Biomedical subjects

S Redner

Publications and source records attributed to S Redner.

At least 19 recordsLinked to original sources

PubMed2006

Evolutionary dynamics on degree-heterogeneous graphs.

The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model dynamics) or by an individual giving birth to an offspring that takes over a random neighbor node (invasion process dynamics). The fixation probability for one species to take over a population of N individuals depends crucially on the dynamics and on the local environment. Starting with a single fitter mutant at a node of degree k, the fixation probability is proportional to k for voter model dynamics and to 1/k for invasion process dynamics.

Animals↗

PubMed2006

Simplest piston problem. I. Elastic collisions.

We study the dynamics of three elastic particles in a finite interval where two light particles are separated by a heavy "piston." The piston undergoes surprisingly complex motion that is oscillatory at short time scales but seemingly chaotic at longer scales. The piston also makes long-duration excursions close to the ends of the interval that stem from the breakdown of energy equipartition. Many of these dynamical features can be understood by mapping the motion of three particles on the line onto the trajectory of an elastic billiard in a highly skewed tetrahedral region. We exploit this picture to construct a qualitative random walk argument that predicts a power-law tail, with exponent -3/2, for the distribution of time intervals between successive piston crossings of the interval midpoint. These predictions are verified by numerical simulations.

Journal Article↗

PubMed2006

Simplest piston problem. II. Inelastic collisions.

We study the dynamics of three particles in a finite interval, in which two light particles are separated by a heavy "piston," with elastic collisions between particles but inelastic collisions between the light particles and the interval ends. A symmetry breaking occurs in which the piston migrates near one end of the interval and performs small-amplitude periodic oscillations on a logarithmic time scale. The properties of this dissipative limit cycle can be understood simply in terms of a effective restitution coefficient picture. Many dynamical features of the three-particle system closely resemble those of the many-body inelastic piston problem.

Journal Article↗

PubMed2005

Dynamics of social balance on networks.

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 a dynamic phase transition from a steady state to "paradise"--all links are friendly--as the propensity p for friendly links in an update event passes through 1/2 . A finite network always falls into a socially balanced absorbing state where no imbalanced triads remain. If the additional constraint that the number of imbalanced triads in the network not increase in an update is imposed, then the network quickly reaches a balanced final state.

Adaptation, Physiological↗

PubMed2005

Voter model on heterogeneous graphs.

We study the voter model on heterogeneous graphs. We exploit the nonconservation of the magnetization to characterize how consensus is reached. For a network of N nodes with an arbitrary but uncorrelated degree distribution, the mean time to reach consensus T(N) scales as Nmu(2)1/mu(2), where mu(k) is the kth moment of the degree distribution. For a power-law degree distribution n(k) approximately k(-nu), T(N) thus scales as N for nu > 3, as N/ln(N for nu = 3, as N((2nu-4)/(nu-1)) for 2 < nu < 3, as (lnN)2 for nu = 2, and as omicron(1) for nu < 2. These results agree with simulation data for networks with both uncorrelated and correlated node degrees.

Journal Article↗

PubMed2005

Statistics of weighted treelike networks.

We study the statistics of growing networks with a tree topology in which each link carries a weight (k(i) k(j))(theta) , where k(i) and k(j) are the node degrees at the end points of link ij . Network growth is governed by preferential attachment in which a newly added node attaches to a node of degree k with rate A(k) =k+lambda . For general values of theta and lambda , we compute the total weight of a network as a function of the number of nodes N and the distribution of link weights. Generically, the total weight grows as N for lambda>theta-1 and superlinearly otherwise. The link weight distribution is predicted to have a power-law form that is modified by a logarithmic correction for the case lambda=0 . We also determine the node strength, defined as the sum of the weights of the links that attach to the node, as function of k . Using known results for degree correlations, we deduce the scaling of the node strength on k and N .

Journal Article↗

PubMed2005

Network growth by copying.

We introduce a growing network model in which a new node attaches to a randomly selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultrasmall network where the average node degree grows logarithmically with network size while the network diameter equals 2. We determine basic geometrical network properties, such as the size dependence of the number of links and the in- and out-degree distributions. We also compare our predictions with real networks where the node degree also grows slowly with time--the Internet and the citation network of all Physical Review papers.

Journal Article↗

PubMed2005

Majority rule dynamics in finite dimensions.

We investigate the long-time behavior of a majority rule opinion dynamics model in finite spatial dimensions. Each site of the system is endowed with a two-state spin variable that evolves by majority rule. In a single update event, a group of spins with a fixed (odd) size is specified and all members of the group adopt the local majority state. Repeated application of this update step leads to a coarsening mosaic of spin domains and ultimate consensus in a finite system. The approach to consensus is governed by two disparate time scales, with the longer time scale arising from realizations in which spins organize into coherent single-opinion bands. The consequences of this geometrical organization on the long-time kinetics are explored.

Journal Article↗

PubMed2004

Dynamics of an unbounded interface between ordered phases.

We investigate the evolution of a single unbounded interface between ordered phases in two-dimensional Ising ferromagnets that are endowed with single-spin-flip zero-temperature Glauber dynamics. We examine specifically the cases where the interface initially has either one or two corners. In both examples, the interface evolves to a limiting self-similar form. We apply the continuum time-dependent Ginzburg-Landau equation and a microscopic approach to calculate the interface shape. For the single corner system, we also discuss a correspondence between the interface and the Young diagram that represents the partition of the integers.

Algorithms↗

PubMed2003

Majority versus minority dynamics: phase transition in an interacting two-state spin system.

We introduce a simple model of opinion dynamics in which binary-state agents evolve due to the influence of agents in a local neighborhood. In a single update step, a fixed-size group is defined and all agents in the group adopt the state of the local majority with probability p or that of the local minority with probability 1-p. For group size G=3, there is a phase transition at p(c)=2/3 in all spatial dimensions. For p>p(c), the global majority quickly predominates, while for p<p(c), the system is driven to a mixed state in which the densities of agents in each state are equal. For p=p(c), the average magnetization (the difference in the density of agents in the two states) is conserved and the system obeys classical voter model dynamics. In one dimension and within a Kirkwood decoupling scheme, the final magnetization in a finite-length system has a nontrivial dependence on the initial magnetization for all p not equal p(c), in agreement with numerical results. At p(c), the exact two-spin correlation functions decay algebraically toward the value 1 and the system coarsens as in the classical voter model.

Journal Article↗

PubMed2003

Dynamics of majority rule in two-state interacting spin systems.

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 finite-dimensional lattices, where a group is a contiguous cluster, the consensus time fluctuates strongly between realizations and grows as a dimension-dependent power of N. The upper critical dimension appears to be larger than 4. The final opinion always equals that of the initial majority except in one dimension.

Journal Article↗

PubMed2002

Statistics of changes in lead node in connectivity-driven networks.

We study statistical properties of the highest degree, or most popular, nodes in growing networks. We show that the number of lead changes increases logarithmically with network size N, independent of the details of the growth mechanism. The probability that the first node retains the lead approaches a finite constant for popularity-driven growth, and decays as N-phi (ln(N)(-1/2), with phi=0.08607 em leader, for growth with no popularity bias.

Journal Article↗

PubMed2002

Infinite-order percolation and giant fluctuations in a protein interaction network.

We investigate a model protein interaction network whose links represent interactions between individual proteins. This network evolves by the functional duplication of proteins, supplemented by random link addition to account for mutations. When link addition is dominant, an infinite-order percolation transition arises as a function of the addition rate. In the opposite limit of high duplication rate, the network exhibits giant structural fluctuations in different realizations. For biologically relevant growth rates, the node degree distribution has an algebraic tail with a peculiar rate dependence for the associated exponent.

Journal Article↗

PubMed2002

Synchronization and coarsening (without self-organized criticality) in a forest-fire model.

We study the long-time dynamics of a forest-fire model with deterministic tree growth and instantaneous burning of entire forests by stochastic lightning strikes. Asymptotically the system organizes into a coarsening self-similar mosaic of synchronized patches within which trees regrow and burn simultaneously. We show that the average patch length grows linearly with time as t--> infinity. The number density of patches of length L, N(L,t), scales as -2N(L/ ), and within a mean-field rate equation description we find that this scaling function decays as N(x) approximately e(-1/x) for x-->0, and as e(-x) for x--> infinity. In one dimension, we develop an event-driven cluster algorithm to study the asymptotic behavior of large systems. Our numerical results are consistent with mean-field predictions for patch coarsening.

Journal Article↗

PubMed2002

Scaling theory for migration-driven aggregate growth.

We give a comprehensive description for the irreversible growth of aggregates by migration from small to large aggregates. For a homogeneous rate K(i;j) at which monomers migrate from aggregates of size i to those of size j, that is, K(ai;aj)similar to a(lambda)K(i;j), the mean aggregate size grows with time as t(1/(2-lambda)) for lambda<2. The aggregate size distribution exhibits distinct regimes of behavior that are controlled by the scaling properties of the migration rate from the smallest to the largest aggregates. Our theory applies to diverse phenomena such as the distribution of city populations, late stage coarsening of nonsymmetric binary systems, and models for wealth exchange.

Cities↗

PubMed2002

Fitness versus longevity in age-structured population dynamics.

We examine the dynamics of an age-structured population model in which the life expectancy of an offspring may be mutated with respect to that of the parent. While the total population of the system always reaches a steady state, the fitness and age characteristics exhibit counter-intuitive behavior as a function of the mutational bias. By analytical and numerical study of the underlying rate equations, we show that if deleterious mutations are favored, the average fitness of the population reaches a steady state, while the average population age is a decreasing function of the average fitness. When advantageous mutations are favored, the average population fitness grows linearly with time t, while the average age is independent of the average fitness. For no mutational bias, the average fitness grows as t2/3.

Life Expectancy↗

PubMed2001

Freezing in Ising ferromagnets.

We investigate the final state of zero-temperature Ising ferromagnets that are endowed with single-spin-flip Glauber dynamics. Surprisingly, the ground state is generally not reached for zero initial magnetization. In two dimensions, the system reaches either a frozen stripe state with probability approximately 1/3 or the ground state with probability approximately 2/3. In greater than two dimensions, the probability of reaching the ground state or a frozen state rapidly vanishes as the system size increases; instead the system wanders forever in an isoenergy set of metastable states. An external magnetic field changes the situation drastically-in two dimensions the favorable ground state is always reached, while in three dimensions the field must exceed a threshold value to reach the ground state. For small but nonzero temperature, relaxation to the final state proceeds first by formation of very long-lived metastable states, as in the zero-temperature case, before equilibrium is reached.

Journal Article↗

PubMed2001

Dissolution in a field.

We study the dissolution of a solid by continuous injection of reactive "acid" particles at a single point, with the reactive particles undergoing biased diffusion in the dissolved region. When acid encounters the substrate material, both an acid particle and a unit of the material disappear. We find that the lengths of the dissolved cavity parallel and perpendicular to the bias grow as t(2/(d+1)) and t(1/(d+1)), respectively, in d dimensions, while the number of reactive particles within the cavity grows as t(2/(d+1)). We also obtain the exact density profile of the reactive particles and the relation between this profile and the motion of the dissolution boundary. The extension to variable acid strength is also discussed.

Journal Article↗