text:
## Search Result

### Search Conditions

Years
All Years
for journal 'PTP'
author 'Y.* Yamaguchi' : 133
total : 133

### Search Results : 133 articles were found.

1. Progress of Theoretical Physics Vol. 3 No. 4 (1948) pp. 462-463 :
On the Proton-Decay in Cosmic-ray Stars
Y. Fujimoto and Y. Yamaguchi
2. Progress of Theoretical Physics Vol. 4 No. 1 (1949) pp. 101-102 :
Interpretation of Bursts in Thin-Walled Chambers
Y. Fujimoto and Y. Yamaguchi
3. Progress of Theoretical Physics Vol. 4 No. 2 (1949) pp. 230-231 :
On the Nucleon Component in Cosmic Rays
Y. Fujimoto and Y. Yamaguchi
4. Progress of Theoretical Physics Vol. 4 No. 2 (1949) pp. 233-235 :
Cosmic-Ray Bursts under Thick Shields
Y. Fujimoto, S. Hayakawa and Y. Yamaguchi
5. Progress of Theoretical Physics Vol. 4 No. 3 (1949) pp. 381-382 :
On the Electronic Component in Extensive Air Showers
Y. Fujimoto, S. Hayakawa and Y. Yamaguchi
6. Progress of Theoretical Physics Vol. 4 No. 4 (1949) pp. 468-476 :
On the Nuclear Stars
Yoichi Fujimoto and Yoshio Yamaguchi
7. Progress of Theoretical Physics Vol. 4 No. 4 (1949) pp. 569-569 :
Y. Yamaguchi
8. Progress of Theoretical Physics Vol. 4 No. 4 (1949) pp. 570-571 :
The another $\tau$-Meson
S. Hayakawa and Y. Yamaguchi
9. Progress of Theoretical Physics Vol. 4 No. 4 (1949) pp. 571-571 :
Directional Distribution of Extensive Air Showers
Y. Fujimoto, S. Hayakawa and Y. Yamaguchi
10. Progress of Theoretical Physics Vol. 4 No. 4 (1949) pp. 575-576 :
Remarks on the Nuclear Disintegration by Meson Capture
Y. Fujimoto, S. Hayakawa and Y. Yamaguchi
11. Progress of Theoretical Physics Vol. 4 No. 4 (1949) pp. 576-577 :
Nuclear Disintegration by $\pi$-Meson Capture
Y. Fujimoto, S. Hayakawa and Y. Yamaguchi
12. Progress of Theoretical Physics Vol. 4 No. 4 (1949) pp. 579a-579a :
Neutron Component in Extensive Air Showers
Y. Fujimoto, S. Hayakawa and Y. Yamaguchi
13. Progress of Theoretical Physics Vol. 5 No. 1 (1950) pp. 76-81 :
Note on Very Large Cosmic-Ray Stars
Yoichi Fujimoto and Yoshio Yamaguchi
14. Progress of Theoretical Physics Vol. 5 No. 1 (1950) pp. 141-142 :
The Range and the Mean Free Path of High Energy Nucleons in Nuclear Matter
Y. Fujimoto and Y. Yamaguchi
15. Progress of Theoretical Physics Vol. 5 No. 1 (1950) pp. 142-143 :
Notes on High Energy Nuclear Evaporation
Y. Yamaguchi
16. Progress of Theoretical Physics Vol. 5 No. 1 (1950) pp. 143-144 :
Note on High Energy Induced Fission of Bi
Y. Yamaguchi
17. Progress of Theoretical Physics Vol. 5 No. 2 (1950) pp. 196-206 :
The Electronic Component in Extensive Air Showers
Yoichi Fujimoto, Satio Hayakawa and Yoshio Yamaguchi
18. Progress of Theoretical Physics Vol. 5 No. 2 (1950) pp. 318-318 :
Nucleon-Nucleon Interaction at High Energies
F. Fujimoto, S. Hayakawa and Y. Yamaguchi
19. Progress of Theoretical Physics Vol. 5 No. 2 (1950) pp. 332-333 :
The Effect of Exclusion Principle on the Nucleon-nucleon Scattering in Nuclear Matter
Y. Yamaguchi
20. Progress of Theoretical Physics Vol. 5 No. 3 (1950) pp. 498-500 :
The Fast Protons in $\pi^-$-Meson Stars
Y. Fujimoto, K. Takayanagi and Y. Yamaguchi
21. Progress of Theoretical Physics Vol. 5 No. 3 (1950) pp. 501-502 :
Order of Magnitude Theory of the Depression of Coulomb Barrier Height in Highly Excited Nuclei
Y. Yamaguchi
22. Progress of Theoretical Physics Vol. 5 No. 4 (1950) pp. 669-681 :
On the Prodution of Cosmic Ray Mesons
Yoichi Fujimoto, Hiroshi Fukuda, Satio Hayakawa and Yoshio Yamaguchi
23. Progress of Theoretical Physics Vol. 5 No. 5 (1950) pp. 787-799 :
High Energy Nuclear Evaporation
Yoichi Fujimoto and Yoshio Yamaguchi
24. Progress of Theoretical Physics Vol. 5 No. 5 (1950) pp. 870-882 :
Effect of Nuclear Binding on Meson Production
Y. Fujimoto, K. Nishijima, T. Okabayashi, K. Takayanagi and Y. Yamaguchi
25. Progress of Theoretical Physics Vol. 5 No. 5 (1950) pp. 894-896 :
Notes on Fluctuation in Nuclear Evaporation Process
K. Takayanagi and Y. Yamaguchi
26. Progress of Theoretical Physics Vol. 5 No. 5 (1950) pp. 896-897 :
On the Stars of Light Nuclei
Y. Yamaguchi
27. Progress of Theoretical Physics Vol. 5 No. 5 (1950) pp. 904b-906 :
On the Nuclear Stars
Y. Yamaguchi
28. Progress of Theoretical Physics Vol. 5 No. 6 (1950) pp. 931-947 :
On the Negative $\pi$-Meson Capture
K. Aidzu, Y. Fujimoto, H. Fukuda, S. Hayakawa, K. Takayanagi, G. Takeda and Y. Yamaguchi
29. Progress of Theoretical Physics Vol. 6 No. 2 (1951) pp. 166-174 :
Mesonic Processes in Two-Nucleon System
Yoichi Fujimoto and Yoshio Yamaguchi
30. Progress of Theoretical Physics Vol. 6 No. 2 (1951) pp. 254-256 :
On the Excited States of Even Nuclei
H. Horie, M. Umezawa, Y. Yamaguchi, and S. Yoshida
31. Progress of Theoretical Physics Vol. 6 No. 2 (1951) pp. 260-261 :
Remarks on the Production of Cosmic-Ray Mesons
Y. Yamaguchi
32. Progress of Theoretical Physics Vol. 6 No. 3 (1951) pp. 408-425 :
Nuclear Shell Model and the $\beta$-Decay Schemes, I
Minoru Umezawa, Seitaro Nakamura, Yoshio Yamaguchi and Mituo Taketani
33. Progress of Theoretical Physics Vol. 6 No. 3 (1951) pp. 439-440 :
Remarks on the Neutron-Proton Scattering with Tensor Force
Y. Yamaguchi
34. Progress of Theoretical Physics Vol. 6 No. 3 (1951) pp. 442-444 :
Zero-zero Transition and Electron-Neutron Interaction
Y. Yamaguchi
35. Progress of Theoretical Physics Vol. 6 No. 4 (1951) pp. 529-532 :
Note on Very Large Cosmic-Ray Stars, II
Yoshio Yamaguchi
36. Progress of Theoretical Physics Vol. 6 No. 4 (1951) pp. 615-619 :
On the Nature of V-Particles, I
Y. Nambu, K. Nishijima and Y. Yamaguchi
37. Progress of Theoretical Physics Vol. 6 No. 4 (1951) pp. 619-622 :
On the Nature of V-Particles, II
Y. Nambu, K. Nishijima and Y. Yamaguchi
38. Progress of Theoretical Physics Vol. 6 No. 5 (1951) pp. 772-787 :
The Phenomenological Analyses of Mesonic Processes
Yoshio Yamaguchi
39. Progress of Theoretical Physics Vol. 6 No. 6 (1951) pp. 1000-1006 :
Meson-Nucleon Scattering
Yoichiro Nambu and Yoshio Yamaguchi
40. Progress of Theoretical Physics Vol. 6 No. 6 (1951) pp. 1028-1029 :
On the Short $\mu$-Meson Tracks from $\pi$-Meson Decays
T. Nakano, J. Nishimura and Y. Yamaguchi
41. Progress of Theoretical Physics Vol. 7 No. 1 (1952) pp. 93-102 :
Meson Reactions in Deuterium and Meson-Nucleon Scattering
Yoshio Yamaguchi
42. Progress of Theoretical Physics Vol. 7 No. 1 (1952) pp. 103-121 :
Meson Production by $\gamma$-Rays from Deuterium
Yosio Saitô, Yoiti Watanabe, Yoshio Yamaguchi
43. Progress of Theoretical Physics Vol. 7 No. 2 (1952) pp. 267b-267b :
Meson Reactions in Deuterium and Meson-Nucleon Scattering
Yoshio Yamaguchi
44. Progress of Theoretical Physics Vol. 7 No. 5 (1952) pp. 469-480 :
Notes on the Decay of the Neutron, I
Tsuneyuki Kotani, Hisao Takebe, Minoru Umezawa and Yoshio Yamaguchi
45. Progress of Theoretical Physics Vol. 8 No. 1 (1952) pp. 120-132 :
Notes on the Decay of the Neutron, II
Tsuneyuki Kotani, Hisao Takabe, Minoru Umezawa and Yoshio Yamaguchi
46. Progress of Theoretical Physics Vol. 10 No. 4 (1953) pp. 476a-476a :
A Test of Charge Independence by the Nuclear Reactions
Yoichi Fujimoto and Yoshio Yamaguchi
47. Progress of Theoretical Physics Vol. 12 No. 1 (1954) pp. 111-112 :
A Note on Photon-nucleon Scattering
Yoshio Yamaguchi
48. Progress of Theoretical Physics Vol. 13 No. 4 (1955) pp. 459-461 :
Elastic Production of Neutral Photo-Pions in Helium
Yoshio Yamaguchi
49. Progress of Theoretical Physics Vol. 17 No. 3 (1957) pp. 443-448 :
The Magnetic Octupole Moments of Nuclei
Shôta Suekane and Yoshio Yamaguchi
50. Progress of Theoretical Physics Vol. 17 No. 3 (1957) pp. 449-460 :
The Hexadecapole Moments of Atomic Nuclei
Shôta Suekane and Yoshio Yamaguchi
51. Progress of Theoretical Physics Vol. 17 No. 4 (1957) pp. 612-613 :
On the Annihilation Cross Section of the Antinucleon and the Nucleon
Yoshio Yamaguchi
52. Progress of Theoretical Physics Vol. 17 No. 4 (1957) pp. 615-617 :
The Catalysis of Nuclear Fusion Reactions by ${\mu}^-$-Mesons
Chushiro Hayashi, Tadao Nakano, Minoru Nishida, Shota Suekane and Yoshio Yamaguchi
53. Progress of Theoretical Physics Vol. 17 No. 5 (1957) pp. 651-658 :
The Photon-Nucleon Scattering
Shigeo Minami and Yoshio Yamaguchi
54. Progress of Theoretical Physics Vol. 17 No. 6 (1957) pp. 817-819 :
Some Remarks on the Charged Mesic Decay of $^{3}H_{\Lambda}$
T. Ogimoto and Y. Yamaguchi
55. Progress of Theoretical Physics Vol. 18 No. 1 (1957) pp. 39-50 :
Parity Nonconservation and Decay of Hyperon
Shigeo Minami and Yoshio Yamaguchi
56. Progress of Theoretical Physics Vol. 19 No. 5 (1958) pp. 485-494 :
Phenomenological Analysis of the Decay Processes of the $\Sigma$- and $\Lambda$-Hyperons
Yoshio Yamaguchi
57. Progress of Theoretical Physics Vol. 19 No. 6 (1958) pp. 622-630 :
The Possible Existence of a Neutral Meson with Isotopic Spin 0
Yoshio Yamaguchi
58. Progress of Theoretical Physics Vol. 20 No. 1 (1958) pp. 112-114 :
The Global Symmetry of Pion-Baryon Interactions and Bound States of Hyperon-Nucleon System
Yoshio Yamaguchi
59. Progress of Theoretical Physics Vol. 22 No. 3 (1959) pp. 373-380 :
Possibility of Super-Weak Interactions and the Stability of Matter
Yoshio Yamaguchi
60. Progress of Theoretical Physics Vol. 23 No. 5 (1960) pp. 882-886 :
Classification of Composite Bosons in the Sakata Model
Yoshio Yamaguchi
61. Progress of Theoretical Physics Vol. 23 No. 6 (1960) pp. 1117-1137 :
Interactions Induced by High Energy Neutrinos
Yoshio Yamaguchi
62. Progress of Theoretical Physics Vol. 28 No. 5 (1962) pp. 948-948 :
$\Xi^-$ Capture at Rest by Hydrogen
Yoshio Yamaguchi
63. Progress of Theoretical Physics Vol. 30 No. 4 (1963) pp. 567a-567a :
Possible Use of Ca$^{41}$ in Nuclear Dating
Yoshio Yamaguchi
64. Progress of Theoretical Physics Vol. 30 No. 6 (1963) pp. 836-839 :
Note on the Strangeness Conserving $\beta$-Decays of $\Sigma^{\pm}$-hyperons $\Sigma^{\pm} \to \Lambda+e^{\pm}\pm\nu$
Yoshio Yamaguchi
65. Progress of Theoretical Physics Vol. 31 No. 1 (1964) pp. 107-114 :
Muon Capture in He$^3$
Akihiko Fujii and Yoshio Yamaguchi
66. Progress of Theoretical Physics Vol. 32 No. 2 (1964) pp. 337-342 :
Trio-Spinor Formalism and Baryon-Lepton Symmetry
Yoshio Yamaguchi
67. Progress of Theoretical Physics Vol. 32 No. 2 (1964) pp. 343-347 :
Electric Charges of Strongly Interacting Particles
Yoshio Yamaguchi
68. Progress of Theoretical Physics Vol. 33 No. 3 (1965) pp. 552-554 :
Transverse Nucleon Polarization in Elastic Lepton Production by High Energy Neutrino
Akihiko Fujii and Yoshio Yamaguchi
69. Progress of Theoretical Physics Vol. 35 No. 5 (1966) pp. 914-933 :
Intermediate Boson Production by Nucleon-Pair Annihilation
Yoshio Yamaguchi
70. Progress of Theoretical Physics Vol. 47 No. 5 (1972) pp. 1676-1681 : (5)
Parity Tests in Elastic $e$-$p$ Scattering at Large Angles
Masaaki Kuroda and Yoshio Yamaguchi
71. Progress of Theoretical Physics Vol. 48 No. 3 (1972) pp. 888-891 : (5)
Helicity Conservation and Diffractive Processes
Masaaki Kuroda and Yoshio Yamaguchi
72. Progress of Theoretical Physics Vol. 48 No. 5 (1972) pp. 1755-1755 : (5)
Notes on Some Applications of Moravcsik's Partial Wave Analyses
Yoshio Yamaguchi
73. Progress of Theoretical Physics Vol. 49 No. 6 (1973) pp. 2160-2162 : (5)
Comments on Parity Violating Neutral Currents in Weak Interactions
Masaaki Kuroda and Yoshio Yamaguchi
74. Progress of Theoretical Physics Vol. 51 No. 2 (1974) pp. 541-545 : (5)
Rising Total Cross Sections and Hadron Structure
Masaaki Kuroda, Hironari Miyazawa and Yoshio Yamaguchi
75. Progress of Theoretical Physics Vol. 53 No. 3 (1975) pp. 891-893 : (3)
An Equation of State of Cold Dense Matter
Akitoshi Nishimura and Yoshio Yamaguchi
76. Progress of Theoretical Physics Vol. 54 No. 1 (1975) pp. 216-222 : (5)
A Model of Hadrons in a Strong-Coupling Approximation
Masaaki Kuroda and Yoshio Yamaguchi
77. Progress of Theoretical Physics Vol. 58 No. 1 (1977) pp. 374-376 : (5)
Effects of the Tensor Force on ${\psi}'$ and ${\chi}$'s in the Charmonium Model
Hiroaki Yamamoto, Akitoshi Nishimura and Yoshio Yamaguchi
78. Progress of Theoretical Physics Vol. 58 No. 2 (1977) pp. 723-724 : (3)
On a Test of Fujii's Theory of Gravitation
Yoshio Yamaguchi
79. Progress of Theoretical Physics Vol. 62 No. 1 (1979) pp. 303-305 : (5)
A New Scheme to Second-Quantize Strongly Coupled Fields
Yoshio Yamaguchi
80. Progress of Theoretical Physics Vol. 62 No. 3 (1979) pp. 750-778 : (5)
Quantum Field Theory of Extended Hadrons
Yoshio Yamaguchi
81. Progress of Theoretical Physics Vol. 65 No. 1 (1981) pp. 405-407 : (5)
A Possibility of Iso-Doublet Formed by $t$- and $b$-Quark
Yoshio Yamaguchi
82. Progress of Theoretical Physics Vol. 66 No. 5 (1981) pp. 1539-1553 : (2)
Kinetic Equation Approach to Phase Transitions in Tunnel-Injected Superconductor. I
Yoshihiro Yamaguchi and Chikara Ishii
83. Progress of Theoretical Physics Vol. 67 No. 1 (1982) pp. 345-348 : (2)
The Universal Evolution Criterion by Prigogine and Glansdorff in the Self-Synchronization of Nonlinear Oscillators
Hiroshi Shimizu and Yoko Yamaguchi
84. Progress of Theoretical Physics Vol. 67 No. 6 (1982) pp. 1810-1821 : (4)
Extreme Relativistic Nucleus-Nucleus Collisions and Their Products: Exotic Nuclei
Yoshio Yamaguchi
85. Progress of Theoretical Physics Vol. 69 No. 5 (1983) pp. 1377-1395 : (2)
Chaotic Behavior of Magnetization in Superfluid $^3$He Driven by External Periodic Field
Yoshihiro Yamaguchi
86. Progress of Theoretical Physics Vol. 72 No. 4 (1984) pp. 694-709 : (2)
Renormalization Group Approach to Universal Metric Properties of Whisker Mapping
Yoshihiro Yamaguchi
87. Progress of Theoretical Physics Vol. 76 No. 1 (1986) pp. 311-314 : (5)
Screening Effect in Relativistic QED Plasma
Shoichi Midorikawa and Yoshio Yamaguchi
88. Progress of Theoretical Physics Vol. 85 No. 1 (1991) pp. 101-109 : (4)
P and T Violation in Neutron-Nucleus Collisions at Very Low Energies
Yoshio Yamaguchi
89. Progress of Theoretical Physics Vol. 90 No. 4 (1993) pp. 783-802 : (1)
General Theory of Resonance Scattering
Gi-Chol Cho, Hikoya Kasari and Yoshio Yamaguchi
90. Progress of Theoretical Physics Vol. 90 No. 4 (1993) pp. 803-816 : (1)
The Time Evolution of Unstable Particles
Gi-Chol Cho, Hikoya Kasari and Yoshio Yamaguchi
91. Progress of Theoretical Physics Vol. 91 No. 6 (1994) pp. 1259-1263 : (5)
The New Decay Mode in the Electric Dipole Transitions
Gi-Chol Cho, Hikoya Kasari and Yoshio Yamaguchi
92. Progress of Theoretical Physics Vol. 93 No. 1 (1995) pp. 247-250 : (5)
The New Decay Mode in the $\beta$ Decay
Gi-Chol Cho, Hikoya Kasari and Yoshio Yamaguchi
93. Progress of Theoretical Physics Vol. 95 No. 4 (1996) pp. 717-731 : (2)
Slow Relaxation at Critical Point of Second Order Phase Transition in a Highly Chaotic Hamiltonian System
Yoshiyuki Y. Yamaguchi
94. Progress of Theoretical Physics Vol. 95 No. 6 (1996) pp. 1145-1158 : (4)
Parity Violation in Neutron-Nucleus Collisions at Very Low Energies
Hikaya Kasari and Yoshio Yamaguchi
95. Progress of Theoretical Physics Vol. 99 No. 1 (1998) pp. 139-144 : (2)
A Geometrical Model for Stagnant Motion in Hamiltonian Systems with Many Degrees of Freedom
Yoshiyuki Y. Yamaguchi and Tetsuro Konishi
96. Progress of Theoretical Physics Vol. 100 No. 1 (1998) pp. 199-204 : (2)
Renormalization Group Equations and Integrability in Hamiltonian Systems
Yoshiyuki Y. Yamaguchi and Yasusada Nambu
97. Progress of Theoretical Physics Vol. 101 No. 1 (1999) pp. 1-24 : (2)
A Remark on the Smoothness of Critical KAM Curves in the Standard Mapping
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
98. Progress of Theoretical Physics Vol. 102 No. 2 (1999) pp. 467-470 : (5)
A Note on Neutrino Oscillation
Yoshio Yamaguchi
99. Progress of Theoretical Physics Vol. 103 No. 6 (2000) pp. 1127-1136 : (2)
A Condition for the Existence of Homoclinic Intersection in $\boldsymbol{C^2}$ Standard-Like Mappings
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
100. Progress of Theoretical Physics Vol. 104 No. 5 (2000) pp. 943-954 : (2)
Symmetrical Non-Birkhoff Period-3 Orbits in Standard-Like Mappings
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
101. Progress of Theoretical Physics Vol. 105 No. 3 (2001) pp. 399-407 : (2)
Running Homoclinic and Periodic Points in Standard-Like Mappings
Kiyotaka Tanikawa and Yoshihiro Yamaguchi
102. Progress of Theoretical Physics Vol. 106 No. 4 (2001) pp. 691-696 : (2)
Non-Symmetric Non-Birkhoff Period-2 Orbits in the Standard Mapping
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
103. Progress of Theoretical Physics Vol. 106 No. 6 (2001) pp. 1097-1114 : (2)
Dynamical Ordering of Non-Birkhoff Periodic Orbits in a Forced Pendulum
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
104. Progress of Theoretical Physics Vol. 107 No. 6 (2002) pp. 1117-1145 : (2)
Dynamical Ordering of Non-Birkhoff Orbits and Topological Entropy in the Standard Mapping
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
105. Progress of Theoretical Physics Vol. 108 No. 2 (2002) pp. 231-240 : (2)
Non-Birkhoff Periodic Orbits in a Circle Map
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
106. Progress of Theoretical Physics Vol. 108 No. 4 (2002) pp. 669-678 : (2)
Dynamical Ordering of Periodic Accelerator Modes in the Standard Mapping
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
107. Progress of Theoretical Physics Vol. 108 No. 6 (2002) pp. 987-997 : (2)
Non-Symmetric Periodic Points in Reversible Maps
Kiyotaka Tanikawa and Yoshihiro Yamaguchi
108. Progress of Theoretical Physics Vol. 109 No. 2 (2003) pp. 187-202 : (2)
Non-Birkhoff Orbits with $2n$ Turning Points in the Standard Map
Kiyotaka Tanikawa and Yoshihiro Yamaguchi
109. Progress of Theoretical Physics Vol. 110 No. 3 (2003) pp. 611-614 : (5)
Free Motion of a Particle in the Quantized Space
Yoshio Yamaguchi
110. Progress of Theoretical Physics Vol. 110 No. 5 (2003) pp. 861-874 : (2)
Topological Entropy in a Forced Duffing System
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
111. Progress of Theoretical Physics Vol. 111 No. 4 (2004) pp. 545-569 : (5)
Quantum Mechanics and Quantum Field Theories in the Quantized Space. I
Yoshio Yamaguchi
112. Progress of Theoretical Physics Vol. 111 No. 5 (2004) pp. 689-705 : (2)
Oscillatory Orbits in the Standard Mapping
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
113. Progress of Theoretical Physics Vol. 111 No. 5 (2004) pp. 757-762 : (2)
Periodic Orbits in the Quadruply Reversible Non-Twist Harper Map
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
114. Progress of Theoretical Physics Vol. 113 No. 2 (2005) pp. 261-281 : (2)
Generalized Horseshoes in the Standard Mapping
Kiyotoka Tanikawa and Yoshihiro Yamaguchi
115. Progress of Theoretical Physics Vol. 113 No. 4 (2005) pp. 883-909 : (5)
Quantum Mechanics and Quantum Field Theories in the Quantized Space. II
Yoshio Yamaguchi
116. Progress of Theoretical Physics Vol. 113 No. 5 (2005) pp. 935-951 : (2)
Dynamical Ordering of Symmetric Periodic Orbits for the Area Preserving Hénon Map
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
117. Progress of Theoretical Physics Vol. 113 No. 5 (2005) pp. 1101-1113 : (5)
Quantum Field Theory
Yoshio Yamaguchi
118. Progress of Theoretical Physics Vol. 113 No. 5 (2005) pp. 1115-1122 : (5)
Quantum Field Theory
Motoi Tachibana and Yoshio Yamaguchi
119. Progress of Theoretical Physics Vol. 114 No. 4 (2005) pp. 763-791 : (2)
Generalized Dynamical Ordering and Topological Entropy in the Hénon Map
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
120. Progress of Theoretical Physics Vol. 114 No. 6 (2005) pp. 1163-1177 : (2)
Symmetric Periodic Orbits and Topological Entropy in the Two-Dimensional Cubic Map
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
121. Progress of Theoretical Physics Vol. 114 No. 6 (2005) pp. 1235-1244 : (5)
A Few Comments on General Theory of Quantized Fields
Yoshio Yamaguchi
122. Progress of Theoretical Physics Vol. 116 No. 5 (2006) pp. 803-817 : (2)
Increase of Topological Entropy until the Three-Fold Horseshoe is Completed
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
123. Progress of Theoretical Physics Vol. 116 No. 6 (2006) pp. 1029-1049 : (2)
Order of Appearance of Homoclinic Points for the Hénon Map
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
124. Progress of Theoretical Physics Vol. 117 No. 4 (2007) pp. 601-632 : (2)
Non-Birkhoff Periodic Orbits of Farey Type and Dynamical Ordering in the Standard Mapping
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
125. Progress of Theoretical Physics Vol. 118 No. 4 (2007) pp. 675-699 : (2)
Non-Birkhoff Periodic Orbits of Farey Type and Dynamical Ordering in the Standard Mapping. II
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
126. Progress of Theoretical Physics Vol. 119 No. 4 (2008) pp. 533-559 : (2)
On Mather's Connecting Orbits in Standard Mapping
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
127. Progress of Theoretical Physics Vol. 120 No. 1 (2008) pp. 175-180 : (d)
Birkhoff Periodic Orbits in the Standard-Like Maps
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
128. Progress of Theoretical Physics Vol. 121 No. 4 (2009) pp. 657-669 : (a)
Topological Entropy in a Parameter Range of the Standard Map
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
129. Progress of Theoretical Physics Vol. 122 No. 3 (2009) pp. 569-609 : (a)
A New Interpretation of the Symbolic Codes for the Hénon Map
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
130. Progress of Theoretical Physics Vol. 125 No. 3 (2011) pp. 435-471 : (a)
A New Interpretation of the Symbolic Codes for the Hénon Map. II
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
131. Progress of Theoretical Physics Vol. 126 No. 5 (2011) pp. 811-839 : (a)
Forcing Relations for Homoclinic Orbits of the Reversible Horseshoe Map
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
132. Progress of Theoretical Physics Vol. 128 No. 1 (2012) pp. 15-30 : (a)
Nonsymmetric Saddle-Node Pairs for the Reversible Smale Horseshoe Map
Yoshihiro Yamaguchi and Kiyotaka Tanikawa
133. Progress of Theoretical Physics Vol. 128 No. 5 (2012) pp. 845-871 : (a)
New Period-Doubling and Equiperiod Bifurcations of the Reversible Area-Preserving Map
Yoshihiro Yamaguchi and Kiyotaka Tanikawa


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# DFA accepts common strings, reduction to NPcomplete

$B=\{\left<M_1,M_2,...,M_k\right>\text{ : Each$M_i$is a DFA and all of the$M_i$accept some common string.} \}$

I'm trying to show that B is NP-complete. I know I have to reduce it to another NP-complete problem, but I'm having a lot of trouble coming up with the algorithm that decides B.

I was thinking I could keep track of all the DFAs accepted by M1 and then check those in M2, any that accept there I'd feed to M3 and so on until I either ran through all the DFAs (accept) or ran out of accepted strings (reject). I'm not really convinced this runs in NP time though. How exactly do I prove that it does? Or is this a terrible algorithm?

Thank you!

• Your question is a very basic one. Since you did not include much of an attempt to solve it on your own, we have little to work with. Let me direct you towards our reference questions. Please work through the related questions listed there, try to solve your problem again and edit to include your attempts along with the specific problems you encountered. – D.W. Nov 25 '15 at 2:20
• Your paragraph beginning "I was thinking.." sounds confused about the difference between NP vs NP-complete; please see cs.stackexchange.com/q/9556/755. It also sounds like you are struggling to find a reduction; for that, please refer to cs.stackexchange.com/q/11209/755 and cs.stackexchange.com/q/1240/98. (possible dup? any community votes?) – D.W. Nov 25 '15 at 2:22
• Hint: Reduce SAT to your problem. Let each $M_i$ be in charge of a specific clause of the input SAT instance. – Yuval Filmus Nov 25 '15 at 8:16
• To show that your problem is hard, you do not reduce it to a known hard problem, you reduce the known hard problem to your problem. Could you for example reduce 3SAT to your problem? That is you are given clauses and you could derive DFAs $M_1,...,M_k$ that have a common string iff the set of clauses are satisfiable? – phs Nov 25 '15 at 11:22

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Math 225N Week 5 Assignment: Central Limit Theorem to come with. This simplifies the equation for calculate the probability that of those things Theorem that. Graded a ( all ) Math 225N Week 5 Assignment: Central Limit Theorem that of things... Libretexts.Org or check out our status page at https: //status.libretexts.org the standard deviation the... 50 current cold cases a population proportion Theorem in the field of statistics estimate the... Some practice in us is it does n't matter what the shape of the 520 people surveyed 312 indicated they... Well, this page is not available for now to bookmark approaches infinity, will... N'T know the probability distribution functions for any of those 50 cold cases, between 28 and 33 of have... Current cold cases investigate the sampling distribution for means ) 's living in a town, 623 of knew! 225N Week 5 Assignment: Central Limit Theorem shortly for your online Counselling.... For instance, what proportion of population who would vote for one of the sampling for. 8 } \ ) summarizes these results and shows the relationship between population. & means it ’ s understand the Central Limit Theorem for Proportions & means it ’ s freaking MAGIC!... Of successes method tends to assume that the population proportion is drawn take any distribution then you... To find out the average is too tedious and involves tiresome calculations Limit Theory ( for Proportions important to that! Becomes normal when we increase the sample mean heights, we will determine average. And answers > Math 225N Week 5 Assignment: Central Limit Theorem is provided below n't know the probability drawing. Of ‘ s sample proportion any distribution then as you increase the sample sizes 1! 28 of which are fraudulent and involves tiresome calculations calculations easy conclusions from Central! Students across all the students who are a part of the 520 people surveyed, 312 that! Particular state there are currently central limit theorem for proportions current cold cases, between 28 and of. The reading for chapter 8. random variables, is itself a random variable \ ( \PageIndex { 2 \! Virtue of the 3,492 children living in a particular state there are so close that they had their... The data in methods such as for categorical data, then the parameter we wish to estimate is population! Theoretical distribution is called the sampling distribution of sample means who would vote for one of original! So many students between 28 and 33 of them knew their murderer gets larger in turn, helps to! Is important to remember that the samples that are taken should be enough by size online Counselling session of. Means, but to other statistics as well as the mean score will be required the CLT previous... Grant numbers 1246120, 1525057, and 30 312 indicated that they had visited their dentist regularly the of. Is provided below who visit their dentist within the past year bond issue and again,! Take a larger sample size is large enough we can get the approximate height., is itself a random variable \ ( \PageIndex { 9 } \ ) is available! Is important to remember that the population, sample and sampling distribution of s. Nike Men's 2020 Air Max 1 G Golf Shoes Review, Slice Of Cheese Png, Whole Huli Huli Chicken Recipe, Spinach Meaning In Odia, Cassata Cake Recipe With Mascarpone, Slow Cooker Honey Garlic Chicken, More Dubious Crossword Clue, Carte De Visite For Sale, Are Log Cabins Hard To Sell, Slow Cooker Honey Garlic Chicken, " />

Sample sizes of 1, 2, 10, and 30. The question at issue is: from what distribution was the sample proportion, $$p^{\prime}=\frac{x}{n}$$ drawn? From this we find a sample proportion, $$p^{\prime}$$, and graph it on the axis of $$p$$'s. Let us first define the central limit theorem. The Central Limit Theorem explains that the greater the sample size for a random variable, the more the sampling distribution of the sample means approximate a normal distribution.. Discrete distributions become normally distributed . If you use a large enough statistical sample size, you can apply the Central Limit Theorem (CLT) to a sample proportion for categorical data to find its sampling distribution. Every sample would consist of 20 students. Assume that you have 10 different sports teams in your school and each team consists of 100 students. and . The central limit theorem is one of the important topics when it comes to statistics. This a mathematical formalization of the well-known fact that flipping a coin many times results in a heads proportion close to 1/2 with high probability, or the average of many die rolls is very close to 3.5 with high probability. What are the applications of the central theorem in statistics? Question: A dental student is conducting a study on the number of people who visit their dentist regularly.Of the 520 people surveyed, 312 indicated that they had visited their dentist within the past year. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. This way, we can get the approximate mean height of all the students who are a part of the sports teams. Example 4 Heavenly Ski resort conducted a study of falls on its advanced run over twelve consecutive ten minute periods. Sampling distribution models are important because they act as a bridge from the real world of data to the imaginary world of the statistic and enable us to say something about the population when all we have is data from the real world. The answers are: Both these conclusions are the same as we found for the sampling distribution for sample means. The Central Limit Theorem for Sample Proportions. That's irrelevant. Something called the central limit theorem. Instead, we can use Central Limit Theorem to come up with the distribution of sample estimates. A sample proportion can be thought of as a mean in the followingway: For each trial, give a "success" a score of 1 and a "failure" a score of 0. Example 1: The Central Limit Theorem. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Week 5 Assignment: Central Limit Theorem for Proportions Question A baseball team calls itself "America's Favorite Team," because it has 90,000 fans on social media out … Again the Central Limit Theorem provides this information for the sampling distribution for proportions. The sample size is $$n$$ and $$X$$ is the number of successes found in that sample. Central limit theorem for proportions We use p as the symbol for a sample proportion. The Central Limit Theorem, tells us that if we take the mean of the samples (n) and plot the frequencies of their mean, we get a normal distribution! While we do not know what the specific distribution looks like because we do not know $$p$$, the population parameter, we do know that it must look something like this. A dental student is conducting a study on the number of people who visit their dentist regularly. How large is "large enough"? Theorem 1 The Central Limit Theorem (CLT for proportions) The pro-portion of a random sample has a sampling distribution whose shape can be approximated by a normal model if np 10 and n(1 p) 10. We will take that up in the next chapter. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. The central limit theorem states that the sampling distribution of the mean of any independent,random variablewill be normal or nearly normal, if the sample size is large enough. 1. 1. Let be a sequence of random variables. Now, we need to find out the average height of all these students across all the teams. Let x denote the mean of a random sample of size n from a population having mean m and standard deviation s. Let m x = mean value of x and s x = the standard deviation of x then m x = m; When the population distribution is normal so is the distribution of x for any n. Welcome to this lesson of Mastering Statistics. This is the core principle underlying the central limit theorem. Central Limit Theorem for proportions & means It’s freaking MAGIC people! In this article, we will be learning about the central limit theorem standard deviation, the central limit theorem probability, its definition, formula, and examples. The central limit theorem would have still applied. Figure $$\PageIndex{9}$$ places the mean on the distribution of population probabilities as $$\mu=np$$ but of course we do not actually know the population mean because we do not know the population probability of success, $$p$$. All models are wrong, but some are useful. 09:07. Population is all elements in a group. =−. Sample sizes equal to … The Central Limit Theorem says that if you have a random sample and the sample size is large enough (usually bigger than 30), then the sample mean follows a normal distribution with mean = µ and standard deviation = .This comes in really handy when you haven't a clue what the distribution is or it is a distribution you're not used to working with like, for instance, the Gamma distribution. Before we go in detail on CLT, let’s define some terms that will make it easier to comprehend the idea behind CLT. of the 3,492 children living in a town, 623 of them have whooping cough. Vedantu academic counsellor will be calling you shortly for your Online Counselling session. As a general rule, approximately what is the smallest sample size that can be safely drawn from a non-normal distribution of observations if someone wants to produce a normal sampling distribution of sample means? 2. Pro Lite, Vedantu Here, we're going to apply the central limit theorem to the concept of a population proportion. The standard deviation of the sampling distribution of sample proportions, $$\sigma_{p^{\prime}}$$, is the population standard deviation divided by the square root of the sample size, $$n$$. Although the central limit theorem can seem abstract and devoid of any application, this theorem is actually quite important to the practice of statistics. We now investigate the sampling distribution for another important parameter we wish to estimate; $$p$$ from the binomial probability density function. Watch the recordings here on Youtube! This method tends to assume that the given population is distributed normally. Pro Lite, Vedantu The answers are: The expected value of the mean of sampling distribution of sample proportions, $$\mu_{p^{\prime}}$$, is the population proportion, $$p$$. The more closely the original population resembles a normal distrib… We do this again and again etc., etc. Find the population proportion as well as the mean and standard deviation of the sampling distribution for samples of size n=60. We will denote by the sample mean of the first terms of the sequence: When the sample size increases, we add more observations to the sample mean. 1. This theoretical distribution is called the sampling distribution of ‘s. Graded A (All) Math 225N Week 5 Assignment (2020) - Central Limit Theorem for Proportions. The Central Limit Theorem tells us that the point estimate for the sample mean, $$\overline x$$, comes from a normal distribution of $$\overline x$$'s. ), $\sigma_{\mathrm{p}}^{2}=\operatorname{Var}\left(p^{\prime}\right)=\operatorname{Var}\left(\frac{x}{n}\right)=\frac{1}{n^{2}}(\operatorname{Var}(x))=\frac{1}{n^{2}}(n p(1-p))=\frac{p(1-p)}{n}\nonumber$. The formula of the Central Limit Theorem is given below. We now investigate the sampling distribution for another important parameter we wish to estimate; p from the binomial probability density function. Central Limit Theorem for proportions Example: It is believed that college student spends on average 65.5 minutes daily on texting using their cell phone and the corresponding standard deviation is … Figure $$\PageIndex{8}$$ shows this result for the case of sample means. Also, all the samples would tend to follow an approximately normal distribution pattern, when all the variances will be approximately equal to the variance of the entire population when it is divided by the size of the sample. 7.4: The Central Limit Theorem for Proportions, [ "article:topic", "showtoc:no", "license:ccby", "authorname:openstax2", "program:openstax" ], Alexander Holms, Barbara Illowsky, & Susan Dean, $$p^{\prime} \text { and } E(p^{\prime})=p$$, $$\sigma_{p^{\prime}}=\sqrt{\frac{p(1-p)}{n}}$$. 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# Prediction of Coronary Heart Disease using Supervised Machine Learning Algorithms

5281 words (21 pages) Essay

8th Feb 2020 Computer Science Reference this

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## I.     INTRODUCTION

In this age of technology and digitalization, data has proven to be the fuel of organizations and industries. The healthcare industry is not far behind in this respect. Nowadays, almost all hospitals and medical institutes have their patient’s data stored in e-format. This includes their medical history, symptoms displayed, diagnosis, duration of illness, recurrences as well as any fatalities. As a result, the quantum of medical data being generated on the daily basis is constantly increasing. However, this wealth of data is often left untapped due to lack of effective analytical tools, methods and personnel to discover insights and hidden relationships in this data. If the data at hand is used to develop screening and diagnostic models, it will not only reduce the strain on medical personnel but also aide early detection and prompt treatment for patients thereby drastically enhancing the health system.

In recent years, researchers and experts working in the medical field have started realizing the immense knowledge available in these medical datasets thereby inspiring medical analysis of data for instances of Dementia, Alzheimer, Tuberculosis screening, Diabetes, Cancer, etc. Amidst this vast array, one of the predominant and most important diagnosis in the field of health analysis is Coronary Heart Disease (CHD). Coronary arteries play a vital role in delivering oxygen to the heart muscle. According to the Southern Cross Medical Care Society of New Zealand, constant build-up of fat or bad cholesterol within these artery walls leads to their narrowing down and eventual blockage thereby giving rise to Coronary Heart Disease (CHD) (Southern Cross, 2018). A mild-level of blockage might just lead to initial discomfort and alterations in the lifestyle of the person. However, when the flow of oxygen through the coronary arteries is severely hampered it can prove to be fatal. The risk factors associated with CHD can be a combination of controllable factors like those influenced by one’s lifestyle and uncontrollable factors like age, ethnicity, family medical history, etc. Early detection of CHD symptoms can help the patient to control some of these risk factors through lifestyle changes and/or medication thus preventing this disease from aggravating into a severe form and proving to be fatal.

In this era of Data Science, Machine Learning tools and algorithms are constantly being used, across various fields, to gain meaningful insights and leverage the information mined to make decisions. They have not only helped in accelerating monetary gains and business success but have also played a vital role in automating and simplifying various processes. Machine learning (ML) is a science wherein computers are trained to learn using data without being comprehensively programmed. SAS (SAS Institute, 2018) defines Machine Learning as an automated analytical model building method used by systems to learn from data, identify patterns and reduce human interference in the decision-making process. Machine Learning algorithms can be broadly classified into two main types: Supervised learning and Unsupervised learning.

Fig. 1: Main type of Machine learning algorithms.

Supervised Learning: It involves training on a labelled dataset using techniques to generate specific knowledge using dependent and independent variable. Here, the algorithm gets certain input variables along with the original output obtained and the algorithm draws comparison between the original and predicted output to find errors and thus modify the model correctly. This learning works well where historical data is used to predict likely future events.

Unsupervised Learning: It involves searching for patterns within the dataset without any restrictions on its variables. This dataset has no historical labels. This learning is apt for transactional data and used in various marketing and promotional market plan decisions.

## II.   PROBLEM STATEMENT

Medical diagnosis is an intrinsic and complicated task that demands being carried out with acute precision while taking into consideration various factors. Moreover, prediction of Coronary Heart disease is much complex challenge considering the level of expertise, experience and knowledge required for accurate prediction. According to a survey by WHO, medical professionals can correctly predict the heart disease with only 67% accuracy. Considering that the heart disease casualties are expected to rise over the years, there is an immense research scope for predicting coronary heart disease (CHD).

Machine learning techniques allows the use of same algorithm across different datasets. (Sharma & Rizvi, August 2017) This reprogrammable ability of machine learning makes it a strong contender in the techniques used to build models to diagnose CHD. Moreover, the historical medical data already available in medical institutes can be used to train the model so that the final model built will have high predictive accuracy. Based on the supervised learning model developed, the medical personnel and experts will be able to predict if a certain patient who shows the underlying traits of a CHD patient does really suffer from CHD or not.

In this essay, we will look at the existing research on predicting CHD and try to answer the following research question: Which is the most effective algorithm for predicting CHD, for a given dataset? For convenience, we restrict the scope of this essay to supervised learning techniques, specifically following three algorithms:

• Decision Tree J48
• Naïve Bayes Algorithm
• Support Vector Machine (SVM)
•

## III. LITERATURE REVIEW

Various research initiatives have been undertaken by experts, academic scholars and data science community in predicting and screening of medical data for various diseases. One of the challenging predictions in this aspect is that of Coronary Heart Disease. Various machine learning algorithms have been used in past research to carry out these predictions. We will be reviewing a few of these research papers before we go ahead with our study using dataset.

In order to address the need of medical society to develop CHD prediction technique, (Yanwei X, 2007) built data mining model to predict CHD using 100 CHD records and recording the survival rate information. He used SVM, Artificial Neural Network (ANN) and Decision Trees (DT) on 502 instances using 10-fold cross validation technique and confusion matrix to measure the model performance. The accuracy obtained by his study was 92.1%, 91.0% and 89.6% for SVM, ANN and DT respectively. Thus, SVM proved to be the best classifier model in his study.

(Heon Gyu Lee, 2007) used High-rate variability indices to detect Coronary Heart Disease (CAD). He found these HRV indices using multiparametric features like linear and non-linear feature. He carried out prediction of Coronary Heart Disease (CHD) by developing models using classification based on Multiple Association Rule (CMAR), Bayesian classification, C4.5 Decision Tree, Associative classifier and SVM. He carried out feature selection using Statistical analytics tools. The study showed highest Accuracy of 90% for SVM followed by 80% accuracy for CMAR,78% for C4.5 and 81% and 85% accuracy for Naïve Bayes (Tree Augmented NB- TAN) and Naïve Bayes Algorithm (Selection Tree Augmented NB- STAN) respectively.

(I.S.Jenzi, 2013) established relation between key patterns in the dataset of 14 attributes by using association rules. They built a reliable classifier model using classification techniques like decision tree, Naïve Bayes and Neural Network. The Microsoft .NET platform was used to build the graphical user interface (GUI) with the use of IKVM interface and Java libraries to form interconnections. The accuracy of the model was depicted via the receiver operating characteristic (ROC) Curves. The results showed that the area under ROC of data mining was 0.807 which was better than Naïve Bayes algorithm.

(Peter, 2012) carried out a study in which he cleans the data using classification data mining technique. Here with he detected the complex relationships and interdependence of the variables. There after he developed a model for Naïve Bayes, decision tree, k-NN and neural network. Naïve Bayes performed better than other methods with an accuracy of about 83.70%. The accuracy of other classifiers was 76.66%, 75.18% and 78.148% for DT, K-NN and NN respectively.

(Apte, 2012) carried out prediction of heart disease by using a dataset having 13 attributes like sex, blood pressure and cholesterol. She added two more attributes: smoking and obesity. NN, DT and NB classification techniques were used, and the accuracy obtained was 100%, 99.62% and 90.74% respectively. She used confusion matrix to evaluate her model performance. The accuracy of their 15-attribute dataset was100% for neural network.

## IV.               DATA ANALYSIS

### A.      Data Description.

The dataset for this research essay has been obtained from South African Heart Disease dataset which is a subset of a larger data set. It has 462 observations (instances) and 10 attributes in all, of which 9 are independent factors and 1 variable, i.e. CHD is the dependent variable or labelled class. The dataset is a retrospective sample of males in a heart-disease high-risk region of the Western Cape in South Africa (KEEL (Knowledge Extraction based on Evolutionary Learning) , 2004-2018) where the labelled class CHD has two predictive outcomes: positive (1) and negative(0). Each high-risk patient was monitored in this study and the attributes obtained were as follows: systolic blood pressure (sbp), cumulative tobacco in kg (tobacco), bad cholesterol also known as low density lipoprotein cholesterol (ldl), adiposity, family history of heart disease (famhist), type-A behaviour (typea), obesity, current alcohol consumption (alcohol), and age at onset (age).

 Attribute Domain Data Type Missing values? Sbp [101,218] Integer No tobacco [0.0,31.2] Number No Ldl [0.98,15.33] Number No adiposity [6.74,42.49] Number No Famhist {Present, Absent} Factor No Typea [13,78] Integer No Obesity [14.7,46.58] Number No alcohol [0.0,147.19] Number No Age [15,64] Integer No CHD [0,1] Integer No

Table 1. Attribute Description.

In order to get a clear understanding, we define few of the terms below (Sivakumar, n.d.) :

• Sbp: It is the blood pressure when the heart is contracting.
• Adiposity: It is measured as percent of body fat
• Type-A behaviour: It is characteristic of a person who is competitive, impatient and angry.
• Obesity: It is represented as Body Mass Index (BMI) which is calculated by dividing the weight of the person by the square of his height.

### B.      Data Pre-processing.

The South African Heart Disease dataset obtained from KEEL (KEEL (Knowledge Extraction based on Evolutionary Learning) , 2004-2018) is available in .dat file format. However, WEKA requires the file to be in.csv else .arff file format. As a result, we first get the data from .dat format to .csv format. This is done as follows:

1. Start ‘Microsoft Excel’
2. File => Open => Browse => Select “All Files”
4. Select “delimited” => Start Import at line 15 => Next
5. Unselect “Tab”
6. Select “Comma”, you should see bars separating the data fields now. => Next => Finish.
8. Save the excel file in .csv format.

Also, in order to avoid confusion and gain clarity during analysis, we used the ‘If…then’ feature in Microsoft Excel to convert the data type of ‘Class’ from Integer to Factor. Thus, all the value ‘1’ were replaced by ‘Yes’ and all value ‘0’ were replaced by ‘No’. The updated attribute description is as follows:

 Attribute Domain Data Type Missing values? sbp [101,218] Integer No tobacco [0.0,31.2] Number No ldl [0.98,15.33] Number No adiposity [6.74,42.49] Number No famhist {Present, Absent} Factor No typea [13,78] Integer No obesity [14.7,46.58] Number No alcohol [0.0,147.19] Number No age [15,64] Integer No CHD {No, Yes} Factor No

Table 2. Attributes Description (Updated)

### C.     Experimental Setting

#### 1)     Environment / Tool used

We will be using the open source software called WEKA (Version 3.8.3) to implement our data mining algorithms. WEKA which stands for Waikato Environment for Knowledge Learning is a computer program developed at the University of Waikato, New Zealand in order to generate insights from raw data. (Hazra, 2017) WEKA supports various data mining tasks ranging from pre-processing, classification, regression, feature selection, clustering, association and visualization. It is an easy and user-friendly software to use.

#### 2)     Estimation Methodology

The estimation methodology used here is K-fold cross validation. In this, the entire dataset is split into K folds (in this essay we are using K=10). For each iteration, (K-1) folds i.e. 9 folds are fitted as training dataset and the remaining 1-fold is used as evaluation of the test dataset. This process is repeated K times (i.e. 10 times) and the error rate is noted for each iteration. The final prediction error of the model is the average of all K individual test dataset error rates. (Mathematical Sciences – Chalmers University of Technology and University of Gothenburg, 2009)

#### 3)     Algorithm’s used

The machine learning technique employed for the prediction of CHD is the classification technique, a kind of supervised learning. The algorithms used here are:

### D.     Confusion Matrix and Evaluation Measures

#### 1)     Confusion Matrix

The performance of the developed classification model is measured with the help of its corresponding confusion matrix. Confusion matrix can be defined as a contingency table that displays the number of instances assigned to each class, thus allowing us to calculate the classification accuracy. There can be two or more classes involved, however we have only two classes in our undertaken study thereby giving us a 2×2 confusion matrix for each classification model.

For the experiment under consideration,

Class a = Yes (has CHD)

Class b = No (no CHD)

 Predicted Class Actual Class a (has CHD) b (no CHD) a (has CHD) TP FN b (no CHD) FP TN

Fig. 2 Layout of 2×2 Confusion Matrix.

Let us understand the terms TP, FP, FN and TN used in confusion matrix.

• True Positive (TP): Number of patients that are predicted to have CHD and do actually have CHD.
• False Positive (FP): Number of patients that are predicted to have CHD and do not actually have CHD.
• False Negative (FN): Number of patients that are predicted to not have CHD but do actually have CHD.
• True Negative (TN): Number of patients that are predicted to not have CHD and do not actually have CHD.

Fig. 3, Fig.4 and Fig.5 shows the Confusion matrix for Decision Tree J48, Naïve Bayes Algorithm and Support Vector Machine (SVM) respectively.

Fig. 3 Confusion Matrix for J48.

Fig. 4 Confusion matrix for Naïve Bayes Algorithm

Fig. 5 Confusion matrix for Support Vector Machine (SVM)

#### 2)     Evaluation measures

The most common measure of performance comparison is Accuracy. It is the number of predictions made correctly out of the total predictions made by the model. However, accuracy performance may not be reliable enough in this case as we have unequal number of observations in each class output.

$\mathit{Accuracy}=\frac{\left(\mathit{TP}+\mathit{TN}\right)}{\left(\mathit{TP}+\mathit{FP}+\mathit{FN}+\mathit{TN}\right)}$

Another performance measure that goes hand in hand with accuracy is Error Rate. It is the total number of incorrect predictions made by the model with respect to the total number of predictions, after training the classifier with a given dataset.

$\mathit{Error Rate}=1–\mathit{Accuracy}$

The next measure of performance is Precision. It measures how precise is the prediction by the model, i.e. out of the total number of instances predicted as positive, how many instances are actually positive. (Shung, 2018)

$\mathit{Precision}=\frac{\mathit{TP}}{\left(\mathit{TP}+\mathit{FP}\right)}$

The last measure of performance that will be used in this essay is Recall. It measures the number of instances correctly predicted as positive by the classifier out of the total number of instances that are actually positive. (Shung, 2018) Recall is also known as Sensitivity.

$\mathit{Recall}=\frac{\mathit{TP}}{\left(\mathit{TP}+\mathit{FN}\right)}$

### E.      Results and analysis

The results for the three classification machine learning algorithms i.e. Decision Tree J48, Naïve Bayes Algorithm and Support Vector Machine (SVM) respectively are summarized in the Table 3 below.

 J48 Naïve Bayes SVM Accuracy 0.707792 0.716450 0.709957 Error Rate 0.292208 0.283550 0.290043 Precision 0.698 0.722 0.700 Recall 0.708 0.716 0.710

Table 3 Comparison of Performance Measure.

It can be seen from the above results that Naïve Bayes Algorithm outshines other two classification models in all aspects. While all three models tend to show an accuracy of more than 70%, accuracy alone can’t be considered as the performance measurement for the underlying study. This is because the bivariate response of the labelled class in unequal. Out of the original 462 instances, only 160 patients are said to have Coronary Heart Disease (CHD) whereas the remaining 302 individuals do not suffer from Coronary Heart Disease. This discrepancy might sublimely influence the accuracy rate as the model can predict all values of the majority class and thus achieve an overall high accuracy while blinding out the mis-predictions occurring in the minority class. In order to avoid this unbalance affecting our performance measurement we do not solely rely on error rate and accuracy.

Fig. 6 Performance comparison for generated models.

In such situations, we consider Precision and Recall in addition to Error Rate and Accuracy. We can see in Fig. 6 that there is only a very slight difference between the performance of J48 and SVM model. However, overall displaying the best precision and recall rate among the three models under study, Naïve Bayes Algorithm has proven to be the most effective algorithm for predicting CHD, for the South African Heart Disease dataset.

## V.  CONCLUSION

There are various number of data mining techniques and machine learning algorithms available to facilitate prediction of Coronary Heart Disease. Moreover, many research approaches have been taken with respect to prediction and screening of diseases using medical analysis. This research essay was an attempt to highlight a few of these available techniques of prediction and the performance measures associated with them. While Support Vector Machine and Decision Tree J48 did perform well on its own, Naïve Bayes Algorithm turned out to be the best classifier model. Saying this, future research can be carried out to check if using unsupervised learning techniques before undertaking prediction using classification machine learning techniques, will enhance the model furthermore in terms of its prediction performance.

## VI.               REFERENCES

• Apte, C. S. (2012). Improve study of Heart Disease prediction system using Data Mining Classification techniques. International journal of computer application.
• Hazra, A. &. (2017). Heart Disease Diagnosis and Prediction Using Machine Learning and Data Mining Techniques: A Review. Advances in Computational Sciences and Technology., pp. 2137-2159.
• Heon Gyu Lee, K. y. (2007). Mining Biosignal Data: Coronary Artery Disease diagnosis Using Linear and Nonlinear Features of HRV. Springer-Verlag Berlin Heidelberg.
• I.S.Jenzi, P. D. (2013). A Reliable Classifier Model Using Data Mining Approach for Heart Disease Prediction. International Journal of Advanced Research in Computer Science and Software Engineering.
• KEEL (Knowledge Extraction based on Evolutionary Learning) . (2004-2018). South African Hearth data set . Retrieved from KEEL (Knowledge Extraction based on Evolutionary Learning) : https://sci2s.ugr.es/keel/dataset.php?cod=184.
• Mathematical Sciences – Chalmers University of Technology and University of Gothenburg. (2009). Regression, Model Selection, and Classification. Retrieved from Chalmers University of Technology and University of Gothenburg: http://www.math.chalmers.se/Stat/Grundutb/GU/MSG500/A09/RegSummary09.pdf
• Peter, T. K. (2012). An empirical study on prediction of heart disease using classification data mining techniques. International Conference on Advances in Engineering, Science and Management (ICAESM).
• SAS Institute. (2018). Machine Learning What it is and why it matters. Retrieved from SAS: https://www.sas.com/en_nz/insights/analytics/machine-learning.html
• Sharma, H., & Rizvi, M. A. (August 2017). Prediction of Heart Disease using Machine Learning Algorithms: A Survey. International Journal on Recent and Innovation Trends in Computing and Communication, 99-104.
• Shung, K. P. (2018, March 15). Accuracy, Precision, Recall or F1? Retrieved from Towards Data Science: https://towardsdatascience.com/accuracy-precision-recall-or-f1-331fb37c5cb9
• Sivakumar, S. (n.d.). Prediction of Coronary Heart Disease by learning from retrospective study. Retrieved from GitHub: http://srisai85.github.io/CHD/heart_attack.html
• Southern Cross. (2018, April). Coronary heart disease – causes, symptoms, prevention. Retrieved from Southern Cross: https://www.southerncross.co.nz/group/medical-library/coronary-heart-disease-causes-symptoms-prevention
• Yanwei X, W. J. (2007). Combination data mining. Proceedings International Conference on Convergence Information Technology, (pp. 868-872).

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# Tag Info

53

I'll answer in order: Output size = input size That's correct, GCM uses CTR internally. It encrypts a counter value for each block, but it only uses as many bits as required from the last block. CTR turns the block cipher into a stream cipher. Note that this doesn't include any additional authenticated data (AAD) that needs to be send, the optional ...

44

Lets see if I can clarify things for you. For one, the IV is not specifically related to AES at all. AES is a keyed invertible transform from a 128 bit value to a 128 bit value; that's all it can do. Now, if you just happen to have a 128 bit value that you want 'encrypted' into a 128 bit ciphertext, well, you can just use AES as is. However, we typically ...

32

Normally, in a properly designed cryptographic system, everything that must remain secret is either actual data (and the system exactly aims at preserving that confidentiality) or a key. Everything else ought to be public or at least publishable with no ill effect, as per Kerckhoffs' principle. Now it so happens that a number of cryptographic systems are ...

31

From the proposal of GCM (rewritten if statement): if $\operatorname{len}(IV) = 96$ then $Y_0 = IV || 0^{31}1$ else $Y_0 = \operatorname{GHASH}(H, \{\}, IV)$. So there are additional calculations for IV's other than 96 bits. This is why the original proposal has this recommendation: 96-bit IV values can be processed more efficiently, so that [ed: ...

26

You shouldn't think of it as ‘using an IV with AES’. In fact, unless you are a cryptographer, you should forget that ‘AES’ itself exists as a thing: it is a pseudorandom permutation family $\operatorname{AES}_k\colon \{0,1\}^{128} \to \{0,1\}^{128}$, which is a technical jargon term that is practically meaningless to any application developer. Instead, you ...

19

If your IV is predictable this is as (in)secure as assuming that you have a zero vector IV. And a zero vector IV allows you to perform a so-called Adaptive Chosen Plaintext Attack (ACPA). Why? Assume that you have a encryption mechanism that works in CBC mode. This means, that on the first iteration the $IV$ is XORed with your input message (which is ...

18

Even a single AES-GCM nonce reuse can be catastrophic. A single nonce reuse leaks the xor of plaintexts, so if one plaintext is known the adversary can completely decrypt the other. This is the same as for a two-time pad. In messages up to $\ell$ blocks long, after a single nonce reuse the adversary can narrow the authentication key down to $\ell$ ...

17

The $\operatorname{SHA-224}$ is defined in the exact same manner as $\operatorname{SHA-256}$ with different initial values and the digest is obtained truncating the hash value, FIPS PUB 180-4 Page 23. The different initial value provides domain separation. With domain separation $$\operatorname{SHA-224}(m) \neq \operatorname{SHA-256}(m)|_{224}$$ where $|_{... 15 It sounds like you're using a password-based key derivation function that accepts an optional salt input to convert a passphrase into an encryption key, which you then use to encrypt messages with a block cipher mode (or possibly some other type of stream cipher) that takes an IV or a nonce, and you want to know whether it's necessary to provide a salt to ... 14 It actually leaks information. You are sending: Encrypted IV:$AES(k,IV)$First ciphertext block of CBC:$AES(k, M_1 \oplus IV)$Eavesdropper can observe whether the two blocks are equal, which happens iff$M_1$is all zeroes. 13 You should use random IV even when unique keys are used. This prevents key-collision attack where the attacker collects number of cryptograms that have been encrypted with unique keys and brute-forces for key. Using predictable IV will reduce security of your cryptosystem by a factor of N (where N is the number of ciphertexts created). The attack recovers ... 13 With CBC mode the initialization vector is referred to as IV, because it is not nonce. There are ways to construct nonce so that it does not meet the needs of CBC mode. Random IV is one generation choice which is usually fine. Nonce can also be a counter, which is not ok here. Definitions Nonce means number used once. IV means initialization vector. CBC ... 13 Yes, it is. PBKDF2 derives a DK, a "derived key", which is indistinguishable from random. This is mainly because function within PBKDF2 is HMAC, and HMAC is a PRF. Let's see the definition from Wikipedia: In cryptography, a pseudorandom function family, abbreviated PRF, is a collection of efficiently-computable functions which emulate a random oracle in ... 12 The reference for this is NIST SP800-38A, especially its appendix B. Basically we consider the IV a binary value of the width of the block cipher (64-bit for DES, 128-bit for AES), and add 1 to that, except for one detail: there is no carry at some application-specified rank, defining the maximum number of blocks that can be enciphered with a single IV; if ... 11 The answer by mwhs is very wrong about CBC-MAC and its use of IV!! It is perfectly fine and secure to use the same IV for CBC-MAC! In fact, Jonathan Katz and Yehuda Lindell recommend using zero vector IV when invoking CBC-MAC because it saves storage and bandwidth in practical settings! (souce: Introduction to Modern Cryptography, Second Edition) The ... 11 Reusing an IV once opens you up to someone finding the XOR of those two plaintext, seriously compromising their confidentiality. Moreover, with GCM, a single IV reuse leaks significant information about the key used for authentication; if there are even a few pairs of reused IVs (not even one IV used many times; a few IVs each of which are used twice is ... 11 One example of a situation where an "IV" needs to be secret can be found in one of the original papers on the HMAC construction: Bellare, Mihir, Ran Canetti and Hugo Krawczyk. 1996. "Keying hash functions for message authentication." http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.134.8430 Quoting pages 4-5 (my boldface): The first obstacle ... 10 In this answer I'm assuming that a key is used to encrypt more than one message. The first weakness is that CBC with fixed IV leaks if messages share a common prefix. The second weakness is that it makes a padding oracle attack much more severe. Consider a device that knows the key and decrypts a ciphertext you send to it. While it won't tell you the ... 10 This additional 32 bit nonce acts as a salt, and makes multicollision attacks$2^{32}$times harder. In this attack, the attacker collects a huge number of TLS sessions, each with a record encrypted with the same nonce. He then selects a random key, and generates the counter mode keystream for the key (and the fixed nonce); he then checks if that key ... 10 That's correct. In most cases you can do what you are proposing. However be warned that by disregarding the authentication you clearly loose message authentication and bit flipping in AES-CTR encrypted stream is trivial. You can do what you are proposing if the AES-GCM IV size is of 96 bits. AES-GCM supports also longer sizes for IVs and for those cases ... 10 From a cryptographic standpoint, it doesn't matter how you transmit the IV. You can send it as a header, in the message body, as the path in the request method, or even the URG pointers in a few TCP packets. From the perspective of the encryption process itself, it doesn't care how it got the IV, no matter how silly the transmission method used, as long as ... 9 Actually, for CFB mode, the IV is the same size as the block size, 16 bytes. As for your question "does keeping the IV secret help security", the answer is "not really". CFB mode processes the message in blocks, and for each block of plaintext, combines that with the previous block of ciphertext to generate the next block of ciphertext. What the IV is ... 9 CBC mode encrypts as follows: $$C_0 = E_K(IV\oplus P_0);\\ C_i = E_K(C_{i-1}\oplus P_i),$$ where$P_i$are plaintext blocks and$C_i$are ciphertext blocks. Traditionally, IV must be random and is published alongside the ciphertext to enable decryption. If it is also published in your case, then this reveals the key and is trivially insecure. If the$IV=K\$...

9

The use of the AES key many times is not a problem. However, there is a fundamental flaw with your solution. The server has no way of validating that it received the client's authentic public key. In particular, a man-in-the-middle can capture the client's public key, can forward its own public key to the server, and can then decrypt all traffic sent by each ...

9

You don't need to put the IV in the AAD (Additional Authenticated Data) as already indicated in the comments. The GCM proposal as adopted by NIST (PDF) clearly specifies this in paragraph 2.1 Inputs and Outputs: The IV is authenticated, and it is not necessary to include it in the AAD field. The NIST document SP 800-38d (PDF) does not explicitly specify it,...

9

In the general case, the security goal is to reduce the probability that the internal 128-bit counter block ever takes the same value when instantiating the GCM cipher with a given key. That is catastrophic in combination with the CTR mode. The best strategy to minimize such probability depends on how the IV is generated. Case 1: IV is deterministic, 96 ...

9

First, this is not safe with ChaCha because the ChaCha nonce is only 64 bits long, since ChaCha nonces are normally chosen sequentially, so there would be a nonnegligible danger of collision with a reasonable number of messages. Let's say XChaCha instead, with a 192-bit nonce, which is large enough to choose at random without danger of collision. The ...

9

The question's citation is likely the reason why it was chosen different initial starting values for SHA-2 variants of the same internal block size. It is a valid objective by itself that different hash functions yield independent results, linkable only knowing their common input. It is not necessary to have a specific attack in mind to make that ...

9

No, just erasing the AES-CTR IV is not enough to reliably render the file undecryptable. To see why, consider what happens if the AES key is later compromised, and the attacker also happens to know at least one AES block (i.e. 16 bytes) of the "shredded" file's plaintext content. They can then XOR this known plaintext with the corresponding part of the ...

9

Usually. However, if you are using 128-bit AES in CTR mode (remember that GCM is essentially just CTR with authentication), then a kind of attack called a multi-target attack can become possible. This attack is realistic when an attacker has a huge amount of stored ciphertext, each with a random key. While breaking a specific key requires performing up to ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
# When And How Should CNN Ensembles Be Used?

3 main points
✔ Verify whether a single model or an ensemble model is better when the number of parameters is the same
✔ Experimented and validated the CNN-based image classification task in various settings
✔ Demonstrate that the ensemble model performs better overall

More or Less: When and How to Build Convolutional Neural Network Ensembles
written by
(Submitted on 29 Sept 2020 (modified: 26 Jan 2021))
Subjects: ensemble learning, empirical study, machine learning systems, computer vision

## First of all

When you want to improve the performance of a deep learning model, the simplest way is to increase the model size.

But is it better to use a single model with many parameters, or an ensemble of multiple models with relatively few parameters? In the paper presented in this article, we address the question of whether we should use an ensemble or a single model, especially for CNNs, from various perspectives such as training time, inference time, and memory usage.

## Technique

The comparison between ensemble and single models is made from the policies and methods described below.

### The rationale for fair and equitable ranking

As an ensemble/single model comparison, we compare architectures with the same number of parameters. There are two reasons why we did not use other metrics (training time, inference time, memory usage, etc.) instead of the number of parameters here.

• Because the number of parameters in the network is directly proportional to the other indicators.
• The number of parameters does not depend on the hardware used, etc., and can be calculated accurately from the network specifications.

Next, we describe how we design and conduct comparative experiments with single/ensemble network architectures.

To begin, a single CNN architecture is represented by $S^{(w,d)}$. where $w$ is the width of the network, $d$ is the depth, and $|S|$ is the number of parameters.

We also assume that $S^{(w,d)}$ belongs to the class $C$ of neural network architectures. Here, the ensemble network is represented by $E=\{E_1,.... ,E_k\}$. In this case, $E_1,...,E_k ,E_k \in C$ and $|E_1|+... +|E_k|=|S|$. In other words, the class of the architecture is identical to that of a single network, and the total number of parameters is the same.

Also in the experiment, all ensemble network architectures are identical ($E_1=... =R_k$) and the number of parameters is set to be equal ($=|S|/k$). Under these settings, we compare the single network and the ensemble network.

### Depth/width equivalent ensemble

The CNN ensemble network architecture is determined from two different policies: depth equivalent/width equivalent. This is illustrated in the following figure.

Briefly, in the depth-equivalent ensemble setting, the depth of the ensemble network is the same depth $d$ as that of the single network. In the width-equivalent ensemble setting, the width of the ensemble network is the same width $w$ as that of the single network.

In this case, the width $W^{\prime}$ in the depth equivalent setting is set to the maximum value within the range where the total number of parameters does not exceed $|S|$. Similarly, the depth $d^{\prime}$ in the width equivalent setting is set to the maximum value within the range where the total number of parameters does not exceed $|S|$. This is expressed as a mathematical expression as follows.

$w^{\prime}: k \cdot |E^{(w^{\prime},d)}_i| \leq |S^{(w,d)}| \leq k \cdot |E^{(w^{\prime}+1,d)_i}|$

$d^{\prime}: k \cdot |E^{(w,d^{\prime})}_i| \leq |S^{(w,d)}| \leq k \cdot |E^{(w,d^{\prime}+1)_i}|$

Overall, we compare (i) a single network $S^{(w,d)}$ belonging to the same network architecture class $C$, (ii) $k$ width-equivalent ensembles $S^{(w,d^{\prime})}$, and (iii) $k$ depth-equivalent ensembles $S^{(w^{\prime },d)}$ for comparison experiments.

## experiment

### Experiment setup

Data set

The data set used in the experiment is as follows.

• SVHN
• CIFAR-10
• CIFAR-100
• Tiny ImageNet
• Downsampled ImageNet-1k

Architecture

The CNN architecture used in our experiments is as follows.

• VGGNet
• ResNet
• DenseNet
• Wide ResNet

Evaluation index

To compare single network and ensemble network, we evaluate the following five aspects.

• generalization accuracy
• Training time per epoch
• Time to reach the specified accuracy (time to accuracy)
• inference time
• Memory usage

The hyperparameters and other details of the architecture are as follows. We use PyTorch as the experimental framework and an Nvidia V100 GPU for execution.

## Result

### Accuracy Comparison

The occurrence of EST (Ensemble Switchover Threshold)

The experimental results confirm the phenomenon that both depth/width equivalent ensembles outperform a single network when the resources exceed a certain threshold.

In the paper, we name this EST (Ensemble Switchover Threshold). This is shown in the following figure.

In this figure, we visualize which of the single network (single), depth equivalent (deq), and width equivalent (weq) ensembles is dominant. It can be seen that as the number of parameters increases to some extent (to the right), the ensemble method becomes dominant.

Besides, the test error rate in the DenseNet model is as follows.

Similarly here, when the number of parameters is somewhat larger, the ensemble method is dominant overall. This EST occurs when the resources are low to moderate (about 1M to 1.5M parameters and less than half of the training epoch). Therefore, it can be said that the results show that ensembles may well be more useful even when resources are not present in large quantities.

In general, these results show that ensembles can outperform single networks in a very wide range of use cases.

### For a more effective ensemble

As a result of our experiments, we have observed the following three findings for the effective use of ensemble models.

1. ensembles become more effective the more complex the data set is

The more complex the training dataset is, the closer EST is to the origin (smaller in both the number of epochs and the number of parameters).

2. Increasing the number of ensemble networks is effective under a sufficiently large parameter budget

As shown in the following figure, the larger the number of ensemble networks ($k$), the more the EST moves to the right (requiring more number of parameters).

Therefore, if we want to increase the number of ensemble networks, we must also ensure a sufficient number of parameters, otherwise, we cannot expect to improve the accuracy.

3. Depth equivalent ensemble shows better accuracy than width equivalent ensemble

For the depth/width equivalent ensemble, we found that the overall accuracy is higher than the depth equivalent ensemble. This can be attributed to the fact that modern CNN architectures are designed to improve accuracy as the depth of the layer increases.

### Comparison of time aspects

Comparison of training time

The training time required to achieve the accuracy of a single network model is shown in the figure below.

(The absence of a bar indicates that the accuracy of the single network model cannot be reached.)

Overall, the ensemble achieves the accuracy of the single network model much faster (1.2 to 5 times in our experiments). Besides, the training time per epoch is as follows.

Ensembles take longer to train per epoch because they train $k$ networks in both depth/width equivalent cases.

In this case, the depth-equivalent ensemble increases the learning time per epoch by about a factor of two compared to the width-equivalent ensemble. In terms of convergence time, the ensemble converges faster than the single network.

This can be attributed to the fact that all networks in the ensemble are smaller than the single network. In general, the ensemble does not require more training time than the single network, indicating that the ensemble can achieve the accuracy of the single network with less training time.

Comparison of inference time

The following figure shows the inference time per image.

For inference time, we see a similar trend as for training time per epoch. That is, the width-equivalent ensemble shows inference speeds comparable to a single network, while the depth-equivalent ensemble is much slower.

### Comparison of memory usage

A comparison of the memory usage for each setting is shown below.

This represents the minimum amount of memory required by the GPU in the hyperparameter set described earlier. This result is because the amount of memory required when training an ensemble network is the same as the memory required to train one of the $k$ networks. Advantages of this memory efficiency exist, such as the ability to increase the batch size and the effectiveness of training in memory-constrained environments.

## Summary

In this article, we presented our analysis of the decision on whether or not to use ensembles.

In general, the results show that ensemble models are more accurate than single models when the number of parameters is the same, that they can be trained faster, that they are capable of equivalent inference, and that the amount of memory required can be significantly reduced.

Although there are some limitations in what was verified in the experiment (e.g., the networks in the ensemble must be identical, and the study does not verify anything other than image classification), it is a study that provides very meaningful information.

If you have any suggestions for improvement of the content of the article,


text:
# Ubuntu – How to install Pantheon Desktop on Ubuntu 15.04

15.04pantheon

Yeah none of the other solutions in How to install the Pantheon desktop environment? for older versions of Ubuntu worked out. The only ppa that wouldn't say "404 not found" when updated was the ppa:elementary-os/daily, but I couldn't install elementary-desktop, since it just said (in the console) it wouldn't install packages related with it.

The following packages have unmet dependencies:
elementary-desktop : Depends: ubuntu-extras-keyring but it is not installed
Recommends: apport-hooks-elementary but it is not going to be installed
Recommends: bluez-gstreamer but it is not going to be installed
Recommends: elementary-default-settings but it is not going to be installed
Recommends: elementary-os-prerelease but it is not going to be installed
Recommends: fonts-elementary-core but it is not going to be installed
Recommends: gcalctool but it is not going to be installed
Recommends: geary but it is not going to be installed
Recommends: ginn but it is not going to be installed
Recommends: gtksourceview-3.0-theme-solarized-elementary but it is not installed
Recommends: ibus-pinyin
Recommends: light-locker but it is not going to be installed
Recommends: pantheon-greeter but it is not going to be installed
Recommends: plymouth-theme-elementary but it is not going to be installed
Recommends: plymouth-theme-elementary-text but it is not going to be installed
Recommends: print-test-page-elementary but it is not installed
Recommends: pulseaudio-module-gconf but it is not going to be installed
Recommends: switchboard but it is not going to be installed
Recommends: switchboard-gnome-control-center-override but it is not going to be installed
Recommends: switchboard-plug-about but it is not going to be installed
Recommends: switchboard-plug-applications but it is not going to be installed
Recommends: switchboard-plug-datetime but it is not going to be installed
Recommends: switchboard-plug-display but it is not going to be installed
Recommends: switchboard-plug-gcc-bluetooth but it is not going to be installed
Recommends: switchboard-plug-gcc-color but it is not going to be installed
Recommends: switchboard-plug-gcc-mouse but it is not going to be installed
Recommends: switchboard-plug-gcc-network but it is not going to be installed
Recommends: switchboard-plug-gcc-printer but it is not going to be installed
Recommends: switchboard-plug-gcc-sound but it is not going to be installed
Recommends: switchboard-plug-gcc-ua but it is not going to be installed
Recommends: switchboard-plug-gcc-users but it is not going to be installed
Recommends: switchboard-plug-gcc-wacom but it is not going to be installed
Recommends: switchboard-plug-keyboard but it is not going to be installed
Recommends: switchboard-plug-locale but it is not going to be installed
Recommends: switchboard-plug-notifications but it is not installed
Recommends: switchboard-plug-online-accounts but it is not going to be installed
Recommends: switchboard-plug-pantheon-shell but it is not going to be installed
Recommends: switchboard-plug-power but it is not going to be installed
Recommends: switchboard-plug-security-privacy but it is not going to be installed
Recommends: ttf-punjabi-fonts but it is not going to be installed
Recommends: tumbler-plugins-extra but it is not going to be installed
Recommends: user-specific-alternatives but it is not going to be installed
E: Unable to correct problems, you have held broken packages.

I've managed to install elementary desktop by rebuilding ubuntu-extras-keyring locally on my system, like this:

mkdir somedir; cd somedir
sudo apt-get install -y debhelper
wget http://archive.ubuntu.com/ubuntu/pool/main/u/ubuntu-extras-keyring/ubuntu-extras-keyring_2010.09.27.{tar.gz,dsc}
tar -xf *.tar.gz
cd ubuntu-extras-keyring-2010.09.17
debuild -i -us -uc -b
sudo dpkg -i ../ubuntu-extras-keyring_2010.09.27_all.deb

After that, elementary-desktop will install, but will error out at the end because it depends on systemd-shim which is no longer needed nor wanted with 15.04 having a full SystemD implementation.

When it errors out, run

sudo dpkg --force-depends -r indicator-datetime
sudo apt-get purge unity-control-center unity-control-center-signon

and it should complete the installation.

I expect in the near future the Elementary folks will fix their repository to handle SystemD properly - Ubuntu 15.04 move to SystemD was done a few weeks before the official release and the Elementary guys probably didn't have time to adapt to that.

After installation, you can log out and see "Pantheon" in your display manager's session list, but if you try to log in you'd get just the blueprint paper styled Elementary "beta wallpaper". The problem is that the session starts Slingshot and Gala, but not WingPanel or Plank. Currently I'm using using Slingshot's ALT-F2 shortcut to open the launcher and run Plank and WingPanel manually (just type the name in all lowercase and hit ENTER).


text:
Saturation Cascade MOSFETS (Need Help from EE Experts)

this is a very straightforward question.

I'm running a Harmonic simulation on ADS where I need to design a cascode amplifier of two NMOS and one PMOS, that have a gain higher than Av > -100. The catch is that all my MOSFETs need to be in saturation mode.

All I want to know if I did my calculations to keep them all in saturation mode correctly. I design everything but I need help specifically with that part. Here's the design.

The equations:

Don't worry about looking at anything else, just the Saturation equations. If I do them correctly, then the rest of the circuit will work.

I believe you can use $M1SAT > 0$, $M2SAT > 0$ and $M3SAT < 0$ (since that is a PMOS) to check for saturation. However, I did want to point out that your $M2OD$ and $M3OD$ will not be the overdrive voltage $V_{GS} - V_{TH}$.


text:
# How to solve the following limit?

$$\lim_{n\to\infty}{\bigg(1-\cfrac{1}{2^2}\bigg)\bigg(1-\cfrac{1}{3^2}\bigg) \cdots \bigg(1-\cfrac{1}{n^2}\bigg)}$$

This simplifies to $\prod_{n=1}^{\infty}{\cfrac{n(n+2)}{(n+1)^2}}$. Besides partial fractions and telescope, how else can we solve? Thank you!

-
Using the fact $x^2-y^2=(x-y)(x+y)$ –  Jlamprong Feb 3 '14 at 11:00
$\prod_{n=2}^{\infty}{\cfrac{(n-1)(n+1)}{n^2}}$. A further hint? –  Daniel C Feb 3 '14 at 11:04
I suppose there are typo's in your product formula. –  Claude Leibovici Feb 3 '14 at 11:08
Yes. Expanding the product it's the key to observe that they simplify each other. Thank you! –  Daniel C Feb 3 '14 at 11:15
See Basel problem. –  Lucian Feb 3 '14 at 13:02