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**MIMS現象数理学カフェセミナー
MIMS Cafe Seminar**

世話人：Nina Sviridova （明治大学MIMS PD）

- 主催： 明治大学先端数理科学インスティテュート(MIMS)
- 会場：明治大学中野キャンパス８階談話室

**Multiscale Set-Oriented Computations for Dynamical Systems**

日時：2017年5月10日（水） 12:40～13:20

Tomoyuki Miyaji 氏 （Meiji University, MIMS）Abstract:

Dynamical systems theory provides a useful framework for understanding phenomena in which the state changes dynamically as time passes. In particular, Conley’s fundamental theorem of dynamical systems tells us that any dynamical system can be decomposed into recurrent components and gradient components which connect between the recurrent components. This allows us to describe a dynamical system by a finite directed graph. Although it is difficult to obtain such a decomposition for a concrete example by hand, recent developments of computers and numerical methods have enabled us to obtain it by utilizing a computer. The finite graph description of a dynamical system associated with the Conley indices, which represents the topology and stability of the corresponding recurrent component, is called the Conley-Morsegraph. We briefly introduce a numerical method for computing the Conley-Morse graph for a given dynamical system, and we would like to share some difficulties to overcome.

**A Mathematical Model for Understanding and Creating Impossible Object Illusion**

日時：2017年4月26日（水） 12:40～13:20

Kokichi Sugihara 氏 （Meiji University, MIMS）Abstract:

Impossible objects were first proposed as imaginary 3D structures that exist only in our brains when we see anomalous pictures. It had long been believed that they cannot be realized as actual 3D solids unless we use tricky structures such as discontinuities that appear continuous or curved surfaces that appear planar. However, we found that some of impossible objects can be constructed without those tricks. Starting with this discovery, we have extended the sense of impossibility to various forms. They include “impossible motions”, “ambiguous cylinders”, “partly invisible objects” and “topology-disturbing objects”. We present a mathematical model for understanding pictures of 3D objects, which was first considered for computer vision but also useful for understanding human vision, and show how it can be used for creating new types of impossible objects.

**An Examination for The Iyashi Structure
by Deep Learning**

日時：2016年12月13日（火） 12:10～12:50

Hiroe Abe 氏 （Meiji University, MIMS）Abstract:

Previously for the analysis of Iyashi structure, the mapping function which is obtained from fixtures of facial expressions to the judge by the subject whether the data is healed or not to the subject. This accuracy is determined by the type of inputs and it is not always the general way to select the input data. In recent years, deep learning has been a great concern, because the input data itself is possibly to be provided from the big amounts of data. However, the amount and quality of big data depend on the problem and not yet general-purpose ones are obtained. In this study, the healing structure is given as an example to consider the quality and quantity in the big data.

**Eigenvalue problems from the topological viewpoint**

日時：2016年11月7日（月） 12:10～12:50

Ayuki Sekisaka 氏 （Meiji University, MIMS）Abstract:

Eigenvalue problems are applied in many applications in physics, engineering and in other areas of science. In many cases of mathematics, they are solved by analytical or algebraic approaches. Here, there are other approaches, that is, topological approaches. The topological viewpoint gives simple and beautiful mechanism of mathematics, and is sometimes very convenient in application. In this talk, we roughly explain what is the topological viewpoint of eigenvalue problem with a brief history of topology.

**Recent topics on the phenomenon with respect to camphor**

日時：2016年10月17日（月） 12:10～12:50

Yumihiko S. Ikura 氏 （Meiji University, MIMS）Abstract:

Previously, the self-propelled system driven by the camphor has been understood not only experimentally but also theoretically, e.g., the traffic jam of camphor boats on an annular water channel. In a lot of these studies, to avoid unnecessary complexity, some elements (such as solutal Marangoni convection and fluctuation of water level) were ignored as inconsequential. However, some further suggestions might become impaired. In this café seminar, I would like to introduce some of camphor systems that these elements are thought to be essential for, and claim that this system will include more suggestions.

**A Brief Story of the Lugiato - Lefever Equation**

日時：2016年7月11日（月） 12:10～12:50

Tomoyuki Miyaji 氏 （Meiji University, MIMS）Abstract:

The Lugiato-Lefever equation (LLequation) is a damped driven nonlinear Schrödinger equation with cubicnonlinearity. It was derived by Lugiato and Lefever as a model equation for pattern formation in nonlinear optics in 1987. It exhibits a rich bifurcation structure, e.g. snaking bifurcation of spatially localized structures, breathing localized structure, and spatiotemporal chaos. Nowadays, it is attracting more and more attention in a different context of nonlinear optics. In his caféseminar, we show a brief history of the LL equation as well as a part of our recent interest in this subject.

**Spherical Laguerre Voronoi Diagram as a Tool for Fitting Real World Tessellations**

日時：2016年6月6日（月） 12:10～12:50

Supanut Chaidee 氏 （Meiji University, MIMS）Abstract:

Recently, we proposed a method for fitting real world tessellations, spike-containing objects, using spherical Voronoi diagram and spherical Laguerre Voronoi diagram (SLVD). From the SLVD fitting experiments using ideal data, it leads to the theoretical study of the properties of a polyhedron corresponding to the SLVD. Using those properties, we can solve the SLVD recognition problem, the judgment whether or not the given convex spherical tessellation is SLVD. We finally apply the recognition algorithm to find the best-fitting SLVD to the given spherical tessellation when generators are not included explicitly in the tessellation, which is a generalization of the spike-containing objects. We are now doing the experiments using sugar apple and raspberry photographic images.

This works is supervised by Prof. Kokichi Sugihara.

**Perfect Victory in NHK TV Show “Sugowaza”
from Development of Vehicle Collision Simulation**

**The Lecture date has been changed to May 9th, 2016

※開催日が5月9日に変更になりました変更後の開催日時：2016年5月9日（月） 12:10～12:50

Ichiro HAGIWARA 氏（Meiji University, MIMS）Abstract:

Around 1970, for boycotting Japanese cars, astrict safety standard was newly provided in U.S. Since a testcar is around 1 billion yen, to reduce the number of testcars for verifying crash characteristics became the biggest subject concerning the continued existence of vehicle companies over the world. At that time, finite element method(FEM) had been exerting high power in vibration analysis, however had been helpless in collision analysis. I'll talk how to develop the technique for collision simulation using FEM. Also, I’ll tell the road to victory in NHK TV show “Sugowaza(Supreme Skills)” by explaining the relationship between origami engineering and vehicle collision simulation.

**Mathematical Modeling and Analysis of Fruit Skin Patterns**

日時：2015年10月21日（水） 12:10～12:50

Supanut Chaidee 氏 （Meiji University, MIMS）Abstract:

In nature, there are many tessellation patterns on curved surfaces that look like Voronoi diagrams. Typical examples are the patterns found on fruit skins. Verifying that a given tessellation is a Voronoi diagram will be useful for constructing mathematical models of polygonal patterns. However, the data are usually obtained as a 2D projected image, and hence it is not easy to compare it with a Voronoi diagram on a curved surface. We propose frameworks for using a photograph of a fruit to measure the difference between the pattern on its skin and a spherical Voronoi diagram. The problem of finding the spherical Voronoi diagram that best fits the fruit skin pattern is reduced to an optimization problem. In addition, we also find the spherical Laguerre Voronoi diagrams which best fit to the planar tessellations. The validity of this formulation is evaluated using jackfruit and lychee.

**Continuous flattening of polyhedral surfaces**

日時：2015年7月22日（水） 12:10～12:50

Chie Nara 氏 （Meiji University, MIMS）Abstract:

Can we flatten an empty box of paper without cutting and stretching? According to the Cauchy rigidity Theorem (1813) and the Sabitov volume Theorem (1996), it is necessary to change the shape of some faces by moving edges for such motion. Generally, a problem which was proposed by Eric Demaine et al. in 2001 asks to find a continuous flattening motion for any given polyhedron. If the polyhedron is convex, such continuous flattening motion was given with a few methods by the author et al. recently. In this talk, the key ideas are introduced and some future works are proposed.

**A reaction diffusion model for understanding phyllotactic
formation**

日時：2015年6月24日（水） 12:10～12:50

Yoshitaro Tanaka 氏 （Meiji University, MIMS）Abstract:

Phyllotactic patterns in plants are well known to be related to the golden ratio and Fibonacci sequence. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biological experiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator. Then, there arises a natural question as tohow the inhibitory effect can be related to the auxin. In this talk, we will propose a reaction diffusion model by taking account of auxin behavior in plant tips. This model can link the auxin behavior of the activator to the inhibitory effect in the stem tip. Moreover, we will show the relationship between Douady and Couder’s model and our model by singular limit analysis. It also provides us with the potential function corresponding to the inhibitory effect, and the bifurcation diagram.

**Concentration points of solutions in a spatially heterogeneous
reaction-diffusion equation**

日時：2015年5月13日（水） 12:10～12:50

Hiroko Yamamoto 氏 （Meiji University, MIMS）Abstract:

We are interested in a point-condensation phenomenon in solutions of a spatially heterogeneous reaction-diffusion equation. This means that distribution of a solution concentrates in a very narrow region around a finitely many points. Hence, it is important to find the candidates for the concentration points since we can know the shape of concentrating solutions. In this talk, we introduce the location of concentration points and the effect of spatial heterogeneity on the points.

**Development of Origami-forming by modeling and simulation**

日時：2015年3月11日（水） 12:10～12:50

Nguyen Thai Tat Hoan 氏 （Graduate School of Advanced Mathematical Sciences, Meiji University）Abstract:

Origami is a forming process from flat papers to 3D shape by following steps: Shape → Partition → Making crease pattern → Cutting material → Folding → Connecting by glue. In this study, a new manufacturing method called Origami-forming is developed, based on traditional Origami approach. The new method follows the same steps as Origami, applying for wider rank of material (soft and hard material such as aluminum, high tensile steel, etc), and folding by a reconfigurable robot system. If the method is successful, it will allow to produce object in short time and get higher stiffness. In this study, the Origami-forming is applied into Truss Core Panel(TCP) manufacturing, to get the shape that is impossible to be produce by current technology, and acountermeasure to reduce the springback is considered. Secondly, a grooving technique inspired fromtradition origami is proposed to bend the material easier than before, hence allow for a dual-arm robot can produce many cases of shape. A optimization process based on Response surface methodology is built to search for best shape of groove. Next, designing handling system and decision-making process are carried out. Modeling and simulation by FEM is used to confirm forming process.

**Bifurcation Analysis of Periodic Traveling Wave Solutions in Excitable Reaction-Diffusion Systems**

日時：2015年2月18日（水） 12:10～12:50

Mohammad Osman Gani 氏 （Graduate School of Advanced Mathematical Sciences, Meiji University）Abstract:

We are interested in the existence and stability of periodic traveling waves in two-variable excitable reaction-diffusion systems numerically. We introduce a system of reaction-diffusion equations to mimic the cardiac electrical activities. Our results based on the method of continuation show a stability change of Eckhaus type of the periodic traveling waves. There are two families of periodic traveling waves:fast and slow. The fast family is stable in the case of standard FitzHugh-Nagumo excitable system. However, we observe that the fast family becomes unstable in our model. Consequently, it bifurcates to an oscillating wave. We explain this phenomenon by numerically calculating the essential spectra of the periodic traveling waves. Moreover, we study the stability of the periodic traveling waves for the Aliev-Panfilov excitable system and compare its results with the proposed model. This is a joint work with Toshiyuki Ogawa in Meiji University.

**Two-scale expansion with drift approach to
a slow smoldering combustion process in a porous media**

日時：2015年1月28日（水） 12:10～12:50

Ijioma Ekeoma Rowland 氏 （Meiji University, MIMS）Abstract:

We are interested in the upscaling of a slow smoldering combustion process, involving a nonlinear chemical reaction of a solid fuel and an oxidizer on the pore surfaces of a heterogeneous porous media. We introduce the two-scale expansion with drift to derive the upscaled system of equations. Specially, we use this approach to study more general velocity fields arising from dominant convection regime of the flow.

日時：2014年11月5日（水） 12:10～12:50

Tommaso Scotti 氏 （Graduate School of Advanced Mathematical Sciences, Meiji University）Abstract:

Blooms of freshwater cyanobacteria are a worldwide spread environmental issue. In fact, some cyanobacteria can produce a variety of toxins that are harmful to a wide range of organisms, including humans. Therefore, monitoring and understanding the dynamics of harmful algal blooms is tremendously important because of their potential impact on drinking and recreational waters.

Despite toxin producing planktonic species are generally expected to be poor competitors for resources, dense blooms of toxic cyanobacteria, such asMicrocystis, do often occur in nature. We employ a Lotka-Volterra reaction-diffusion system in order to investigate the coupled role of toxicity and zooplankton's predation in the persistence of the toxic species, and to study the mechanisms behind the formation of spatially local toxic blooms. We show that the presence of a toxic prey may destabilize the spatially homogeneous coexistence and trigger the formation of spatial patterns. We also show that local blooms more likely occur when predators avoid the toxic prey and the toxicity is at an intermediate level.

日時：2014年9月24日（水） 12:10～12:50

Kohta Suzuno 氏 （Graduate School of Advanced Mathematical Sciences, Meiji University）

Abstract:

In this talk many types of spontaneous pattern formation in human flow are shown. It is well known that biological entities (fish, birds, ants etc.) behave "as one" and show amazing order without any central controlling unit. Recent development of mathematical science has revealed that the collective motion of pedestrian could also be viewed as a self-organized system. Actually, we can observe self-organized lanes, arches and various structures in simulations and experiments ｏｆ pedestrians, and they are ｎｉｃｅ eｘａmples of the spontaneous order iｎ non-equilibrium finite particle systems. ln this presentation, we review some of the self-organized phenomena observed in crowd simulation and give possible explanations to them via mathematical modeling.

日時：2014年9月10日（水） 12:10～12:50

Takamichi Sushida 氏 （Meiji University, MIMS）

Abstract:

Phyllotaxis is the arrangements of leaves, florets and other organs of plants. In particular, it is well known that typical phyllotactic patterns which appear to plants such as sunflower and pine cone are intimately related to the golden section and Fibonacci sequence. In the classical subject of phyllotaxis, helical models of the cylinder and spiral models of the disk were studied by using the Voronoi diagram and the optimal circle packing, etc. As one of plane tilings, Akio Hizume devised triangular spiral tilings called Fibonacci tornado. Ｔｈｅｙ are tilings which admit a transitive action by a similarity transformation generated by the golden section. Moreover, he presented origami developments of Fibonacci Tornado by one sheet. In this presentation, we will introduce mathematical researches of spiral tilings with phyllotactic properties. In particular, we will consider spiral tilings given as a Voronoi diagram.

日時：2014年8月19日（火） 12:10～12:50

Ryo Ooizumi 氏 （Meiji University, MIMS）

Abstract:

Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the min subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. ln order to analyze the optimal control under internal stochasticity, we need to make use of "Stochastic Control Theory" in the optimal life schedule problems. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension ｏｆ optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models . We apply our theory to a two-resource utilization model for semelparity. Consequently, we show that the diversity of resources is important for species in a case.

日時：2014年7月16日（水） 12:10～12:50

Yujing Liao 氏 （Meiji University, MIMS）

Abstract:

Computer-based surface models are indispensable in several fields of science and engineering. Reverse engineering is the process of reconstructing digital representations from physical models. Rapid modeling the objects from 2-3 dimensional data is very important task in the scientific research and the market applications. The presented approach is connected to the modeling of 3D objects from the given images. In this talk I will present our technique and related with it applications of the results. (co-researcher: Maria Savchenko)

日時：2013年11月20日（水） 12:10～12:50

Shintaro Kondo 氏 （Meiji University, MIMS）

Abstract:

My research theme is plasma phenomena appearing in nuclear fusion research. When l was a student of the master course of fundamental science and technology at Keio university, I selected it and have researched it. There are many instabilities in plasma phenomena, and drift wave turbulence is a kind of plasma instabilities. In this talk I will speak about plasma phenomena, application, my motivation and the point of my research.

日時：2013年10月23日（水） 12:10～12:50

Yutaka Kobayashi 氏 （Meiji University, MIMS）

Abstract:

One of the most prominent aspects of modern humans' culture, compared with other animals, is said to be its cumulative nature. Namely, humans' culture evolves from generation to generation through accumulation of modifications by individuals. The cumulativeness, however, is not really useful to distinguish modern humans from extinct human species because the latter must also have had cumulative culture. For example, the Levallois flint-knapping technique of Neanderthals for making stone tools is so complex that any single individual could never have invented it alone. One key feature to characterize modern humans' culture then may be its explosive evolution rate. My recent preliminary analysis suggests that explosive culture is possible if knowledge promotes innovation. The presence of a cognitive ability that allows such a feedback however remains to be confirmed. I argue in this talk that "creativity" may be one of cognitive abilities with this property.

Pattern Formation in a Reaction-Diffusion-Advection System

日時：2013年7月3日（水） 12:00～12:50

出原浩史 氏 （明治大学MIMS研究員）

Abstract:

拡散の速さの異なる2種の物質が適当な条件のもとで反応し合うことにより自己組織的に周期的空間構造を作り出すというTuringのパラドックスは、今なお多くの研究を生み出す源となっている。本セミナーでは、Turingのパラドックス、つまり反応拡散系と呼ばれる系に現れる拡散誘導不安定性という一見不可思議な現象を紹介し、それに関連する最近行っているパターン形成に閏する研究についてもお話ししたい。

Modeling Cultural Evolution on Prehistoric Archaeological Data

日時：2013年6月5日（水） 12:00～12:50

青木健一 氏 （明治大学研究・知財戦略機構客員教授）

Abstract:

先史時代とは文字(ましてはマスコミ)以前の時代であり、文化の伝播は人と人の直接の出会いによって主に起きた｡従って、先史時代の文化のダイナミックスは、現代の文化のダイナミックスと異なることが予想される｡本発表では、先史考古学データが物語る2つの現象について、数理モデルを用いた解釈を試みる。 １つ目が、中東からヨーロッパへの初期農耕の地理的伝播である｡Ammerman＆Cavalli-Sforza(1971)によるこの伝播の等速性の発見を受けて、我々(Aoki,Shida,＆Shigesada、l996)は、ヨーロッパに先住する狩猟採集民が進出する農民との接触によって農耕に転向する、反応拡散モデルを提案した｡このモデルから得られる予測は、諸経験的知見と矛盾しない。 ２つ目が、旧人ネアンデルタールと新人サピエンスで異なるとされる文化進化速度である。我々(Aoki,Lehmann,＆Feldman、2011)は、集団遺伝学の分子進化理論を転用して文化進化速度を理論的に定義した｡また、その一応用例として、新人では考古学的に実証されている一対多伝達(一人の熟練者が多くの初心者に教示する)のモデルを提案し先行研究が主張する文化進化の加速効果、文化進化速度に対する集団サイズの影響などについて検討した。

Origami Theory to Design Deployable Structures

日時：2013年5月15日（水） 12:00～12:50

石田祥子 氏 （明治大学特任講師）

Abstract:

折り畳み傘や折り畳み自転車など、“折り畳み”と名のつく製品は私たちの生活になじみ深い。“折り畳む”ことにより持ち運びがしやすく、また省収納スペースを図ることができる。本講演では、曰本古来の文化であり芸術である折紙に着目し、折り畳みが自在な構造物を数学的に設計する手法について論じる。山折線と谷折線を規則的に配置し、軸方向に折り畳み自在な円筒や円錐、中心周りに巻き取ることのできる円形膜などを紹介する。

Propagation Speed of a Starting Wave in a Queue of Pedestrians

日時：2013年5月1日（水） 12:00～12:50

友枝明保 氏 （明治大学MIMS研究員）

Abstract:

渋滞を解消するためには、何を考えれば良いだろうか？ 例えば、高速道路での車の渋滞を考えた場合、渋滞の後方に加わる車の台数を前方から抜けて行く台数よりも少なくすることができれば、渋滞列を短くすることができる。つまり、渋滞にゆっくりと近づき(slow-in)、渋滞から素早く抜け出す(fast-out)ことが実現できれば、渋滞を解消できると言える。本講演では、fast-outに注目し、人が行列から動き出す際の反応の連鎖(発進波)の伝播速度について、その特徴を数理モデルと実証実験の双方から議論する。