MASセミナー 2010年度

第30回 MASセミナー

タイトル :Fluctuation theorem applied to bio-motors

講演者 : 林 久美子氏(大阪大学)

日時: 2010年10月14日(月) 16:30 ~ 18:00

場所:明治大学生田校舎・第2校舎A館・2階A207室

アブストラクト: Fluctuation theorem (FT) is the physical law of entropy productioncaused when an operation is added to a small system, which issensitive to thermal noise. When applied to a macroscopic system, FT is equivalent to the second law of thermodynamics. Since 1993when FT was discovered, it has been studied theoretically andexperimentally for various physical systems. In our study, FT was first applied to bio-motors in order to measuretheir driving forces. For example we applied FT to F1-ATPase, whichis a rotary motor protein, and measured its rotary torque by using FT.Being practically useful for rotary motors when our results werecompared with those obtained in previous studies, FT has begun tobe used for the torque measurements of ofF1 mutants and V1 mutants. Now we try to apply FT to measure driving forces exerted by motorproteins in vivo or in a cell. Concretely we observed mitochondriontransported by motor proteins in the axon of PC12 cells. We wouldlike to discuss whether we can measure the driving force acting on amitochondria. We will show our primitive data related to this issue.
Reference:
[1] Kumiko Hayashi,Hiroshi Ueno, RyotaIino and Hiroyuki Noji ,Phys. Rev. Lett.104, 218103 (2010).

第30回MASセミナーポスター


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第29回 MASセミナー

タイトル :Turing patterns in network-organized activator-inhibitor systems

講演者 : 中尾 裕也氏(京都大学)

日時: 2010年9月27日(月) 16:30 ~ 18:00

場所:明治大学生田校舎・第2校舎A館・2階A207室

アブストラクト: Turing instability in activator–inhibitor systems provides a paradigm of non-equilibrium self-organization; it has been extensively investigated for biological and chemical processes. Turing instability should also be possible in networks, and general mathematical methods for its treatment have been formulated previously by Othmer& Scrivenin 1971. However, only examples of regular lattices and small networks were explicitly considered. We study Turing patterns in large random networks with strong degree heterogeneity, using the classical Mimura-Murray model on scale-free networks as an example, which reveal striking differences from the classical behavior. The initial linear instability leads to spontaneous differentiation of the network nodes into activator-rich and activator-poor groups but periodic structures are not formed. The emerging Turing patterns become furthermorestrongly reshaped at the subsequent nonlinear stage. Multiple coexisting stationary states and hysteresis effects are observed. This peculiar behavior can be understood in the framework of a mean-field theory. Our results offer a new perspective on self-organization phenomena in systems organized as complex networks. Potential applications include ecological metapopulations, cellular networks of early biological morphogenesis, etc. If time permits, I would also like to touch on diffusion-induced chaos in coupled limit-cycle oscillators on scale-free networks, which can be understood almost in parallel with the network Turing patterns.
[1] H. Nakao& A. S. Mikhailov, Turing patterns in network-organized activator-inhibitor systems. Nature Phys. 6, 544-550 (2010).
[2] H. Nakao& A. S. Mikhailov, Diffusion-induced instability and chaos in random oscillator networks. Phys. Rev. E 79, 036214 (2009).

第29回MASセミナーポスター


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第28回 MASセミナー

タイトル :The generalized t-distribution on the circle

講演者 : Hai-Yen Siew 氏(明治大学)

日時: 2010年7月22日(木) 16:30 ~ 18:00

場所:明治大学生田校舎・第2校舎A館・2階A207室

アブストラクト: An extended version oft-distribution on the unit circle is generated by conditioning a normal mixture distribution, which is broadened to include not only unimodalityand symmetry, but also bimodality and asymmetry, depending on the values of parameters. After reparametrization, the distribution contains four circular distributions as special cases: symmetric Jones-Pewsey, generalized von Mises, generalized cardioidand generalized wrapped Cauchy distributions. As illustrative examples, the proposed model is fitted to the number of occurrences of the thunder in a day and the monthly wind directions of Ryoriin 1995.

第28回MASセミナーポスター


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第27回 MASセミナー

タイトル :Strategies for Chemotaxis of Amoeboid Cells

講演者 : 西村 信一郎 氏(広島大学)

日時: 2010年7月8日(木) 16:30 ~ 18:00

場所:明治大学生田校舎・第2校舎A館・2階A207室

アブストラクト: Chemotactic behaviors in eukaryotic cellsanimal cells are widely known phenomena. Though a straight motion toward the chemical source can be observed in chemotaxis, cells do not necessarily move in a straight way but often move in fluctuated zigzag ways. For understanding such variety of behaviors, we build a simple model for chemotactic eukaryotic cells, which describes changes in cell shape on the two-dimensional plane by considering a cell membrane, actin filaments embedded in the membrane, and an intracellular control factor. We also introduce three models of environment around cells: (a) simple chemical gradient, in which the chemical guidance (chemotactic signal) spreads everywhere in a two-dimensional field with a uniform gradient; (b) flipping chemical gradient, with which the uniform gradient is reversed at a moment everywhere in the space; and (c) a maze around a chemical source, in which maze-like walls separate the source and cells to block cell’s locomotion. Some parts in those walls permeate the chemical guidance to confuse cells. The simulated results show that in the case (a) cell’s behavior is most efficient when the cell takes a crescent shape like “keratocyte” and moves in a straight way. In contrast, in cases of (b) and (c) the behavior is efficient when the cell takes a typical amoeboid-like shape and moves in zigzag ways. These results suggest that the fluctuated zigzag locomotion of amoeboid cell has an advantage in some “complex” environment.

第27回MASセミナーポスター


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第26回 MASセミナー

タイトル :Mathematical models in biosignals

講演者 : 高田 宗樹 氏(福井大学)

日時: 2010年6月24日(木) 16:30 ~ 18:00

場所:明治大学生田校舎・第2校舎A館・2階A207室

アブストラクト: The aim of mathematical modeling is to understand the mechanisms that govern the working of complex systems and to detect anomalous signals by using model coefficients or theoretical indices. For instance, detection is effective for diagnosing diseases. Anomalous signals can be generated by the degeneration of the potential function in the dynamical equation systems (DESs) or by fundamental changes in the DESs themselves, for instance, an increase in the degrees of freedom or the addition of stochastic factors. Visible determinism in the latter case would be different from that in the case without random variables. DESs were obtained as mathematical models that regenerated time series data such as those obtained from electrocardiography, electrogastrography, body sway, etc. It is especially well known that the mathematical models of some biosignalscan be developed by using stochastic processes. A correspondence has been obtained between the distributions of time series and temporally averaged potential functionsin stochastic differential equations. By performing time series analysis of the biosignals, the authors have succeeded in identifying the nonlinearity in a potential function that has several minima. Fluctuations could be observed in the neighborhood of the minima. We discuss the metamorphism in the potential function due to the application of a specific artificial load.

第26回MASセミナーポスター


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第25回 MASセミナー

タイトル :Issues on coupled oscillator networks: feedback engineering of synchronization and dependence of temporal precision on network structure

講演者 : 郡 宏 氏(お茶の水女子大学)

日時: 2010年6月10日(木) 16:30 ~ 18:00

場所:明治大学生田校舎・第2校舎A館・2階A207室

アブストラクト: In nature, there are many situations in which a population of oscillators forms a collective oscillation. Understanding dynamical properties of oscillator networks is an important issue because oftheir broad applications in disciplines ranging from biology to engineering. In this presentation, I will first review synchronization. In particular, useful mathematical models, called phase models, will be briefly explained. Then, I will talk about a few issues from my recent works.

Reference:[1] I. Z. Kiss, C. G. Rusin, H. Kori, J. L. Hudson, "Engineering Complex Dynamical Structures: Sequential Patterns and Desynchronization", Science 316, 1886-1889 (2007)
[2] Y. Kobayashi and H. Kori, "Design principle of multi-cluster and desynchronized states in oscillatory media via nonlinear global feedback ", New Journal Physics 11, 033018 (2009)
[3] N. Masuda, Y. Kawamura, H. Kori: "Collective fluctuations in networks of noisy components", arXiv/0911.5013

第25回MASセミナーポスター


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第24回 MASセミナー

タイトル :Noise Inhomogeneitywithin Biological Modeling

講演者 : 長谷川 禎彦 氏(東京大学)

日時: 2010年5月27日(木) 16:30 ~ 18:00

場所:明治大学生田校舎・第2校舎A館・2階A207室

アブストラクト: Since many biological mechanisms function under fluctuant environments, their dynamics can be well accounted for by Langevinequations driven by white noise. Although the white noise can reflect the nature of microscopic aspect of fluctuations, it is regular in a mesoscopictime scale and does not capture long-range fluctuations. In this presentation, we show effects of noise inhomogeneityon biological mechanisms. An approximation method considering the inhomogeneityis also presented.

第24回MASセミナーポスター


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第23回 MASセミナー

タイトル : Pattern formation in autocatalytic proliferation systems

講演者 : 小田切 健太 氏(お茶の水女子大学)

日時: 2010年5月13日(木) 16:30 ~ 18:00

場所:明治大学生田校舎・第2校舎A館・2階A207室

アブストラクト: Autocatalytic process is often associated with pattern formation, ranging from the atomic scale phenomena to the morphology of living bodies. In my talk, I focus on pattern formation and its dynamics in autocatalytic proliferation systems. I will first present the very simple model that represents autocatalytic cell proliferation subject to the distribution of nutrition and natural death of the cells by starvation. I will show what is essential togenerate a branching pattern like actual bacterial colonies in the model, by comparing the cellular automata approach with the reaction-diffusion equation approach. I next present two kinds of three-component autocatalytic proliferation systems. One consists of consumer (X), its inhibitor (I), and nutrition (N), and the other consists of two different consumers (A, B) and N. Focusing on the“competitive” relation in these models, I will show various kinds of pattern formation and its transitionphenomena induced by the change of control parameters of the competition.

第23回MASセミナーポスター


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第22回 MASセミナー

タイトル :The limit theorems for a time-dependent discrete-time quantum walk on the line

講演者 : 町田 拓也 氏(明治大学)

日時: 2010年4月27日(火) 16:30 ~ 18:00

場所:明治大学生田校舎・第2校舎A館・2階A207室

アブストラクト: The quantum walks describes quantum versions of classical random walks. Relating with computer science, quantum walks are investigated as quantum search algorithms. The quantum search algorithms, e.g. Grover's algorithm, expressed by quantum wakls are expected more exponentially faster than their classical counterparts. We study time-dependent discrete-time quantum walks on the one-dimensional lattice. By using the Fourier analysis, we can compute the limit distribution of a two-period quantum walk defined by two orthogonal matrices or special unitary matrices. For the symmetric case, the distrivution is determined by one of two matrices. Moreover, we consider two special cases and present limit theorems. In this case, the probability distribution becomes a one-period (usual) quantum walks.

第22回MASセミナーポスター


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第21回 MASセミナー

タイトル : Characteristics finite element schemes for flow problems

講演者 : 野津 浩史 氏(明治大学)

日時: 2010年4月13日(火) 16:30 ~ 18:00

場所:明治大学生田校舎・第2校舎A館・2階A207室

アブストラクト: In this talk, finite element schemes based on the method of characteristics are considered. It is known that the converntional Galerkin method gives oscillating results for high Peclet/Reynolds number problems. To deal with such phenomena, many upwind type schemes have been developed. We focus on schemes based on the method of characteristics in the upwind type ones. The method rests on an approximation of the material derivative along the trajectory of the fluid particle, and is natural from the physical point of view. Moreover, the method has an advantage that the matrix for the system of linear equations is symmetric, which leads to symmetric linear solvers, e.g., CG method, although the convection term usually gives a non-symmetric matrix. We show usefulness of the schemes including ours with numerical examples.

第21回MASセミナーポスター


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MASセミナーは明治大学グローバルCOEプログラム 『現象数理学の形成と発展』(http://gcoe.mims.meiji.ac.jp/)の援助を受けております。

明治大学先端数理科学インスティテュート・現象数理・基礎数理部門 (世話人:三村昌泰、上山大信、若野友一郎、池田幸太、木下修一)