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- P L Krapivsky, S Redner, F Leyvraz
- Physical review letters
- 2000

A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites that link to earlier sites with a probability A(k) which depends on the number of preexisting links k to that site. For homogeneous connection kernels, A(k) approximately k(gamma), different behaviors arise for… (More)

- P L Krapivsky, S Redner
- Physical review. E, Statistical, nonlinear, and…
- 2001

The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively, and linking each to an earlier node of degree k with an attachment probability A(k). When A(k) grows more slowly than linearly with k, the number of nodes with k links, N(k)(t), decays faster than a power law in k, while… (More)

We study an opinion dynamics model in which agents reach compromise via pairwise interactions. When the opinions of two agents are sufficiently close, they both acquire the average of their initial opinions; otherwise, they do not interact. Generically, the system reaches a steady state with a finite number of isolated, noninteracting opinion clusters ("… (More)

- I Ispolatov, P L Krapivsky, A Yuryev
- Physical review. E, Statistical, nonlinear, and…
- 2005

We investigate a very simple model describing the evolution of protein-protein interaction networks via duplication and divergence. The model exhibits a remarkably rich behavior depending on a single parameter, the probability to retain a duplicated link during divergence. When this parameter is large, the network growth is not self-averaging and an average… (More)

- Tibor Antal, P L Krapivsky
- Physical review. E, Statistical, nonlinear, and…
- 2007

Synthetic biomolecular spiders with "legs" made of single-stranded segments of DNA can move on a surface which is also covered by single-stranded segments of DNA complementary to the leg DNA. In experimental realizations, when a leg detaches from a segment of the surface for the first time it alters that segment, and legs subsequently bind to these altered… (More)

- V Spirin, P L Krapivsky, S Redner
- Physical review. E, Statistical physics, plasmas…
- 1999

We study the low-temperature coarsening of an Ising chain subject to spin-exchange dynamics and a small driving force. This dynamical system reduces to a domain diffusion process, in which entire domains undergo nearest-neighbor hopping, except for the shortest domains-dimers-which undergo long-range hopping. This system exhibits anomalous ordering dynamics… (More)

- T Antal, P L Krapivsky, S Redner
- Physical review. E, Statistical, nonlinear, and…
- 2005

We study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes. The network is endowed with dynamics in which the sense of a link in an imbalanced triad--a triangular loop with one or three unfriendly links--is reversed to make the triad balanced. With this dynamics, an infinite network undergoes… (More)

- P L Krapivsky, S Redner
- Physical review letters
- 2003

We introduce a two-state opinion dynamics model where agents evolve by majority rule. In each update, a group of agents is specified whose members then all adopt the local majority state. In the mean-field limit, where a group consists of randomly selected agents, consensus is reached in a time that scales ln(N, where N is the number of agents. On… (More)

- Paul L. Krapivsky, Sidney Redner
- Computer Networks
- 2002

Approaches from statistical physics are applied to investigate the structure of network models whose growth rules mimic aspects of the evolution of the World Wide Web. We first determine the degree distribution of a growing network in which nodes are introduced one at a time and attach to an earlier node of degree k with rate A k $ k c. Very different… (More)

- Tibor Antal, P L Krapivsky, Kirone Mallick
- Journal of statistical mechanics
- 2007

Molecular spiders are synthetic bio-molecular systems which have "legs" made of short single-stranded segments of DNA. Spiders move on a surface covered with single-stranded DNA segments complementary to legs. Different mappings are established between various models of spiders and simple exclusion processes. For spiders with simple gait and varying number… (More)