Search results for: hypergraphs

Authors: Siliang Wang, Minghui Wang

Abstract:

Many exist studies always use Markov decision processes (MDPs) in modeling optimal route choice in stochastic, time-varying networks. However, taking many variable traffic data and transforming them into optimal route decision is a computational challenge by employing MDPs in real transportation networks. In this paper we model finite horizon MDPs using directed hypergraphs. It is shown that the problem of route choice in stochastic, time-varying networks can be formulated as a minimum cost hyperpath problem, and it also can be solved in linear time. We finally demonstrate the significant computational advantages of the introduced methods.

Keywords: Markov decision processes (MDPs), stochastictime-varying networks, hypergraphs, route choice.

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Authors: Nicole Pearcy, Jonathan J. Crofts, Nadia Chuzhanova

Abstract:

In this paper, we employ a directed hypergraph model to investigate the extent to which environmental variability influences the set of available biochemical reactions within a living cell. Such an approach avoids the limitations of the usual complex network formalism by allowing for the multilateral relationships (i.e. connections involving more than two nodes) that naturally occur within many biological processes. More specifically, we extend the concept of network reciprocity to complex hyper-networks, thus enabling us to characterise a network in terms of the existence of mutual hyper-connections, which may be considered a proxy for metabolic network complexity. To demonstrate these ideas, we study 115 metabolic hyper-networks of bacteria, each of which can be classified into one of 6 increasingly varied habitats. In particular, we found that reciprocity increases significantly with increased environmental variability, supporting the view that organism adaptability leads to increased complexities in the resultant biochemical networks.

Keywords: Complexity, hypergraphs, reciprocity, metabolism.

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