage of the underlying geometry and topology of the data, the regression task is performed on the basis of the first several eigenfunctions of the Laplace-Beltrami operator of the manifold, which are regularized with topological penalties. The proposed penalties are based on the topology of the sub-level sets of either the basis eigenfunctions or the estimated function. We will give a gentle introduction to all required notions in topology and statistics and no prior knowledge in these fields is required. The presentation will be based on the paper
https://arxiv.org/abs/2110.13749
and is a joint work with Krishnakumar Balasubramanian (UC Davis), Gilles Blanchard (Université Paris-Saclay), Clément Levrard (Université Rennes I) and Wolfgang Polonik (UC Davis)
- 15:00--
-
Yasuhide NUMATA (Hokkaido Univeristy)
-
On the annalysis of the image schema of the preposition "in".
-
It is said that
the image schema of the preposition "in" is something like a container.
It, however, seems that
there exisists difference between native speakers and non-native sperkers.
We discuss a way to analyze quantitatively.
This talk is based on a joint work with T. Fujiwara (Matsumoto Univ.).
-
Free discussion.
Announce
If you want to join to this workshop,
then please let orginizer know by
email
(nu at math.sci.hokudai.ac.jp).
In Wakkanai,
we have NO ATMs of banks
in convenience stores.
Since it is too difficult to get cash in Wakkanai,
the organizers strongly recommend to prepare cache before your flight.
(稚内のコンビニには`銀行'のATMはありません.
信金系統のATMはありますが, 銀行のキャッシュカードは使えません(でした. 少なくとも数年前には.)
銀行自体はまちなかにはあり, 銀行系のキャッシュカードはそこでは使えますが,
大学からは遠いですし, 土日はしまっていますので,
使えないと思ったほうが良いです.
出発前に現金を用意されることを強くおすすめします.)
Wakkanai is the nothernmost city in Japan and seaside.
So it will be very cold.
Please check
not only maximal temparature but also minimum temparature and strength of wind
by weather forecast e.g., jma.
A web site
recomends
to wear T-shirts in the daytime and a cardigan in the night.
On Sunday
We have a bus (route #5). which will arrive
at the bus stop, Daigaku Mae (Ikueikan Daigaku)/大学前［育英館大］,
around 12:48.
The bus will depart
at Teminal of Wakkanai Station 2 (駅前ターミナル2),
close to Wakkanai Station,
on 12:21.
The bus will depart
at Minami Eki Mae (南駅前), close to Wakkanai Minami Station,
on 12:29.
On Moday
We have a bus (route #5). which will arrive
at the bus stop, Daigaku Mae (Ikueikan Daigaku)/大学前［育英館大］,
around 9:39.
The bus will depart
at Teminal of Wakkanai Station 2 (駅前ターミナル2),
close to Wakkanai Station,
on 9:12.
The bus will depart
at Minami Eki Mae (南駅前), close to Wakkanai Minami Station,
on 9:20.
On Sunday evening, we will have a banquet.
If you are interested in it,
then please contact to the organizer by email (nu at maht.sci.hokudai.ac.jp)
There is no restaurant close to the university.
Moreover the cafeteria is basically closed due to summer vacation.
The organizer will provide some lunch on Monday.
Please contact the organizer if you need lunch on Monday.
On Sunday, basically, the buildings will be locked.
Please enter from "新館".
Kuriki's talk was canceled
Organizer(s)
Yasuhide NUMATA (Hokkaido University)/沼田泰英 (北海道大学).
Kohki MATSUZAKA (Ikueikan University)/松坂公暉 (育英館大学).