Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half.

Abstract: This is an introduction to multiple zeta values (MZVs). Although the study of MZVs is related to various areas of mathematics, we will concentrate on the algebraic structures of MZVs themselves. The key point is that MZVs have two kinds of representations: nested series and iterated integrals. We present how these two representations yield rich algebraic relations among MZVs.

The iron-based superconductor FeTexSe1−x is one of the material candidates hosting Majorana vortex modes residing in the vortex cores. It has been observed by recent scanning tunneling spectroscopy measurement that the fraction of vortex cores possessing zero-bias peaks decreases with increasing magnetic field on the surface of FeTexSe1−x. The hybridization of two Majorana vortex modes cannot simply explain this phenomenon. We construct a three-dimensional tight-binding model simulating the physics of over a hundred Majorana vortex modes in FeTexSe1−x. Our simulation shows that the Majorana hybridization and disordered vortex distribution can explain the decreasing fraction of the zero-bias peaks observed in the experiment; the statistics of the energy peaks off zero energy in our Majorana simulation are in agreement with the experiment.

This workshop is supported by RIKEN iTHEMS (RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program).

Organizers
Emiko Hiyama (Kyushu U./RIKEN)
Hiroshi Suzuki (Kyushu U.)
Tetsuo Hatsuda (RIKEN)

He will talk about theoretical study on complex network data, including clinical data.

His talk consists of two parts:
14:00-15:00: Detecting the tipping points of dynamic processes by dynamic network biomarkers
15:00-15:30: Coffee break
15:30-16:30: Predicting future dynamics of short-term time-series data by randomly distributed embedding

First part of his talk is for general audience.
In second part of his talk, he will explain mathematical basis of his study in detail.

Animals adapt to the environment for survival. Synaptic plasticity is considered a major mechanism underlying this process. However, the best-known form of synaptic plasticity, i.e., Hebbian plasticity that depends on pre- and post-synaptic activity, can surge coincident activity in model neurons beyond a physiological range. Our lab has explored how neural circuits learn about the environment by synaptic plasticity. The instability of Hebbian plasticity could be mitigated by a global factor that modulates its outcome. For example, TNF-alpha that mediates homeostatic synaptic scaling is released by glia, reflecting the activity level of surrounding neurons. I show that a specific interaction of Hebbian plasticity with this global factor accounts for the time course of adaptation to the altered environment (Toyoizumi et al. 2015). At a more theoretical level, I ask what is the optimal synaptic plasticity rule for achieving an efficient representation of the environment. A solution is the error-gated Hebbian rule, whose update is proportional to the product of Hebbian change and a specific global factor. I show that this rule, suitable also in neuromorphic devices, robustly extracts hidden independent sources in the environment (Isomura and Toyoizumi 2016, 2018, 2019). Finally, I introduce that synapses change by intrinsic spine dynamics, even in the absence of synaptic plasticity. I show that physiological spine-volume distribution and stable cell assemblies are both achieved when intrinsic spine dynamics are augmented in a model (Humble et al.2019).