TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Sarich, Marco A1 - Schütte, Christof T1 - Estimating the eigenvalue error of Markov State Models JF - Multiscale Modeling & Simulation Y1 - 2012 UR - http://publications.imp.fu-berlin.de/914/ U6 - https://doi.org/10.1137/100798910 VL - 10 IS - 1 SP - 61 EP - 81 ER - TY - CHAP A1 - Djurdjevac Conrad, Natasa A1 - Sarich, Marco A1 - Schütte, Christof T1 - On Markov State Models for Metastable Processes T2 - Proceedings of the International Congress of Mathematics, Hyderabad, India, Section Invited Talks. (ICM) 2010 Y1 - 2010 UR - http://publications.imp.fu-berlin.de/991/ ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Helfmann, Luzie A1 - Zonker, Johannes A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - Human mobility and innovation spreading in ancient times: a stochastic agent-based simulation approach JF - EPJ Data Science N2 - Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochastic simulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution. Y1 - 2018 U6 - https://doi.org/10.1140/epjds/s13688-018-0153-9 VL - 7 IS - 1 PB - EPJ Data Science ET - EPJ Data Science ER - TY - JOUR A1 - Becker, Fabian A1 - Djurdjevac Conrad, Natasa A1 - Eser, Raphael A. A1 - Helfmann, Luzie A1 - Schütt, Brigitta A1 - Schütte, Christof A1 - Zonker, Johannes T1 - The Furnace and the Goat—A spatio-temporal model of the fuelwood requirement for iron metallurgy on Elba Island, 4th century BCE to 2nd century CE JF - PLOS ONE Y1 - 2020 UR - https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0241133 U6 - https://doi.org/10.1371/journal.pone.0241133 VL - 15 SP - 1 EP - 37 PB - Public Library of Science ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Fuerstenau, Daniel A1 - Grabundzija, Ana A1 - Helfmann, Luzie A1 - Park, Martin A1 - Schier, Wolfram A1 - Schütt, Brigitta A1 - Schütte, Christof A1 - Weber, Marcus A1 - Wulkow, Niklas A1 - Zonker, Johannes T1 - Mathematical modeling of the spreading of innovations in the ancient world JF - eTopoi. Journal for Ancient Studies Y1 - 2018 U6 - https://doi.org/10.17171/4-7-1 SN - ISSN 2192-2608 VL - 7 ER - TY - JOUR A1 - Thiel, Denise A1 - Djurdjevac Conrad, Natasa A1 - Ntini, Evgenia A1 - Peschutter, Ria A1 - Siebert, Heike A1 - Marsico, Annalisa T1 - Identifying lncRNA-mediated regulatory modules via ChIA-PET network analysis JF - BMC Bioinformatics N2 - Background: Although several studies have provided insights into the role of long non-coding RNAs (lncRNAs), the majority of them have unknown function. Recent evidence has shown the importance of both lncRNAs and chromatin interactions in transcriptional regulation. Although network-based methods, mainly exploiting gene-lncRNA co-expression, have been applied to characterize lncRNA of unknown function by means of ’guilt-by-association’, no strategy exists so far which identifies mRNA-lncRNA functional modules based on the 3D chromatin interaction graph. Results: To better understand the function of chromatin interactions in the context of lncRNA-mediated gene regulation, we have developed a multi-step graph analysis approach to examine the RNA polymerase II ChIA-PET chromatin interaction network in the K562 human cell line. We have annotated the network with gene and lncRNA coordinates, and chromatin states from the ENCODE project. We used centrality measures, as well as an adaptation of our previously developed Markov State Models (MSM) clustering method, to gain a better understanding of lncRNAs in transcriptional regulation. The novelty of our approach resides in the detection of fuzzy regulatory modules based on network properties and their optimization based on co-expression analysis between genes and gene-lncRNA pairs. This results in our method returning more bona fide regulatory modules than other state-of-the art approaches for clustering on graphs. Conclusions: Interestingly, we find that lncRNA network hubs tend to be significantly enriched in evolutionary conserved lncRNAs and enhancer-like functions. We validated regulatory functions for well known lncRNAs, such as MALAT1 and the enhancer-like lncRNA FALEC. In addition, by investigating the modular structure of bigger components we mine putative regulatory functions for uncharacterized lncRNAs. Y1 - 2019 U6 - https://doi.org/10.1186/s12859-019-2900-8 VL - 20 IS - 1471-2105 ER - TY - JOUR A1 - Banisch, Ralf A1 - Djurdjevac Conrad, Natasa A1 - Schütte, Christof T1 - Reactive flows and unproductive cycles for random walks on complex networks JF - The European Physical Journal Special Topics, vol. 224, iss. 12 (2015) pp. 2369-2387 Y1 - 2015 U6 - https://doi.org/10.1140/epjst/e2015-02417-8 ER - TY - GEN A1 - Djurdjevac Conrad, Natasa A1 - Weber, Marcus A1 - Schütte, Christof T1 - Finding dominant structures of nonreversible Markov processes N2 - Finding metastable sets as dominant structures of Markov processes has been shown to be especially useful in modeling interesting slow dynamics of various real world complex processes. Furthermore, coarse graining of such processes based on their dominant structures leads to better understanding and dimension reduction of observed systems. However, in many cases, e.g. for nonreversible Markov processes, dominant structures are often not formed by metastable sets but by important cycles or mixture of both. This paper aims at understanding and identifying these different types of dominant structures for reversible as well as nonreversible ergodic Markov processes. Our algorithmic approach generalizes spectral based methods for reversible process by using Schur decomposition techniques which can tackle also nonreversible cases. We illustrate the mathematical construction of our new approach by numerical experiments. T3 - ZIB-Report - 15-40 KW - nonreversible Markov processes KW - metastable sets KW - cycle decomposition KW - Schur decomposition Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55739 SN - 1438-0064 ER - TY - GEN A1 - Banisch, Ralf A1 - Djurdjevac Conrad, Natasa A1 - Schütte, Christof T1 - Reactive flows and unproductive cycles for random walks on complex networks N2 - We present a comprehensive theory for analysis and understanding of transition events between an initial set A and a target set B for general ergodic finite-state space Markov chains or jump processes, including random walks on networks as they occur, e.g., in Markov State Modelling in molecular dynamics. The theory allows us to decompose the probability flow generated by transition events between the sets A and B into the productive part that directly flows from A to B through reaction pathways and the unproductive part that runs in loops and is supported on cycles of the underlying network. It applies to random walks on directed networks and nonreversible Markov processes and can be seen as an extension of Transition Path Theory. Information on reaction pathways and unproductive cycles results from the stochastic cycle decomposition of the underlying network which also allows to compute their corresponding weight, thus characterizing completely which structure is used how often in transition events. The new theory is illustrated by an application to a Markov State Model resulting from weakly damped Langevin dynamics where the unproductive cycles are associated with periodic orbits of the underlying Hamiltonian dynamics. T3 - ZIB-Report - 15-19 KW - Complex networks KW - molecular transition networks KW - transition path theory KW - cycle decomposition KW - reactive trajectories KW - Markow State Methods Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-54239 SN - 1438-0064 ER - TY - GEN A1 - Djurdjevac Conrad, Natasa A1 - Banisch, Ralf A1 - Schütte, Christof T1 - Modularity of Directed Networks: Cycle Decomposition Approach N2 - The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarsegrained description of complex systems, often revealing functional subunits of these systems. A variety of module detection algorithms have been proposed, mostly oriented towards finding hard partitionings of undirected networks. Despite the increasing number of fuzzy clustering methods for directed networks, many of these approaches tend to neglect important directional information. In this paper, we present a novel random walk based approach for finding fuzzy partitions of directed, weighted networks, where edge directions play a crucial role in defining how well nodes in a module are interconnected. We will show that cycle decomposition of a random walk process connects the notion of network modules and information transport in a network, leading to a new, symmetric measure of node communication. Finally, we will use this measure to introduce a communication graph, for which we will show that although being undirected it inherits all necessary information about modular structures from the original network. T3 - ZIB-Report - 14-31 KW - directed networks, modules, cycle decomposition, measure of node communication Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-51166 SN - 1438-0064 ER -