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Creation and control of Fractal spatiotemporal hierarchical structure

分形时空层次结构的创建与控制

基本信息

批准号：
17300069
负责人：
GOHARA Kazutoshi
金额：
$ 10.07万
依托单位：
Hokkaido University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17300069/
关键词：
Nonlinear Dynamics Fractal Hierarchy Cultured Neuron Multi-electrode Ssytem 培養ニュートン

项目摘要

views the system as being closed, I.e. an autonomous system. Another views the system as being open, I.e. a non-autonomous system. The former approach assumes the external environment to be composed of constituent subsystems. In relation to this approach, many researchers have been interested in chaotic phenomena. Consequently, for the autonomous system, chaos has been established as a prominent research area that might be key to developing an understanding of complex systems in nature. On the other hand, the investigation into non-autonomous systems is still in its initial phase, and no clear theoretical framework has yet been established. We believe that the main reason that little research has thus far been done in this area is the difficulty in examining the interaction between systems. Therefore, we must attempt to determine how we can describe this interaction from a dynamical systems point of view. A theory for continuous dynamical systems stochastically excited by temporal exte … More rnal inputs has been presented. The theory suggests that the dynamics of continuous-time recurrent neural networks (RNNs) is generally characterized by a set of continuous trajectories with a fractal-like structure in hyper-cylindrical phase space. We refer to this dynamics as the fractal transition. Three types of numerical experiments are discussed in order to investigate the learning process and noise effects in terms of the fractal transition. First, to analyze how an RNN learns desired input {output transformations, a simple example with a single state was examined in detail. A fractal structure similar to a Cantor set was clearly observed in the learning process. This finding sheds light on the learning of RNNs, I.e. it suggests that the learning is a process of adjusting the fractal dimension. Second, input noise effects on the fractal structure were investigated. The results show that small-scale hierarchical structures are broken by noise. Third, using a network with twenty states, we show that fractal transition is a universal characteristic of RNNs driven by switching inputs. Less

将系统视为封闭的，即自治系统。另一种观点认为系统是开放的，即非自治系统。前一种方法假设外部环境由子系统组成。与这种方法有关，许多研究人员对混沌现象感兴趣。因此，对于自治系统，混沌已被确立为一个突出的研究领域，这可能是理解自然界复杂系统的关键。另一方面，对非自治系统的研究仍处于起步阶段，尚未建立明确的理论框架。我们认为，迄今为止在这一领域很少进行研究的主要原因是难以研究系统之间的相互作用。因此，我们必须试图确定如何从动力系统的角度来描述这种相互作用。受时间外激励的随机连续动力系统的一个理论 ...更多信息已经呈现了RNAL输入。该理论表明，连续时间递归神经网络（RNN）的动力学通常由超圆柱相空间中具有分形结构的一组连续轨迹来表征。我们把这种动力学称为分形过渡。三种类型的数值实验进行了讨论，以调查的学习过程和噪声的分形过渡方面的影响。首先，为了分析RNN如何学习所需的输入输出转换，我们详细研究了一个具有单个状态的简单示例。在学习过程中，可以清楚地观察到类似于Cantor集的分形结构。这一发现揭示了RNN的学习，即它表明学习是一个调整分形维数的过程。其次，研究了输入噪声对分形结构的影响。结果表明，小尺度的等级结构被噪声破坏。第三，使用一个有20个状态的网络，我们证明了分形转换是由切换输入驱动的RNN的普遍特征。少

项目成果

期刊论文数量（0）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

A Policy-Improving System with a Mixture of Bayesian Networks Adapting Agents to Continuously Changing Environments

混合贝叶斯网络的策略改进系统，使代理适应不断变化的环境

DOI：
发表时间：
2006
期刊：
影响因子：
0
作者：
M. Uchida;et. al.;M. Nagayama;J. Sekimoto;M. Nagayama I;Daisuke Kitakoshi
通讯作者：
Daisuke Kitakoshi

Unsupervised Weight Parameter Estimation Method for Ensemble Learning

DOI：
10.1007/s10852-011-9157-1
发表时间：
2011-12
期刊：
Journal of Mathematical Modelling and Algorithms
影响因子：
0
作者：
M. Uchida;Y. Maehara;H. Shioya
通讯作者：
M. Uchida;Y. Maehara;H. Shioya

Anomaly of fractal dimensions observed in stochastically switched systems

DOI：
10.1103/physreve.77.036210
发表时间：
2008-03-01
期刊：
PHYSICAL REVIEW E
影响因子：
2.4
作者：
Nishikawa, Jun;Gohara, Kazutoshi
通讯作者：
Gohara, Kazutoshi

Analysis for Adaptability of Policy-Improving System with a Mixture Model of Bayesian Networks to Dynamic Environments

贝叶斯网络混合模型政策改进系统对动态环境的适应性分析

DOI：
发表时间：
2005
期刊：
KES 2005 Lecture Notes in Artificial Intelligence 3684
影响因子：
0
作者：
J. Motomura;et. al.;J. Motomura;M. Shimizu;内田努;永山昌史;T.Uchida;M.Nagayama;Hiroyuki Shioya and Kazutoshi Gohara;H.Shioya;K.Gohara;M.Uchida;D.Kitakoshi;Daisuke Kitakoshi;Daisuke Kitakoshi
通讯作者：
Daisuke Kitakoshi

Electron Microscope Imaging for Caveolae of Adipocyte

脂肪细胞小窝的电子显微镜成像