Conformations of Randomly Linked Polymers

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N; its mean squared end to end distance growing as r^2 ~ M/N. A possible collapse transition (to a region of order unity) is related to percolation in a one dimensional model with long--ranged connections. A directed version of the model is also solved exactly. Based on these results, we conjecture that the typical size of a self-avoiding polymer is reduced by the links to R > (N/M)^(nu). The number of links needed to collapse a polymer in three dimensions thus scales as N^(phi), with (phi) > 0.43.Comment: 6 pages, 3 Postscript figures, LaTe

Local search heuristics for the multidimensional assignment problem

The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate that a combination of two neighborhoods may yield a heuristics which is superior to both of its components

Formation of microdomains in a quenched disordered heteropolymer

A replica trick similar to that used in spin glass theory is implemented to study a structure of large heteropolymeric globule or a heteropolymeric melt with random quenched sequence of monomers of two types (A and B). It is shown that a microphase separation third order phase transition occurs when the system of torn A and B links becomes thermodynamically incompatible. A periodic structure of A- and B-rich domains is formed, and the symmetry of this phase depends on the fraction of A and B monomers. When this fraction is 0.5 the lamellar structure is favored.Nous étudions par une méthode de répliques analogue à celle utilisée pour les verres de spin un large globule ou un fondu hétéropolymérique composés d'une chaîne désordonnée de monomères de deux types (A et B). Nous montrons qu'une séparation en microphase du troisième ordre se produit quand le système des maillons A et B étirés est thermodynamiquement incompatible. Une structure périodique de domaines riches en A et B se forme et la symétrie de cette phase dépend des fractions de monomères A et B. Quand cette fraction vaut 0,5, la structure lamellaire est favorisée