List of contributors |
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xvii | |
I PLENARY LECTURES |
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3 | (254) |
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1 Roger Penrose--A Personal Appreciation |
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3 | (6) |
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1 Personal and historical remarks |
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3 | (1) |
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4 | (1) |
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3 Integrable systems and solitons |
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5 | (1) |
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5 | (1) |
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6 | (1) |
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6 | (1) |
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7 | (2) |
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2 Hypercomplex Manifolds and the Space of Framings |
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9 | (22) |
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9 | (1) |
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10 | (3) |
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13 | (1) |
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14 | (6) |
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5 Twistor spaces and isomonodromic deformations |
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20 | (4) |
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6 Holonomy and hypergeometric functions |
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24 | (5) |
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29 | (2) |
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3 Gauge Theory in Higher Dimensions |
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31 | (18) |
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31 | (1) |
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31 | (2) |
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33 | (4) |
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37 | (1) |
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5 The two-dimensional picture |
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38 | (2) |
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6 Adiabatic limits and dimension reduction |
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40 | (2) |
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7 An example: quadrics in P(5) |
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42 | (1) |
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8 Vanishing cycles and pseudoholomorphic curves |
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43 | (2) |
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45 | (2) |
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47 | (2) |
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4 Noncommutative Differential Geometry and the Structure of Space-Time |
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49 | (32) |
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Foreword |
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49 | (1) |
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49 | (5) |
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54 | (10) |
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3 The local index formula and the transverse fundamental class |
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64 | (5) |
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4 The notion of manifold and the axioms of geometry |
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69 | (6) |
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5 The spectral geometry of space-time |
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75 | (3) |
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78 | (3) |
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5 Einstein's Equation and Conformal Structure |
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81 | (18) |
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81 | (1) |
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2 Asymptotic simplicity and conformal Einstein equations |
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82 | (2) |
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3 De Sitter-type space-times |
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84 | (1) |
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4 Anti-de Sitter-type space-times |
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84 | (2) |
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5 Minkowski-type space-times |
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86 | (8) |
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5.1 Conformal Minkowski space |
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86 | (1) |
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5.2 Some existence results |
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87 | (1) |
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88 | (1) |
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5.4 Assumptions on the data |
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89 | (1) |
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5.5 Gauge conditions and conformal field equations |
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90 | (1) |
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5.6 The finite regular initial value problem near space-like infinity |
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91 | (1) |
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5.7 The total characteristic at space-like infinity |
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92 | (1) |
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5.8 Comments on our procedure |
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93 | (1) |
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94 | (3) |
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97 | (2) |
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6 Twistors, Geometry, and Integrable Systems |
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99 | (10) |
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99 | (1) |
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2 Twistors for 3-dimensional space-time |
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99 | (2) |
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3 An integrable Yang-Mills-Higgs system |
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101 | (2) |
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103 | (1) |
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104 | (2) |
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106 | (1) |
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107 | (2) |
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7 On Four-Dimensional Einstein Manifolds |
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109 | (14) |
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109 | (1) |
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2 The curvature of 4-manifolds |
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110 | (1) |
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3 The Hitchin-Thorpe inequality |
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111 | (2) |
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113 | (1) |
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5 Seiberg-Witten techniques |
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114 | (3) |
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117 | (3) |
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120 | (1) |
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120 | (3) |
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8 Loss of Information in Black Holes |
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123 | (12) |
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1 Personal and historical remarks |
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123 | (1) |
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124 | (11) |
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9 Funda-mental Geometry: the Penrose-Hameroff `Orch OR' Model of Consciousness |
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135 | (26) |
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1 Introduction: on the trail of an enigma |
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135 | (1) |
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2 Philosophy: a panexperiential `funda-mentality' |
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135 | (3) |
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3 Physics: objective reduction (OR) |
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138 | (2) |
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4 Biology: quantum coherence in microtubules? |
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140 | (10) |
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140 | (1) |
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4.2 Frohlich's biological coherence |
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141 | (1) |
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4.3 Quantum isolation--avoiding environmental interaction and decoherence |
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142 | (2) |
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4.4 Macroscopic quantum coherence and gap junctions |
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144 | (2) |
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4.5 Evolution, Orch OR and the Cambrian explosion |
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146 | (4) |
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5 Summary of the `Orch OR' model of consciousness |
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150 | (2) |
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6 Assumptions and testable predictions of Orch OR |
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152 | (2) |
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7 Conclusion: Penrose's Platonic world |
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154 | (1) |
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155 | (6) |
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10 Implications of Transience for Spacetime Structure |
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161 | (12) |
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170 | (3) |
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11 Geometric Issues in Quantum Gravity |
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173 | (22) |
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173 | (4) |
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173 | (2) |
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175 | (2) |
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177 | (5) |
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177 | (1) |
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2.2 Quantum configuration space |
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178 | (2) |
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2.3 Kinematical Hilbert space |
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180 | (2) |
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182 | (7) |
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182 | (1) |
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183 | (2) |
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185 | (2) |
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3.4 Properties of area operators |
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187 | (2) |
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189 | (3) |
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192 | (1) |
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192 | (3) |
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12 From Quantum Code-making to Quantum Code-breaking |
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195 | (20) |
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1 What is wrong with classical cryptography? |
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195 | (2) |
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2 Is the Bell theorem of any practical use? |
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197 | (2) |
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3 Quantum key distribution |
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199 | (2) |
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201 | (2) |
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5 Public key cryptosystems |
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203 | (2) |
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6 Fast and slow algorithms |
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205 | (1) |
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206 | (3) |
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209 | (2) |
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211 | (1) |
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212 | (3) |
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13 Penrose Tilings and Quasicrystals Revisited |
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215 | (12) |
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215 | (3) |
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2 New approach to Penrose tiling: single tile/matching rule |
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218 | (2) |
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3 New approach to Penrose tiling: maximizing cluster density |
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220 | (3) |
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223 | (2) |
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225 | (2) |
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14 Decaying Neutrinos and the Geometry of the Universe |
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227 | (8) |
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227 | (1) |
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2 Relic neutrinos as dark matter |
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228 | (2) |
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3 Decaying neutrinos and the ionisation of the universe |
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230 | (2) |
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4 A new observational test of the decaying neutrino theory |
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232 | (1) |
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233 | (2) |
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15 Quantum Geometric Origin of All Forces in String Theory |
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235 | (10) |
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235 | (1) |
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2 Forces and local symmetries |
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235 | (1) |
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3 Field-theoretic Kaluza-Klein |
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236 | (2) |
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238 | (2) |
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5 String-theoretic Kaluza-Klein |
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240 | (1) |
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6 S-duality and the big fix |
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241 | (2) |
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243 | (2) |
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16 Space from the Point of View of Loop Groups |
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245 | (12) |
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1 Loop groups and quantum field theory |
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246 | (3) |
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2 Loop groups and low-dimensional topology |
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249 | (1) |
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250 | (2) |
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252 | (5) |
II PARALLEL SESSION I: QUANTUM THEORY AND BEYOND |
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257 | (50) |
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17 The Twistor Diagram Programme |
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257 | (8) |
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262 | (3) |
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18 Geometric Models for Quantum Statistical Inference |
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265 | (12) |
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265 | (1) |
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266 | (3) |
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269 | (1) |
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270 | (1) |
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5 Quantum statistical estimation |
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271 | (1) |
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6 Higher order variance bounds |
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272 | (2) |
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7 Quantum geometry vs information geometry |
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274 | (1) |
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274 | (3) |
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19 Spin Networks and Topology |
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277 | (14) |
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277 | (1) |
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2 Networks and discrete space |
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277 | (1) |
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3 The bracket state summation and the Jones polynomial |
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278 | (4) |
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3.1 The Reidemeister moves |
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279 | (3) |
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282 | (5) |
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287 | (4) |
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20 The Physics of Spin Networks |
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291 | (16) |
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291 | (1) |
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2 Spin networks in non-perturbative quantum gravity |
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292 | (7) |
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299 | (2) |
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301 | (6) |
III PARALLEL SESSION II: GEOMETRY AND GRAVITY |
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307 | (42) |
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21 The Sen Conjecture for Distinct Fundamental Monopoles |
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307 | (10) |
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307 | (1) |
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308 | (1) |
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3 Weak XXX strong coupling |
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308 | (1) |
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4 Bound states at threshold |
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309 | (1) |
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309 | (3) |
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312 | (1) |
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313 | (1) |
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314 | (1) |
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9 Bound states in the continuum |
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315 | (1) |
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315 | (2) |
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22 An Unorthodox View of GR via Characteristic Surfaces |
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317 | (8) |
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317 | (2) |
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2 The null surface formulation of GR |
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319 | (3) |
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319 | (1) |
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2.2 Imposing the Einstein equations |
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319 | (1) |
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2.3 Self-dual Einstein equations |
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320 | (1) |
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2.4 Asymptotically flat GR |
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321 | (1) |
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3 Discussion and applications |
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322 | (1) |
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323 | (2) |
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23 Amalgamated Codazzi-Raychaudhuri Identity for Foliation |
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325 | (12) |
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325 | (3) |
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328 | (2) |
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3 The adapted foliation connection |
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330 | (1) |
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4 The amalgamated foliation curvature tensor |
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331 | (3) |
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334 | (3) |
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24 Abstract/Virtual/Reality/Complexity |
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337 | (12) |
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337 | (1) |
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338 | (2) |
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340 | (2) |
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342 | (1) |
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343 | (2) |
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345 | (4) |
IV PARALLEL SESSION III: FUNDAMENTAL QUESTIONS IN QUANTUM MECHANICS |
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349 | (34) |
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25 Interaction-Free Measurements |
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349 | (8) |
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1 The Penrose bomb testing problem |
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349 | (2) |
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2 The Elitzur-Vaidman bomb testing problem |
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351 | (1) |
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3 Experimental realization of the IFM |
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352 | (1) |
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353 | (1) |
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5 Applications of the IFM |
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354 | (1) |
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6 The IFM as counterfactuals |
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354 | (1) |
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355 | (2) |
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26 Quantum Measurement Problem and the Gravitational Field |
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357 | (12) |
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357 | (1) |
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2 Quantum measurement problem |
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358 | (2) |
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3 Efforts to resolve the measurement problem |
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360 | (3) |
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4 Gravitational reduction of the wave packet |
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363 | (4) |
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367 | (2) |
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27 Entanglement and Quantum Computation |
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369 | (14) |
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369 | (1) |
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2 Quantum computation and complexity |
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370 | (3) |
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3 Superposition and entanglement in quantum computation |
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373 | (3) |
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4 Entanglement and the super-fast quantum Fourier transform |
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376 | (1) |
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377 | (1) |
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378 | (5) |
V PARALLEL SESSION IV: MATHEMATICAL ASPECTS OF TWISTOR THEORY |
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383 | (40) |
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28 Penrose Transform for Flag Domains |
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383 | (12) |
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1 The Penrose transform in formulas |
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383 | (3) |
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383 | (1) |
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384 | (1) |
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1.3 Inverse Penrose transform |
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385 | (1) |
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1.4 Holomorphic cohomology |
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385 | (1) |
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1.5 Boundary integral formula |
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386 | (1) |
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2 Generalized Penrose transform (geometrical problems) |
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386 | (4) |
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2.1 Holomorphic cohomology |
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386 | (1) |
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387 | (1) |
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388 | (1) |
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389 | (1) |
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3 Generalized Penrose transform (analytic problems) |
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390 | (2) |
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392 | (3) |
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29 Twistor Solution of the Holonomy Problem |
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395 | (8) |
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395 | (1) |
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395 | (2) |
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3 Twistor theory of holonomy groups |
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397 | (4) |
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401 | (2) |
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30 The Penrose Transform and Real Integral Geometry |
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403 | (8) |
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403 | (1) |
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403 | (1) |
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3 The holomorphic Penrose transform |
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404 | (1) |
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4 The connection with integral geometry |
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405 | (1) |
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5 A new method in real integral geometry |
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406 | (3) |
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5.1 Pull-back from RP(3) to F |
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406 | (1) |
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5.2 Push-down from F to Gr(2)(R(4)) |
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407 | (1) |
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408 | (1) |
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409 | (2) |
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31 Pythagorean Spinors and Penrose Twistors |
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411 | (12) |
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411 | (1) |
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411 | (2) |
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3 Projective quadrics and twistors |
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413 | (5) |
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414 | (3) |
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417 | (1) |
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418 | (5) |
VI AFTERWORD |
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1 Geometry, and the roots and aims of twistor theory |
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423 | (1) |
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2 Towards a twistor description of Einsteinian physics |
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424 | (5) |
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3 Further issues of physics and biology |
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