From Linear Operators to Computational Biology Essays in Memory of Jacob T. Schwartz

Cover......Page 1
From Linear Operators to Computational Biology......Page 3
Recollecting Jack Schwartz......Page 6
Contents......Page 8
Contributors......Page 9
1 Introduction......Page 10
References......Page 13
1 Quantum Theories......Page 14
1.1 Canonical Quantum Theories......Page 18
2 Yang Space-Times......Page 19
3 Whither Physics?......Page 20
4 Below Hilbert Space......Page 22
5 Quantification......Page 23
6 Palev Statistics......Page 24
7 Neutral Metrics......Page 25
8 Quantum Events......Page 27
9 Quantum Gauges......Page 29
References......Page 30
Jack Schwartz Meets Karl Marx......Page 32
1 Prologue: Contemporary Issues......Page 33
2 Hegel and Marx......Page 37
3 Marx's Enigmatic 00......Page 42
4 Conclusion......Page 44
References......Page 45
1 The Origins of the SETL Project......Page 47
2 Executable Specifications......Page 49
3 Optimizing at the Algorithmic Level......Page 51
4 Improving Programming Productivity......Page 52
References......Page 53
1 Prologue......Page 55
2 Introduction......Page 56
3 Multi-level Syllogistic......Page 57
3.1 A Tableau-Based Decision Procedure for MLSS......Page 67
4 Extensions of Multi-level Syllogistic......Page 71
4.1 Monotone Functions......Page 74
4.2 Monotone Functions Having a Known Order Relationship......Page 75
4.4 Additive Functions......Page 76
4.5 arb Function......Page 77
4.7 Total Ordering Relationships on Sets......Page 78
4.8 Multiple Functions with Known Ranges and Domains......Page 79
4.9 Pairs of Mutually Inverse Functions f, g......Page 80
4.11 car, cdr, and cons Functions......Page 81
4.13 Predicates Representable by Functions......Page 82
5 Further Extensions of Multi-level Syllogistic......Page 84
5.1 MLS with the General Union Operator......Page 86
5.2 MLS with the Powerset Operator......Page 88
References......Page 91
1.1 Jack Schwartz and Robotics, and Me......Page 94
2 Jack and Motion Planning: The Piano Movers Papers I, II......Page 96
2.1 Piano Movers I......Page 97
Discussion......Page 100
2.2 Piano Movers II......Page 101
Piano Movers III, IV, and V......Page 102
Cell Decompositions......Page 103
Lower Bounds......Page 104
Efficient Motion Planning Algorithms......Page 106
3.1 Jack and Robotics at Large......Page 107
References......Page 108
1 Opening......Page 112
2 Gripping......Page 114
2.1 Closure Grasps......Page 117
2.2 Synthesizing a Grasp......Page 119
Synthesizing a Equilibrium Grasp with Seven Fingers......Page 121
3 Groping......Page 122
4 Closing......Page 124
References......Page 125
1 Introduction......Page 127
2 Architecture of a Proof Scenario......Page 129
3 Definition Mechanisms......Page 132
4 Inferential Armory......Page 134
Appendix:  Claw-Free Graphs as Sets......Page 137
A.1 Basic Laws on the Union-Set Global Operation......Page 138
A.2 Transitive Sets......Page 140
A.3 Basic Laws on the Finitude Property......Page 142
A.4 Some Combinatorics of the Union-Set Operation......Page 143
A.5 Claw-Free, Transitive Sets and Their Pivots......Page 145
A.6 Hanks, Cycles, and Hamiltonian Cycles......Page 152
A.7 Hamiltonicity of Squared Claw-Free Sets......Page 163
A.8 Perfect Matchings......Page 165
A.9 Each Claw-Free Set Admits a Near-Perfect Matching......Page 168
A.10 From Membership Digraphs to General Graphs......Page 171
References......Page 173
Computational Approaches to RNAi and Gene Silencing......Page 174
2 Gene Silencing and RNA Interference......Page 175
2.1 siRNA......Page 176
2.2 miRNA......Page 177
2.3 miRNAs in Development and Disease......Page 178
3 miRNA Genes Prediction......Page 180
4 Prediction of miRNA Targets......Page 181
4.1 Tools for the Prediction of miRNA Targets......Page 183
5 Design of Synthetic miRNAs......Page 185
5.1 Tools for the Design of siRNA and miRNA......Page 186
6.1 The miRò System......Page 188
6.2 The miRò Web Interface......Page 190
6.3 The miRò Data Mining Facilities......Page 191
7 Conclusions......Page 193
References......Page 195
1 Taming the Robot......Page 200
2 Genomes as Searchable Strings......Page 201
3 Phylogeny of Mitochondria......Page 202
5 Illusions......Page 204
6 Memory......Page 205
7 The End Game......Page 206
References......Page 207
1963......Page 208
1979......Page 209
1985......Page 210
1995......Page 211
Index......Page 212