## 過去の記録

### 2016年01月27日(水)

#### 統計数学セミナー

13:00-14:10   数理科学研究科棟(駒場) 052号室
Ajay Jasra 氏 (National University of Singapore)
Multilevel SMC Samplers
[ 講演概要 ]

The approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs) is considered herein; this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a discretisation bias, with step-size level h_L. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multi-level Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretisation levels \infty>h_0>h_1\cdots>h_L. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence of probability distributions. A sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. It is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained in the SMC context. The approach is numerically illustrated on a Bayesian inverse problem. This is a joint work with Kody Law (ORNL), Yan Zhou (NUS), Raul Tempone (KAUST) and Alex Beskos (UCL).

#### 数理人口学・数理生物学セミナー

13:30-16:30   数理科学研究科棟(駒場) 128号室

HIV 感染リンパ器官ネットワークモデルの数理解析 (JAPANESE)
[ 講演概要 ]
バクテリアやウィルスからの感染を防御する働きを担う上で重要な T細胞は、通常リンパ節やリンパ器官に存在する。リンパ器官は免疫応答を活性化する場であると同時に、扁桃炎などウィルス感染の場になることもある。ヒト免疫不全ウィルス(HIV) は、T 細胞に感染するが、T 細胞が常駐するリンパ節に常駐している。リンパ節が HIV感染存続において重要であると示唆されているが、薬剤投与時でも HIV が消滅しない機構については、未だ明らかになっていない。

[ 講演概要 ]
We discuss the problem of approximating stability radius appearing
in the design procedure of finite-dimensional stabilizing controllers
for an infinite-dimensional dynamical system. The calculation of
stability radius needs the value of the H-infinity norm of a transfer
function whose realization is described by infinite-dimensional
operators in a Hilbert space. From the practical point of view, we
need to prepare a family of approximate finite-dimensional operators
and then to calculate the H-infinity norm of their transfer functions.
However, it is not assured that they converge to the value of the
H-infinity norm of the original transfer function. The purpose of
this study is to justify the convergence. In a numerical example,
we treat parabolic distributed parameter systems with distributed
control and distributed/boundary observation.

バックステッピング法に基づく感染人口の増減予測 (JAPANESE)
[ 講演概要 ]

Kermack and McKendrick (1927) から現在に至るまで長く研究されている。その
モデルは数学的には1階偏微分方程式の境界値問題と見なすことができ、その境

の境界値問題に対し、自明平衡解の安定化のための境界フィードバック制御を導

ルエンザの報告データに対してこの予測法を適用すると、その精度は8割を超え
ることが確認された。本研究は佐野英樹教授（神戸大学大学院システム情報学研

[ 講演概要 ]
マラリアは蚊によって媒介される感染症であるため、その流行を考察するにあたってヒトと蚊と両方の動態を考えることが必要である。主な流行地域の一つである南アフリカでは一つ一つの村(人口密集地)間の間隔が広く、村から村へとマラリアの感染を伝播させているのは主に車などの移動手段によるヒトの移動・交流であると考えられる。本研究では村間のヒトの往来に焦点を当て、マラリア流行の古典的なモデルであるRossモデルを下敷きとした数理モデルを構築した。また実際の村間のネットワーク構造を用いて南アフリカにおける感染報告データと比較しながら、何がマラリア感染の伝播のリスク要因となっているのかを解析してゆくために、今回は基本的なモデル解析を行った結果を報告する。

### 2016年01月26日(火)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Salomé Oudet 氏 (University of Tokyo)
Hamilton-Jacobi equations for optimal control on 2-dimensional junction (English)
[ 講演概要 ]
We are interested in infinite horizon optimal control problems on 2-dimensional junctions (namely a union of half-planes sharing a common straight line) where different dynamics and different running costs are allowed in each half-plane. As for more classical optimal control problems, ones wishes to determine the Hamilton-Jacobi equation which characterizes the value function. However, the geometric singularities of the 2-dimensional junction and discontinuities of data do not allow us to apply the classical results of the theory of the viscosity solutions.
We will explain how to skirt these difficulties using arguments coming both from the viscosity theory and from optimal control theory. By this way we prove that the expected equation to characterize the value function is well posed. In particular we prove a comparison principle for this equation.

### 2016年01月25日(月)

#### 東京確率論セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室

Hamilton-Jacobi equations in metric spaces
[ 講演概要 ]
ハミルトン・ヤコビ方程式は解析力学の基礎的な方程式の一つであると同時に前

コビ方程式の研究を進めてきた。そこで本講演ではまずハミルトン・ヤコビ方程

して、一般の完備測地的距離空間上のハミルトン・ヤコビ方程式を導入し、最近
の研究成果である粘性解の時間漸近挙動を紹介する。なお、本講演の内容の一部
は東京大学の難波時永氏との共同研究に基づく。

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
このセミナーは悪天候の影響によりキャンセルになりました。

[ 講演概要 ]

### 2016年01月22日(金)

#### FMSPレクチャーズ

15:00 -16:00   数理科学研究科棟(駒場) 056号室

Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏 (ENGLISH)
Functor categories and stable homology of groups (8) (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### FMSPレクチャーズ

16:30-17:30   数理科学研究科棟(駒場) 056号室

Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (9) (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### 作用素環セミナー

15:00-17:00   数理科学研究科棟(駒場) 118号室

$C^*$テンソル圏入門

### 2016年01月21日(木)

#### FMSPレクチャーズ

15:00-16:00   数理科学研究科棟(駒場) 056号室

Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (6) (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### FMSPレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 056号室

Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (7) (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### 作用素環セミナー

15:00-17:00   数理科学研究科棟(駒場) 118号室

$C^*$テンソル圏入門

### 2016年01月20日(水)

#### FMSPレクチャーズ

16:00-18:00   数理科学研究科棟(駒場) 056号室

Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (5) (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### 作用素環セミナー

15:00-17:00   数理科学研究科棟(駒場) 118号室

$C^*$テンソル圏入門

#### 統計数学セミナー

13:00-17:00   数理科学研究科棟(駒場) 123号室
Enzo Orsingher 氏 (Sapienza University of Rome)
Fractional calculus and some applications to stochastic processes
[ 講演概要 ]
1) Riemann-Liouville fractional integrals and derivatives
2) integrals of derivatives and derivatives of integrals
3) Dzerbayshan-Caputo fractional derivatives
4) Marchaud derivative
5) Riesz potential and fractional derivatives
6) Hadamard derivatives and also Erdelyi-Kober derivatives
7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives
8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)
9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)
10) Time-fractional telegraph Poisson process
11) Space fractional Poisson process
13) Other fractional point processes (birth and death processes)
14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.

In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.

### 2016年01月19日(火)

#### FMSPレクチャーズ

13:30 -14:30   数理科学研究科棟(駒場) 056号室

Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (3) (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### FMSPレクチャーズ

16:30 -18:00   数理科学研究科棟(駒場) 056号室

Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (4) (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### 作用素環セミナー

15:00-17:00   数理科学研究科棟(駒場) 118号室

$C^*$テンソル圏入門

#### トポロジー火曜セミナー

15:00-16:00   数理科学研究科棟(駒場) 056号室

Ricci-mean curvature flows in gradient shrinking Ricci solitons (JAPANESE)
[ 講演概要 ]
A Ricci-mean curvature flow is a coupled parabolic PDE system of a mean
curvature flow and a Ricci flow.
In this talk, we consider a Ricci-mean curvature flow in a gradient
shrinking Ricci soliton, and give a generalization of a well-known result
of Huisken which states that if a mean curvature flow in a Euclidean space
develops a singularity of type I, then its parabolic rescaling near the singular
point converges to a self-shrinker.

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Hao Wu 氏 (Fudan University)
Well-posedness and stability of the full Ericksen-Leslie system for incompressible nematic liquid crystal flows
[ 講演概要 ]
In this talk, the general Ericksen-Leslie (E-L) system modelling the incompressible nematic liquid crystal flow will be discussed.
We shall prove the well-posedness and long-time behavior of the E-L system under proper assumptions on the viscous Leslie coefficients.
In particular, we shall discuss the connection between Parodi's relation and stability of the E-L system.

### 2016年01月18日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Holomorphic motions and the monodromy (Japanese)
[ 講演概要 ]
Holomorphic motions, which was introduced by Mane, Sad and Sullivan, is a useful tool for Teichmuller theory as well as for complex dynamics. In particular, Slodkowski’s theorem makes a significant contribution to them. The theorem says that every holomorphic motion of a closed set on the Riemann sphere parametrized by the unit disk is extended to a holomorphic motion of the whole Riemann sphere parametrized by the unit disk. In this talk, we consider a generalization of the theorem. If time permits, we will discuss applications of our results.

#### FMSPレクチャーズ

15:00-16:00   数理科学研究科棟(駒場) 056号室

Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (1) (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### FMSPレクチャーズ

16:30-17:30   数理科学研究科棟(駒場) 056号室

Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (2) (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### 作用素環セミナー

15:00-17:00   数理科学研究科棟(駒場) 118号室

$C^*$テンソル圏入門 (日本語)

#### 統計数学セミナー

13:00-17:00   数理科学研究科棟(駒場) 123号室
Enzo Orsingher 氏 (Sapienza University of Rome)
Fractional calculus and some applications to stochastic processes
[ 講演概要 ]
1) Riemann-Liouville fractional integrals and derivatives
2) integrals of derivatives and derivatives of integrals
3) Dzerbayshan-Caputo fractional derivatives
4) Marchaud derivative
5) Riesz potential and fractional derivatives
6) Hadamard derivatives and also Erdelyi-Kober derivatives
7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives
8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)
9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)
10) Time-fractional telegraph Poisson process
11) Space fractional Poisson process
13) Other fractional point processes (birth and death processes)
14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.

In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.

#### FMSPレクチャーズ

14:00-15:00   数理科学研究科棟(駒場) 126号室
Samuli Siltanen 氏 (University of Helsinki)
Blind deconvolution for human speech signals (ENGLISH)
[ 講演概要 ]
The structure of vowel sounds in human speech can be divided into two independent components. One of them is the “excitation signal,” which is a kind of buzzing sound created by the vocal folds flapping against each other. The other is the “filtering effect” caused by resonances in the vocal tract, or the confined space formed by the mouth and throat. The Glottal Inverse Filtering (GIF) problem is to (algorithmically) divide a microphone recording of a vowel sound into its two components. This “blind deconvolution” type task is an ill-posed inverse problem. Good-quality GIF filtering is essential for computer-generated speech needed for example by disabled people (think Stephen Hawking). Also, GIF affects the quality of synthetic speech in automatic information announcements and car navigation systems. Accurate estimation of the voice source from recorded speech is known to be difficult with current glottal inverse filtering (GIF) techniques, especially in the case of high-pitch speech of female or child subjects. In order to tackle this problem, the present study uses two different solution methods for GIF: Bayesian inversion and alternating minimization. The first method takes advantage of the Markov chain Monte Carlo (MCMC) modeling in defining the parameters of the vocal tract inverse filter. The filtering results are found to be superior to those achieved by the standard iterative adaptive inverse filtering (IAIF), but the computation is much slower than IAIF. Alternating minimization cuts down the computation time while retaining most of the quality improvement.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Siltanen.pdf