Mathematical Seminar

1.(13:30-15:30)
Speaker: Kazuyoshi Yata
(Institute of Mathematics, University of Tsukuba)

Title:
Statistical theories and methodologies for high-dimensional data

Abstract:
In this talk, we consider statistical theories and methodologies for
high-dimensional data. We first clarify the limit of the conventional
principal component analysis (PCA) for high-dimensional data. In order
to overcome the curse of dimensionality, we introduce two effective PCAs
called the noise-reduction methodology and the cross-data-matrix
methodology. We show that the new PCAs hold consistency properties even
in high-dimension, low-sample-size settings. Based on the new PCAs, we
provide high-dimensional statistical methodologies: a two-sample test
and a discriminant procedures.
Finally, we demonstrate the new procedures by using genetic data sets.
[The talk is based on joint work with Prof. Makoto Aoshima (University of Tsukuba)]

2.(15:30-17:30)
Speaker:
Takenobu Nakamura
(National Institute of Advanced Industrial Science and Technology)

Title:
The Unique and Physical Definition of the Free-Energy Landscape

Abstract :
It is well-known that the conventionally defined free-energy landscape
(FEL) in a small system exhibits unphysical dependence on the choice of
reaction coordinates. We  propose a new definition of FEL that is
invariant under any smooth one-to-one transformation (diffeomorphism) of
reaction coordinates. Our definition can be used to  unambiguously
extract physical properties such as the energy barrier or the transition
state. A practical procedure for determining the FEL from time-series
data will be discussed.