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5 will position neuron ab closer to kj, with the chance that more patterns will be removed from neuron kj A value larger than 05 will have the opposite effect The quantization error threshold, A, is important to ensure that a sufficient map size is constructed A small value for A may result in too large a map architecture, while too large a A may result in longer training times to reach a large enough architecture An upper bound on the size of the map is easy to determine: it is simply the number of training patterns, PT This is, however, undesirable The maximum map size is rather expressed as PT, with (3 6 (0, 1) The optimal value of is problem dependent, and care should be taken to ensure that is not too small if a growing SOM is not used.

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12. Develop a ciphertext only attack on the Enigma, assuming that all you know about the plaintext is that it is English. Analyze the work factor of your proposed attack and also estimate the minimum amount of ciphertext necessary for your attack to succeed. Assume that Enigma rotors, the rotor order, the movable ring positions, and the reflector are all known. Then you need to solve for the initial settings of the three rotors and the stecker. Hint: Since E is the most common letter in English, guess that the plaintext is EEEEEE.. . and use this noisy plaintext to solve for the rotor and stecker settings.

The first time you go to export your images to Facebook, you need to set up access to your Facebook account from within Aperture. Start by selecting a group of images to share.

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13. Suggest niodifications to the Enigma design that would make the attack discussed in Section 2.2 infeasible. Your objective is to make minor modifications to the design.

If this is the case, the final map may not converge to the required quantization error, since the map size will be too small..

14. Suppose that the sixes in the Purple cipher consist of the vowels, AEIOUY. What is the expected frequency of each of the sixes and what is the expected frequency of each of the twenties Suppose instead that the sixes consist of JKQVXZ. What is the expected frequency of each of the sixes and what is the expected frequency of each of the twenties To answer these questions, use the English letter frequency distribution given in Table 1.3 in 1.

1. 2.

15. Consider the Purple cipher. For each of the = 217.8 choices for the sixes, let E6 be the average frequency for each of the sixes letters and

the let Ezo be the average frequency for each of the corresponding twenties letters. For how many of these 217.8 selections is - E 0 < 0.1 21 To answer this question, use the English letter frequency distribution in Table 1.3 in 1.

Training of SOMs is slow, due to the large number of weight updates involved (all the weights are updated for standard SOM training) . Several mechanisms have been developed to reduce the number of training calculations, thereby improving speed of convergence. BatchMap is one such mechanism. Other approaches include the following:

Choose File Share Facebook. Aperture asks if you want to set up access to your Facebook account. Click the Set Up button. Type your login e-mail and password in the Facebook Login sheet that appears, as shown in Figure 8.30. To have Aperture store your Facebook information, select the Keep me logged in to Aperture Uploader check box. If you don t have a Facebook account, click the Sign up for Facebook link at the bottom left of this sheet to create an account.

16. Suppose that we have two ciphers, both of which encrypt elements of { 0 , 1 , 2 , .. . ,7} using permutations, where the permutation varies with each step. One of these, known as cipher A , is a rotor machine, analogous to the Enigma, while the other, known as cipher B , is a switch-based machine, analogous to Purple. Which of the permutations P,Q, . . . , W , below, could have been generated by the A cipher and which could have been generated by the B cipher In each case, justify your answer.

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