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capturing the variations in the target output random
variables of interest (e. g. , classes). The optimization effect
is more difficult to tease out because the top two layers of a
deep neural net can just overfit the training set whether the
lower layers compute useful features or not, but there are | [
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these factors would typically be relevant for any particular
example, justifying sparsity of representation. These factors
are expected to be related to simple (e. g. , linear) depen-dencies, with subsets of these explaining different random
variables of interest (inputs, tasks) and varying in struc- | [
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] |
domain, while only unlabeled data DTare available in the
target domain. More specifically, let the source domain data
beDS={(xS1, yS1), . . . , ( xSn1, ySn1)}, w h e r e xSi∈Xis the
input and ySi∈Yis the corresponding output. Similarly, let
the target domain data be DT={xT1, . . . , xTn2}, w h e r et h e | [
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] |
the distance (measured w. r. t. the MMD) between the projected
source and target domain data while maximizing the embeddeddata variance. By virtue of the kernel trick, it can be shown that
the MMD distance in Section III-A can be written as tr (KL), where K=[φ(x
i)⊤φ(xj)], a n d Lij=1/n2
1ifxi, xj∈XS, | [
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] |
(i, j)∈Nmij[W⊤K]i−[W⊤K]j2
=tr(W⊤KLKW). (11)
B. Formulation and Optimization Procedure
Combining all three objectives, we thus want to find a W
that maximizes (10) while simultaneously minimizing (5) and(11). The final optimization problem can be written as
min
Wtr(W⊤KLKW )+μtr(W⊤W)+λ
n2tr(W⊤KLKW) | [
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] |
208 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 22, NO. 2, FEBRUARY 2011
0 5 10 15 20 25 30 35 40 45 50 551. 52. 54. 58153055100
# DimensionsAED ( unit: m)KPCA
SSTCATCA
TCARed uced
SSA
(a)0 100 200 300 400 500 600 700 800 9002345678
# Unlabeled Data in the Tar get Domain for Trainin gAED ( unit: m)RLSR | [
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72. 33 (2. 32) 75. 86 (1. 55) 76. 70 (1. 05) 81. 59 (1. 36) 90. 51 (0. 70)
TCAlinear 10 70. 41 (6. 84) 87. 67 (2. 12) 82. 83 (3. 07) 84. 51 (5. 04) 89. 79 (2. 54) 88. 67 (3. 01)
kernel 20 69. 04 (5. 07) 81. 52 (8. 86) 83. 86 (3. 24) 82. 23 (2. 64) 89. 73 (4. 04) 92. 03 (2. 05)
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84. 44 (2. 29) 79. 81 (4. 20) 91. 81 (2. 38) 92. 23 (2. 41)
Laplacian 10 69. 12 (13. 27) 78. 68 (8. 23) 79. 58 (8. 12) 69. 02 (5. 31) 82. 29 (2. 57) 90. 01 (1. 02)
kernel 20 69. 37 (11. 22) 79. 57 (4. 31) 78. 71 (9. 22) 74. 71 (3. 01) 85. 59 (1. 59) 92. 68 (1. 12)
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74. 40 (2. 49) 87. 89 (2. 22) 92. 63 (0. 84)
RBF 10 74. 88 (3. 51) 82. 51 (7. 65) 78. 34 (6. 58) 81. 65 (4. 08) 82. 69 (2. 24) 89. 15 (0. 69)
kernel 20 72. 60 (5. 60) 77. 47 (2. 62) 78. 09 (6. 88) 79. 54 (1. 89) 83. 51 (3. 32) 90. 77 (0. 83)
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kernel 20 64. 28 (3. 48) 60. 69 (14. 87) 77. 45 (5. 30) 78. 19 (4. 17) 86. 71 (3. 36) 91. 81 (2. 13)
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Laplacian 10 75. 29 (3. 92) 79. 84 (5. 03) 72. 70 (10. 69) 73. 10 (2. 10) 85. 26 (2. 25) 91. 72 (0. 64)
kernel 20 71. 99 (4. 73) 81. 77 (3. 44) 72. 99 (9. 99) 74. 94 (2. 28) 84. 28 (1. 27) 92. 47 (0. 74)
30 69. 71 (4. 99) 82. 09 (4. 42) 72. 34 (10. 82) 74. 67 (1. 79) 85. 30 (1. 80) 92. 73 (0. 76)
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73. 76 (3. 25) 74. 50 (7. 85) 78. 51 (7. 50) 77. 61 (1. 49) 83. 09 (. 0287) 90. 35 (1. 18)
kernel 20 70. 87 (7. 51) 75. 49 (6. 67) 79. 28 (7. 20) 79. 46 (1. 27) 80. 02 (. 0287) 90. 62 (0. 83)
30 70. 16 (5. 98) 77. 03 (5. 56) 79. 06 (7. 60) 79. 88 (1. 52) 81. 30 (. 0287) 90. 21 (0. 96)
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88. 26 (5. 85) 68. 59 (10. 00) 81. 42 (6. 67) 87. 33 (3. 56) 91. 24 (1. 84)
kernel 20 69. 18 (6. 27) 82. 59 (7. 07) 71. 46 (7. 41) 80. 22 (3. 81) 89. 49 (3. 34) 93. 44 (1. 92)
30 70. 55 (2. 81) 80. 94 (11. 63) 78. 90 (8. 33) 77. 92 (4. 32) 91. 36 (1. 51) 93. 66 (1. 81)
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54. 42 (7. 33) 80. 37 (. 0252) 58. 87 (4. 97) 58. 47 (2. 35)
kernel 20 49. 08 (10. 46) 55. 67 (6. 35) 50. 42 (1. 01) 72. 67 (. 0252) 75. 71 (6. 83) 73. 94 (3. 75)
30 45. 24 (8. 17) 63. 13 (7. 76) 50. 43 (1. 03) 69. 36 (. 0252) 75. 07 (10. 64) 74. 18 (4. 24)
RBF 10 53. 82 (6. 23) 78. 50 (4. 23) 51. 64 (2. 11) | [
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fects of randomness are seen to be controlled. Some results oftheparticleswarmoptimizer, usingmodificationsderivedfromtheanalysis, arepresented;theseresultssuggestmethodsforal-
tering the original algorithm in ways that eliminate some prob-
lemsandincreasetheoptimizationpoweroftheparticleswarm. II. A | [
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] |
choice. The probabilities for messages are implicitly determined bystating
oura priori knowledge of the enemy's language habits, thetactical situation
(which will influence the probable content of the message) and any special
information we may have regarding the cryptogram. . . . . , ~. , . . . ----::;:;~ | [
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] |
integers. Thus, for d=5, we might have 2 3 1 54as the permutation. This means that:
mim2mam4m6m6m7ms mg mlO. . . becomes
~ma mi m«m4m7msm6mIDmg. . . . Sequential application of two or more transpositions will be called compound
transposition. Ifthe periods are dl, d2, "', d. it isdear that the result is | [
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] |
6. Matrix System?
One method ofn-gram substitution is to operate on successive n-grams
with a matrix having an inverse. The letters are assumed numbered from
oto25, making them elements of an algebraic ring. From the n-gram m, m~. . . m;of message, the matrix ajjgives an n-gram of cryptogram
"e, =Lau m, | [
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] |
674 BELL SYSTEM TECHNICAL JOURNAL
bethesame as theMspace, i. e. that thesystem beendomorphic. The
fractional transposition is as homogeneous as the ordinary transposition
without being endomorphic. The proper definition is the following: A cipher
Tispure if for every T, , T, , T»there is a T. such that | [
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] |
identifying Bwith the message gives the second result. The last result fol
lows from
[fB(M) ~HB(K, M) =HE(K)+HB. K(M)
and the fact that HB, K(M) =0 since KandEuniquely determine M. Since the message and key are chosen independently we have:
H(M, K)=H(M)+H(K). Furthermore, H(M, K)=H(E, K)=H(E)+HE(K), | [
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] |
tions of the system. The lower limit is achieved if all the systems R, S, . . . , Ugo to completely different cryptogram spaces. This theorem is also
proved by the general inequalities governing equivocation, HAB)sH(B) ::::;H(A)+HA(B). Weidentify Awith the particular system being used and Bwith the key | [
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-0.030040884390473366,
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0.035630084574222565,
-0.09731242060661316,
0.05315323546528816,
0.01810373179614544,
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0.007897724397480488,
-0.029294461011886597,
0.026126280426979065,
0.04418908804655075,
0.002489208709448576,
-0.06768801063299179,
0.0363021194934845,
-0.06471896916627884,
0.04184487462043762,
-0.0021577132865786552,
-0.04681945964694023,
-0.05126263573765755,
0.0017427902203053236,
0.019658299162983894,
-0.015206621028482914,
-0.009855061769485474,
-0.041596781462430954,
-0.023180902004241943,
0.047679875046014786,
0.023363905027508736,
-0.00754965515807271,
0.04555603489279747,
-0.04148498922586441,
0.01241979468613863,
-0.0022912246640771627,
-0.05501934885978699,
0.07137630879878998,
0.02090446464717388,
0.05861096456646919,
0.0270913727581501,
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-0.0024646352976560593,
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0.04220058023929596,
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0.017143217846751213,
0.00722554000094533,
0.02272479236125946,
0.08328349143266678,
0.042165618389844894,
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0.06521885842084885,
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0.0019481431227177382,
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0.0006837655091658235,
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2.6469749059288006e-7,
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0.022487854585051537,
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-0.04867464303970337,
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0.05087244138121605,
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0.01064974907785654,
-0.008610410615801811,
0.019020123407244682,
0.03770553693175316,
0.0120399110019207,
0.027697887271642685,
0.04293489083647728,
0.012549703940749168,
0.048583053052425385,
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0.01716724969446659,
0.010101406835019588,
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0.01932760514318943,
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0.03968210518360138,
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0.014807562343776226,
0.012248361483216286,
-0.015801947563886642,
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0.021711919456720352,
0.047303494065999985,
0.006308925803750753,
-0.015022212639451027,
0.021728169173002243,
2.428735943925709e-34,
0.0006247815326787531,
-0.06547459959983826,
0.03778478503227234,
0.011857555247843266,
-0.01970515586435795,
0.000453638203907758,
0.04795624688267708,
-0.032667260617017746,
0.06426995992660522,
-0.03385606408119202,
-0.0020649991929531097
] |
for 0 and 1, and successive letters chosen independently. We have
HB(M) =HB(K) = -L: P(E)PB(K) logP. (K)
The probability that Econtains exactly sO's in a particular permutation is:
!(p. qN-. +q'pN-. )
""-, \ r-, \ r-, \<, "-<, \<, . . . . . . . P"'11, q"'1~
\r-, . . . . . . . \i""""--. r-. . I
f\r--r-. \ --\. | [
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0.008282099850475788,
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692 BELL SYSTEM TECHNICAL JOURNAL
mkeys from high probability messages each with probabilityf. Hence the
equivocation is:
T k(k)(S)m( s)~m -L: - 1 - - InlogmSkm_1 m T T
We wish to find a simple approximation to this when kis large. Ifthe
expected value of m, namely iii=SkiT, is»1, thevariation of log m | [
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] |
each L, weighted in accordance with its Pi. The mean equivocation char
acteristic will be a line somewhere in the midst of these ridges and may not
give a very complete picture of the situation. This is shown in Fig. 11. A
similar effect occurs if the system is not pure butmade up of several systems | [
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] |
secrecy" afforded by the system. For a simple substitution on English the work and equivocation char
acteristics would be somewhat as shown in Fig, 12. The dotted portion of. :". . . . . . -. \, , , , , , , \, . , ', I, . , . •, , . I•, , , •, , , , , , , , , , , . , , . Fig. 12-Typical work and equivocation characteristics. | [
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] |
therefore be complex in the kj, and involve many of them. Otherwise the
enemy can solve the simple ones and then the more complex ones by sub
stitution. From thepoint of view of increasing confusion, it is desirable to have the
f. involve several mi, especially ifthese are not adjacent and hence less | [
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(e-mail: cheewooi@iastate. edu; liu@iastate. edu; gmani@iastate. edu). Digital Object Identifier 10. 1109/TPWRS. 2008. 2002298Since the 1970s, the control center framework has gradually
evolved from a closed monolithic structure to a more opennetworked environment. With the recent trend of using stan- | [
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0.02671477198600769,
0.011532084085047245,
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0.00565449520945549,
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2.9043333818399737e-34,
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0.014011957682669163,
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0.01256561279296875,
-0.018941493704915047,
0.03530603274703026
] |
, represents the level
of impact on a power system when a substation is removed, i. e. , electrically disconnected, by switching actions due to the attack. The impact caused by an attack through an access point will
be evaluated by a logic- and power flow-based procedure. The
steady state probabilities | [
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0.012783889658749104,
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0.010205082595348358,
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0.01967683993279934,
0.0008378201746381819,
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0.050690460950136185,
0.0000014572671034329687,
0.008700431324541569,
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0.04710628092288971,
0.019070379436016083,
0.012229138053953648,
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0.012889666482806206,
0.013678085058927536,
0.01430569402873516,
0.017763540148735046,
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0.07893995940685272,
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0.009283777326345444,
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0.004052178468555212,
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0.04538818821310997,
0.007156153209507465,
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0.025098349899053574,
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0.0019235539948567748,
0.09272405505180359,
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0.042093612253665924,
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0.002214965410530567,
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0.04853988066315651,
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0.0003339129325468093,
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0.004730090498924255,
0.052182409912347794,
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0.016863664612174034,
0.04601389542222023,
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bound on transmission rate of 2, 3, and 4 b/s/Hz. It follows also from the above that there is a fundamental
tradeoff between constellation size, diversity, and the trans-mission rate. We relate this tradeoff to the trellis complexityof the code. Lemma 3. 3. 1: The constraint length of an
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uses the RBF kernel, whose two optimal hyperparame-
tersσandλ(the regularization parameter to balance the
training and testing errors) can be determined by fivefold
cross validation in the range σ=[2−3, 2−2, . . . , 24]and
λ=[10−2, 10−1, . . . , 104]. 4) For the 1-D CNN, we use one convolutional block, | [
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] |
including a 1-D convolutional layer with a filter size
of 128, a BN layer, a ReLU activation layer, and a
softmax layer with the size of P, w h e r e Pdenotes the
dimension of network output. 3https://www. csie. ntu. edu. tw/ ∼cjlin/libsvm/TABLE IV
GENERAL NETWORK CONFIGURATION IN EACH LAYER OF OURFUNET. | [
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