Text only print
Full screen print
Seminar information archive
Seminar information archive ～02/06｜Today's seminar 02/07 | Future seminars 02/08～
2008/08/25
Lectures
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Ronald C. King (Emeritus Professor, University of Southampton)
Affine Weyl groups, grids, coloured tableaux and characters of affine algebras
Ronald C. King (Emeritus Professor, University of Southampton)
Affine Weyl groups, grids, coloured tableaux and characters of affine algebras
[ Abstract ]
It is shown that certain coloured Young diagrams serve to specify not
only all the elements of the affine Weyl groups of the classical
affine Lie algebras but also their action on an arbitrary weight
vector. Through a judicious choice of coset representatives with
respect to the finite Weyl groups of the corresponding maximal rank
simple Lie algebras, both denominator and numerator formulae are
derived and exemplified, along with the explicit calculation of
characters of irreducible representations of the affine Lie algebras.
It is shown that certain coloured Young diagrams serve to specify not
only all the elements of the affine Weyl groups of the classical
affine Lie algebras but also their action on an arbitrary weight
vector. Through a judicious choice of coset representatives with
respect to the finite Weyl groups of the corresponding maximal rank
simple Lie algebras, both denominator and numerator formulae are
derived and exemplified, along with the explicit calculation of
characters of irreducible representations of the affine Lie algebras.
2008/08/21
thesis presentations
15:00-15:40 Room #126 (Graduate School of Math. Sci. Bldg.)
鎌谷研吾 (東京大学大学院数理科学研究科)
On some asymptotic properties of the Expectation-Maximization Algorithm and the Metropolis-Hastings Algorithm (EMアルゴリズムとメトロポリス-ヘイスティングスアルゴリズムの漸近的性質)
鎌谷研吾 (東京大学大学院数理科学研究科)
On some asymptotic properties of the Expectation-Maximization Algorithm and the Metropolis-Hastings Algorithm (EMアルゴリズムとメトロポリス-ヘイスティングスアルゴリズムの漸近的性質)
2008/08/06
Seminar on Mathematics for various disciplines
10:30-14:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Kazufumi Ito (North Carolina State University) 10:30-11:30
Adaptive Tikhonov Regularization for Inverse Problems
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
Kazufumi Ito (North Carolina State University) 10:30-11:30
Adaptive Tikhonov Regularization for Inverse Problems
[ Abstract ]
Tikhonov regularization method plays a critical role in ill-posed inverse problems, arising in applications including computerized tomography, inverse scattering and image processing. The goodness of the inverse solution heavily depends on selection of the regularization parameter. Commonly used methods rely on a priori knowledge of the noise level. A method that automatically estimates the noise level and selects the regularization parameter automatically is presented.
Yimin Wei (Fudan University) 13:00-14:00Tikhonov regularization method plays a critical role in ill-posed inverse problems, arising in applications including computerized tomography, inverse scattering and image processing. The goodness of the inverse solution heavily depends on selection of the regularization parameter. Commonly used methods rely on a priori knowledge of the noise level. A method that automatically estimates the noise level and selects the regularization parameter automatically is presented.
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
[ Abstract ]
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this talk, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this talk, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.
Mathematical Finance
17:30-19:00 Room #122 (Graduate School of Math. Sci. Bldg.)
楠岡 成雄 (東京大)
オペレーショナルリスクと fat tail を持つ iid 確率変数の和に対する極限定理
楠岡 成雄 (東京大)
オペレーショナルリスクと fat tail を持つ iid 確率変数の和に対する極限定理
2008/08/01
Number Theory Seminar
13:00-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Olivier Brinon (Paris北大学) 13:00-14:00
B_dR-representations and Higgs bundles
Henrik Russell (Duisburg-Essen大学) 14:15-15:15
Generalized Albanese and duality
Thomas Geisser (南California大学) 15:45-16:45
Negative K-theory, homotopy invariance and regularity
On Iwasawa theory for abelian varieties over function fields of positive characteristic
Olivier Brinon (Paris北大学) 13:00-14:00
B_dR-representations and Higgs bundles
Henrik Russell (Duisburg-Essen大学) 14:15-15:15
Generalized Albanese and duality
Thomas Geisser (南California大学) 15:45-16:45
Negative K-theory, homotopy invariance and regularity
[ Abstract ]
The topic of my talk are two classical conjectures in K-theory:
Weibel's conjecture states that a scheme of dimension d
has no K-groups below degree -d, and Vorst's conjecture
states that homotopy invariance of the K-theory of rings
implies that the ring must be regular.
I will give an easy introduction to the conjectures, and discuss
recent progress.
Fabien Trihan (Nottingham大学) 17:00-18:00The topic of my talk are two classical conjectures in K-theory:
Weibel's conjecture states that a scheme of dimension d
has no K-groups below degree -d, and Vorst's conjecture
states that homotopy invariance of the K-theory of rings
implies that the ring must be regular.
I will give an easy introduction to the conjectures, and discuss
recent progress.
On Iwasawa theory for abelian varieties over function fields of positive characteristic
2008/07/29
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
小木曽 岳義 (城西大学)
Clifford代数の表現から作られる局所関数等式を満たす多項式とそれに付随する空間について(佐藤文広氏との共同研究)
小木曽 岳義 (城西大学)
Clifford代数の表現から作られる局所関数等式を満たす多項式とそれに付随する空間について(佐藤文広氏との共同研究)
[ Abstract ]
概均質ベクトル空間の理論の基本定理(局所関数等式)は、大雑把に言うと、正則概均質ベクトル空間の相対不変式の複素ベキのFourier変換が双対概均質ベクトル空間の相対不変式の複素ベキにガンマ因子をかけたものと一致することを主張している。
この講演では、概均質ベクトル空間の相対不変式ではないにもかかわらず、その複素ベキが同種の局所関数等式を満たすような多項式が、Clifford代数の表現より構成できることを報告する。
概均質ベクトル空間の理論の基本定理(局所関数等式)は、大雑把に言うと、正則概均質ベクトル空間の相対不変式の複素ベキのFourier変換が双対概均質ベクトル空間の相対不変式の複素ベキにガンマ因子をかけたものと一致することを主張している。
この講演では、概均質ベクトル空間の相対不変式ではないにもかかわらず、その複素ベキが同種の局所関数等式を満たすような多項式が、Clifford代数の表現より構成できることを報告する。
2008/07/28
Kavli IPMU Komaba Seminar
17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Lin Weng (Kyushu University)
Symmetries and the Riemann Hypothesis
http://xxx.lanl.gov/abs/0803.1269
Lin Weng (Kyushu University)
Symmetries and the Riemann Hypothesis
[ Abstract ]
Associated to each pair of a reductive group
and its maximal parabolic, we will introduce an abelian zeta function.
This zeta, defined using Weyl symmetries, is expected
to satisfy a standard functional equation and the Riemann Hypothesis.
Its relation with the so-called high rank zeta,
a very different but closely related non-abelian zeta,
defined using stable lattices and a new geo-arithmetical cohomology,
will be explained.
Examples for $SL, SO, Sp$ and $G_2$ and confirmations of
(Lagarias and) Masatoshi Suzuki on the RH for zetas
associated to rank 1 and 2 groups will be presented
as well.
[ Reference URL ]Associated to each pair of a reductive group
and its maximal parabolic, we will introduce an abelian zeta function.
This zeta, defined using Weyl symmetries, is expected
to satisfy a standard functional equation and the Riemann Hypothesis.
Its relation with the so-called high rank zeta,
a very different but closely related non-abelian zeta,
defined using stable lattices and a new geo-arithmetical cohomology,
will be explained.
Examples for $SL, SO, Sp$ and $G_2$ and confirmations of
(Lagarias and) Masatoshi Suzuki on the RH for zetas
associated to rank 1 and 2 groups will be presented
as well.
http://xxx.lanl.gov/abs/0803.1269
2008/07/26
Infinite Analysis Seminar Tokyo
13:30-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)
星野歩 (上智大理) 13:30-14:30
変形W代数とMacdomald多項式のtableau表示
Entanglement Entropy in Conventional and Topological Orders
星野歩 (上智大理) 13:30-14:30
変形W代数とMacdomald多項式のtableau表示
[ Abstract ]
A型変形W代数の自由場表示を用いてA型Macdomald多項式のtableau表示を構成する。さらにD型変形W代数の自由場表示を用いて、第一基本ウェイトの正数倍のウェイトを持つD型Macdomald多項式のtableau表示を構成する。尚、本研究は白石潤一氏(東京大学)との共同研究である。
古川俊輔 (理化学研究所) 15:00-16:00A型変形W代数の自由場表示を用いてA型Macdomald多項式のtableau表示を構成する。さらにD型変形W代数の自由場表示を用いて、第一基本ウェイトの正数倍のウェイトを持つD型Macdomald多項式のtableau表示を構成する。尚、本研究は白石潤一氏(東京大学)との共同研究である。
Entanglement Entropy in Conventional and Topological Orders
[ Abstract ]
量子多体系の基底状態には、しばしば、個々の粒子の状態の直積では表せない構造、すなわち、エンタングルメントが現れる。これを、エンタングルメント・エントロピーという指標を用いて測ることにより、系のユニヴァーサリティを特徴づける重要な情報が得られることが近年、明らかにされてきた。セミナーでは、エンタングルメントについての基礎的な知識から始め、私が取り組んできた(いる)、次の二つのテーマについてご紹介したい。
(1)量子ダイマー模型におけるトポロジカル・エントロピー
トポロジカル秩序を持つ系においては、エンタングルメント・エントロピーに、背景のゲージ理論を特徴づける、負の定数項が含まれることが、Kitaevらによって予想された。我々は、Z2トポロジカル秩序を示すと考えられる量子ダイマー模型において、予想の数値的検証を行い、予想が精度よく成り立つことを示した。
Ref. S. Furukawa & G. Misguich, Phys. Rev. B 75, 214407 (2007).
(2)自発的対称性の破れとマクロスコピック・エンタングルメント
自発的対称性の破れを示す系においては、有限系の基底状態に、秩序を持った状態のマクロな重ね合わせ構造が見られる。この構造がエンタングルメント・エントロピーにも反映され、基底状態縮退度の情報を含む、正の定数項が現れることを示した。
量子多体系の基底状態には、しばしば、個々の粒子の状態の直積では表せない構造、すなわち、エンタングルメントが現れる。これを、エンタングルメント・エントロピーという指標を用いて測ることにより、系のユニヴァーサリティを特徴づける重要な情報が得られることが近年、明らかにされてきた。セミナーでは、エンタングルメントについての基礎的な知識から始め、私が取り組んできた(いる)、次の二つのテーマについてご紹介したい。
(1)量子ダイマー模型におけるトポロジカル・エントロピー
トポロジカル秩序を持つ系においては、エンタングルメント・エントロピーに、背景のゲージ理論を特徴づける、負の定数項が含まれることが、Kitaevらによって予想された。我々は、Z2トポロジカル秩序を示すと考えられる量子ダイマー模型において、予想の数値的検証を行い、予想が精度よく成り立つことを示した。
Ref. S. Furukawa & G. Misguich, Phys. Rev. B 75, 214407 (2007).
(2)自発的対称性の破れとマクロスコピック・エンタングルメント
自発的対称性の破れを示す系においては、有限系の基底状態に、秩序を持った状態のマクロな重ね合わせ構造が見られる。この構造がエンタングルメント・エントロピーにも反映され、基底状態縮退度の情報を含む、正の定数項が現れることを示した。
2008/07/24
Lectures
16:00-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Noriko Yui (Queen's University)
On the modularity of Calabi-Yau varieties over $\\mathbf{Q}$
Noriko Yui (Queen's University)
On the modularity of Calabi-Yau varieties over $\\mathbf{Q}$
2008/07/23
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Andrei Constantinescu (Ecole Polytechnique)
Identification of residual stresses: problem settings and results.
Andrei Constantinescu (Ecole Polytechnique)
Identification of residual stresses: problem settings and results.
[ Abstract ]
Identification of residual stresses is an important task in many engineering fields such as fatigue or fracture mechanics, where their presence can significantly increase or decrease the apparent strength of mechanical components.
The present talk will try to make a review of existing problem settings identification results.
More precisely we shall:
1. discuss the linearization procedure strain and materials behaviour in finite elasticity around a stressed state in order to define in a mathematical precise way the problem settings for the identification of residual stresses.
2. present a series of measurement techniques currently used in industry and research for the measurement of residual stresses like the X-ray technique and strain measurements.
3. present existing results in the identification of residual stresses for the different
Identification of residual stresses is an important task in many engineering fields such as fatigue or fracture mechanics, where their presence can significantly increase or decrease the apparent strength of mechanical components.
The present talk will try to make a review of existing problem settings identification results.
More precisely we shall:
1. discuss the linearization procedure strain and materials behaviour in finite elasticity around a stressed state in order to define in a mathematical precise way the problem settings for the identification of residual stresses.
2. present a series of measurement techniques currently used in industry and research for the measurement of residual stresses like the X-ray technique and strain measurements.
3. present existing results in the identification of residual stresses for the different
Seminar on Mathematics for various disciplines
10:30-14:00 Room #056 (Graduate School of Math. Sci. Bldg.)
伊東一文 (North Carolina State University) 10:30-11:30
Adaptive Tikhonov Regularization for Inverse Problems
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
伊東一文 (North Carolina State University) 10:30-11:30
Adaptive Tikhonov Regularization for Inverse Problems
[ Abstract ]
Tikhonov regularization method plays a critical role in ill-posed inverse problems, arising in applications including computerized tomography, inverse scattering and image processing. The goodness of the inverse solution heavily depends on selection of the regularization parameter. Commonly used methods rely on a priori knowledge of the noise level. A method that automatically estimates the noise level and selects the regularization parameter automatically is presented.
Yimin Wei (Fudan University) 13:00-14:00Tikhonov regularization method plays a critical role in ill-posed inverse problems, arising in applications including computerized tomography, inverse scattering and image processing. The goodness of the inverse solution heavily depends on selection of the regularization parameter. Commonly used methods rely on a priori knowledge of the noise level. A method that automatically estimates the noise level and selects the regularization parameter automatically is presented.
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
[ Abstract ]
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this talk, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this talk, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.
2008/07/17
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
George Elliott (Univ. Toronto)
A canonical AF-algebra construction for rank two subgroups of R
(A new description of the Pimsner-Voiculescu embedding)
George Elliott (Univ. Toronto)
A canonical AF-algebra construction for rank two subgroups of R
(A new description of the Pimsner-Voiculescu embedding)
2008/07/16
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Valentina Di Proietto (Padova大学)
On p-adic differential equation on semi-stable varieties
Valentina Di Proietto (Padova大学)
On p-adic differential equation on semi-stable varieties
2008/07/15
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
松田 浩 (広島大学大学院理学研究科)
One-step Markov Theorem on exchange classes
松田 浩 (広島大学大学院理学研究科)
One-step Markov Theorem on exchange classes
[ Abstract ]
The main theorem in this talk claims the following.
``Let L_A and L_B denote a closed a-braid and a closed b-braid,
respectively, that represent one link type.
After at most (a^2 b^2)/4 exchange moves on L_A,
we can 'see' the pair of closed braids."
In this talk, we explain the main theorem in details, and
we present some applications.
In particular, we propose a strategy to construct an algorithm
that determines whether two links are ambient isotopic.
The main theorem in this talk claims the following.
``Let L_A and L_B denote a closed a-braid and a closed b-braid,
respectively, that represent one link type.
After at most (a^2 b^2)/4 exchange moves on L_A,
we can 'see' the pair of closed braids."
In this talk, we explain the main theorem in details, and
we present some applications.
In particular, we propose a strategy to construct an algorithm
that determines whether two links are ambient isotopic.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
廣惠 一希 (東大数理)
GL(4,R)の退化主系列表現の一般Whittaker関数
http://akagi.ms.u-tokyo.ac.jp/seminar.html
廣惠 一希 (東大数理)
GL(4,R)の退化主系列表現の一般Whittaker関数
[ Abstract ]
$GL(n,R)$の退化球主系列表現の一般Whittaker模型の空間は,対称空間$GL(n,R)/O(n)$上の$C^\\infty$級関数の中で,ある微分作用素達のkernelとして特徴付けられる.この微分作用素達は,大島利雄氏による退化主系列表現に対するPoisson変換の像の特徴付けに用いられたものであり,その明示的な表示が氏によって得られている.また,こうしたkernel定理は山下博氏のユニタリ最低ウエイト加群の一般Whittaker模型に対する定理の類似にあたる.こういった背景の下,$GL(4,R)$の退化主系列表現に対し、いくつかの具体例を考えたい.そこでは一般Whittaker模型は一変数変形Bessel関数、Hornの二変数合流型超幾何関数によって実現される.
[ Reference URL ]$GL(n,R)$の退化球主系列表現の一般Whittaker模型の空間は,対称空間$GL(n,R)/O(n)$上の$C^\\infty$級関数の中で,ある微分作用素達のkernelとして特徴付けられる.この微分作用素達は,大島利雄氏による退化主系列表現に対するPoisson変換の像の特徴付けに用いられたものであり,その明示的な表示が氏によって得られている.また,こうしたkernel定理は山下博氏のユニタリ最低ウエイト加群の一般Whittaker模型に対する定理の類似にあたる.こういった背景の下,$GL(4,R)$の退化主系列表現に対し、いくつかの具体例を考えたい.そこでは一般Whittaker模型は一変数変形Bessel関数、Hornの二変数合流型超幾何関数によって実現される.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2008/07/12
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
刈山和俊 (尾道大学経済情報学部
) 13:30-14:30
On certain types and the Hecke algebras for unramified p-adic unitary groups
鍛治匠一 (東京大学数理科学研究科) 15:00-16:00
The $(\\mathfrak{g},K)$-module structures of the principal series resentations for $SL(4,R)$
刈山和俊 (尾道大学経済情報学部
) 13:30-14:30
On certain types and the Hecke algebras for unramified p-adic unitary groups
鍛治匠一 (東京大学数理科学研究科) 15:00-16:00
The $(\\mathfrak{g},K)$-module structures of the principal series resentations for $SL(4,R)$
[ Abstract ]
$SL(4,R)$ の主系列表現 $H$ の $(\\mathfrak{g},K)$-module としての構造を
明示的に与えることを目標とする。
具体的には、まず $H$ の基底として $K$-module の weight vector になっているものを取り、その基底が $\\mathfrak{g}$ の作用でどのように移るかを記述する。
$SL(4,R)$ の主系列表現 $H$ の $(\\mathfrak{g},K)$-module としての構造を
明示的に与えることを目標とする。
具体的には、まず $H$ の基底として $K$-module の weight vector になっているものを取り、その基底が $\\mathfrak{g}$ の作用でどのように移るかを記述する。
2008/07/10
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
竹崎正道 (UCLA名誉教授)
The Structure of a Hyponormal Operator (a joint work with Kotaro
Tanahashi)
竹崎正道 (UCLA名誉教授)
The Structure of a Hyponormal Operator (a joint work with Kotaro
Tanahashi)
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
渡辺 達也 (早稲田大学・理工学術院)
Two positive solutions for an inhomogeneous scalar field equation
渡辺 達也 (早稲田大学・理工学術院)
Two positive solutions for an inhomogeneous scalar field equation
[ Abstract ]
We consider the following nonlinear elliptic equation:
$$-\\Delta u+u=g(u)+f(x), x \\in R^N,$$
where $N\\ge 3$. When $f(x)\\equiv 0$, it is known that there is a nontrivial solution for a wide class of nonlinearities. Even though $f(x) \\not\\equiv 0$, we can expect the existence of a nontrivial solution if $f(x)$ is small in a suitable sense. Our purpose is to show the existence of two positive solutions via the variational approach when $\\| f\\|_{L^2}$ is small. The first solution is characterized as a local minimizer. The second solution will be obtained by the Mountain Pass Method. Since we do not impose any global condition on the nonlinearity, we will need a presice interaction estimate.
We consider the following nonlinear elliptic equation:
$$-\\Delta u+u=g(u)+f(x), x \\in R^N,$$
where $N\\ge 3$. When $f(x)\\equiv 0$, it is known that there is a nontrivial solution for a wide class of nonlinearities. Even though $f(x) \\not\\equiv 0$, we can expect the existence of a nontrivial solution if $f(x)$ is small in a suitable sense. Our purpose is to show the existence of two positive solutions via the variational approach when $\\| f\\|_{L^2}$ is small. The first solution is characterized as a local minimizer. The second solution will be obtained by the Mountain Pass Method. Since we do not impose any global condition on the nonlinearity, we will need a presice interaction estimate.
Seminar on Probability and Statistics
16:20-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
吉田 亮 (統計数理研究所)
Bayesian learning of biological pathways on genomic data assimilation
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/06.html
吉田 亮 (統計数理研究所)
Bayesian learning of biological pathways on genomic data assimilation
[ Abstract ]
States of living cells are controlled by networks of biochemical reactions, referred to as biological pathways, which comprise of, for instance, phosphorylation and binding of protein molecules, gene expressions mediated by transcription factor activities. In systems biology, mathematical modeling and simulation, based on biochemical rate equations, have proved to be a popular approach for unraveling complex machinery of cellular mechanisms. To proceed to simulations, however, it is vital to find the effective values of kinetic rate constants that are difficult to measure directly from in vivo and in vitro experiments. Furthermore, once a set of hypothetical models is given, a proper statistical criterion is needed to test the reliability of the constructed models in terms of predictability and biological robustness. The aim of this research is to present a new statistical technology, called Genomic Data Assimilation, for handling data-driven model construction of biological pathways. The method starts with a knowledge-based pathway modeling with hybrid functional Petri net. It then proceeds to the Bayesian learning of model parameters for which experimental data are available. This process uses time course measurements of biochemical reactants, e.g. gene expression profiles. Another important issue that we consider is statistical evaluation and comparison of the constructed hypothetical models. For this purpose, we developed a new Bayesian information-theoretic measure that assesses the predictability and the biological robustness of models. In this talk, I will detail mathematical aspects of the proposed method, and then, show some statistical issues to be addressed.
[ Reference URL ]States of living cells are controlled by networks of biochemical reactions, referred to as biological pathways, which comprise of, for instance, phosphorylation and binding of protein molecules, gene expressions mediated by transcription factor activities. In systems biology, mathematical modeling and simulation, based on biochemical rate equations, have proved to be a popular approach for unraveling complex machinery of cellular mechanisms. To proceed to simulations, however, it is vital to find the effective values of kinetic rate constants that are difficult to measure directly from in vivo and in vitro experiments. Furthermore, once a set of hypothetical models is given, a proper statistical criterion is needed to test the reliability of the constructed models in terms of predictability and biological robustness. The aim of this research is to present a new statistical technology, called Genomic Data Assimilation, for handling data-driven model construction of biological pathways. The method starts with a knowledge-based pathway modeling with hybrid functional Petri net. It then proceeds to the Bayesian learning of model parameters for which experimental data are available. This process uses time course measurements of biochemical reactants, e.g. gene expression profiles. Another important issue that we consider is statistical evaluation and comparison of the constructed hypothetical models. For this purpose, we developed a new Bayesian information-theoretic measure that assesses the predictability and the biological robustness of models. In this talk, I will detail mathematical aspects of the proposed method, and then, show some statistical issues to be addressed.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/06.html
2008/07/08
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Otto van Koert (北海道大学大学院理学研究科, JSPS)
Contact homology of left-handed stabilizations and connected sums
Otto van Koert (北海道大学大学院理学研究科, JSPS)
Contact homology of left-handed stabilizations and connected sums
[ Abstract ]
In this talk, we will give a brief introduction to contact homology, an invariant of contact manifolds defined by counting holomorphic curves in the symplectization of a contact manifold. We shall show that certain left-handed stabilizations of contact open books have vanishing contact homology.
This is done by finding restrictions on the behavior of holomorphic curves in connected sums. An additional application of this behavior of holomorphic curves is a long exact sequence for linearized contact homology.
In this talk, we will give a brief introduction to contact homology, an invariant of contact manifolds defined by counting holomorphic curves in the symplectization of a contact manifold. We shall show that certain left-handed stabilizations of contact open books have vanishing contact homology.
This is done by finding restrictions on the behavior of holomorphic curves in connected sums. An additional application of this behavior of holomorphic curves is a long exact sequence for linearized contact homology.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
直井 克之 (東大数理)
construction of extended affine Lie algebras from multiloop Lie algebras
http://akagi.ms.u-tokyo.ac.jp/seminar.html
直井 克之 (東大数理)
construction of extended affine Lie algebras from multiloop Lie algebras
[ Abstract ]
affine Lie algebra の Kac-Moody Lie algebra とは異なる一般化として、extended affine Lie algebra と呼ばれる Lie algebra の class を考える。
ほとんどの extended affine Lie algebra は、有限次元 simple Lie algebra と、有限個の互いに可換な有限位数自己同型を用いて構成できることがすでに知られている。
この講演では、上の構成によって得られる extended affine Lie algebra がどのような場合に(適当な意味で)同型となるか、という問題に関する結果をお話ししたい。
[ Reference URL ]affine Lie algebra の Kac-Moody Lie algebra とは異なる一般化として、extended affine Lie algebra と呼ばれる Lie algebra の class を考える。
ほとんどの extended affine Lie algebra は、有限次元 simple Lie algebra と、有限個の互いに可換な有限位数自己同型を用いて構成できることがすでに知られている。
この講演では、上の構成によって得られる extended affine Lie algebra がどのような場合に(適当な意味で)同型となるか、という問題に関する結果をお話ししたい。
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2008/07/07
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
石井 豊 (九大数理)
Henon 写像の複素力学系
石井 豊 (九大数理)
Henon 写像の複素力学系
2008/07/03
Seminar on Probability and Statistics
16:20-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
西山 陽一 (統計数理研究所)
拡散過程のノンパラメトリック適合度検定
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/05.html
西山 陽一 (統計数理研究所)
拡散過程のノンパラメトリック適合度検定
[ Abstract ]
独立同一分布に従う確率変数列に対する適合度検定問題を考えるとき, Kolmogorov-Smirnov 検定統計量が漸近的に分布不変であることはよく知られて いる.ところが,拡散過程モデルにおいて,例えばエルゴード性を仮定してその 不変分布の経験分布関数から Kolmogorov-Smirnov 型の検定統計量を構成しても, 漸近的分布不変にはならない.本報告では,この問題に対し,score marked empirical process に基づく新しいアプローチを用いて漸近的分布不変な検定統 計量を構成し,かつそれが一致性をもつことを紹介する.モデルとしては小拡散 過程とエルゴード的拡散過程を扱い,また連続観測・離散観測の双方を考察する ので,合計4通りの場合を調べ尽くす.同時期に提案された Dachian and Kutoyants (2008) の結果にも触れる.
本報告は Ilia Negri 氏と共同で執筆した3編の論文(うち1編は増田弘毅氏と も共同)にもとづくものであるが、概要は日本語によるサーベイ論文
http://www.ism.ac.jp/~nisiyama/pism080626.pdf
にまとめてある。
[ Reference URL ]独立同一分布に従う確率変数列に対する適合度検定問題を考えるとき, Kolmogorov-Smirnov 検定統計量が漸近的に分布不変であることはよく知られて いる.ところが,拡散過程モデルにおいて,例えばエルゴード性を仮定してその 不変分布の経験分布関数から Kolmogorov-Smirnov 型の検定統計量を構成しても, 漸近的分布不変にはならない.本報告では,この問題に対し,score marked empirical process に基づく新しいアプローチを用いて漸近的分布不変な検定統 計量を構成し,かつそれが一致性をもつことを紹介する.モデルとしては小拡散 過程とエルゴード的拡散過程を扱い,また連続観測・離散観測の双方を考察する ので,合計4通りの場合を調べ尽くす.同時期に提案された Dachian and Kutoyants (2008) の結果にも触れる.
本報告は Ilia Negri 氏と共同で執筆した3編の論文(うち1編は増田弘毅氏と も共同)にもとづくものであるが、概要は日本語によるサーベイ論文
http://www.ism.ac.jp/~nisiyama/pism080626.pdf
にまとめてある。
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/05.html
2008/07/02
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
近藤 智 (東京大学数物連携宇宙研究機構)
有限体上のスキームのふたつのモチビックコホモロジー群の計算
(安田正大氏との共同研究)
近藤 智 (東京大学数物連携宇宙研究機構)
有限体上のスキームのふたつのモチビックコホモロジー群の計算
(安田正大氏との共同研究)
2008/07/01
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
奥田 隆幸 (東大数理)
不変式のzeta多項式の零点と、微分作用素の関係について
奥田 隆幸 (東大数理)
不変式のzeta多項式の零点と、微分作用素の関係について
[ Abstract ]
MacWilliams変換と呼ばれる変換で不変な複素2変数斉次多項式に対して、zeta多項式と呼ばれる複素1変数多項式を定義する。
TypeIV extremal と呼ばれる不変式の無限列に対し、deg = 0 (mod 6) の場合には、対応する全ての zeta多項式の零点が同一円周上に乗るという事が証明されているが、deg = 2,4 (mod 6) の場合は未解決であった。
この講演では、不変式に対する微分作用素を用いて、deg = 4 (mod6) の場合にも全てのzeta多項式の零点が同一円周上に乗るということを示したい。
MacWilliams変換と呼ばれる変換で不変な複素2変数斉次多項式に対して、zeta多項式と呼ばれる複素1変数多項式を定義する。
TypeIV extremal と呼ばれる不変式の無限列に対し、deg = 0 (mod 6) の場合には、対応する全ての zeta多項式の零点が同一円周上に乗るという事が証明されているが、deg = 2,4 (mod 6) の場合は未解決であった。
この講演では、不変式に対する微分作用素を用いて、deg = 4 (mod6) の場合にも全てのzeta多項式の零点が同一円周上に乗るということを示したい。
< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176 Next >
