Derrida

B. Derrida. Can disorder induce several phase transitions Phys Rep 705 29-39, 1984. 

Derrida and Flyvberg [flyvb88] and Derrida and Bessis [derrida88] have examined the overlap between two attractors by looking at the probability that two randomly chosen initial state.s evolve toward the same attractor. These studies find that the distribution is very similar to that found in certain spin-glass models. 

This charm, this spellbinding virtue, this power of fascination, can be— alternately or simultaneously—beneficent or maleficent. The pharmakon would be a substance— with all that that word can connote in terms of matter with occult virtues, cryptic depths refusing to submit their ambivalence to analysis, already paving the way for alchemy—if we didn t have eventually to come to recognize it as antisubstance itself that which resists any philosopheme. (Derrida 70)... 

Derrida, Jacques. La dissemination. Paris Seuil, 1972. Translated by Barbara Johnson as Dissemination (Ghicago University of GJdcago Press, 1981). 

B. Derrida, J. L. Lebowitz, and E. R. Speer, Free energy functional for nonequilibrium systems an exactly solvable case. Phys. Rev. Lett. 87, 150601 (2001). 

B. Derrida, Random-energy model limit of a family of disordered models. Phys. Rev. Lett. 45, 79-82 (1980). 

In the limit K = N — 1, the TVA-lanclscape becomes the random energy model (Derrida, 1980 Derrida, 1981). The fitness function is written as... 

Simulations of RNA secondary structure landscapes provide insight into the necessary mutation rate to drive adaptation. Huynen etal. (1996) found that the ability of a population to adapt is determined by the error threshold of the fitness and not the sequence. Indeed, they found that any mutation rate greater than zero will cause the population to drift on the neutral network [The error threshold on landscapes with high neutrality approaches zero (Derrida and Peliti, 1991).] A second, higher mutation threshold causes the fitness information to be lost. To accelerate the diffusion of the population on the neutral network, it is necessary to be above the sequence error threshold and as close to the fitness error threshold as possible. Under these criteria, the population will diffuse rapidly without losing fitness information. On a flat landscape, the diffusion constant D0 for a population of M sequences of length N can be approximated by Eq. (37). 

Values ascribed to the critical exponent s in the literature are somewhat controversial. Results (Derrida and Vannimenus, 1982) indicate that s is close to 1.28. Below pc the bulk conductance is zero, since the network fails to form an infinite cluster whose existence would permit current to be conducted through the system. 

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