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The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept–representing highly nonlinear dynamical systems by infinite-dimensional linear operators–has been known for a long time, the availability of large data sets and efficient machine learning algorithms for estimating the Koopman operator from data make this framework extremely powerful and popular. Koopman operator theory allows us to gain insights into the characteristic global properties of a system without requiring detailed mathematical models. We will show how these methods can also be used to analyze complex networks and highlight relationships between Koopman operators and graph Laplacians.
We introduce an agent-based model for co-evolving opinions and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents’ movements are governed by the positions and opinions of other agents and similarly, the opinion dynamics are influenced by agents’ spatial proximity and their opinion similarity. Using numerical simulations and formal analyses, we study this feedback loop between opinion dynamics and the mobility of agents in a social space. We investigate the behaviour of this ABM in different regimes and explore the influence of various factors on the appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution, and, in the limit of infinite number of agents, we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples, we show that a resulting PDE model is a good approximation of the original ABM.
Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models.
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.
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.