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References

1
V. I. Abkevich, A. M. Gutin and E. I. Shakhnovich, ``Impact of Local and Non-Local Interactions on Thermodynamics and Kinetics of Protein Folding,'' J. Mol. Biol. 252, 460 (1995).

[Academic] reading, after a certain age, diverts the mind too much from its creative pursuits. Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.ALBERT EINSTEIN

INVERSE PROTEIN FOLDING

2
D. J. Amit, Modeling Brain Function (Cambridge University Press, Cambridge, UK, 1989), Ch. 6, Ch. 7.

3
C. B. Anfinsen et al., ``The Kinetics of Formation of Native Ribonuclease during Oxidation of the Reduced Polypeptide Chain,'' Proc. Natl. Acad. Sci. USA 47, 1309 (1961).

4
J. D. Bryngelson and P. G. Wolynes, ``Spin Glasses and the Statistical Mechanics of Protein Folding,'' Proc. Nat. Acad. Sci. USA 84, 7524 (1987).

5
Joseph D. Bryngelson et al., ``Funnels, Pathways and the Energy Landscape of Protein Folding: A Synthesis,'' Proteins: Structure, Function and Genetics, 21, 167 (1995).

6
Thomas E. Creighton, Protein Folding (W. H. Freeman and Company, New York, 1992).

7
Ken A. Dill et al., ``Principles of Protein Folding -- A Perspective from Simple Exact Models,'' Protein Sci. 4, 561 (1995).

8
Ken A. Dill and Sun Chan, ``From Levinthal to Pathways to Funnels,'' Nature Struct. Biol. 4, 10 (1997).

9
Thomas M. Fink and Robin C. Ball, ``Robustness and Efficiency in Inverse Protein Folding,'' Physica D 107, 199 (1997).

10
Thomas M. Fink and Robin C. Ball, ``Inverse Protein Folding as an Associative Memory,'' submitted to Phys. Rev. Lett. (1997).

11
Thomas M. Fink and Robin C. Ball, ``Kinetically Oriented Sequence Selection,'' for Phys. Rev. Lett. (1998).

12
P. J. Flory, ``The Configuration of Real Polymer Chains,'' J. Chem. Phys. 17, 303 (1949).

13
A. M. Gutin, V. I. Abkevich and E. I. Shakhnovich, ``Evolution-Like Selection of Fast-Folding Model Proteins,'' Proc. Natl. Acad. Sci. USA 92, 1282 (1995).

14
Mehul Khimasia and Robin C. Ball, ``Off-Lattice Protein Folding,'' in preparation (1998).

15
C. Levinthal, ``Are there Pathways for Protein Folding?'' J. Chim. Phys. 65, 44 (1968).

16
S. Miyazawa and R. Jernigan, ``Residue-Residue Potentials with a Favorable Contact Pair Term and an Unfavorable High Packing Density Term, for Simulation and Threading'' J. Mol. Biol. 256, 623 (1996).

17
W. J. C. Orr, Trans. Faraday Soc. 43, 12 (1947).

18
E. I. Shakhnovich and A. M. Gutin, ``Engineering of Stable and Fast-Folding Sequences of Model Proteins,'' Proc. Natl. Acad. Sci. USA 90, 7195 (1993).

19
E. I. Shakhnovich, ``Proteins with Selected Sequences Fold into Unique Native Conformation,'' Phys. Rev. Lett. 72, 3907 (1994).

20
E. I. Shakhnovich, ``Chain Length Scaling of Protein Folding Time,'' Phys. Rev. Lett. 77, 5433 (1996).

HIERARCHICAL OPTIMISATION

21
Robin C. Ball and Thomas M. Fink, ``Stochastic Annealing,'' for Phys. Rev. Lett. (1998).

22
D. J. Bertsimas, Probabilistic Combinatorial Optimisation Problems, Ph.D. thesis, MIT (1988).

23
D. J. Bertsimas, P. Jaillet and A. R. Odoni, ``A Priori Optimization,'' Opns. Res. 38, 1019 (1990).

24
Thomas M. Fink and Robin C. Ball, ``Exactly Solvable Hierarchical Optimization Problem Related to Percolation,'' Phys. Rev. Lett. 76, 2827 (1996).

25
Thomas M. Fink and Robin C. Ball, ``Hierarchical Optimization Problems,'' in preparation (1997).

26
R. J. Glauber, ``Time-Dependent Statistics of the Ising Model,'' J. Math. Phys. 4, 294 (1963).

27
P. Jaillet, Probabilistic Travelling Salesman Problems, Ph.D. thesis, MIT (1985).

28
M. Kubo and H. Kasugai, ``Randomized Decision Strategy for the Hierarchical-Optimization Problems,'' Opns. Res. Soc. Jap. 33, 335 (1990).

29
N. Metropolis et al., ``Equation of State Calculations for Fast Computing Machines,'' J. Chem. Phys. 21, 1087 (1953).

30
D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1992), p. 60.

TIE KNOTS

31
Hardy Amies, The Englishman's Suit (Quartet, London, 1994), Ch. 6.

32
Thomas M. Fink and Yong Mao, ``Tie Knots and Random Walks,'' Nature, in press (1998).

33
Thomas M. Fink and Yong Mao, ``A Mathematical Theory of Tie Knots,'' submitted to J. Phys. A (1998).

34
Sarah Gibbings, The Tie (Studio Editions, London, 1990).

35
Thomas P. Harte and Luke S. G. E. Howard, private communication.

36
Charles Livingston, Knot Theory (Mathematical Association of America, Washington, 1993).



Thomas Fink
Tue Jun 16 17:14:36 BST 1998