Quantum Bio-informatics IV: From Quantum Information to Bio-informatics (Qp-Pq: Quantum Probability and White Noise Analysis)

CONTENTS......Page 8
Preface......Page 6
1. QP-DYN algorithms: general scheme......Page 12
2. Dynamical systems underlying the QP-DYN algorithms......Page 15
3. From sequences of vectors to sequences of bits......Page 16
3.1. Recursive construction of the sequence (K,n)......Page 17
3.2. KGF by left concatenation......Page 18
4. Modifications of the dynamical law......Page 19
5. Orbit jump function......Page 20
7. Use of multiple dynamical systems......Page 21
7.1. The 2 prime protocol......Page 22
8. Attacks to the 1-matrix algorithm......Page 23
9. Attacks to the 2-matrix algorithm......Page 24
References......Page 25
1. Introduction......Page 28
3. Available Cis-Module Data in public database......Page 29
4.3. Extraction and Comparison upstream region (Fig4-3, 4-4)......Page 31
5. Explanation of User Interface and Advantage of Cis-Module Database......Page 34
6.2. Prediction of gene network for caloric restriction Rat......Page 35
6.3. Evaluation CE pattern predicted in USR of genes......Page 36
7. Conclusion and Future works......Page 37
References......Page 38
1. Introduction......Page 40
2. Murray-von Neumann's result......Page 42
3.1.1. Strong Resolvent Topology......Page 43
3.1.2. T-Measure Topology......Page 44
3.2. Main Results......Page 45
4. Categorical Characterization of......Page 47
References......Page 49
1. Introduction......Page 52
2. Time Operators of a Hamiltonian with Discrete Eigenvalues (I)......Page 53
2.1. A general class of time operators of H......Page 54
2.2. Necessary condition for H to have time operators and the general form of them......Page 56
2.3. Non-existence theorems of time operators......Page 57
3. Time Operators of a Hamiltonian with Discrete Eigenvalues (II)......Page 58
References......Page 61
1. Introduction......Page 62
References......Page 70
1. Introduction......Page 72
2.1. Normal states, densities and pairings......Page 74
2.2. Examples: the standard and the qubit paring......Page 75
2.3. Coupling operators......Page 77
2.4. Mixed entangled states......Page 78
2.6. The standard entanglement......Page 79
3.1. Entanglement measures......Page 80
3.2. The general information divergences......Page 81
3.3. The relative l-entropies of types A&B......Page 83
3.4. The entropy increase, its concavity and additivity......Page 84
3.5. A new type of relative l-entropy C......Page 86
3.6. Other new entropy types D&E......Page 87
4.2. The proper quantum entropies......Page 89
4.4. Entanglement as quantum encoding......Page 91
5.1. The quantum and semiclassical capacities......Page 92
5.3. Block encoding for quantum product channels......Page 93
5.4. The additivity problem for quantum capacities......Page 94
5.6. The additivity of true quantum capacities......Page 95
7. Appendix: The standard pairing......Page 97
References......Page 99
1. Introduction......Page 102
2. Local vs. non-local approach......Page 104
3. Examples......Page 105
References......Page 109
1. Introduction......Page 112
2. Some biological facts and experiments......Page 113
3. The Space of Signals......Page 116
4. The Process of Recognition......Page 118
5. A Markov Chain with Discrete Time......Page 122
References......Page 124
1. Introduction......Page 128
2.1. Historical Development......Page 130
2.2. General Setup of a Statistical Test......Page 131
2.3. Specialties for Testing of RNGs......Page 133
3. Test Results......Page 136
References......Page 138
1. Introduction......Page 140
2. A new measure taking entangled effects of two consecutive pairs in residues......Page 141
3. Evaluation......Page 143
4. Results......Page 144
References......Page 146
1. Prologue......Page 148
2. An i.i.d. random variables as a representation of parameter set......Page 149
3. Poisson noise......Page 151
4. Calculus of Poisson noise functionals......Page 152
References......Page 154
1. Introduction......Page 156
2. The Degree of Entanglement......Page 157
3.1. Circulant states......Page 159
3.2. Horodecki state......Page 162
4. Bell diagonal states......Page 163
5. Conclusions......Page 165
References......Page 166
1. Introduction......Page 168
2. Basic notations......Page 169
3. A Special Type of a Stochastic Partial Differential Equation......Page 171
4. Some Lemmas......Page 175
5. Proof......Page 176
References......Page 182
2. Quantum Algorithm......Page 184
3. OMV SAT Algorithm......Page 186
3.1. Chaos Amplifier......Page 188
4. Language Classes......Page 189
5.1. Representation of a Game......Page 190
5.2. Pebble Game......Page 191
5.3. Computational Complexity of a Classical Algorithm for Pebble Game......Page 192
7. Computational Complexity......Page 193
References......Page 194
1. Introduction......Page 196
2. Identification of quantum states......Page 199
3. Stroboscopic tomography of open quantum systems......Page 200
4. Algebraic approach to identification problems......Page 204
5. Examples. Low dimensional cases......Page 206
References......Page 208
1. Introduction......Page 210
2. Detecting and measuring entanglement......Page 211
3. Estimations of concurrence......Page 213
4. Main result......Page 214
5. Examples......Page 216
References......Page 219
1. Introduction......Page 220
2.1. LTP and classical decision making......Page 222
2.2. Violation of LTP from contextuality of probabilities......Page 223
2.3. Violation of LTP in cognitive science......Page 224
3. Prequantum classical statistical field theory: noncomposite systems......Page 225
4. Composite systems......Page 228
5.2. Precognitive time scale......Page 232
References......Page 233
1. Introduction......Page 234
2. Entanglement mapping and its classification......Page 236
3. Quantum conditional probability operator and its classification......Page 239
4. The relation between entanglement mapping and QCPO......Page 240
5. Mutual entropy and conditional entropy vs. quantum entanglement......Page 241
References......Page 246
1. Introduction......Page 248
2. Multipartite entanglement......Page 250
3. Construction of entanglement witnesses......Page 253
4. Example: Anisotropic Heisenberg spin chains......Page 258
References......Page 265
1. Introduction......Page 266
2. Preliminaries......Page 267
3. Quantum quadratic operators with Kadison-Schwarz property on M2 (C)......Page 268
4. An Example of q.q.o. which is not Kadision-Schwarz one......Page 272
References......Page 276
1. Introduction......Page 278
2. Preliminaries......Page 280
3. Constructions of Quantum d-Markov chains on the Cayley tree......Page 282
4. Quantum d-Markov chains associated with XY-model......Page 284
References......Page 288
1.1. "Theory of Everything" vs. Duheme-Quine thesis......Page 290
1.2. "Geometrization principle" vs. Physical emergence of space-time......Page 291
2. Universality inherent in Macro-levels......Page 292
3. "Sector bundle" associated with broken symmetry......Page 294
4. Emergence of space(-time) as symmetry breaking......Page 296
References......Page 299
1. Introduction......Page 302
2.1. Spaces......Page 303
2.2. Functions......Page 304
2.3. Global variables and further definitions......Page 305
3.1. Coding......Page 306
3.3. Preliminary observations......Page 307
4.2. Functions and implementation......Page 308
4.3. Observation......Page 310
5. The role of the Coding Functions......Page 311
6.1. Cryptanalysis......Page 312
6.2. OUT Idea......Page 313
6.3.3. The Data......Page 314
6.4.1. The Experiment......Page 315
6.4.4. The Results......Page 316
6.5. First Results - Differences......Page 317
6.6.4. Phase II - Strategies......Page 318
6.8. New Results - Differences......Page 319
References......Page 320
1. Introduction......Page 322
2. Analysis of white noise functionals......Page 323
4. Operators : from discrete to continuous form......Page 324
References......Page 329
Introduction......Page 332
1. Symplectic locally convex spaces and Hamilton's equations.......Page 333
2. Liouville's equations with respect to measures.......Page 334
3. Systems of equations with respect to finite-dimensional distributions of probabilities.......Page 337
4. Bogolyubov's systems of equations.......Page 339
5. Wigner measures.......Page 341
6. Generalization of Poincare's model.......Page 346
References......Page 347
1. Introduction......Page 350
2. Review of generalized total uncertainty measure......Page 354
3. Approximate confidence interval for measure......Page 355
4. Analysis of data......Page 356
5. Remarks......Page 357
7. Discussion......Page 358
References......Page 359
1. Introduction......Page 366
2. Quantum Hall Effects......Page 367
3. Magnetoplasmon Dispersion Plateaus......Page 368
4. Radiation-induced Magnetoresistance Oscillations......Page 370
References......Page 372
1. Introduction......Page 374
2. Anharmonic oscillator......Page 377
3. Newtonian and Averaged Trajectories Comparison......Page 378
4. Numerical Approach......Page 379
References......Page 383
1. Introduction......Page 384
2.1. Plant genome information......Page 386
2.5. Interspecies Quantile-Quantile Plots......Page 387
3.1. DNA-motif variance as a measure of information content......Page 388
3.2. Quantile-quantile (QQ)-plots for interspecies promoter comparison......Page 389
References......Page 396
1. Introduction......Page 398
2. Quantum Channels......Page 399
2.1. Noisy optical channel......Page 400
3.1.1. (1) von Neumann entropy......Page 401
3.1.2. (2) S-mixing entropy......Page 402
3.2.2. (2) Ohya mutual entropy for general C*-system......Page 403
4. Quantum Mean Mutual Entropy of K-S type......Page 404
4.1. Computation of mean mutual entropy for modulated states of OOK and PSK......Page 406
4.1.1. Mean mutual entropy for modulated state of OOK and PSK......Page 407
References......Page 411
1. Introduction......Page 414
2. A biased-sampling attack on Ekert protocol......Page 415
3. Countermeasures......Page 418
4. Conclusion......Page 422
References......Page 423
1. Introduction......Page 424
2.1. Estimation of diffusion tensor of a macromolecule from atomic structure......Page 425
2.2. Brownian dynamics for arbitrarily shaped objects......Page 427
2.4. Simulation conditions and analysis......Page 429
3.1. Estimation of diffusion tensor of a macromolecule from atomic structure......Page 430
3.2. Construction of the intracellular environment......Page 431
3.3. Effect of molecular shapes on diffusion......Page 432
4. Discussion......Page 434
References......Page 435
1. Calcium ion as a key element in information processingl......Page 438
2. Ca2+ -mediated signaling and plant immunity4.6......Page 439
3. Regulation of spatio-temporal patterns of cytosolic Ca2+ concentration triggered by signal molecules from pathogens......Page 440
4. Ca2+-permeable cation channels and plant immunityl-3......Page 442
6. Decoding of Ca2+ -mediated signals by Ca2+ sensor proteins1,20.22......Page 443
Acknowledgement......Page 446
References......Page 447
1. Introduction......Page 448
1.2. Modularity......Page 449
2. A Few Words on Graphs......Page 450
2.1. How to plot a graph......Page 451
2.2. Modularity of Graphs......Page 452
3. What NetzCope does......Page 453
4.2. The Adjacency Matrix......Page 455
4.3. Plotting the Graph......Page 457
4.5. The Network Portrait......Page 458
6. Conclusion......Page 460
References......Page 461
1. Introduction......Page 462
2.1. The Code Structure of HIV-I......Page 463
2.2. The Evolutionary Changes of HIV-I by Entropic Chaos Degree......Page 464
2.3. Longitudinal Sequence Data......Page 465
3. Results and Discussion......Page 466
References......Page 470
1. Introduction......Page 472
2. Modeling of NTNHA structures......Page 474
3. Modeling of HA-70 structure......Page 477
References......Page 478
1. Introduction......Page 480
2.2. The energy landscape of CU06 octahedron......Page 483
2.3. Kamimura-Suwa model (K-S model)......Page 486
2.4. Effective Hamiltonian for the Kamimura-Suwa model (K-S) model......Page 487
3.1. Effective energy band......Page 488
3.2. The shape of Fermi surface......Page 489
4.2. Effective inter-hole interaction via phonon......Page 491
4.3. Calculated results of the hole-concentration dependence of Tc and of isotope effect......Page 495
5. Conclusion and concluding remarks......Page 498
References......Page 499