6 research outputs found
Unanimity Rule on networks
We introduce a model for innovation-, evolution- and opinion dynamics whose
spreading is dictated by unanimity rules, i.e. a node will change its (binary)
state only if all of its neighbours have the same corresponding state. It is
shown that a transition takes place depending on the initial condition of the
problem. In particular, a critical number of initially activated nodes is
needed so that the whole system gets activated in the long-time limit. The
influence of the degree distribution of the nodes is naturally taken into
account. For simple network topologies we solve the model analytically, the
cases of random, small-world and scale-free are studied in detail.Comment: 7 pages 4 fig
Schumpeterian economic dynamics as a quantifiable minimum model of evolution
We propose a simple quantitative model of Schumpeterian economic dynamics.
New goods and services are endogenously produced through combinations of
existing goods. As soon as new goods enter the market they may compete against
already existing goods, in other words new products can have destructive
effects on existing goods. As a result of this competition mechanism existing
goods may be driven out from the market - often causing cascades of secondary
defects (Schumpeterian gales of destruction). The model leads to a generic
dynamics characterized by phases of relative economic stability followed by
phases of massive restructuring of markets - which could be interpreted as
Schumpeterian business `cycles'. Model timeseries of product diversity and
productivity reproduce several stylized facts of economics timeseries on long
timescales such as GDP or business failures, including non-Gaussian fat tailed
distributions, volatility clustering etc. The model is phrased in an open,
non-equilibrium setup which can be understood as a self organized critical
system. Its diversity dynamics can be understood by the time-varying topology
of the active production networks.Comment: 21 pages, 11 figure
A self-organized model for cell-differentiation based on variations of molecular decay rates
Systemic properties of living cells are the result of molecular dynamics
governed by so-called genetic regulatory networks (GRN). These networks capture
all possible features of cells and are responsible for the immense levels of
adaptation characteristic to living systems. At any point in time only small
subsets of these networks are active. Any active subset of the GRN leads to the
expression of particular sets of molecules (expression modes). The subsets of
active networks change over time, leading to the observed complex dynamics of
expression patterns. Understanding of this dynamics becomes increasingly
important in systems biology and medicine. While the importance of
transcription rates and catalytic interactions has been widely recognized in
modeling genetic regulatory systems, the understanding of the role of
degradation of biochemical agents (mRNA, protein) in regulatory dynamics
remains limited. Recent experimental data suggests that there exists a
functional relation between mRNA and protein decay rates and expression modes.
In this paper we propose a model for the dynamics of successions of sequences
of active subnetworks of the GRN. The model is able to reproduce key
characteristics of molecular dynamics, including homeostasis, multi-stability,
periodic dynamics, alternating activity, differentiability, and self-organized
critical dynamics. Moreover the model allows to naturally understand the
mechanism behind the relation between decay rates and expression modes. The
model explains recent experimental observations that decay-rates (or turnovers)
vary between differentiated tissue-classes at a general systemic level and
highlights the role of intracellular decay rate control mechanisms in cell
differentiation.Comment: 16 pages, 5 figure
On singularities and black holes in combination-driven models of technological innovation networks
It has been suggested that innovations occur mainly by combination: the more inventions accumulate, the higher the probability that new inventions are obtained from previous designs. Additionally, it has been conjectured that the combinatorial nature of innovations naturally leads to a singularity: at some finite time, the number of innovations should diverge. Although these ideas are certainly appealing, no general models have been yet developed to test the conditions under which combinatorial technology should become explosive. Here we present a generalised model of technological evolution that takes into account two major properties: the number of previous technologies needed to create a novel one and how rapidly technology ages. Two different models of combinatorial growth are considered, involving different forms of ageing. When long-range memory is used and thus old inventions are available for novel innovations, singularities can emerge under some conditions with two phases separated by a critical boundary. If the ageing has a characteristic time scale, it is shown that no singularities will be observed. Instead, a "black hole" of old innovations appears and expands in time, making the rate of invention creation slow down into a linear regime.This work was supported by the Fundacion Botin and by the Spanish Ministry of Economy and Competitiveness, Grant FIS2013-44674-P and FEDER and by the Santa Fe Institute, where most of this work was done