http://popups.lib.uliege.be/1373-5411/index.php?id=2845 Publications of Auteurs Taichi Haruna fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=4660 We propose a new data analytical tool for directed networks by using category theory. We develop a category theoretical treatment of directed networks in order to obtain functional networks for real networks. By applying our method to concrete data on real information processing biological networks, we find a distinguishing global structure of functional networks. A possibility of a new hypothesis on network motifs is also indicated based on our theory and data analvsis. Mon, 14 Oct 2024 15:52:45 +0200 Mon, 14 Oct 2024 15:52:50 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4660 http://popups.lib.uliege.be/1373-5411/index.php?id=3959 We address the excess entropy, which is a measure of complexity for stationary time series, from the ordinal point of view. We show that the permutation excess entropy is equal to the mutual information between two adjacent semi-infinite blocks in the space of orderings for finite-state stationary ergodic Markov processes. This result may spread a new light on the relationship between complexity and anticipation. Tue, 01 Oct 2024 16:48:42 +0200 Tue, 01 Oct 2024 16:50:15 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3959 http://popups.lib.uliege.be/1373-5411/index.php?id=2842 We propose an algebraic description of emergence of new levels in trophic level networks. Trophic level networks are described by directed graphs. Their properties are surveyed in terms of an adjunction on a subcategory of the category of directed graphs. In particular, it is shown that trophic level networks are invariant under the composition of the right adjoin functor and the left adjoin functor. This invariance of trophic level networks can be broken by introducing the notion of time into the left adjoint functor. This leads to changes in trophic level networks. We show that the left adjoin functor consists of an intra-level process and an inter-level process. An inconsistency between them arises by the introduction of time. Negotiation between the intra-level process and the inter-level process can resolve the inconsistency at a level, however, a new inconsistency can arises at an emerged new level. Thus our algebraic description can follow indefinite development of trophic hierarchy. Tue, 03 Sep 2024 15:22:17 +0200 Tue, 03 Sep 2024 15:22:26 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2842