因為外界的訊息在生物體內傳遞及處理需要時間，因此生物體需要預測物體未來的位置，如此一來才能即時的反應，成功得躲避獵殺或者捕獲食物。透過等速運動以及方向反轉光帶的研究，科學家們發現這樣的預測行為早在視網膜的反應就已經開始了。然而這樣的刺激過於簡單，因為在自然界中，生物體接觸到的刺激總是含有許多的雜訊。因此，我們利用隨機運動光帶來刺激牛蛙的視網膜以及利用時變互信息的分析來研究神經節細胞的預測行為。藉由時變互信息，我們可以計算物體位置和視網膜發放頻率之間共享的訊息含量。研究結果顯示在含有雜訊的隨機運動光帶刺激底下，視網膜也展現了預測物體未來位置的編碼能力。我們更進一步測試不同的刺激性質對於預測能力的影響，結果發現光帶運動的方位、刺激的相關時間以及刺激的統計性質都會影響視網膜對於物體未來位置的預測編碼。在這些影響的因素中，光帶的運動方位對於預測能力的影響和前人的等速運動光帶的研究形成了強烈的對比。在等速運動光帶的研究中，刺激的運動方位對於視網膜預測未來的位置是沒有影響的。因此，我們認為未來在視網膜的預測編碼研究中，關於光帶的運動方位和預測編碼之間的關係是一個值得投入的方向，會對視網膜神經迴路的建構帶來更多的了解。

To successfully catch the prey or escape from hunting, organisms need to make prediction of the future trajectory of the object in order to compensate the time delay resulting from signal transmission and processing. The anticipative ability of retina has been demonstrated in simple motion such as a moving bar with constant velocity or with directional reversal. However, these studies lack a general applicability under noisy stimulations as in most cases in nature. Therefore, a stochastic moving bar is applied to the bullfrog’s retina and we use time-shifted mutual information to quantify the predictive information shared between bar positions and firing rates of a single ganglion cell. Results show that retina reveals predictive computation of the future bar position under stochastic moving bar. Furthermore, we found that the orientation of moving bar, correlation times and the statistics of motion will influence the retinal prediction ability of future position. Among these factors, the orientation-selective prediction of HMM forms a stark contrast to the predictive firing pattern under motion with constant velocity, which is general in different motion orientations. More concentrated studies of the effect of motion orientation on prediction is needed in order to understand the retinal circuit of prediction.

1 Introduction 1
1.1 Retina as a study model 1
1.2 Anticipative computation of retina under simple motion 4
1.3 Characterizing predictive information under stochastic stimulation 10
1.4 Purpose and organization of the thesis 11
2 Material and Method 14
2.1 Sample preparation 14
2.2 Experimental setup 15
2.3 Recording and data processing 16
2.3.1 Recording setup 16
2.3.2 Spike sorting 19
2.4 Calibration of stimulation 21
2.4.1 Calibration for spatial distortion of stimuli image 22
2.4.2 Calibration for luminance distortion of stimuli image 23
2.4.3 Recalculating bar positions 25
2.5 Stimulation forms and protocols 26
2.5.1 Stimulation protocols 26
2.5.2 Moving bar with direction reversal 29
2.5.3 Stochastic motion: Hidden Markovian model (HMM) 29
2.5.4 Stochastic motion: Ornstein Uhlenbeck process (OU) 31
2.5.5 Flickering checkerboard 34
2.6 Visual stimulation problems of skipped/delayed frames 35
2.7 Analysis method 38
2.7.1 Information Theory 38
2.7.2 Spike trigger average 40
2.7.3 Categorizing MI types under HMM stimulation 42
3 Results 45
3.1 Receptive field 45
3.2 Response under motion with constant velocity 49
3.3 Response of motion reversal 51
3.4 Firings across space under HMM moving bar 54
3.5 Mutual information under HMM stimulation 55
3.6 Different responses of MI under various correlation times 56
3.7 Analysis of cells with MI trend of P type and N type 62
3.8 Orientation-selective prediction of MI 66
3.9 Comparison to OU stimulation 69
3.10 STA of electrodes locating at different positions 72
4 Conclusion and Discussions 75
4.1 Firing pattern under HMM stimulation 75
4.2 Prediction defined by MI peak location 77
4.3 Orientation-selective prediction of HMM moving bar 78
4.4 Higher order encoding - comparison to OU 79
4.5 Conclusion and future work 80
Reference 81
Supplementay material 85

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