self-tuning and stochastic resonance-theory and application of information processing with use of noise

(A)自校正和随机共振-阈值系统的数学方面我们选择一个阈值和噪声强度作为简单阈值系统的重要参数，通过对这些参数单独或同时应用自校正机制，我们基于互信息和信噪比来估计系统的性能。我们还研究了阈值对缓慢变化的外部输入信号的响应。由于反馈的作用，我们发现阈值系统的响应变慢了，并且出现了遍历-非遍历的转变。(B)自校正和随机共振-双态系统的数学方面。作为双势垒系统的近似描述，д双态系统得到了深入的研究。在两态模型中引入了自校正的机理，研究了自校正的影响，讨论了自校正与随机共振的关系。(C)自校正和信息处理-滤波及其在图像处理中的应用基于自校正的思想解释了我们的听觉系统的高灵敏度。放置听觉系统的环境可能非常嘈杂或非常安静。因此，为了获得与环境无关的良好性能，我们希望有某种机制来调整阈值以适应环境的噪声强度。(D)Fitzhugh-Nagumo模型中的随机共振。Fitzhugh-Nagumo模型通常用一个微分方程来描述。引入并定义了连续时间系统的互信息(M)，讨论了基于互信息的随机共振

(A) selftuning and stochastic resonance-mathematical aspects of threshold systemsWe choose a threshold value and the noise intensity as important parameters to characterize a simple threshold system.By applying the self-tuning mechanism to these parameters, separately or simultaneously, we estimate perforniance of the system based on mutual information and signal to noise ratio (SNR). We also studied how the response of the threshold value to slowly varying external input signals.. Due to the feedback we found that the response become slower and there occurs an ergodic-nonergodic transition in the threshold system.(B) self-tuning and stochastic resonance-mathematical aspects of two-state system.As an approximate description of the double-well system,дwo-state system has been studied intensively. We introduced the mechanism of self-tuning to the two-state model and studied its effects and discussed the relation between the self-tuning and stochastic resonance.(C) self-tuning and information processing-filtering and its application to picture processing High sensitivity of our auditory system is explained based on the idea of selftuning. The environment where the auditory system is put may be very noisy or very quiet. So in order to achieve good performance irrespective of the environment it is put in, it is desirable to have some mechanism by which we can adjust the threshold value to the noise intensity of the environment. We applied this idea to the picture reproduction in conjunction with the filter theory.(D) Stochastic resonance in the FitzHugh-Nagumo model.The FitzHugh-Nagumo model is usually described by a differential equation. We introduce and define the mutual information (M) to this Continuous time system and discussed stochastic resonance based on the MI