Biomedical subjects

Konstantin Klemm

Publications and source records attributed to Konstantin Klemm.

10 recordsLinked to original sources

PubMed2006

Statistics of cycles in large networks.

The occurrence of self-avoiding closed paths (cycles) in networks is studied under varying rules of wiring. As a main result, we find that the dependence between network size and typical cycle length is algebraic, (h) proportional to Nalpha, with distinct values of for different wiring rules. The Barabasi-Albert model has alpha=1. Different preferential and nonpreferential attachment rules and the growing Internet graph yield alpha<1. Computation of the statistics of cycles at arbitrary length is made possible by the introduction of an efficient sampling algorithm.

Journal Article↗

PubMed2005

Topology of biological networks and reliability of information processing.

Survival of living cells and organisms is largely based on highly reliable function of their regulatory networks. However, the elements of biological networks, e.g., regulatory genes in genetic networks or neurons in the nervous system, are far from being reliable dynamical elements. How can networks of unreliable elements perform reliably? We here address this question in networks of autonomous noisy elements with fluctuating timing and study the conditions for an overall system behavior being reproducible in the presence of such noise. We find a clear distinction between reliable and unreliable dynamical attractors. In the reliable case, synchrony is sustained in the network, whereas in the unreliable scenario, fluctuating timing of single elements can gradually desynchronize the system, leading to nonreproducible behavior. The likelihood of reliable dynamical attractors strongly depends on the underlying topology of a network. Comparing with the observed architectures of gene regulation networks, we find that those 3-node subgraphs that allow for reliable dynamics are also those that are more abundant in nature, suggesting that specific topologies of regulatory networks may provide a selective advantage in evolution through their resistance against noise.

Biological Evolution↗

PubMed2005

Stable and unstable attractors in Boolean networks.

Boolean networks at the critical point have been a matter of debate for many years as, e.g., the scaling of numbers of attractors with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a common earlier expectation of sublinear scaling. We point out here that these results are obtained using deterministic parallel update, where a large fraction of attractors are an artifact of the updating scheme. This limits the significance of these results for biological systems where noise is omnipresent. Here we take a fresh look at attractors in Boolean networks with the original motivation of simplified models for biological systems in mind. We test the stability of attractors with respect to infinitesimal deviations from synchronous update and find that most attractors are artifacts arising from synchronous clocking. The remaining fraction of attractors are stable against fluctuating delays. The average number of these stable attractors grows sublinearly with system size in the numerically tractable range.

Journal Article↗

PubMed2005

Scaling in the structure of directory trees in a computer cluster.

We describe the topological structure and the underlying organization principles of the directories created by users of a computer cluster. Users create trees with a scale-free degree distribution whose properties are reproduced by a growth and preferential attachment mechanism with a single parameter. The degree distribution has a nonuniversal exponent associated with different values of the parameter. However, the distribution of branch sizes has a universal exponent analytically obtained from the model.

Journal Article↗

PubMed2003

Effective dimensions and percolation in hierarchically structured scale-free networks.

We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial character of this network that displays scale-free connectivity among other features, it turns out to be approximately one dimensional. The dimensional characterization is in agreement with the results on statistics of site percolation and other dynamical processes implemented on such a network.

Journal Article↗

PubMed2003

Global culture: a noise-induced transition in finite systems.

We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the dissemination of culture. The disordered multicultural frozen configurations are found not to be stable. This general result is proven rigorously in d=1, where the dynamics is described in terms of a Lyapunov potential. In d=2, the dynamics is governed by the average relaxation time T of perturbations. Noise at a rate r or =T(-1) sustains disorder. In the thermodynamic limit, the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence.

Journal Article↗

PubMed2003

Nonequilibrium transitions in complex networks: a model of social interaction.

We analyze the nonequilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small-world network, we find a transition between an ordered homogeneous state and a disordered state. The transition point is shifted by the degree of spatial disorder of the underlying network, the network disorder favoring ordered configurations. In random scale-free networks the transition is only observed for finite size systems, showing system size scaling, while in the thermodynamic limit only ordered configurations are always obtained. Thus, in the thermodynamic limit the transition disappears. However, in structured scale-free networks, the phase transition between an ordered and a disordered phase is restored.

Journal Article↗

PubMed2002

Epidemic threshold in structured scale-free networks.

We analyze the spreading of viruses in scale-free networks with high clustering and degree correlations, as found in the Internet graph. For the susceptible-infected-susceptible model of epidemics the prevalence undergoes a phase transition at a finite threshold of the transmission probability. Comparing with the absence of a finite threshold in networks with purely random wiring, our result suggests that high clustering (modularity) and degree correlations protect scale-free networks against the spreading of viruses. We introduce and verify a quantitative description of the epidemic threshold based on the connectivity of the neighborhoods of the hubs.

Disease Outbreaks↗

PubMed2002

Growing scale-free networks with small-world behavior.

In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small-world effect. While the average shortest path length increases logarithmically as in random networks, the clustering coefficient assumes a large value independent of system size. We derive analytical expressions for the clustering coefficient in two limiting cases: random [C approximately (ln N)(2)/N] and highly clustered (C=5/6) scale-free networks.

Journal Article↗

PubMed2002

Highly clustered scale-free networks.

We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power-law distribution of degree, linear preferential attachment of new links, and a negative correlation between the age of a node and its link attachment rate. Notably, the degree distribution is conserved even though only the most recently grown part of the network is considered. As the network grows, the clustering reaches an asymptotic value larger than that for regular lattices of the same average connectivity and similar to the one observed in the networks of movie actors, coauthorship in science, and word synonyms. These highly clustered scale-free networks indicate that memory effects are crucial for a correct description of the dynamics of growing networks.

Journal Article↗