http://popups.lib.uliege.be/1373-5411/index.php?id=154 Index terms 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=2678 In graph-based systems there are many methods to compose (possibly different) graphs. However, none of these usual compositions are adequate to naturally express semantics of systems with dynamic topology, i.e., systems whose topology admits successive transformations through its computation. We constructed a categorical semantic domain for graph based systems with dynamic topology using a new way to compose edges of (possible different) graphs. ln this context, sequences of different graphs represent successive transformations of system topology during its computation and the edges composition between those graphs, the semantics of the corresponding dynamic system. Then we show how the proposed approach can be used to give semantics to concurrent anticipatory systems. Fri, 30 Aug 2024 10:23:17 +0200 Thu, 10 Oct 2024 10:52:38 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2678 http://popups.lib.uliege.be/1373-5411/index.php?id=2043 Aiming at developing a theoretical framework for the formal study of NP-hard optimisation problems, we have focused on structural properties of optimisation problems related to approximative issue. From the observation that, intuitively, there are many connections among categorical concepts and structural complexity notions, in this work we present a categorical approach to cope with some questions originally studied within Computational Complexity Theory. After defining the polynomial time soluble optimisation problems category OPTS and the optimisation problems category OPT, we introduce a comparison mechanism between them following the basic idea of categorical shape theory, in such way the hierarchical structure of approximation to each optimisation problem can be modelled. Fri, 26 Jul 2024 15:48:26 +0200 Thu, 10 Oct 2024 10:52:10 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2043 http://popups.lib.uliege.be/1373-5411/index.php?id=790 The goal of the paper is to manifest a special arrow diagram logic developed in mathematical category theory as capable to provide a general specification framework for information system engineering. We show that, unexpectedly, abstract ideas developed in categorical logic are of extremely high relevance for approaching some difficult specification problems in the field. Correspondingly, the arrow thinking underlying the diagram logic is suggested as a working way of thinking in information system engineering. Mon, 01 Jul 2024 13:57:30 +0200 Mon, 07 Oct 2024 15:24:44 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=790 http://popups.lib.uliege.be/1373-5411/index.php?id=3688 At the end of the last century, Planck opened the door onto the quantum mechanical world. Yet, ever since, despite enormous advances, science has resisted the precept implicit in the quantum mechanical formalism now increasingly confirmed by the experimental evidence, that reality is fundamentally non-local and reducible only locally to the classical Newtonian understanding that subsumed science before Planck's discovery. Even now such advanced ideas for the unification of physics such as string theory begin by quantizing an essentially classical model. Yet the expanding science and emerging technology of quantum cybernetics and information processing will, I am now convinced, change this. In particular, quantum holography/holochory offers such quantum non-local modelling such as quantum neural information processing or the completion began by Einstein, for Riemann's programme for the geometrization of physics, where the local classical models emerge as invariants. It is not therefore that neural networking or Einstein's general relativity are wrong, but that they are of limited application to modelling the reality in which we live, and that quantum models offer a new category of explanatory power, as this paper attempts to demonstrate, the breadth of which has yet to be fully appreciated. Thu, 26 Sep 2024 10:45:32 +0200 Thu, 26 Sep 2024 10:46:12 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3688 http://popups.lib.uliege.be/1373-5411/index.php?id=2994 Consistent structure of a Hamiltonian dynamical system with constant energy is shown in terms of category theory. A colimit of the dynamical system corresponds to a set of pairs of an initial state and a final state. Expansion of the colimit based on a concept of internal measurement induces heterarchical structure in the dynamical system and derives interaction between the system and the other one. Dynamical change of potential functions derived from that expansion is relevant to a concept of emergence based on the viewpoint of the Hamiltonian system. Wed, 04 Sep 2024 09:24:35 +0200 Wed, 04 Sep 2024 09:24:55 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2994 http://popups.lib.uliege.be/1373-5411/index.php?id=363 A theory of organization of complexity was constructed in order to create a common semiotic lineage among the diverse symbol systems used by various disciplines (Chandler, t996, L997). The foundations of the theory are developed from observations on the nonlinear dynamics of organisms within ecoments -- ecoments being defined as the immediate surroundings of one hierarchical degree of an emergent system. Each system (sub-system, sub-sub-system ... ) is assigned four primitives attributes (closure, conformation, concatenation and cyclicity) which are subject to scaling and semiotic constraints. In principle, each of these four terms is enumerable for a local system. Degrees of organization (symbolized as Oo) are composed from lesser organized systems to higher organized systems in terms of the enumeration of the four primitives. The emergent organizations are enumerated: 1,2,3, ... The patterns of organization at any particular level, Oo, are composed from patterns at other levels. Thus, no particular science or philosophy is assigned a privileged role in the unfolding of the dynamics. Mathematically, the organized systems are composed under the scientific representations of categories as developed in Chandler, 1991, and Ehresmann and Vanbremeersch 1987, 1997. Categorical objects have the unique mathematical characteristic of creating a 'logical shell' for other classes of mathematical structures. (see S. Mac Lane, Mathematics, Form and Structure, 1986.) This 'logical shell' character of category theory is used here to construct hierarchical relationships between scientific observations and mathematical structures. This notation parallels natural history and allows the facile accounting of the molecular biological mechanisms within a living system. Implications of this theory of natural organization for the design of artifrcial hierarchical systems arc apparent. Wed, 26 Jun 2024 11:41:38 +0200 Fri, 28 Jun 2024 16:58:07 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=363 http://popups.lib.uliege.be/1373-5411/index.php?id=175 The purpose of this paper is to consider a number of conceptual and linguistic issues associated with the nature and occurrence of collection concepts in the biological sciences. Collections are very common in biology and may be conflated with the idea of a system. The relations between collections (in the linguistic/psychological sense) and systemic metaphors in the biosciences will be examined. Two important systemic constructs that are relevant to both collections and systems are verbs and 'glue'. Examination of certain aspects of these ideas leads to a consideration of potentially valuable insights into the construction of descriptive biosystemic concepts using the source metaphor of category theory. Wed, 19 Jun 2024 11:00:17 +0200 Wed, 19 Jun 2024 11:00:26 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=175 http://popups.lib.uliege.be/1373-5411/index.php?id=149 A categorial framework for structured graph based systems with or without distinguished nodes or labeling on both arcs and nodes is proposed. Requirements for the existence of limits and colimits in the resulting categories are set. In this context, unrestricted and bicomplete categories of graph based systems such as Petri Nets, Labeled Transition Systems, Nonsequential Automata, etc., are easily defined. Then it is shown how limits and colimits can be interpreted as structuring and anticipatory properties of systems. The proposed framework called duo-internalization generalizes the notion of intemal graphs allowing that nodes and arc may be objects from different categories. The results about limits and colimits of (reflexive) duo-intemal (labeled) graphs (with distinguished nodes) are, for our knowledge, new. Tue, 18 Jun 2024 16:30:02 +0200 Tue, 18 Jun 2024 16:30:21 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=149