Biomedical subjects

Barbara Drossel

Publications and source records attributed to Barbara Drossel.

9 recordsLinked to original sources

PubMed2006

Scaling in a general class of critical random Boolean networks.

We derive analytically the scaling behavior in the thermodynamic limit of the number of nonfrozen and relevant nodes in the most general class of critical Kauffman networks for any number of inputs per node, and for any choice of the probability distribution for the Boolean functions. By defining and analyzing a stochastic process that determines the frozen core we can prove that the mean number of nonfrozen nodes in any critical network with more than one input per node scales with the network size N as N2/3, with only N1/3 nonfrozen nodes having two nonfrozen inputs and the number of nonfrozen nodes with more than two inputs being finite in the thermodynamic limit. Using these results we can conclude that the mean number of relevant nodes increases for large N as N1/3, with only a finite number of relevant nodes having two relevant inputs, and a vanishing fraction of nodes having more than three of them. It follows that all relevant components apart from a finite number are simple loops, and that the mean number and length of attractors increases faster than any power law with network size.

Journal Article↗

PubMed2005

Scaling in critical random Boolean networks.

We derive mostly analytically the scaling behavior of the number of nonfrozen and relevant nodes in critical Kauffman networks (with two inputs per node) in the thermodynamic limit. By defining and analyzing a stochastic process that determines the frozen core we can prove that the mean number of nonfrozen nodes scales with the network size N as N(2/3), with only N(1/3) nonfrozen nodes having two nonfrozen inputs. We also show the probability distributions for the numbers of these nodes. Using a different stochastic process, we determine the scaling behavior of the number of relevant nodes. Their mean number increases for large N as N(1/3), and only a finite number of relevant nodes have two relevant inputs. It follows that all relevant components apart from a finite number are simple loops and that the mean number and length of attractors increases faster than any power law with network size.

Journal Article↗

PubMed2005

Dynamics of critical Kauffman networks under asynchronous stochastic update.

We show that the mean number of attractors in a critical Boolean network under asynchronous stochastic update grows like a power law and that the mean size of the attractors increases as a stretched exponential with the system size. This is in strong contrast to the synchronous case, where the number of attractors grows faster than any power law.

Computer Simulation↗

PubMed2005

Number of attractors in random Boolean networks.

The evaluation of the number of attractors in Kauffman networks by Samuelsson and Troein is generalized to critical networks with one input per node and to networks with two inputs per node and different probability distributions for update functions. A connection is made between the terms occurring in the calculation and between the more graphic concepts of frozen, nonfrozen, and relevant nodes, and relevant components. Based on this understanding, a phenomenological argument is given that reproduces the dependence of the attractor numbers on system size.

Journal Article↗

PubMed2005

Number and length of attractors in a critical Kauffman model with connectivity one.

The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a frozen and a disordered phase, and is therefore used for studies of real network problems. We prove here that the mean number and mean length of attractors in critical random Boolean networks with connectivity one both increase faster than any power law with network size. We derive these results by generating the networks through a growth process and by calculating lower bounds.

Economics↗

PubMed2004

The impact of nonlinear functional responses on the long-term evolution of food web structure.

We investigate the long-term web structure emerging in evolutionary food web models when different types of functional responses are used. We find that large and complex webs with several trophic layers arise only if the population dynamics is such that it allows predators to focus on their best prey species. This can be achieved using modified Lotka-Volterra or Holling/Beddington functional responses with effective couplings that depend on the predator's efficiency at exploiting the prey, or a ratio-dependent functional response with adaptive foraging. In contrast, if standard Lotka-Volterra or Holling/Beddington functional responses are used, long-term evolution generates webs with almost all species being basal, and with additionally many links between these species. Interestingly, in all cases studied, a large proportion of weak links result naturally from the evolution of the food webs.

Animals↗

PubMed2002

Complex scaling behavior of nonconserved self-organized critical systems.

The Olami-Feder-Christensen earthquake model is often considered the prototype dissipative self-organized critical model. It is shown that the size distribution of events in this model results from a complex interplay of several different phenomena, including limited floating-point precision. Parallels between the dynamics of synchronized regions and those of a system with periodic boundary conditions are pointed out, and the asymptotic avalanche size distribution is conjectured to be dominated by avalanches of size 1, with the weight of larger avalanches converging towards zero as the system size increases.

Journal Article↗

PubMed2002

p-Spin model in finite dimensions and its relation to structural glasses.

The p-spin spin-glass model has been studied extensively at mean-field level because of the insights which it provides into the mode-coupling approach to structural glasses and the nature of the glass transition. We demonstrate explicitly that the finite-dimensional version of the three-spin model is in the same universality class as an Ising spin glass in a magnetic field. Assuming that the droplet picture of Ising spin glasses is valid we discuss how this universality may provide insights into why structural glasses are either "fragile" or "strong."

Journal Article↗

PubMed2002

Self-organized critical forest-fire model on large scales.

We discuss the scaling behavior of the self-organized critical forest-fire model on large length scales. As indicated in earlier publications, the forest-fire model does not show conventional critical scaling, but has two qualitatively different types of fires that superimpose to give the effective exponents typically measured in simulations. We show that this explains not only why the exponent characterizing the fire-size distribution changes with increasing correlation length, but allows us also to predict its asymptotic value. We support our arguments by computer simulations of a coarse-grained model, by scaling arguments and by analyzing states that are created artificially by superimposing the two types of fires.

Journal Article↗