Friday, 6 December, 2024

12:40-12:50  Opening

12:50-13:40  稲津 将 (北大), 中高緯度大気の予測可能性

中高緯度大気はそのカオス的振る舞いのため、気象予報の限界は高々２週間程度とされている。しかし、中高緯度大気であっても予測限界が長い場合と短い場合があることが知られている。その中でも中高緯度の予測可能性に重要な因子となる大気ブロッキングをキーワードに講演者が取り組んだ２つの研究を紹介する。大気ブロッキングの発達の原因として低周波・高周波の渦フラックス収束の効果があるとされている。しかし、予測データにその診断をしようとすると、未来時間のデータにフィルタを適用する必要がある。研究[2]ではまず、準地衡系で行われているモード展開法をプリミティブ系に拡張し、モード方程式を導出する。その後、Barriopedroに従い定義したブロッキング事例の合成として、ブロッキングをZ500主成分の線型結合の持続として再定義する。これにより、導出したモード方程式によるブロッキング診断が可能になる。本研究では予測データを使わず、あくまで再解析データでの診断を行う。次に、大気ブロッキングを含む多様な長周期変動を自己組織化写像で生成された潜在空間上で表現し、気象予測可能性を診断した[1]。まず、解析データから基準となる潜在空間を生成する。次に、S2Sプロジェクトによる各国気象機関の１か月アンサンブル予報データに射影する。潜在空間上のノードをまとめたクラスタ分析から大気状態を少数に分類することで、予測限界が長い場合と短い場合が、予報モデルによらず共通していることがわかった。これは物理的に考えられる予測可能性に一致するものと期待される。以上は、講演者が過去に行った主成分で張った相空間上での単一モデルの予測可能性研究[3]と整合する結果である。

[1] Inatsu, M., M. Matsueda, N. Nakano, and S. Kawazoe, 2023: Prediction skill and practical predictability depending on the initial atmospheric states in S2S forecasts. Journal of Atmospheric Sciences, 80, 1449–1462.

[2] Aikawa, T., M. Inatsu, N. Nakano, and T. Iwano, 2019: Mode-decomposed equation diagnosis for atmospheric blocking development. Journal of the Atmospheric Sciences, 76, 3151–3167.

[3] Inatsu, M., N. Nakano, and H. Mukougawa, 2013: Dynamics and practical predictability of extratropical wintertime low-frequency variability in a low-dimensional system. Journal of the Atmospheric Sciences, 70, 939–952.

13:50-14:40  斎​木 ​吉隆 (​一​橋​大), Laminar chaotic saddle within a turbulent attractor

Chaotic dynamics can be quite heterogeneous in that, in some regions, the dynamics are unstable in more directions than in other regions. We say a chaotic invariant set is heterogeneous when arbitrarily close to each point of the set there are different periodic points with different numbers of unstable dimensions. We call such dynamics heterochaos [1, 2, 3]. 

In the study of (phase) synchronization, a heterochaotic saddle has sometimes been used to characterize a coherent state. However, such studies mainly examine symmetrically coupled identical oscillators or directionally coupled dynamics [4]. We investigate intermittency in asymmetric coupled dynamics, including model turbulence and coupled chaotic oscillators. Our approach focuses on the appearance or disappearance of a chaotic saddle and thus gives new insight into characterizing the destabilization of coherent dynamics. Using our idea, intermittency is judged by the existence of a heterochaotic saddle within a chaotic attractor. We confirm the occurrence of phase synchronization in the shell model, which indicates that turbulence models can be generalized as coupled chaotic models. In high-dimensional systems, phases are not generally defined appropriately. Even in such cases, a laminar heterochaotic saddle, like in the cases in this study, can be used to generalize a phase-synchronized state. The talk is mainly based on the joint work with H. Kato, M. U. Kobayashi, Y. Saiki, and J. A. Yorke [5].

[1] Y. Saiki, M. F. Sanjuán and J. A. Yorke, Chaos 28, 103110, 2018

[2] Y. Saiki, H. Takahasi and J. A. Yorke, Nonlinearity 36, 1776-1788, 2021

[3] Y. Saiki, H. Takahasi and J. A. Yorke, SIAM J. App. Dyn. Sys. 22, 1852-1876, 2023

[4] M. Inubushi, Y. Saiki, M. U. Kobayashi and S. Goto, Phys. Rev. Lett. 131, 254001, 2023

[5] H. Kato, M. U. Kobayashi, Y. Saiki, and J. A. Yorke, Phys. Rev. E 110, L052202, 2024

14:50-15:10 髙橋 海斗 (東京理科大), Optimization of Infection Spread Dynamics in Many-Body Brownian Motion

TBA

15:20-15:40 吉原 爽太 (名大), Dynamical Systems in One-on-One Pursuit and Evasion: With Examples of Circular and Elliptical Cases

In 1921, Hathaway found an interesting property of the one-on-one pursuit and evasion problem when the evader followed a circle. If the pursuer's speed is times the speed of the evader, the pursuer's trajectory will converge to a circle with a radius reduced by n. This property does not hold when the evader follows an ellipse. The evader's trajectory converges to an unknown closed curve that is neither an ellipse nor a circle. This talk aims to explain the difference between the circular and elliptical cases by using the simultaneous differential equation derived by Barton and Eliezer, which formulates the one-on-one pursuit and evasion problem. This equation allows us to assume that the evader's speed remains constant if we want to know only the shape of the pursuer's trajectory. Based on this assumption, we derive a dynamical system that involves two new variables: the angular difference between the velocity vectors of the two players and the distance between them. When the evader orbits a circle, the dynamical system is autonomous and has an asymptotically stable equilibrium point. By contrast, if the evader orbits an ellipse, the dynamical system becomes non-autonomous and lacks an equilibrium point. We use a second-order nonlinear differential equation concerning the angular difference between the velocity vectors of the two players to prove these properties. In conclusion, lack of asymptotic stability causes the difference between circular and elliptical pursuit and evasion.

(tea)

16:00-16:50 Riccardo Muolo (東京科学大), Higher-order structures and their effects on nonlinear dynamics

Networks are powerful tools in the modeling of complex systems, but they may not capture the right interactions when multiple units are involved simultaneously. Such many-body interactions are encoded by higher-order structures which can be thought as extensions of networks [1]. The most general form is a hypergraph, in which interactions of any order can coexist without any constraint. Over the last years, higher-order structures have been the focus of great excitement, since this novel framework has enormous potential for applications [2].

In this talk I will introduce higher-order structures and nonlinear dynamics on top of them. I will start by discussing nonlinear dynamical systems on networks and how such a framework can be extended to account for higher-order interactions, to then proceed towards some structural properties of higher-order structures such as hypergraphs and simplicial complexes. In the second part, I will discuss some examples of nonlinear dynamics on networks, namely, synchronization of phase [3] and chaotic oscillators [4] and Turing patterns [5], and their recent extensions on hypergraphs [6,7,8,9]. 

[1] Battiston F et al., 2020 Phys. Rep. 84: 1-92.

[2] Bianconi G, 2021 Higher-Order Networks: An introduction to simplicial complexes. Cambridge University Press.

[3] Nakao H, 2016 Cont. Phys. 57(2): 188-214.

[4] Fujisaka H and Yamada T, 1983 Prog. Theor. Phys. 69 32–47.

[5] Nakao H and Mikhailov A, 2010 Nat. Phys. 6, 544.

[6] Tanaka T and Aoyagi T, 2011 Phys. Rev. Lett. 106 224101.

[7]  León I et al, 2023 Chaos 34, 013105.

[8] Gambuzza L et al., 2021 Nat. Comm. 12 1–13.

[9] Muolo R et al, 2023 Chaos Solit. Fractals 166, 112912.

17:00-17:50 Ettore Barbieri (JAMSTEC), Reconstructing Food Webs: A Superposition

Method Using Only Trophic Positions

Understanding trophic positions is essential for analyzing complex food webs. While calculating these positions can be straightforward with knowledge of feeding relationships and their proportions, determining diet coefficients traditionally requires significant time and effort. Fortunately, modern analytical techniques, such as stable isotope analysis, provide an efficient alternative for identifying trophic positions. Stable isotope analysis estimates trophic positions, but this information alone does not offer insights into prey-predator relationships. To reconstruct food webs, a method is needed to convert trophic positions into diet coefficients. Our method employs a superposition of probable prey pairs, where the weighting coefficients are probabilities computed using Bayesian statistics. We present a way to reconstruct diet coefficients using a minimal dataset—trophic positions. This innovative approach is robust and effectively reveals critical ecological traits of food webs, such as the structure of ecological pyramids and the role of keystone species.

Saturday, 7 December, 2024

1​0​:00​​-1​0:​5​​0  白坂 将 (阪大), Estimating Principal Koopman Eigenfunctions for Dynamical Dimension Reduction

TBA

​1​1​:​00​-​1​1:​50​ ​水野 雄太 (北大), Quantum algorithm for dynamic mode decomposition integrated with a quantum differential equation solver

We present a quantum algorithm that analyzes time series data simulated by a quantum differential equation solver. The proposed algorithm is a quantum version of a dynamic mode decomposition algorithm used in diverse fields such as fluid dynamics, molecular dynamics, and epidemiology. The complexity of our quantum algorithm is 𝑂⁡(polylog⁡𝑁) for an 𝑁-dimensional system. This is an exponential speedup over known classical algorithms with at least 𝑂⁡(𝑁) complexity. Thus, our quantum algorithm is expected to enable high-dimensional dynamical systems analysis intractable for classical computers. [This work has been published: Phys. Rev. Research 6, 043031 (2024)]

1​2:00-12:20 片山 夏樹 (京大), Koopman Analysis of the Singularly Perturbed van der Pol Oscillator

The Koopman operator framework holds promise for spectral analysis of nonlinear dynamical systems based on linear operators. Eigenvalues and eigenfunctions of the Koopman operator, the so-called Koopman eigenvalues and Koopman eigenfunctions, respectively, mirror global properties of the system’s flow. In this presentation, we perform the Koopman analysis of the singularly perturbed van der Pol system. First, we show the spectral signature depending on singular perturbation: how two Koopman principal eigenvalues are ordered and what distinct shapes emerge in their associated Koopman eigenfunctions. Second, we discuss the singular limit of the Koopman operator, which is derived through the concatenation of Koopman operators for the fast and slow subsystems. From the spectral properties of the Koopman operator for the singularly perturbed system and the singular limit, we suggest that the Koopman eigenfunctions inherit geometric properties of the singularly perturbed system. These results are applicable to general planar singularly perturbed systems with stable limit cycles.

12:30-12:50 堤 夏輝 (一橋大), データ駆動低次元力学系モデリング手法を用いた全リアプノフ指数の推定

データ駆動型カオス力学系モデリングにおいて，時系列予測の精度が良くても，元の力学系の負のリアプノフ指数を再現することは簡単ではない．我々はこれまでに，時間遅れ座標とガウス型動径基底関数を用いてスカラー時系列から力学系をモデリングする手法[1,2,3]を提案した．本研究では，その手法を用いて元の力学系の全リアプノフ指数の再現を行う．モデリングされた力学系を分析すると，低次元部分空間の中にモデルアトラクタが再構成されていることが確認できる．その構造を用いても上記と同じ元の力学系のリアプノフ指数を得ることができる．これらの手法は未知の力学系から生成された時系列にも適用可能である．

本研究は齊木吉隆教授（一橋大学）と中井拳吾講師（岡山大学）との共同研究である．

[1] N. Tsutsumi, K. Nakai, and Y. Saiki, Chaos 32, 091101 (2022)

[2] N. Tsutsumi, K. Nakai, and Y. Saiki, Phys. Rev. E 108, 054220 (2023)

[3] N. Tsutsumi, K. Nakai, and Y. Saiki, arXiv:2409.00668

(lunch)

14:00-14:50 加藤 譲 (はこだて未来大), Quantum asymptotic phase function for quantum limit-cycle oscillations and quantum synchronization

The asymptotic phase is a fundamental quantity for analyzing classical nonlinear oscillators. Recently, we propose a fully quantum-mechanical definition of the asymptotic phase for quantum nonlinear oscillators, which naturally extends the definition of the asymptotic phase for classical oscillatory systems from the Koopman-operator viewpoint. In this presentation, we briefly overview quantum limit-cycle oscillation and quantum synchronization,  introduce our definition of quantum asymptotic phase function, and discuss its usage for analyzing quantum synchronization. 

15:00-15:50 笹本 智弘 (東京科学大), Exact solutions for current fluctuations of one dimensional exclusion process

The talk will consist of two parts. In the first part, we review basic properties of exclusion process 

and discuss KPZ universality and large deviation through macroscopic fluctuation theory (MFT). 

In the second part we explain recent developments of solving the MFT equation by mapping it 

to classical integrable systems.  The talk is based on a joint work with Kirone Mallick, Hiroki Moriya, Cristian Giardina, Hayate Suda. 

[1] K. Mallick, H. Moriya, T. Sasamoto,

Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process,

Phys. Rev. Lett. 129, 040601 (2022).

[2] K. Mallick, H. Moriya, T. Sasamoto,

Exact solutions to macroscopic fluctuation theory through classical integrable systems, 

JSTAT 2024 074001 (2024). 

[3] A. Grabsch, H. Moriya, K. Mallick, T. Sasamoto, O. Benichou, 

Semi-infinite simple exclusion process: from current fluctuations to target survival,

Phys. Rev. Lett. 133, 117102 (2024).

[4] K. Mallick, C. Giardina, T. Sasamoto, H. Suda, in preparation. 

(tea)

16:10-17:00 秋元 琢磨 (東京理科大), Anomalous Diffusion of Subrecoil-Laser-Cooled Atoms: Insights for Quantum Technologies

TBA

17:00-17:20 堺 一世 (東京理科大), Current fluctuations in the symmetric simple exclusion process with quenched disorder

TBA

Sunday, 8 December, 2024 

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1​0:00​-1​0​:​2​0 中垣 俊之 (北大), Cell behaviors driven by spiral swimming

TBA 

​10:30-11:20 飯間 信 (広大), Elegant light algorithms: from single-cell sensing to control of bioconvection spots 

TBA

11:30-12:20 石川 拓司 (東北大), Ciliary fluid dynamics of swimming, feeding, pumping, and sensing

Cilia are cell organelles acquired by eukaryotes more than a billion years ago that induce flow in the surrounding fluid by periodically beating in waves. Many eukaryotes, from microorganisms to humans, possess cilia. From the viewpoint of biofluid mechanics, cilia perform four major functions: swimming, feeding, pumping, and sensing. In this talk, I will explain the flow produced by cilia and its biological functions. Our studies illustrate that ciliary flow can generate a variety of crucial biological functions and is indispensable for organisms, including humans.

(lunch)

14:00-14:50 柴山 允瑠 (京大), Some applications of KAM and Converse KAM Theories 

The Liouville-Arnold theorem states that, for integrable systems, the phase space is foliated by invariant tori, and the flow on each torus is a Kronecker flow. According to KAM theory, in a perturbed system, many of these invariant tori persist. However, with larger perturbations, the invariant tori are expected to vanish. Converse KAM theory provides a theoretical guarantee of this phenomenon. In this talk, I will discuss the existence and non-existence of invariant tori in the Henon map, billiard map, and Origami map. This work includes joint research with Y. Higashihama, H. Tateishi, and R. Ichikawa.

15:00-15:20 平岩 尚樹 (九大),  Dynamical Structures of Lobe Dynamics for Spacecraft Trajectory Design

Lobe dynamics reveals phase space volume transport on Poincaré maps in Hamiltonian systems. We demonstrate a new trajectory design method to connect a few chaotic orbits based on lobe dynamics. Application of this type of trajectory design method in higher-dimensional Poincaré maps is also discussed by utilizing a three-dimensional map called the ABC map.

(tea)

15:40-16:30 小西 哲郎 (中部大), 多自由度力学系と基準振動解析：多重振り子を例として

自由度の大きな古典力学系の振舞いを調べる研究としておそらくもっともよく知られているものは、Fermi-Pasta-Ulam-Tsingou model (FPUTモデル、FPUモデルとも呼ばれる）の数値計算であろう。この研究およびそれ以降の発展は、その後、ソリトンの発見へとつながり、非線形物理学の一つの潮流となった。しかし、もともとのFPUTモデルの研究で目指していた目的、大自由度系での（いまで言うところの）カオス的な振舞いの発生については、それ以外に適切なモデルが提唱されていないこともあり、まだよくわからないことが多い。本公演では、多重振り子を例として、基準振動解析をもとに規則的な運動とカオス的な運動を見ていきたい。

16:30-17:20 山口 義幸 (京大), バネ玉系における形状の力学的安定性

倒立振子の支点を上下に高速で振動させると倒立状態を安定化することができる。これと似た現象は自励ハミルトン系でも起こる。分子モデルとしても使われる、質点がバネで結合されたバネ玉系を考えよう。バネ振動がない場合の形状はポテンシャルエネルギーで決まるが、バネ振動の励起により形状に対する実効ポテンシャルエネルギーが誘導され、ベアなポテンシャルでは不安定であった形状を安定化できる。興味深いことに、実効ポテンシャルによる安定性はバネ振動の励起モードに依存し、安定だった形状を不安定化することもできる。本発表ではこの現象のメカニズムを説明し、いくつかの系における例を紹介する。

Monday, 9 December, 2024 

​​​10:00-​1​0:​50 西浦 康政 (北大), Annihilation tongue

In this talk, we present a new and completely different type of annihilation arising in a ”weak” interaction regime. It is even counterintuitive in the sense that the spots/pulses come together very slowly but do not merge, and then they start to repel each other for a certain time. Finally, up and down oscillatory instability emerges and its amplitude grows enough for patterns to be destroyed eventually [1]. There is a kind of hidden instability embedded in the traveling patterns, which causes the above annihilation dynamics. It turns out to be a codimension 2 point consisting of drift and Hopf (DH) instabilities. Annihilation regime emanating from the codimension 2 point forms a tongue shape in an appropriate parameter space. The above scenario can be proved analytically up to the onset of annihilation by reducing it to a finite-dimensional system. This is a joint work with Kei-Ichi Ueda (Toyama university) and Takashi Teramoto (Kyoto Women’s University).

[1] Y. Nishiura, T. Teramoto and K. Ueda, Arbitrarily weak head-on collision can induce annihilation: the role of hidden instabilities. Japan Journal of Industrial and Applied Mathematics, 40 (2023) 1695-1743, https://doi.org/10.1007/s13160-023-00607-5

1​​1:00-​1​1:​50 多賀 圭理 (早稲田大), Universality in the pattern formation of the tape-peeling trace

TBA

12:00-12:20 小澤 歩 (JAMSTEC), Phase reduction approach to oscillatory patterns in reaction-diffusion systems with delay

過去の状態に依存して時間発展するシステムではしばしば振動現象がみられ、それらは時間遅れを伴う力学系の振動解としてモデル化される。特にシステムが空間自由度をもつ場合には、振動する空間パターンが現れることがあり、その理解には遅延偏微分方程式が有用である。様々な遅延偏微分方程式において振動解の生じる条件が研究されてきたが、生じた振動解が摂動に対してどのように応答するのかを解析する手段は乏しい。本研究では、反応項に時間遅れをもつ反応拡散方程式の位相縮約理論を定式化する。具体例として時間遅れを含むSchnakenberg systemの振動解に対して縮約理論を適用し、時間遅れや空間の効果を議論する。本研究はJAMSTEC 河村洋史氏との共同研究である。

(lunch)

14:00-14:20 山本 泰智 (東大), Gaussian Process Phase Interpolation for estimating the asymptotic phase of a limit cycle oscillator from time series data

Rhythmic activity commonly observed in biological systems is typically modeled as limit cycle oscillators. Phase reduction theory provides a useful analytical framework for elucidating the synchronization mechanism of oscillators. In essence, this theory describes the dynamics of a multi-dimensional nonlinear oscillator using a single variable, called the asymptotic phase. Estimating the asymptotic phase from the observed data is crucial for understanding and controlling the rhythmic phenomena in the real world. In this study, we propose Gaussian Process Phase Interpolation (GPPI), a novel method for estimating the asymptotic phase from time series data. GPPI first evaluates the asymptotic phase on the limit cycle and then estimates the asymptotic phase outside the limit cycle using Gaussian process regression. The proposed method captures a variety of functions and it is easily applicable even as the dimension of the system increases.

We test GPPI on simulation data from the Stuart-Landau oscillator and the Hodgkin-Huxley oscillator. Our results show that GPPI accurately estimates the asymptotic phase even in the presence of high observation noise and strong nonlinearity. Additionally, we demonstrate that GPPI is an effective tool for data-driven control of a Hodgkin-Huxley oscillator.  Therefore, the GPPI method will facilitate the data-driven modeling of the limit cycle oscillators. (The paper's on arXiv:2409.03290)

14:30-14:50 小池 元 (東京科学大), Chaotic behavior in the gravity interaction model

Transport is a ubiquitous phenomenon in fundamental components of our society. Typical examples include world trade, human migration, commuting, and business transaction between companies. Gravity law is a model of flux in these systems. These systems are networks as well, because sites interact with each other heterogeneously. From this perspective, physicists introduced a mathematical model called “gravity interaction model” as a model of time evolution of node sizes in the network, to connect microscopic nonlinear interaction between nodes by gravity law with macroscopic state, that is, the distribution of wealth over network. Originally introduced as a model to obtain stationary state, recent study revealed that this model exhibits limit cycles and chaos, as well as fixed points. In this talk, we first review the results of bifurcation points and hysteresis of the model. As a main part, we will show that even a simple ring network of several nodes exhibit chaotic behavior. The main part is based on a recent preprint [1].

[1] Hajime Koike, Hideki Takayasu, Misako Takayasu. “New type of chaotic solutions found in Gravity model of network transport”, arXiv:2411.02919

1​5:00-15:20 大石 悟 (阪大), Suppression of Overembedding in Reservoir Computing

Reservoir Computing (RC) is a machine learning framework that has successfully forecasted chaotic time series and achieved attractor reconstruction.

Attractor reconstruction in RC means that there is a diffeomorphic map from the attractor in the phase space onto its image in the reservoir space.

To evaluate the quality of attractor reconstruction, some statistics that quantify the regularity of the reconstruction, such as continuity, homeomorphism, and differentiability, have been proposed.

These statistics have been applied to optimize the delay coordinate for good reconstruction.

In this study, we utilize these statistics from the reservoir space for evaluating the reconstruction quality in RCs and optimize RCs based on these statistics before training.

1​5:20-15:50 小島 瑛貴 (北大), Resonance and chaos in the stochastic Mackey-Glass equation

Stochastic resonance is a noise-induced phenomena showing time-scale matching to a characteristic period of external forces, or delay in time-delay system. We investigate noise-induced phenomena in the stochastic Mackey-Glass equation (SMG) from a viewpoint of random dynamical systems. A random map reduction of slow dynamics of SMG reproduces the bifurcation scenario of the original dynamics. We show that SR in time-delayed system (stochastic Mackey-Glass equation) exhibits harmonics, while SR with external forces (Benzi-Sutera-Vulpiani equation) does not.

16:00-​1​8:00 Poster session 

Tuesday, 10 December, 2024 

1​​​0:00-​12​:​00  Poster session and discussion

1​​​4:00-​17​:​20  Poster session and discussion

Wednesday, 11 December, 2024 

10:00-10:50 Songhao Yin (東大), Nonequilibrium thermodynamics of populations of weakly-coupled low-temperature-differential Stirling engines with synchronous and asynchronous transitions

TBA

11:00-11:20 藤井 成美 (東京科学大), Phase control of the high-dimensional Kuramoto model using dynamical reduction approaches and its application to jet lag

TBA

11:30-12:20 小林 幹 (立正大), Analysis of global supply chains using network theory

TBA

(lunch)

14:00-14:50 佐藤 譲 (北大), Noise-induced phenomena in high dimensions

Noise-induced phenomena are caused by interactions between deterministic dynamics and external noise. When a transition occurs owing to small noise, the stationary distribution of the deterministic dynamical system is substantially altered, and the unobservable structure of the original dynamics becomes observable. In such cases, nonlinear phenomena, which qualitatively differ from deterministic dynamics, emerge in the noised dynamics. This talk includes a brief review of classical noise-induced phenomena from random dynamical systems point of view. Recent results on multiple noise-induced transitions proved by validated numerics, and heterogeneous noise-induced phenomena in a class of high-dimensional dynamical systems are presented as well.

15:00-15:50 三ツ井 孝仁 (順天堂大), Reducing extreme events through local interventions based on multi-scenario ensemble forecasts: the Lorenz 96 model case

The control simulation experiment (CSE) is a recently proposed approach for investigating the controllability of dynamical systems, particularly weather systems (Miyoshi and Sun, 2022). It can also be viewed as an application of chaos control within the framework of numerical weather prediction. Recently, Sun et al. (2023) designed a CSE to reduce extreme events in the Lorenz 96 model. Their method exploits the system's sensitivity to initial conditions to guide trajectories toward desired outcomes using small control inputs. However, their study revealed that the success rate of control dropped to approximately 60% when the number of perturbed sites was small, such as one or three—a limitation that could be significant in real-world applications where control inputs are often constrained. In this study, we propose a new method to reduce extreme events in the Lorenz 96 model using simple intervention strategies. Our method achieves a success rate of approximately 94% when the number of perturbed sites per step is as low as one, and up to 99% when it is up to two.

(tea)​

16:10-16:50 中野 雄史 (北大), 摂動安定でない区分拡大写像の準安定極限定理

TBA

17:00-17:40 高橋 博樹 (慶應大), 間欠区間力学系のバースト時間における等差数列について

今から約50年前にセメレディは「上密度が正の自然数の集合は任意の長さの等差数列を含む」ことを驚くべき組み合わせ論法で証明した。セメレディの定理にインスパイアされたフルステンベルクは多重再帰定理を確立し、セメレディの定理の鮮やかな別証明を与えた。多重再帰定理は離散数学の問題を力学系・エルゴード理論に関連づけることになり、この基本的な結びつきが「素数の集合は任意の長さの等差数列を含む」というグリーン・タオの定理など、多くのさらなる発展へとつながっている。このような歴史的経緯からしても、与えられた力学系が定義する種々の自然数の無限部分集合において、いくらでも長い等差数列の存在・非存在を考察することは面白い問題のように思える。本講演では、典型例としてC2級Manneville-Pomeau写像のバースト時間の集合を考え、いくらでも長い等差数列の存在を議論する。

Thursday, 12 December, 2024 

1​​​0:00-​10​:50 茶碗谷 毅 (​阪大), The fractalization of torus and relevant phenomena 

TBA

1​​1:00-​11​:​50 末谷 大道 (大分大), ランダム神経回路網における弱い一般化同期の発生とその時系列予測問題への影響

時系列予測はデータ科学における重要な課題の一つであり、最近ではリザバーコンピューティングに基づくアプローチも注目されている。これまでのRCを用いた時系列予測の研究では、いわゆる「カオスの縁」にあるハイパラメータ領域において最適な予測パフォーマンスが達成されることが示唆されてきた。しかし、一般的にリザバーは外部入力によって駆動される非自励的な力学系であるため、この概念は問題がある。まず第一に、一般にリザバーは外部入力によって駆動される非自励的な力学系であるため、「カオスの縁」ではなく「条件付き安定性の縁」と呼ぶべきである。さらに、本研究ではこれは単なる用語の問題にとどまらず、「条件付き安定性の縁」が最適な予測性能を提供するとは限らないことを主張する。そのために、「弱い一般化同期」の概念との関連性に注目し、カオス的な入力によって駆動されるランダム神経回路網が弱い一般化同期を示すことを実証し、一般化同期の特性と予測性能との関係について議論する。

12:00-12:10 Closing 

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Supported by

• JSPS Grant in aid for scientific research (B) 21H01002 (PI: Yuzuru Sato)

• JSPS Grant in aid for scientific research (C) 23K03188 (PI: Yushi Nakano)

• JSPS Grant in aid for scientific research (B) 23K2578503 (PI: Takao Namiki)