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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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Neural networks. A neural network is a group of interconnected units called neurons that send signals to one another. neurons can be either biological cells or mathematical models. while individual neurons are simple, many of them together in a network can perform complex tasks. there are two main types of neural
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Neural networks. Neurons in an artificial neural network are usually arranged into layers, with information passing from the first layer (the input layer) through one or more intermediate layers (hidden layers) to the final layer (the output layer). the "signal" input to each neuron is a number, specifically a
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Neural networks. Linear combination of the outputs of the connected neurons in the previous layer. the signal each neuron outputs is calculated from this number, according to its activation function. the behavior of the network depends on the strengths (or weights) of the connections between neurons. a network
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3. 3 Analysis To compare the quantitative performance of the different decoder variants, we use three commonly used perfor- mance measures: global accuracy (G) which measures the percentage of pixels correctly classified in the dataset, class average accuracy (C) is the mean of the predictive accuracy
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FCN 81. 97 54. 38 46. 59 22. 86 82. 71 56. 22 47. 95 24. 76 83. 27 59. 56 49. 83 27. 99 200 K FCN (learnt deconv) 83. 21 56. 05 48. 68 27. 40 83. 71 59. 64 50. 80 31. 01 83. 14 64. 21 51. 96 33. 18 160 K DeconvNet 85. 26 46. 40 39. 69 27. 36 85. 19 54. 08 43. 74 29. 33 89. 58 70. 24 59. 77 52. 23 260 K
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previous section is sharp for the Protocol Model, by exhibiting ascenariowhereitisachieved. Thisscenarioisalsofeasiblefor the Physical Model. Theorem 3. 1: There is a placement of nodes and an as- signment of traffic patterns such that the network can achieve bit-meterspersecondundertheProtocolModel,
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and bit-meterspersecondunderthePhysicalModel, bothwhenever is a multiple of Proof:Consider the Protocol Model. Define Recallthatthedomainisadiskofunitarea, i. e. , ofradius in theplane. Withthecenterofthedisklocatedattheorigin, place transmitters at locations and where is even. Also place receivers at and
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where isodd. Eachtransmittercantransmittoitsnearest receiver, whichisatadistance away, withoutinterferencefrom any other transmitter–receiver pair. It can be verified that there are at least transmitter–receiver pairs all located within thedomain. (This is done by noting that for a tessellation of the
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Lemma 4. 4 for the Physical Model. Theorem 4. 1: (i) ForRandomNetworkson intheProtocolModel, there isadeterministicconstant notdependingon, , or, such that bits per second is feasible whp. ii) ForRandomNetworkson inthePhysicalModel, there aredeterministicconstants andnotdependingon, , , , o r, such that
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Scene Train Test Extent (m) (Uses RGB-D) Nearest Neighbour PoseNet Dense PoseNet King’s College 1220 343 140 x 40m N/A 3. 34m, 2. 96◦1. 92m, 2. 70◦1. 66m, 2. 43◦ Street 3015 2923 500 x 100m N/A 1. 95m, 4. 51◦3. 67m, 3. 25◦2. 96m, 3. 00◦ Old Hospital 895 182 50 x 40m N/A 5. 38m, 4. 51◦2. 31m, 2. 69◦2. 62m, 2. 45◦
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Shop Fac ¸ade 231 103 35 x 25m N/A 2. 10m, 5. 20◦1. 46m, 4. 04◦1. 41m, 3. 59◦ St Mary’s Church 1487 530 80 x 60m N/A 4. 48m, 5. 65◦2. 65m, 4. 24◦2. 45m, 3. 98◦ Chess 4000 2000 3x2x1 m 0. 03m, 0. 66◦0. 41m, 5. 60◦0. 32m, 4. 06◦0. 32m, 3. 30◦ Fire 2000 2000 2. 5x1x1 m 0. 05m, 1. 50◦0. 54m, 7. 77◦0. 47m, 7. 33◦0. 47m, 7. 02◦
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Red Kitchen 7000 5000 4x3x1. 5m 0. 04m, 0. 76◦0. 58m, 5. 65◦0. 59m, 4. 32◦0. 58m, 4. 17◦ Stairs 2000 1000 2. 5x2x1. 5m 0. 32m, 1. 32◦0. 56m, 7. 71◦0. 47m, 6. 93◦0. 48m, 6. 54◦ Figure 6: Dataset details and results. We show median performance for PoseNet on all scenes, evaluated on a single 224x224 center crop
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reprints@ieee. org, and reference the Digital Object Identifier below. Digital Object Identifier no. 10. 1109/TC. 2016. 25199142986 IEEE TRANSACTIONS ON COMPUTERS, VOL. 65, NO. 10, OCTOBER 2016 0018-9340 /C2232016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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The value of corr (U;V) falls in a definite closed interval [/C01, 1]. A value close to either /C01 or 1 indicates a strong rela- tionship between the two variables. A value close to 0 infers a weak relationship between them. Algorithm 2 shows our proposed algorithm based on LCC, and this algorithm is
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(a) Feature ranking results on the KDD Cup 99 dataset Algorithm # Feature Feature ranking FMIFS 19 f5, f23, f6, f3, f36, f12, f24, f37, f2, f32, f9, f31, f29, f26, f17, f33, f35, f39, f34 MIFS ( b¼0:3)2 5 f5, f23, f6, f9, f32, f18, f19, f15, f17, f16, f14, f7, f20, f11, f21, f13, f8, f22, f29, f31, f41, f1, f26, f10, f37
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MIFS ( b¼1)2 5 f5, f7, f17, f32, f18, f20, f9, f15, f14, f21, f16, f8, f22, f19, f13, f11, f29, f1, f41, f31, f10, f27, f26, f12, f28 FLCFS 17 f23, f29, f12, f24, f3, f36, f32, f2, f8, f31, f25, f1, f11, f39, f10, f4, f19 (b) Feature ranking results on the NSL-KDD dataset Algorithm # Features Feature ranking
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FMIFS 18 f5, f30, f6, f3, f4, f29, f12, f33, f26, f37, f39, f34, f25, f38, f23, f35, f36, f28 MIFS ( b¼0:3)2 3 f5, f3, f26, f9, f18, f22, f20, f21, f14, f8, f11, f12, f7, f17, f16, f19, f1, f15, f41, f32, f13, f28, f36 MIFS ( b¼1)2 8 f5, f22, f9, f26, f18, f20, f14, f21, f16, f8, f11, f1, f17, f7, f12, f19, f15, f40, f32, f13, f10, f28, f31, f27, f2, f36, f23, f3
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LSSVM-IDS + FMIFS 99. 46 0. 13 99. 79 98. 76 0. 28 99. 91 99. 64 0. 13 99. 77 LSSVM-IDS + MIFS ( b¼0:3) 99. 38 0. 23 99. 70 95. 96 0. 53 97. 96 98. 59 0. 16 99. 32 LSSVM-IDS + MIFS ( b¼1) 89. 26 0. 34 97. 63 93. 26 0. 47 96. 75 98. 10 0. 58 99. 12 LSSVM-IDS + FLCFS 98. 47 0. 61 98. 41 92. 29 0. 41 96. 45 98. 07 0. 82 98. 99
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LSSVM-IDS + All features 99. 16 0. 97 99. 19 91. 12 0. 38 95. 96 94. 29 0. 33 97. 42 Fig. 2. Building and testing times of LSSVM-IDS using all features and LSSVM-IDS combined with FMIFS, respectively, on three datasets. TABLE 3 Feature Ranking Results for the Four Types of Attacks on the KDD Cup 99 Dataset
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Class # Feature Feature ranking DoS 12 f23, f5, f3, f6, f32, f24, f12, f2, f37, f36, f8, f31 Probe 19 f5, f27, f3, f35, f40, f37, f33, f17, f41, f30, f34, f28, f22, f4, f24, f25, f19, f32, f29 U2R 23 f37, f17, f8, f18, f16, f1, f4, f15, f7, f22, f20, f21, f31, f19, f12, f13, f14, f6, f32, f29, f3, f40, f2
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DR FPR Train ðsÞ TestðsÞ DR FPR Train ðsÞ TestðsÞ 1 96. 01 0. 84 0. 152 0. 246 79. 65 4. 54 1. 823 7. 76 2 97. 01 0. 64 0. 296 0. 396 84. 72 4. 03 3. 463 10. 363 3 97. 13 0. 64 0. 505 0. 656 85. 58 3. 92 5. 26 15. 443 4 97. 18 0. 64 1. 140 1. 343 86. 08 3. 80 9. 662 19. 532 5 97. 26 0. 60 1. 475 1. 773 86. 81 3. 54 11. 302 22. 735
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R2L LSSVM-IDS + FMIFS 90. 08 1. 06 0. 44 PLSSVM + MMIFS 98. 70 54 Overall LSSVM-IDS + FMIFS 97. 33 6. 51 3. 85 PLSSVM + MMIFS 93. 50 21. 4 9. 20TABLE 8 Detection Rate (%) for Different Algorithm Performances on the Test Dataset with Corrected Labels of KDD Cup 99 Dataset (n/a Means no Available Results)
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state transition probability function, and ρi:X×U×X→R, i=1, . . . , n are the reward functions of the agents. In the multiagent case, the state transitions are the result of the joint action of all the agents, uk=[uT 1, k, . . . , uT n, k]T, uk∈ U, ui, k∈Ui(Tdenotes vector transpose). Consequently, the
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available, the task would reduce to a Markov decision process, the action space of which would be the joint action space of the SG. In this case, the goal could be achieved by learning the optimal joint-action values with Q-learning Q k+1(xk, uk)=Qk(xk, uk) +α[ rk+1+γmax u′Qk(xk+1, u′)−Qk(xk, uk)] (7)
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¯h∗ i(x)=argmax uimax u1, . . . , u i−1, ui+1, . . . , u nQ∗(x, u). (8) Fig. 3. (Left) Two mobile agents approaching an obstacle need to coordinate their action selection. (Right) The common Q-values of the agents for the state depicted to the left. However, the greedy action selection mechanism breaks ties
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Q1(x, u1, u2)+Q2(x, u1, u3)+Q3(x, u3, u4). The decompo- sition might be different for different states. Typically (like in this example), the local Q-functions have smaller dimensions than the global Q-function. Maximization of the joint Q-value is done by solving simpler, local maximizations in terms of
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principle to compute strategies and values for the stage games, and a temporal-difference rule similar to Q-learning to propa- gate the values across state-action pairs. The algorithm is given here for agent 1 h 1, k(xk, ·)=argm1(Qk, xk) (13) Qk+1(xk, u1, k, u2, k)=Qk(xk, u1, k, u2, k) +α[rk+1+γm1(Qk, xk+1)
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inherently compositional: secure subsystems combine to form a larger secure system as long as the external type signatures of the subsystems agree. The recent development of seman- tics-based security models (i. e. , models that formalize security intermsofprogrambehavior)hasprovidedpowerfulreasoning
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mitted on the basis of a static analysis of process authority andrelationshipsbetweenprincipals. Securitylabelshaveadditionalstructure that describes the entities capable of performing de-classification. Thismodelsupportsthelabelingofcomputationsperformed on behalf of mutually distrusting principals.
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13:d. Calculate gradient ∇w(l) kand∇b(l) kfor weights∇w(l) kand bias respectively for each layer 14: Gradient calculated in the following sequence 15: i. convolution layer 16: ii. pooling layer 17: iii. fully connected layer 18:e. Update weights 19: w(l) ji←w(l) ji+1w(l) ji 20:f. Update bias 21: b(l)
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e. g. , ears, eyes, etc. , and the third layer can go further up the complexity order by even learning facial shapes of various persons. Even though each layer might learn or detect a defined feature, the sequence is not always designed for it, especially in unsupervised learning. These feature extrac-
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get the best results for specific problems. The training algo- rithms can be finetuned at different levels by incorporating heuristics, e. g. , for hyperparameter optimization. The time to train a deep learning network model is a major factor to gauge the performance of an algorithm or network. Instead
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into the well-known training algorithms and architectures. We highlighted their shortcomings, e. g. , getting stuck in the local minima, overfitting and training time for large prob- lem sets. We examined several state-of-the-art ways to over- come these challenges with different optimization methods.
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Y. Bengio is with the D ´epartement d’Informatique et de Recherche Op´erationelle, Universit ´edeMontr ´eal, Montr ´eal, Qu´ebecH3C3J7Canada. Publisher Item Identifier S 0018-9219(98)07863-3. NN Neural network. OCR Optical character recognition. PCA Principal component analysis. RBF Radial basis function.
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1. Introduction Action recognition methods based on skeleton data have been widely investigated and attracted considerable atten-tion due to their strong adaptability to the dynamic circum-stance and complicated background [31, 8, 6, 27, 22, 29, 33, 19, 20, 21, 14, 13, 23, 18, 17, 32, 30, 34]. Conventional
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is divided into a training set (40, 320 videos)and a validation set (16, 560 videos), where the actors inthe two subsets are different. 2). Cross-view (X-View): thetraining set in this benchmark contains 37, 920 videos thatare captured by cameras 2 and 3, and the validation set con-tains 18, 960 videos
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can be adopted as the loss function to learn the trainable parameters /Theta1in DnCNN. Here {(yi, xi)}N i=1represents N noisy-clean training image (patch) pairs. Fig. 1 illustrates thearchitecture of the proposed DnCNN for learning R(y). I n the following, we explain the architecture of DnCNN and the
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many candidate patches to find the most likely location. /C15The authors are with the Institute of Systems and Robotics, University of Coimbra, Coimbra, Portugal. E-mail: {henriques, ruicaseiro, pedromartins, batista}@isr. uc. pt. Manuscript received 17 Mar. 2014; revised 11 July 2014; accepted 28 July
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The cyclic shifts of each base sample xican be expressed in a circulant matrix Xi. Then, replacing the data matrix X0¼X1 X2. . . 2 643 75in Eq. (3) results in w¼X jX iXH iXiþ/C21I !/C01 XH jy; (60) by direct application of the rule for products of block matri- ces. Factoring the bracketed expression,
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Corresponding author: Young-Gab Kim (alwaysgabi@sejong. ac. kr) This work was supported by the National Research Foundation of Korea (NRF) funded by the Korean Government (MSIT) under Grant 2021R1A2C2012635. ABSTRACT Unlike previous studies on the Metaverse based on Second Life, the current Metaverse
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other hand, another type of object is imaginary animals (e. g. , unicorns, dragons) and anthropomorphic objects (e. g. , talking chairs) that do not exist. 4) SOUND AND SPEECH SYNTHESIS Sound synthesis is a field that gives the user a sense of immersion, but research is insufficient compared to vision.
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much different from what it is now, although a translucent display window tablet is used. 6) DISCUSSION AND OPEN CHALLENGES Player Ready One shows negative aspects of the Metaverse (e. g. , surrogate exam, taste cheating, and mirroring). The problem of over-addiction is explained in the appearance of
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a connection relationship (e. g. , Metaverse access, messenger) must be maintained continuously in a relatively low-spec mobile device that can always be accessed. Using an episodic memory that effectively manages the user’s log allows the user to feel the comfort and advantage of accessing Metaverse
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dimensions three and four are provided. A reader who is only interested in code construction and the application of space–time block codes may choose to read Section V-B, Definition 5. 4. 1, Definition 5. 5. 2, the proof ofTheorem 5. 5. 2, Corollary 5. 5. 1, the remark after Corollary5. 5. 1, and Section V-F.
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during the experiment. The random noise obeys the Gaussian distribution N∈(0, σ2), w h e r e σ∈(0. 2, 0. 4, 0. 8, 1, 2)and the Poisson distribution P(λ), w h e r e λ∈(1, 2, 4, 8, 16). Then, we normalize the values of the noise matrices turn to be between 0 and 1. Using different evaluation metrics, the results
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isitselfalinearsystemwhosecomplexitydecreasesasthenumberof outputquantitiesavailableincreases. Theobservermaybeincorpo- ratedinthecontrolofasystemwhichdoesnothaveitsstatevector availableformeasurement. Theobserversuppliesthestatevector, butattheexpenseofaddingpolestotheover-allsystem. I. INTRODUCTION
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Supposethatsuchatransformation didexist;i. e. , supposethatforallt z(t)=Ty(t). Thetwosystemsaregovernedby y=Ay, x=Bz+Cy, (1) (2)Fig. 1-Asimpleobserver. Fig. 2-Observation ofafirst-ordersystem. So, iftheinitialconditiononz(o)ischosenas az(o)=y(o), X_p thenforallt>0, az(t)=y(t), butusingtherelationz=Ty,
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Assume, now, thattheplantorsystem, Si, thatisto beobservedisgovernedby y=Ay+Dx, (11) wherexisaninputvector. Asbefore, anobserverfor thissystemwillbedrivenbythestatevectory. In addition, itisnaturaltoexpectthattheobservermust alsobedrivenbytheinputvectorx. Considerthesys- temS2governedby =Bz+Cy+Gx. (12)
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Luenberger: StateofaLinearSystem Proof:AsafirstattemptletS1drivethenth-order system Mi 0= OFig. 4-Reduction ofthedynamicorder. 011 Y2 1Z+V I. AnIjjJ(22) Itisappropriate atthispointtoreviewthedefinitions ofcontrollability andobservability forlineartime- invariantsystems. Adiscussionofthephysicalinter-
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controllable. LetTbetheuniquesolutionofTA-BT =ba'. ThenTisinvertible. WiththisTheoremitiseasytoderivearesultconcern- ingthedynamicorderofanobserverforasingleoutput system. Theorem3:LetSi:y=Ay, v=a'ybeannth-order completelyobservablesystem. Let1, u2, . . I*nbea setofdistinctcomplexconstantsdistinctfromthe
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x=c'ytheresultingclosed-loop systemwillhave AliA2***, A, asitseigenvalues. Proof:Firstassumethateach, uiisdistinctfromthe eigenvalues ofA. LetBbeamatrixinJordanform whichhastheuiasitseigenvaluesandhasonlyone Jordanblockassociatedwitheachdistincteigenvalue[31. Letc1beanyvectorsuchthat(B, c1')iscompletely
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server, S2, maybebuiltforS1usingonlyn-mdynamic elements. (Asillustratedbytheproof, theeigenvalues oftheobserver areessentiallyarbitrary. ) Proof:Letthemoutputsbegivenbyal'y, a2'y, * ainy. ThensinceS1iscompletelyobservablethecollec- tionofvectors (A')iaji-O1, l2, *, n1 j. 1-1, 2;, *, m spansndimensions.
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Lemma1guaranteesthateachbiisnotzero. Itwillbeshownthatthevectors(A'-ujI)-'aj, i=1, 2, **, p, generatethesamespaceasthevectors (A')ka, , k=1, 2, **, n. Assumethatwecanfindai's suchthat p ai(A'-ujI) =0. (42) i=1 Thiscanberewritten as P(A')fi(A-ujI)-l =0(43) i=lwherePisapolynomialofdegreelessthanp. Butsince
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