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S Bornholdt

Publications and source records attributed to S Bornholdt.

8 recordsLinked to original sources
PubMed2001

World Wide Web scaling exponent from Simon's 1955 model.

The statistical properties of the World Wide Web have attracted considerable attention recently since self-similar regimes were first observed in the scaling of its link structure. One characteristic quantity is the number of (in-)links k that point to a particular web page. Its probability distribution P(k) shows a pronounced power-law scaling P(k) approximately k(-gamma) that is not readily explained by standard random graph theory. Here, we recall a simple and elegant model for scaling phenomena in general copy- and growth-processes as proposed by Simon in 1955. When combined with an experimental measurement of network growth in the World Wide Web, this classical model is able to model the in-link dynamics and predicts the scaling exponent gamma=2.1 in accordance with observation.

Journal Article↗
PubMed2001

Modeling genetic networks and their evolution: a complex dynamical systems perspective.

After finishing the sequence of the human genome, a functional understanding of genome dynamics is the next major step on the agenda of the biosciences. New approaches, such as microarray techniques, and new methods of bioinformatics provide powerful tools aiming in this direction. In the last few years, important parts of genome organization and dynamics in a number of model organisms have been determined. However, an integrated view of gene regulation on a genomic scale is still lacking. Here, genome function is discussed from a complex dynamical systems perspective: which dynamical properties can a large genomic system exhibit in principle, given the local mechanisms governing the small subsystems that we know today? Models of artificial genetic networks are used to explore dynamical principles and possible emergent dynamical phenomena in networks of genetic switches. One observes evolution of robustness and dynamical self-organization in large networks of artificial regulators that are based on the dynamic mechanism of transcriptional regulators as observed in biological gene regulation. Possible biological observables and ways of experimental testing of global phenomena in genome function and dynamics are discussed. Models of artificial genetic networks provide a tool to address questions in genome dynamics and their evolution and allow simulation studies in evolutionary genomics.

Biological Evolution↗
PubMed2000

Robustness as an evolutionary principle.

We suggest simulating evolution of complex organisms using a model constrained solely by the requirement of robustness in its expression patterns. This scenario is illustrated by evolving discrete logical networks with epigenetic properties. Evidence for dynamical features in the evolved networks is found that can be related to biological observables.

Animals↗
PubMed2000

Topological evolution of dynamical networks: global criticality from local dynamics.

We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the critical value K(c) = 2 in the limit of large system size N. How this principle could generate self-organization in natural complex systems is discussed for two examples: neural networks and regulatory networks in the genome.

Algorithms↗
PubMed2000

Beyond Hebb: exclusive-OR and biological learning.

A learning algorithm for multilayer neural networks based on biologically plausible mechanisms is studied. Motivated by findings in experimental neurobiology, we consider synaptic averaging in the induction of plasticity changes, which happen on a slower time scale than firing dynamics. This mechanism is shown to enable learning of the exclusive-OR (XOR) problem without the aid of error backpropagation, as well as to increase robustness of learning in the presence of noise.

Brain↗