KiDS

2013年

「ノイズ誘起現象」

日時:2013 年 7 月15日(金)午後2時〜16日(土)午後4時ころ

場所:京都大学理学部3号館(数学教室)110講義室

7 月15日(金)

	2:00-2:50	佐藤 譲 氏(北海道大学・電子科学研究所)
				Noise-induced phenomena in one-dimensional maps
	3:00-3:50	岩田友紀子 氏(FIRST 合原数理モデルプロジェクト/東京大学・生産技術研究所)
				Study on limit distributions of random perturbations of non-singular transformations on [0,1]
	4:00-4:50	北城圭一 氏(理化学研究所・脳科学総合研究センター)
				ヒトの脳での確率共振とノイズ誘起現象
	5:00-5:50	中尾裕也 氏(東京工業大学・情報理工学研究科)
				非線形リズムとノイズ
	6:30-		懇親会(場所未定)

7 月16日(土)

	10:00-10:50	角 大輝 氏(大阪大学・理学研究科)
				ランダムな複素力学系における協調原理と安定性
	11:00-11:50	中田一紀 氏(九州大学・稲盛フロンティア研究センター)
				半導体/磁性体集積電子デバイスにおける雑音誘起現象
	1:30-2:20	高橋 亮 氏(京都大学・工学研究科)
				Stochastic resonance in spin systems
	2:30-3:20	寺前順之介 氏(理化学研究所・脳科学総合研究センター)
				神経情報処理におけるノイズの起源と機能
	3:30-4:20	矢野孝次 氏(京都大学・理学研究科)
				マルコフ連鎖の流れの合流性について

2010年

2010年10月25日Professor Masa Tsuchiya (Institute for Advanced Biosciences, Keio University)
時間・場所15:30-17:30 京都大学桂キャンパス A1棟大会議室
題目Roles of Global Response: The Existence of Genome Vehicle for Cell Fate Decision
あらましt is intriguing to grasp how a specific path can be chosen by a cell having enormous number of molecules, among the uncountable number of possibilities that can arise, through the complex multi-molecular interactions during cellular process such as differentiation. The basis for such determinism may stem from the averaging effect caused by the reduction of response fluctuations according to the law of large numbers demonstrating by our recent investigations on microarray dataset. In the innate immune response of macrophages to lipopolysaccharide (LPS) and the neutrophil differentiation process, we showed that correlation fluctuations reduced when genes were grouped, thereby, deciphering the hidden collective genome-wide average expression dynamics. For LPS response, the ensemble property, in wildtype and mutant conditions, uncovered the collective genome-wide expression behaviors which exhibited local and global effects of LPS stimulated macrophages; local being the well-known pro-inflammatory response of a small number of highly expressed genes, while global being the novel collective activation of diverse processes comprising the rest of the lowly expressed genes (Tsuchiya et al., PLoS ONE ; 4(3):e4905, 2009 and Tsuchiya et al., Physica A ; 388(8): 1738-1746, 2009). These works have shed new light on innate immune response, providing significance role of lowly expressed genes, which are often considered as noisy and insignificant in microarray experiments. Elucidating further understanding of significance role of the global response (Tsuchiya et al., FEBS J. 274:2878-2886, 2007), our study on neutrophil differentiation led to find evidence for the existence of specific self-regulating gene ensembles (named “genome vehicle”) guiding cell fate decision in rigorous statistical manner. Notably, the collective motion of lowly and moderately variable genes within the genome vehicle plays an important role in the cell fate decision (Tsuchiya et al., PLoS ONE 5(8): e12116, 2010), providing potentially completely new comprehensive mechanistic view of cell fate decision. It will be very interesting to know how the concerted motion of the genome vehicle, together with well-known master instructive genes, such as Yamanaka factors, drives the differentiation of pluripotent stem cells as well as other biological processes that could acquire a completely different perspective.
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2010年10月25日Professor Kumar Selvarajoo (Institute for Advanced Biosciences, Keio University)
時間・場所14:00-15:30 京都大学桂キャンパス A1棟大会議室
題目Find Organizing Principles in Biology – A study of the innate response in macrophages
あらましRemarkably, cellular systems display robust and stable functional processes such as division, differentiation and apoptosis. Within a single cell, the highly heterogeneous environment with enormous number of molecular species and interactions produce fluctuations of cellular dynamics. However, at population level, the cells are able to execute well-defined deterministic processes indicating the existence of self-organizing principles. To reveal such governing principles for signaling pathways, we studied the dynamics of the innate immune response using perturbation-response approach. Without the requirement of detailed in vivo biochemical parameters, we analyzed the Toll-like receptor signaling and found that the activation dynamics of nuclear factor-kB and Mitogen-activated protein kinases, in wildtype and genetically mutated macrophages, obeyed simple linear rules. Using these, we deciphered novel reaction pathways, intermediates and key regulatory species. It is surprising to know how and why such simplifications hold in an environment where diffusion, molecular crowding and stochastic processes are anticipated to make the response highly complex and non-linear. Providing insights into the origins will aid in uncovering the law of self-organization in complex biological systems.
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2007年

2007年8月1日Dr. M. J. Ogorzalek (AGH Univ. Sci. and Tech.)
時間・場所13:30-15:00 京都大学桂キャンパス A1棟講義室2
題目Fractals for electronic design
あらましGeometric objects possessing properties impossible to describe using Euclidean notion of dimensionality are wide-spread in nature and are also encountered in many scientific experiments. Mathematical description of such objects has been focus of research for very long time - probably starting with the works of Georg Cantor, through von Koch to Julia/Fatou and Sierpinski just to name the most important contributors. The notion of fractal was coined by B. Mandelbrot and it is used for description of structures having non-integer dimension. Fractal geometric objects have several intriguing properties apart from its non-integer dimension, namely they can have finite area while showing infinite perimeter or infinite area for a finite volume object. They show also the self-similarity property - similar fine structure observed at any magnification scale. These fundamental properties of fractal objects can found very interesting applications in electical and electronic engineering. We present some of the most spectacular of these applications: 1). fabrication of very large capacitances thanks to technological possibilities of making huge conducting areas in a limited volume; 2). enhancement of attainable capacitance values in IC design thanks to usage of lateral capacitances obtained by fractioning the available chip area; 3). Fabrication of multiband antennas with improved impedance matching in a very small volume exploiting the self-similar properties of meandring structures and packaging of very long wires in a small volume. Some of these applications came now to mass production.
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2007年3月31日Dr. Marian Wiercigroch (College of Physical Sciences, University of Aberdeen)
題目Dynamics of Non-smooth Systems
あらましIn this lecture I will introduce and discuss a practically important concept of non-smoothness where a dynamical system can be considered as smooth in a finite size subspace of global hyperspace. Global solution is generated by matching local solutions obtained by standard methods. To illustrate the non-smooth dynamical systems and the methodology of solving them, two mechanical engineering systems will be presented. Firstly a vibro-impact system will be analysed to understand its performance can be maximised. Periodic trajectories can be reconstructed as they go through three linear subspaces. The second problem comes from rotordynamics, where understanding of intermittent interactions between the rotor and the snubber ring are studied. The results obtained from the developed mathematical model confronted with the experiment have shown a good degree of correlation. The lecture will close with the latest results on the new archetypal oscillator allowing to study transitions from smooth to discontinuous dynamics.
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2007年1月23日土屋政輝 博士 (慶應義塾大学 先端生命科学研究所)
題目Systems Biology Approach to Understanding Activation of Innate Immune Systems: Dynamic control of gene regulatory networks
あらましこれまで, 遺伝子発現制御メカニズムを理解するのに, 転写因子の, 生化学反応(微分方程式モデル)からのアプローチ, 統計力学的なモデル, 転写機能の論理回路(combinatorial logic)モデル等, 様々な数理モデルが世界中の研究者達で考案された. だが, 遺伝子発現のメカニズムを解明し, 生体内での遺伝子発現の定量的動的コントールの成功には至っていない. 我々は, 転写因子の活性化が, シグナル伝達経路を通し, 化学修飾, 複合体の形成等, 様々に時間的変化を起こし, その結果として, 転写因子の機能に動的変化が起こり, 遺伝子発現をダイナミックに制御・調整している動的機構を解明する数理モデルを構築した.  具体的には, 転写因子によるプロモーター上のcis-DNA結合部位の活性化の時間的変化が遺伝子発現(mRNA)を動的に変化させると考え, 結合部位の活性化とmRNA発現量を共に離散化することで, 遺伝子発現レベルの遷移は, 転写因子群の結合部位の活性化レベルと遺伝子発現レベルで決まるとする有限オートマトン(Finite State Machine)を順次論理で表現(Sequential Logic Modeling, SLM)し, 遺伝子発現の動的制御機構の解明に成功した: 1) SLM は, 時系列な, 結合部位の活性化のデータとmRNA発現量を離散化することで, モデルを構築(non-parametric)することができ, これまで数理モデルに固有にあったパラメーターの最適化問題が存在しないことである. 2) これまで解析が困難であった, 転写因子の動的機能, 転写因子群の動的な相互作用関係を遺伝子発現の変化から解明することができるだけでなく, 転写因子群の時系列活性化に対する遺伝子発現の動的シミュレーション(Forward mapping), cis-DNA結合部位の変異による遺伝子発現の動的変化の予測(in silico Mutagenesis), 遺伝子発現の時間的変化から, 転写因子群の動的な活性化を予測(Reverse mapping)することが, 可能となった. 3) このことは, シグナル伝達経路とそれに特徴的に対応する転写因子群の活性化を解析することで, 遺伝子発現の時間的変化からシグナル伝達経路の活性化を予測することができること意味する. この動的制御システムを, endo16遺伝子によるウニの消化器官の発生モデルで立証した; 遺伝子発現の動的制御機構を解明するSLMの特徴は, 網羅的に遺伝子発現を観測できるマイクロアレイデータの統計的解析から, 遺伝子間, 遺伝子クラスター間の因果相関(causality relation)を見出すことで, それらを動的にマップすることで, ネットワーク制御の動的メカニズムの解明に応用できる. 現在, 生物学的応用として, Toll受容体(TLR)などを用いて病原体感染を認識し, 自然免疫に中心的な役割を果たしている樹状細胞の活性化過程における遺伝子発現の変化を網羅的にとらえ, 動的な免疫活性化のメカニズムを解明し, シミュレーションを可能にするシステム生物学的手法の開発に取り組んでいる.

2006年

2006年12月7日Dr. Pawel Pilarcyzk (京都大学大学院理学研究科数学教室)
題目Computational Dynamics and Cubical Homology
あらましIn this talk, an algorithmic approach to the analysis of dynamical systems will be described. This approach is based on cubical grids and appears to be most natural from the computational point of view, where geometric objects are represented as sets of pixels (bitmap images), voxels, or n-dimensional hypercubes described with respect to the integerlattice. Cubical homology, a recently developed algebraic-topological tool, is used to retrieve certain invariants (like the Conley index) that are useful in the analysis of asymptotic dynamics, or to measure the complexity of spatial-temporal patterns that appear in simmulations of PDEs or in physicalexperiments. Efficient algorithms that allow the effective computation of homology will be described, and their software implementation freely available at the Computational Homology Project website (http://www.math.gatech.edu/~chomp/) will be introduced. Some specific applications of the homology computation will also be pointed out.
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2006年8月17日Dr. Igor Mezic (UCSB)
題目Biomolecules as nonlinear oscillators: Life-enabling dynamics
あらましWe present a study of complex biomolecules from the perspective of nonlinear dynamical systems theory. The basic - so-called minimalist - models used in molecular dynamics consist of a Hamiltonian part that captures the internal interactions among the atoms the molecule consists of, and viscous and stochastic interactions with the surrounding solvent. The question of particular interest is that of switching from one conformed configuration of a biomolecule to another. In fact, understanding the mechanism of fast transitions between conformed states of large biomolecules is central to reconciling the dichotomy between the relatively high speed of metabolic processess and slow (random-walk based) estimates on the speed of biomolecular processess. Here we utilize the dynamical systems approach to suggest that the reduced time of transition between different conformations is due to features of the dynamics of molecules that are a consequence of their structural features. Long-range and local effects both play a role. Long-range molecular forces account for the robustness of final states and nonlinear resonant processes that channel localized, bounded disturbances into collective, modal motions. Local interconnecions provide fast transition dynamics. We also present some experimental evidence of effect of resonance in conformational transitions.
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2006年7月12日Dr. Vakhtang Putkaradze (Colorado State University), collaborator Darryl Holm (Mathematics, Imperial College)
題目Mathematical models of self-aggregation of particles at nano-scales (or cheerios at 50 nanometers)
あらましWe derive a non-local evolution equation for self-assembly of particles at the nano-scale. The physical assumptions underpinning the problem are the presence of interaction potential between the particles and mobility dependence on the averaged local density. We show that for almost any choice of sufficiently smooth potential and averaging functions the evolution is reduced to a finite-dimensional system of ODEs describing the dynamics of particle clumps, and the order of that system is generally very low. Analytical stationary states of the problem in one and two dimension are derived. Next, we present results of numerical simulations showing that the energy density of a realistic particle clump of arbitrary shape is described by a surprisingly simple formula (but is not equal to the half-sum of binary particle interactions), and that the continuum approximation may be used for clumps with as few as five particles. We use this new energy density to predict the evolution of particle density in the continuum model.
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2005年

2005年6月9日Dr. Ralph Abraham (UCSC)
題目Patterns in Complex Dynamical Systems
あらましMathematics is the study of patterns and pattern processes, and dynamical systems theory traditionally has provided models for pattern formation processes, or morphogenesis. The computer revolution has produced radically new models, generalizing those of partial differential equations, for example. In this talk we will explore some of these new modeling strategies, with applications to synchronization, emergence, morphogenesis. We may touch upon -- and view graphics and animations of -- chaotic (fractal) attractors, bifurcations, and applications to various arts and sciences.

2004年

2004年12月6日Dr. Philip Holmes (Princeton University)
題目Piecewise-holonomic mechanics, hybrid dynamical systems, and escaping cockroaches
あらましI will discuss joint work with John Schmitt, Raffaele Ghigliazza and Justin Seipel, in which nonlinear mechanics and hybrid dynamical systems meet biology. Motivated by Robert Full's experimental studies of insects at UC Berkeley, we propose a mechanical model for the dynamics of legged locomotion in the horizontal plane. Our three-degree-of freedom rigid body model with massless, compliant legs in intermittent contact with the ground allows for passive and prescribed (active muscle) force and torque generation. Starting with energetically conservative bipedal models (each leg corresponding to the front/rear/opposite-middle tripod used in rapid running by many insect species), we move on to include active muscles and a central pattern generator of bursting neurons, and begin to develop hexapedal models with more realistic leg geometries. We show that piecewise holonomic mechanics due to intermittent foot contacts can confer strong asymptotic stability, and compare our models' behaviors with experiments on running insects. We stress the relevance of simple models, and show how phase reductions and averaging allow significant simplifications of complex neuromechanical models.
2004年10月1日土居伸二 博士 (大阪大学)
題目Hodgkin-Huxley型微分方程式の非線形力学 --- 分岐, ロバスト性, カオス ---
あらましHodgkin-Huxley型微分方程式は, ヤリイカ神経細胞における活動電位生成のモデルとして著名なHodgkin-Huxley (HH)方程式の拡張として, 種々の神経細胞のみならず, 筋肉細胞, 心筋細胞, 膵臓β細胞, ある種の植物細胞等々, 実に多様な細胞の電気的興奮現象のモデル化に用いることのできるパワフルな数理モデルである. また, HH型方程式は, 巨視的な生命現象を定量的に再現・予測することのできる唯一の数理モデルであると言っても過言ではない. 近年, システムバイオロジーやインシリコバイオロジーなど, 数理モデルを用いた生命現象の研究が盛んであるが, HH型方程式は, それらの研究の中でも中心的位置を占めることが期待される. また, HH型方程式は, 分岐現象を始めとする非線形現象の宝庫であり, 力学系理論の重要な研究対象でもある. 本講演では, 電気生理やHH型方程式に関する入門とHH型方程式の示す非線形現象をいくつか紹介する. 時間があれば, 最近のトピックスである, HH方程式のカオスや特異摂動系のHopf分岐近傍におけるカオスやホモクリニック軌道, などの話題にも触れたい.
天野 晃 博士 (京都大学)
題目包括的心筋細胞モデルと組織・臓器モデル
あらまし心筋細胞の電気生理学モデルは,Hodgkin-Huxleyの神経繊維活動モデルを原型に発展してきている.現在,イオンチャネルに代表される細胞の機能要素に関する研究が進んでおり,これらの要素を共通部品として同じ機能要素を使って複数種類の心筋細胞モデルを実現する包括的心筋細胞モデルが京都大学の野間らにより提案されている.一方,臓器としての心臓は,多数の心筋細胞が複雑な構造で組み合わされたモデルであり,細胞特性の違い,刺激伝導系,非線形力学特性等様々な非線形特性を持つ要素の集合である.本発表では,包括的心筋細胞モデルについて解説し,このモデルを使って心筋組織,心臓がどのように構成されるかを解説する.
2004年6月11日Dr. Ralph H. Abraham (UCSC)
題目Synchronization of coupled oscillators: prediction of phase differences
あらましCoupled oscillators arise in many areas, such as electrical circuits, medical physiology, neural networks, and so on. It is well known that two coupled oscillators entrain in frequency and phase. Less well known is an invisible structure that determines the entrained phase difference called the isochron foliation. In this talk we will explain the isochron structure, and how to uncover it with computational techniques, in the context of an example from biological neural networks.

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Last-modified: 2016-04-01 (金) 09:29:41 (422d)