Towards a Calculus of Biological Networks

Reidys, Christian M.; Mortveit, Henning S.

doi:10.1524/zpch.2002.216.2.235

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…Dynamical Systems and Graph Theory are naturally coupled since any real phenomenon is usually described as a complex graph in which the evolution of time produces changes in specific measures on nodes or links among them [ 1 , 2 ]. In this work, the starting point is any structural network, including a parcelling of the brain, possessing an intrinsic dynamics.…”

Section: Introductionmentioning

confidence: 99%

Informational structures: A dynamical system approach for integrated information

et al. 2018

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Integrated Information Theory (IIT) has become nowadays the most sensible general theory of consciousness. In addition to very important statements, it opens the door for an abstract (mathematical) formulation of the theory. Given a mechanism in a particular state, IIT identifies a conscious experience with a conceptual structure, an informational object which exists, is composed of identified parts, is informative, integrated and maximally irreducible. This paper introduces a space-time continuous version of the concept of integrated information. To this aim, a graph and a dynamical systems treatment is used to define, for a given mechanism in a state for which a dynamics is settled, an Informational Structure, which is associated to the global attractor at each time of the system. By definition, the informational structure determines all the past and future behavior of the system, possesses an informational nature and, moreover, enriches all the points of the phase space with cause-effect power by means of its associated Informational Field. A detailed description of its inner structure by invariants and connections between them allows to associate a transition probability matrix to each informational structure and to develop a measure for the level of integrated information of the system.

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Section: Introductionmentioning

confidence: 99%

Informational structures: A dynamical system approach for integrated information

et al. 2018

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“…Specifically, signal pathways are being rendered in ways that are strikingly similar to logic circuits ''hot-wiring'' signal-activated metabolic or genomic subsystems (e.g., Klipp and Heinrich, 1999;Cabanac and Russek, 2000;Bhalla and Iyengar, 2001;Fox and Hill, 2001;Aoki et al, 2002;Mortveit and Reidys, 2002;Suzuki, 2002). In this respect, many biologists are converging on the pictorial and analytical conventions used by engineers and computer scientists who regularly deal with large networked systems.…”

mentioning

confidence: 99%

“…In this respect, many biologists are converging on the pictorial and analytical conventions used by engineers and computer scientists who regularly deal with large networked systems. Specifically, signal pathways are being rendered in ways that are strikingly similar to logic circuits ''hot-wiring'' signal-activated metabolic or genomic subsystems (e.g., Klipp and Heinrich, 1999;Cabanac and Russek, 2000;Bhalla and Iyengar, 2001;Fox and Hill, 2001;Aoki et al, 2002;Mortveit and Reidys, 2002;Suzuki, 2002).…”

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confidence: 99%

TheBio‐Logic and machinery of plant morphogenesis

Niklas

2003

American J of Botany

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Morphogenesis (the development of organic form) requires signal-trafficking and cross-talking across all levels of organization to coordinate the operation of metabolic and genomic networked systems. Many biologists are currently converging on the pictorial conventions of computer scientists to render biological signaling as logic circuits supervising the operation of one or more signal-activated metabolic or gene networks. This approach can redact and simplify complex morphogenetic phenomena and allows for their aggregation into diagrams of larger, more "global" networked systems. This conceptualization is discussed in terms of how logic circuits and signal-activated subsystems work, and it is illustrated for examples of increasingly more complex morphogenetic phenomena, e.g., auxin-mediated cell expansion, entry into the mitotic cell cycle phases, and polar/lateral intercellular auxin transport. For each of these phenomena, a posited circuit/subsystem diagram draws rapid attention to missing components, either in the logic circuit or in the subsystem it supervises. These components must be identified experimentally if each of these basic phenomena is to be fully understood. Importantly, the power of the circuit/subsystem approach to modeling developmental phenomena resides not in its pictorial appeal but in the mathematical tools that are sufficiently strong to reveal and quantify the synergistics of networked systems and thus foster a better understanding of morphogenesis.

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Voltage Graphs

Groß¹

2013

Discrete Mathematics and Its Applications

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Towards a Calculus of Biological Networks

Cited by 3 publications

References 9 publications

Informational structures: A dynamical system approach for integrated information

Informational structures: A dynamical system approach for integrated information

TheBio‐Logic and machinery of plant morphogenesis

Voltage Graphs

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