Chemical Organizations in a Toy Model of the Political System

Dittrich, Peter; Winter, Lars

doi:10.1142/s0219525908001878

Cited by 28 publications

(18 citation statements)

References 11 publications

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“…Indeed, if I ∩ O n 0 = ∅ for l = i, j we may simply choose y = x , = 1, 2. Otherwise, x 1 , x 2 are in some O n 1 and O n 2 respectively with n 1 , n 2 > n 0 , hence by (14), there exist paths as described. By (13), there exist θ 0 , θ 1 , a 1 > 0 and a probability measure ν on E such that, for all y ∈ O n 0 and all s ∈ [θ 1 , θ 1 + θ 0 ], P y (X s ∈ ·) ≥ a 1 ν.…”

Section: Lemmasmentioning

confidence: 98%

Existence of a unique quasi-stationary distribution in stochastic reaction networks

Hansen¹,

Wiuf²

2020

Electron. J. Probab.

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In the setting of stochastic dynamical systems that eventually go extinct, the quasi-stationary distributions are useful to understand the long-term behavior of a system before evanescence. For a broad class of applicable continuous-time Markov processes on countably infinite state spaces, known as reaction networks, we introduce the inferred notion of absorbing and endorsed sets, and obtain sufficient conditions for the existence and uniqueness of a quasi-stationary distribution within each such endorsed set. In particular, we obtain sufficient conditions for the existence of a globally attracting quasi-stationary distribution in the space of probability measures on the set of endorsed states. Furthermore, under these conditions, the convergence from any initial distribution to the quasi-stationary distribution is exponential in the total variation norm.

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Section: Lemmasmentioning

confidence: 98%

Existence of a unique quasi-stationary distribution in stochastic reaction networks

Hansen¹,

Wiuf²

2020

Electron. J. Probab.

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“…One avenue for future work in this direction involves application of reaction networks to cognitive and social phenomena [21]. The dynamics of the system-whether chemical, cognitive, or social-is described by a set of highly coupled non-linear differential equations.…”

Section: Applying Communal Exchange To Cultural Evolutionmentioning

confidence: 99%

An evolutionary framework for cultural change: Selectionism versus communal exchange

Gabora

2013

Physics of Life Reviews

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Dawkins' replicator-based conception of evolution has led to widespread misapplication of selectionism across the social sciences because it does not address the paradox that inspired the theory of natural selection in the first place: how do organisms accumulate change when traits acquired over their lifetime are obliterated? This is addressed by von Neumann's concept of a self-replicating automaton (SRA). A SRA consists of a self-assembly code that is used in two distinct ways: (1) actively deciphered during development to construct a self-similar replicant, and (2) passively copied to the replicant to ensure that it can reproduce. Information that is acquired over a lifetime is not transmitted to offspring, whereas information that is inherited during copying is transmitted. In cultural evolution there is no mechanism for discarding acquired change. Acquired change can accumulate orders of magnitude faster than, and quickly overwhelm, inherited change due to differential replication of variants in response to selection. This prohibits a selectionist but not an evolutionary framework for culture and the creative processes that fuel it. The importance non-Darwinian processes in biological evolution is increasingly recognized. Recent work on the origin of life suggests that early life evolved through a non-Darwinian process referred to as communal exchange that does not involve a self-assembly code, and that natural selection emerged from this more haphazard, ancestral evolutionary process. It is proposed that communal exchange provides an evolutionary framework for culture that enables specification of cognitive features necessary for a (real or artificial) society to evolve culture. This is supported by a computational model of cultural evolution and a conceptual network based program for documenting material cultural history, and it is consistent with high levels of human cooperation. Evolutionary Framework Culture 3Keywords: creativity, cultural evolution, meme, natural selection, replicator, selfreplicating automaton Evolutionary Framework Culture 4 IntroductionLike organisms, elements of culture exhibit descent with modification; new ideas and artifacts build adaptively on previous ones. If it were possible to root the social and behavioral sciences in an evolutionary framework, they might achieve a unification comparable with Darwin's unification of the life sciences. Thus it is unsurprising that, dating back to Herbert Spencer's introduction of the notion of social Darwinism a few years after Darwin's Origin of Species, Darwinian thinking has been applied to a range of phenomena outside of biology, including creativity [14,111], neural copying and pruning [11,12,13,23,26], law [55], cosmology [118], computer-mediated communication [74], and perhaps most extensively, cultural and economic change [7,8,15,71,86,87,107,108]. Elements of culture build on one another cumulatively, as demonstrated even in laboratory settings [10]. Not only does culture accumulate over time, but it adapts, diversifies,...

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“…In [31], Dittrich and Winter developed a reaction network that represents a toy-model of the political system based on Luhmann's concept of communication. They define 13 communication species, e.g., social movement demands 'SBFor' (acronym from the German: Soziale Bewegung Forderung), social movement members 'SBMit' (Soziale Bewegung Mitglieder), potential collective binding decisions 'KVEPot' (Potenzielle Kollectiv Verbindliche Entscheidungen), etc., and a set of 20 reactions to model the interactions among these communications.…”

Section: Social System: Political Structurementioning

confidence: 99%

“…Representing systems by reaction networks not only permits the incorporation of different perspectives into play but also the possibility to represent and study the long-term dynamics of systems with a large number of entities and interactions. Attempts of modeling systems using reaction networks beyond the biochemical domain have been developed in political, decision-making, and economical systems [31][32][33]. Remarkably, these applications have been carried out combining scholars in various fields including social science, bioinformatics, and mathematics.…”

Section: Introductionmentioning

confidence: 99%

Reaction Networks as a Language for Systemic Modeling: Fundamentals and Examples

Veloz

Razeto‐Barry

2017

Systems

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Abstract:The basic processes that bring about living systems are conventionally represented in the framework of chemical reaction networks. Recently, it has been proposed that this framework can be exploited for studying various other phenomena. Reaction networks are specially suited for representing situations where different types of entities interact in contextual ways leading to the emergence of meta-structures. At an abstract level, a reaction network represents a universe whose evolution corresponds to the transformation of collections of entities into other collections of entities. Hence, we propose that systems correspond to the sub-networks that are stable enough to be observed. In this article, we discuss how to use reaction networks for representing systems. Namely, we introduce the different representational levels available (relational, stoichiometric, and kinetic), we show how to identify observable systems in the reaction network, discuss some relevant systemic notions such as context, emergence, and meta-system, and present some examples.

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Chemical Organizations in a Toy Model of the Political System

Cited by 28 publications

References 11 publications

Existence of a unique quasi-stationary distribution in stochastic reaction networks

Existence of a unique quasi-stationary distribution in stochastic reaction networks

An evolutionary framework for cultural change: Selectionism versus communal exchange

Reaction Networks as a Language for Systemic Modeling: Fundamentals and Examples

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