Publications (64)146.18 Total impact
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ABSTRACT: Elementary flux modes (EFMs) are a concept from Systems Biology, where they serve as an indicator of component relevance in metabolic networks. An elementary flux mode is a functionally relevant, nondecomposable path through a given network. In this paper, we apply elementary flux mode analysis to manufacturing systems, with the aim of using the number of EFMs as a predictor for resource significance in the manufacturing system. For this, we formulate a network representation of a manufacturing process, which allows us to define the manufacturing equivalent of a stoichiometric matrix to draw an analogy between metabolic and manufacturing systems. This, in turn, allows the computation of EFMs, which we conduct in a casestudy for a real manufacturing system. We further show that the change of EFMs under resource breakdown is a good indicator of the average order lateness in the manufacturing system. In this way, EFMs provide insight into the relationship of network structure and function in manufacturing.  [Show abstract] [Hide abstract]
ABSTRACT: Author Summary Pattern formation is abundant in nature—from the rich ornaments of sea shells and the diversity of animal coat patterns to the myriad of fractal structures in biology and patternforming colonies of bacteria. Particularly fascinating are patterns changing with time, spatiotemporal patterns, like propagating waves and aggregation streams. Bacteria form large branched and nested aggregationlike patterns to immobilize themselves against water flow. The individual amoeba in Dictyostelium discoideum colonies initiates a transition to a collective multicellular state via a quorumsensing form of communication—a cAMP signal propagating through the community in the form of spiral waves—and the subsequent chemotactic response of the cells leads to branchlike aggregation streams. The theoretical principle underlying most of these spatial and spatiotemporal patterns is selforganization, in which local interactions lead to patterns as largescale collective”modes” of the system. Over more than half a century, these patterns have been classified and analyzed according to a”physics paradigm,” investigating such questions as how parameters regulate the transitions among patterns, which (types of) interactions lead to such largescale patterns, and whether there are "critical parameter values" marking the sharp, spontaneous onset of patterns. A fundamental discovery has been that simple local interaction rules can lead to complex largescale patterns. The specific pattern "layouts" (i.e., their spatial arrangement and their geometric constraints) have received less attention. However, there is a major difference between patterns in physics and chemistry on the one hand and patterns in biology on the other: in biology, patterns often have an important functional role for the biological system and can be considered to be under evolutionary selection. From this perspective, we can expect that individual biological elements exert some control on the emerging patterns. Here we explore spiral wave patterns as a prominent example to illustrate the regulation of spatiotemporal patterns by biological variability. We propose a new approach to studying spatiotemporal data in biology: analyzing the correlation between the spatial distribution of the constituents’ properties and the features of the spatiotemporal pattern. This general concept is illustrated by simulated patterns and experimental data of a model organism of biological pattern formation, the slime mold Dictyostelium discoideum. We introduce patterns starting from Turing (stripe and spot) patterns, together with target waves and spiral waves. The biological relevance of these patterns is illustrated by snapshots from real and theoretical biological systems. The principles of spiral wave formation are first explored in a stylized cellular automaton model and then reproduced in a model of Dictyostelium signaling. The shaping of spatiotemporal patterns by biological variability (i.e., by a spatial distribution of celltocell differences) is demonstrated, focusing on two Dictyostelium models. Building up on this foundation, we then discuss in more detail how the nonlinearities in biological models translate the distribution of cell properties into pattern events, leaving characteristic geometric signatures.  [Show abstract] [Hide abstract]
ABSTRACT: Random walks are one of the best investigated dynamical processes on graphs. A particularly fascinating phenomenon is the scaling relationship of fluctuations $\sigma $ with the average flux $\langle f \rangle $. Here we analyze how network topology and nodes with finite capacity lead to deviations from a simple scaling law $\sigma \sim \langle f \rangle ^\alpha$. Sources of randomness are the random walk itself (internal noise) and the fluctuation of the number of walkers (external noise). We obtained exact results for the extreme case of a star network which are indicative of the behavior of large scale systems with a broad degree distribution.The latter are subsequently studied using Monte Carlo simulations. We find that the network heterogeneity amplifies the effects of external noise. By computing the `effective' scaling of each node we show that multiple scaling relationships can coexist in a graph with a heterogeneous degree distribution at an intermediate level of external noise. Finally, we analyze the effect of a finite capacity of nodes for random walkers and find that this also can lead to a heterogeneous scaling of fluctuations.  [Show abstract] [Hide abstract]
ABSTRACT: We study the interplay between correlations, dynamics, and networks for repeated attacks on a socioeconomic network. As a model system we consider an insurance scheme against disasters that randomly hit nodes, where a node in need receives support from its network neighbors. The model is motivated by gift giving among the Maasai called Osotua. Survival of nodes under different disaster scenarios (uncorrelated, spatially, temporally and spatiotemporally correlated) and for different network architectures are studied with agentbased numerical simulations. We find that the survival rate of a node depends dramatically on the type of correlation of the disasters: Spatially and spatiotemporally correlated disasters increase the survival rate; purely temporally correlated disasters decrease it. The type of correlation also leads to strong inequality among the surviving nodes. We introduce the concept of disaster masking to explain some of the results of our simulations. We also analyze the subsets of the networks that were activated to provide support after fifty years of random disasters. They show qualitative differences for the different disaster scenarios measured by path length, degree, clustering coefficient, and number of cycles.  [Show abstract] [Hide abstract]
ABSTRACT: The relationship between the structural connectivity (SC) and functional connectivity (FC) of neural systems is a central focus in brain network science. It is an open question, however, how strongly the SCFC relationship depends on specific topological features of brain networks or the models used for describing excitable dynamics. Using a basic model of discrete excitable units that follow a susceptible excited refractory dynamic cycle (SER model), we here analyze how functional connectivity is shaped by the topological features of a neural network, in particular its modularity. We compared the results obtained by the SER model with corresponding simulations by another well established dynamic mechanism, the FitzhughNagumo model, in order to explore general features of the SCFC relationship. We showed that apparent discrepancies between the results produced by the two models can be resolved by adjusting the time window of integration of coactivations from which the FC is derived, providing a clearer distinction between coactivations and sequential activations. Thus, network modularity appears as an important factor shaping the FCSC relationship across different dynamic models.  [Show abstract] [Hide abstract]
ABSTRACT: Genome signatures are statistical properties of DNA sequences that provide information on the underlying species. It is not understood, how such speciesdiscriminating statistical properties arise from processes of genome evolution and from functional properties of the DNA. Investigating the interplay of different genome signatures can contribute to this understanding. Here we analyze the statistical dependences of two such genome signatures: word frequencies and symbol correlations at short and intermediate distances. We formulate a statistical model of word frequencies in DNA sequences based on the observed symbol correlations and show that deviations of word counts from this correlationbased null model serve as a new genome signature. This signature (i) performs better in sorting DNA sequence segments according to their species origin and (ii) reveals unexpected species differences in the composition of microsatellites, an important class of repetitive DNA. While the first observation is a typical task in metagenomics projects and therefore an important benchmark for a genome signature, the latter suggests strong species differences in the biological mechanisms of genome evolution. On a more general level, our results highlight that the choice of null model (here: word abundances computed via symbol correlations rather than shorter word counts) substantially affects the interpretation of such statistical signals.  [Show abstract] [Hide abstract]
ABSTRACT: Topological cycles in excitable networks can play an important role in maintaining the network activity. When properly activated, cycles act as dynamic pacemakers, sustaining the activity of the whole network. Most previous research has focused on the contributions of short cycles to network dynamics. Here, we identify the specific cycles that are used during different runs of activation in sparse random graphs, as a basis of characterizing the contribution of cycles of any length. Both simulation and a refined meanfield approach evidence a decrease in the cycle usage when the cycle length increases, reflecting a tradeoff between long time for recovery after excitation and low vulnerability to outofphase external excitations. In spite of this statistical observation, we find that the successful usage of long cycles, though rare, has important functional consequences for sustaining network activity: The average cycle length is the main feature of the cycle length distribution that affects the average lifetime of activity in the network. Particularly, use of long, rather than short, cycles correlates with higher lifetime, and cutting shortcuts in long cycles tends to increase the average lifetime of the activity. Our findings, thus, emphasize the essential, previously underrated role of long cycles in sustaining network activity. On a more general level, the findings underline the importance of network topology, particularly cycle structure, for selfsustained network dynamics.  [Show abstract] [Hide abstract]
ABSTRACT: The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of random graphs. Hypotheses about the supposed role of prominent topological features (for instance, the roles of modularity, network motifs or hierarchical network organization) are derived from these deviations. An alternative strategy could be to study deviations of network architectures from regular graphs (rings and lattices) and consider the implications of such deviations for selforganized dynamic patterns on the network. Following this strategy, we draw on the theory of spatiotemporal pattern formation and propose a novel perspective for analysing dynamics on networks, by evaluating how the selforganized dynamics are confined by network architecture to a small set of permissible collective states. In particular, we discuss the role of prominent topological features of brain connectivity, such as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the notion of networkguided pattern formation with numerical simulations and outline how it can facilitate the understanding of neural dynamics.  [Show abstract] [Hide abstract]
ABSTRACT: Following the work of Krumov et al. [Eur. Phys. J. B 84, 535 (2011)] we revisit the question whether the usage of large citation datasets allows for the quantitative assessment of social (by means of coauthorship of publications) influence on the progression of science. Applying a more comprehensive and wellcurated dataset containing the publications in the journals of the American Physical Society during the whole 20th century we find that the measure chosen in the original study, a score based on small induced subgraphs, has to be used with caution, since the obtained results are highly sensitive to the exact implementation of the author disambiguation task.  [Show abstract] [Hide abstract]
ABSTRACT: Pharmacology is currently transformed by the vast amounts of genomeassociated information available for systemlevel interpretation. Here I review the potential of systems biology to facilitate this interpretation, thus paving the way for the emerging field of systems pharmacology. In particular, I will show how gene regulatory and metabolic networks can serve as a framework for interpreting high throughput data and as an interface to detailed dynamical models. In addition to the established connectivity analyses of effective networks, I suggest here to also analyze higher order architectural properties of effective networks.  [Show abstract] [Hide abstract]
ABSTRACT: Diversityinduced resonance, the emergence of coherent spatiotemporal patterns at intermediate parameter disorder, is a wellknown phenomenon in lattices of excitable elements. Here we study the pattern events behind diversityinduced resonance in a lattice of coupled FitzHughNagumo oscillators. Starting out with the observation that maximal spiral wave counts occur at intermediate values of parameter diversity, we analyze the competition between spiral and target wave patterns in the asymptotic collective state. We devise stylized numerical “in silico” competition experiments of (individual) patterns to understand the regulating parameters of the competing pattern events occurring stochastically in the full (“in vivo”) numerical simulation. Our analysis shows that pattern competition is a principal driving mechanism behind this form of diversityinduced resonance and that different types of competition take place: some follow the frequency composition of target and spiral waves, others are dictated by the statistics of parameter distributions. In particular, the increase and decrease of spiral wave counts with increasing diversity are statistically regulated by the number of oscillatory elements in the lattice, rather than by the frequency differences between target and spiral waves.  [Show abstract] [Hide abstract]
ABSTRACT: A new paper shows that a characteristic feature of the arrangement of brain networks, their modular organization across several scales, is responsible for an expanded range of critical neural dynamics. This finding solves several puzzles in computational neuroscience and links fundamental aspects of neural network organization and brain dynamics.  [Show abstract] [Hide abstract]
ABSTRACT: Modules are common functional and structural properties of many social, technical and biological networks. Especially for biological systems it is important to understand how modularity is related to function and how modularity evolves. It is known that timevarying or spatially organized goals can lead to modularity in a simulated evolution of signaling networks. Here, we study a minimal model of material flow in networks. We discuss the relation between the shared use of nodes, i.e., the cooperativity of modules, and the orthogonality of a prescribed output pattern. We study the persistence of cooperativity through an evolution of robustness against local damages. We expect the results to be valid for a large class of flowbased biological and technical networks. 
Article: Predictability of spatiotemporal patterns in a lattice of coupled FitzHughNagumo oscillators
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ABSTRACT: In many biological systems, variability of the components can be expected to outrank statistical fluctuations in the shaping of selforganized patterns. In pioneering work in the late 1990s, it was hypothesized that a drift of cellular parameters (along a 'developmental path'), together with differences in cell properties ('desynchronization' of cells on the developmental path) can establish selforganized spatiotemporal patterns (in their example, spiral waves of cAMP in a colony of Dictyostelium discoideum cells) starting from a homogeneous state. Here, we embed a generic model of an excitable medium, a lattice of diffusively coupled FitzHughNagumo oscillators, into a developmentalpath framework. In this minimal model of spiral wave generation, we can now study the predictability of spatiotemporal patterns from cell properties as a function of desynchronization (or 'spread') of cells along the developmental path and the drift speed of cell properties on the path. As a function of drift speed and desynchronization, we observe systematically different routes towards fully established patterns, as well as strikingly different correlations between cell properties and pattern features. We show that the predictability of spatiotemporal patterns from cell properties contains important information on the pattern formation process as well as on the underlying dynamical system.  [Show abstract] [Hide abstract]
ABSTRACT: Recent publications on traffic control in urban road networks have presented strategies for adaptive flow control under varying network load. Traffic lights are modeled as independent, periodic devices, which take decisions on a local level. Despite the not actively coordinated decisions at single network nodes, such a strategy can perform better in terms of waiting time for the whole system than applying a standard optimization approach. First results from an ongoing simulation study indicate that adaptive control algorithms can also be applied successfully to different network topologies, e.g., logistic networks. This article presents the outcome of an extended simulation study. The simulation experiments have been carried out on artificially generated networks as well as networks derived from real manufacturing environments. We are able to show that the promising findings from traffic control regarding waiting time reduction and the emergence of synchronized behavior can be reproduced for production logistics. Furthermore, we illustrate how the variance of the network degree as an indicator for network connectivity influences the logistic performance. 
Article: How do production systems in biological cells maintain their function in changing environments?
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ABSTRACT: Metabolism is a fascinating natural production and distribution process. Metabolic systems can be represented as a layered network, where the input layer consists of all the nutrients in the environment (raw materials entering the production process in the cell), subsequently to be processed by a complex network of biochemical reactions (middle layer) and leading to a welldefined output pattern, optimizing, for example, cell growth. Mathematical frameworks exploiting this layerednetwork representation of metabolism allow the prediction of metabolic fluxes (the cell’s ‘material flow’) under diverse conditions. In combination with suitable minimal models, it is possible to identify fundamental design principles and understand the efficiency and robustness of metabolic systems. Here, we summarize some design principles of metabolic systems from the perspective of production logistics and explore, how these principles can serve as templates for the design of robust manufacturing systems.  [Show abstract] [Hide abstract]
ABSTRACT: Metabolism has frequently been analyzed from a network perspective. A major question is how network properties correlate with biological features like growth rates, flux patterns and enzyme essentiality. Using methods from graph theory as well as established topological categories of metabolic systems, we analyze the essentiality of metabolic reactions depending on the growth medium and identify the topological footprint of these reactions. We find that the typical topological context of a mediumdependent essential reaction is systematically different from that of a globally essential reaction. In particular, we observe systematic differences in the distribution of mediumdependent essential reactions across threenode subgraphs (the network motif signature of mediumdependent essential reactions) compared to globally essential or globally redundant reactions. In this way, we provide evidence that the analysis of metabolic systems on the fewnode subgraph scale is meaningful for explaining dynamic patterns. This topological characterization of mediumdependent essentiality provides a better understanding of the interplay between reaction deletions and environmental conditions.  [Show abstract] [Hide abstract]
ABSTRACT: Fewnode subgraphs are the smallest collective units in a network that can be investigated. They are beyond the scale of individual nodes but more local than, for example, communities. When statistically over or underrepresented, they are called network motifs. Network motifs have been interpreted as building blocks that shape the dynamic behaviour of networks. It is this promise of potentially explaining emergent properties of complex systems with relatively simple structures that led to an interest in network motifs in an evergrowing number of studies and across disciplines. Here, we discuss artefacts in the analysis of network motifs arising from discrepancies between the network under investigation and the pool of random graphs serving as a null model. Our aim was to provide a clear and accessible catalogue of such incongruities and their effect on the motif signature. As a case study, we explore the metabolic network of Escherichia coli and show that only by excluding ever more artefacts from the motif signature a strong and plausible correlation with the essentiality profile of metabolic reactions emerges.  [Show abstract] [Hide abstract]
ABSTRACT: Understanding the interplay of topology and dynamics of excitable neural networks is one of the major challenges in computational neuroscience. Here we employ a simple deterministic excitable model to explore how networkwide activation patterns are shaped by network architecture. Our observables are coactivation patterns, together with the average activity of the network and the periodicities in the excitation density. Our main results are: (1) the dependence of the correlation between the adjacency matrix and the instantaneous (zero time delay) coactivation matrix on global network features (clustering, modularity, scalefree degree distribution), (2) a correlation between the average activity and the amount of small cycles in the graph, and (3) a microscopic understanding of the contributions by 3node and 4node cycles to sustained activity.  [Show abstract] [Hide abstract]
ABSTRACT: The pattern of over and underrepresentations of threenode subgraphs has become a standard method of characterizing complex networks and evaluating how this intermediate level of organization contributes to network function. Understanding statistical properties of subgraph counts in random graphs, their fluctuations, and their interdependences with other topological attributes is an important prerequisite for such investigations. Here we introduce a formalism for predicting subgraph fluctuations induced by perturbations of unidirectional and bidirectional edge densities. On this basis we predict the overand underrepresentation of subgraphs arising from a density mismatch between a network and the corresponding pool of randomized graphs serving as a null model. Such mismatches occur, for example, in modular and hierarchical graphs.
Publication Stats
545  Citations  
146.18  Total Impact Points  
Top Journals
Institutions

20072015

Jacobs University
 SES  School of Engineering & Science
Bremen, Bremen, Germany


20062014

Universität Bremen
Bremen, Bremen, Germany


20032007

Technical University Darmstadt
Darmstadt, Hesse, Germany
