arXiv subjects

Konstantin Klemm

Publications and source records attributed to Konstantin Klemm.

48 records · Page 3Linked to original sources

arXiv2004

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 when storing his/her own files. We analyze degree distributions, average distance between files, distribution of communities and allometric scaling exponents of the directory trees. We find that users create trees with a broad, scale-free degree distribution. The structure of the directories is well captured by a growth model with a single parameter. The degree distribution of the different trees has a non-universal exponent associated with different values of the parameter of the model. However, the distribution of community sizes has a universal exponent analytically obtained from our model.

cond-mat.dis-nn↗

arXiv2004

Topology of biological networks and reliability of information processing

Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches, neurons, etc.). Such noise poses severe stability problems to system behavior as it tends to desynchronize system dynamics (e.g. via fluctuating response or transmission time of the elements). Synchronicity in parallel information processing is not readily sustained in the absence of a central clock. Here we analyze the influence of topology on synchronicity in networks of autonomous noisy elements. In numerical and analytical studies we find a clear distinction between non-reliable and reliable dynamical attractors, depending on the topology of the circuit. In the reliable cases, synchronicity is sustained, while in the unreliable scenario, fluctuating responses of single elements can gradually desynchronize the system, leading to non-reproducible behavior. We find that the fraction of reliable dynamical attractors strongly correlates with the underlying circuitry. Our model suggests that the observed motif structure of biological signaling networks is shaped by the biological requirement for reproducibility of attractors.

q-bio.MN↗

arXiv2003

Robust gene regulation: Deterministic dynamics from asynchronous networks with delay

We compare asynchronous vs. synchronous update of discrete dynamical networks and find that a simple time delay in the nodes may induce a reproducible deterministic dynamics even in the case of asynchronous update in random order. In particular we observe that the dynamics under synchronous parallel update can be reproduced accurately under random asynchronous serial update for a large class of networks. This mechanism points at a possible general principle of how computation in gene regulation networks can be kept in a quasi-deterministic ``clockwork mode'' in spite of the absence of a central clock. A delay similar to the one occurring in gene regulation causes synchronization in the model. Stability under asynchronous dynamics disfavors topologies containing loops, comparing well with the observed strong suppression of loops in biological regulatory networks.

q-bio.MN↗

arXiv2003

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.

cond-mat↗

arXiv2002

Emergence of memory

We propose a new self-organizing mechanism behind the emergence of memory in which temporal sequences of stimuli are transformed into spatial activity patterns. In particular, the memory emerges despite the absence of temporal correlations in the stimuli. This suggests that neural systems may prepare a spatial structure for processing information before the information itself is available. A simple model illustrating the mechanism is presented based on three principles: (1) Competition between neural units, 2) Hebbian plasticity, and (3) recurrent connections.

cond-mat.dis-nn↗

arXiv2002

Nonequilibrium transitions in complex networks: a model of social interaction

We analyze the non-equilibrium 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.

cond-mat↗

arXiv2002

Cultural transmission and optimization dynamics

We study the one-dimensional version of Axelrod's model of cultural transmission from the point of view of optimization dynamics. We show the existence of a Lyapunov potential for the dynamics. The global minimum of the potential, or optimum state, is the monocultural uniform state, which is reached for an initial diversity of the population below a critical value. Above this value, the dynamics settles in a multicultural or polarized state. These multicultural attractors are not local minima of the potential, so that any small perturbation initiates the search for the optimum state. Cultural drift is modelled by such perturbations acting at a finite rate. If the noise rate is small, the system reaches the optimum monocultural state. However, if the noise rate is above a critical value, that depends on the system size, noise sustains a polarized dynamical state.

cond-mat↗

arXiv2002

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 Suscetible-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 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.

cond-mat↗

arXiv2002

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 configurations are found to be metastable. 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 < 1/T induces monocultural configurations, whereas r > 1/T sustains disorder. In the thermodynamic limit, the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence.

cond-mat↗

arXiv2001

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. This feature is relevant because real-world networks truncated in the same way exhibit a power-law distribution in the degree. As the network grows, the clustering reaches an asymptotic value larger than for regular lattices of the same average connectivity. These high-clustering scale-free networks indicate that memory effects could be crucial for a correct description of the dynamics of growing networks.

cond-mat↗

arXiv2001

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 logartihmically as in random networks, the clustering coefficient assumes a large value independent of system size. We derive expressions for the clustering coefficient in two limiting cases: random (C ~ (ln N)^2 / N) and highly clustered (C = 5/6) scale-free networks.

cond-mat↗

arXiv2000

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 back-propagation, as well as to increase robustness of learning in the presence of noise.

adap-org↗