系统与计算神经科学MATLAB作业_psychometric function
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1 / 6 Systems and Computational Neuroscience --- Homework #1 Experiment 1 Matlab Code 1 (See Appendix A) is written according to the demands of the homework instruction, by running which a total of 100 click sequences are generated. The 100 click sequences are supposed to be divided into 10 groups, and each group is characterized by a specific ICI ranging from 10 msec to 100 msec in 10 logarithmic steps (that is 10, 12, 16, 21, 27, 35, 46, 59, 77, 100 msec). When the experiment begins, the first click sequence will be released automatically and followed by a pause during which the number 0 or 1 is expected to be input to the computer, and not until then will the second click sequence be released. The computer is programmed to record the number that the subject has input. After the subject hear all the 100 click sequences and input 100 numbers, a 2×100 matrix is given. Every column of the matrix contains two elements: one is the exact ICI of every click sequence and the other is the number that the subject input correspondingly. Then re-arrange the matrix and classify the 100 columns into 10 groups based on the specific ICI. Eventually, the probability that the subject hears click sequences at every ICI as being continuous is obtained. 1) The probability that the subject hears click sequences at every ICI as being continuous: ICI (msec) Number of ‘1’ Number of ‘0’ Probability 10 10 0 100% 12 10 0 100% 16 10 0 100% 21 9 1 90% 27 6 4 60% 35 1 9 10% 46 0 10 0% 59 0 10 0% 77 0 10 0% 100 0 10 0% Table (1) 2 / 6 2) Psychometric function Run Matlab Code 2 (See Appendix B) to present the psychometric function in a chart. The dots in red represent the probability in Table (1). The curve in blue represents the result of cubic interpolation.
Chart (1) Psychometric function for Exp. 1 3) Find the boundary ICI. As is displayed in Chart (1), the threshold is approximately 28.5 msec. It is feasible to tell the demanding ICI with accuracy to 1 decimal place when Matlab Code 2 is applied. Part of the result of the interpolation is displayed in the following table. Result of interpolation: Probability 0.50146 0.50074 0.50001 0.49928 0.49856
0.49783 ICI (msec) 28.52 28.53 28.54 28.55 28.56 28.57 Table (2) As you can see from Table (2), the boundary ICI must be between 28.54 and 28.55 msec. So, the boundary ICI can be determined to be 28.5 msec. 3 / 6 Experiment 2 In experiment 2, we are demanded to obtain psychometric functions for the perception of periodicity and to calculate “boundary jitter” values in three conditions where the mean ICI varies. Matlab Code 3 (See Appendix C) is written for Experiment 2. First in the program, 60 jitter values which can be divided into 6 groups (that is 0%, 5%, 10%, 15%, 20%, 25%, and each group has 10 elements) are generated in a random order. Next, 60 click sequences are generated based on the corresponding jitter value. In every click sequence, ICIs are drawn from a uniform distribution with a deliberately-set mean (10, 30 or 100 msec) and a jitter. After the subject hear a click sequence, a number is asked to be input to the computer and is recorded automatically by the program. Then, psychometric functions and “boundary jitter” values can be achieved in the same way as we do in Experiment 1. (a) Mean ICI: 10 msec The probability that the subject hears click sequences with different jitter values as being periodic: Jitter value Number of ‘1’ Number of ‘0’ Probability 0% 10 0 100% 5% 10 0 100% 10% 4 6 40% 15% 1 9 10% 20% 0 10 0% 25% 0 10 0% Table (3) The psychometric function: (Use Matlab Code 4 which is enclosed as Appendix D)
Chart (2) Psychometric function for Exp. 2(a) 4 / 6 Result of interpolation: Probability 0.5038 0.5025 0.5011 0.4997 0.4984 0.4970 Jitter value(%) 9.07 9.08 9.09 9.1 9.11 9.12 Table (4) The “boundary jitter” value: 9.1% (b) Mean ICI: 30 msec The probability that the subject hears click sequences with different jitter values as being periodic: Jitter value Number of ‘1’ Number of ‘0’ Probability 0% 10 0 100% 5% 10 0 100% 10% 8 2 80% 15% 7 3 70% 20% 3 7 30% 25% 2 8 20% Table (5) The psychometric function: Chart (3) Psychometric function for Exp. 2(b) Result of interpolation: Probability 0.5021
0.5010 0.5000 0.49890 0.49792 0.4969 Jitter value(%) 17.48 17.49 17.50 17.51 17.52 17.53 Table (6) The “boundary jitter” value: 17.5% 5 / 6 (c) Mean ICI: 100 msec The probability that the subject hears click sequences with different jitter values as being periodic: Jitter value Number of ‘1’ Number of ‘0’ Probability 0% 10 0 100% 5% 9 1 90% 10% 6 4 60% 15% 4 6 40% 20% 3 7 30% 25% 2 8 20% Table (7) The psychometric function:
