611 research outputs found
When do generalized entropies apply? How phase space volume determines entropy
We show how the dependence of phase space volume of a classical
system on its size uniquely determines its extensive entropy. We give a
concise criterion when this entropy is not of Boltzmann-Gibbs type but has to
assume a {\em generalized} (non-additive) form. We show that generalized
entropies can only exist when the dynamically (statistically) relevant fraction
of degrees of freedom in the system vanishes in the thermodynamic limit. These
are systems where the bulk of the degrees of freedom is frozen and is
practically statistically inactive. Systems governed by generalized entropies
are therefore systems whose phase space volume effectively collapses to a
lower-dimensional 'surface'. We explicitly illustrate the situation for
binomial processes and argue that generalized entropies could be relevant for
self organized critical systems such as sand piles, for spin systems which form
meta-structures such as vortices, domains, instantons, etc., and for problems
associated with anomalous diffusion.Comment: 5 pages, 2 figure
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
Dynamics of gene expression and the regulatory inference problem
From the response to external stimuli to cell division and death, the
dynamics of living cells is based on the expression of specific genes at
specific times. The decision when to express a gene is implemented by the
binding and unbinding of transcription factor molecules to regulatory DNA.
Here, we construct stochastic models of gene expression dynamics and test them
on experimental time-series data of messenger-RNA concentrations. The models
are used to infer biophysical parameters of gene transcription, including the
statistics of transcription factor-DNA binding and the target genes controlled
by a given transcription factor.Comment: revised version to appear in Europhys. Lett., new titl
Opinion Formation in Laggard Societies
We introduce a statistical physics model for opinion dynamics on random
networks where agents adopt the opinion held by the majority of their direct
neighbors only if the fraction of these neighbors exceeds a certain threshold,
p_u. We find a transition from total final consensus to a mixed phase where
opinions coexist amongst the agents. The relevant parameters are the relative
sizes in the initial opinion distribution within the population and the
connectivity of the underlying network. As the order parameter we define the
asymptotic state of opinions. In the phase diagram we find regions of total
consensus and a mixed phase. As the 'laggard parameter' p_u increases the
regions of consensus shrink. In addition we introduce rewiring of the
underlying network during the opinion formation process and discuss the
resulting consequences in the phase diagram.Comment: 5 pages, eps fig
CO_2 on Titan
A sharp stratospheric emission feature at 667 cm^(−1) in the Voyager infrared spectra of Titan is associated with the ν_2 Q branch of CO_2. A coupling of photochemical and radiative transfer theory yields an average mole fraction above the 110 mbar level of ƒCO_2 = 1.5 ± ^(1.5)_(0.8) x 10^(-9), with most of the uncertainty being due to imprecise knowledge of the vertical distribution. CO_2 is found to be in a steady state, with its abundance being regulated principally by the ∼72 K cold trap near the tropopause and secondarily by the rate at which water-bearing meteoritic material enters the top of the atmosphere. An influx of water about 0.4 times that at the top of the terrestrial atmosphere is consistent with a combination of the observed CO_2 abundance and a steady state CO mole fraction of 1.1×10^(−4); the theoretical value for CO is close to the value observed by Lutz et al. (1983), although there are large margins for error in both numbers. If steady state conditions for CO prevail, little information is available regarding the evolution of Titan's atmosphere
Mapping the Structure of Human Values through Conceptual Representations
The present research provides the first direct examination of human values through concept categorization tasks that entail judging the meaning of values. Seven studies containing data from nine samples (N = 1086) in two countries (the UK and Brazil) asked participants to compare the meaning of different values found within influential quasi-circumplex model of values. Different methods were used across experiments, including direct similarity judgment tasks, pile sorting, and spatial arrangement. The results of these diverse conceptual assessments corresponded to spatial configurations that are broadly convergent with Schwartz's model, both between and within participants
Coexistence of opposite opinions in a network with communities
The Majority Rule is applied to a topology that consists of two coupled
random networks, thereby mimicking the modular structure observed in social
networks. We calculate analytically the asymptotic behaviour of the model and
derive a phase diagram that depends on the frequency of random opinion flips
and on the inter-connectivity between the two communities. It is shown that
three regimes may take place: a disordered regime, where no collective
phenomena takes place; a symmetric regime, where the nodes in both communities
reach the same average opinion; an asymmetric regime, where the nodes in each
community reach an opposite average opinion. The transition from the asymmetric
regime to the symmetric regime is shown to be discontinuous.Comment: 14 pages, 4 figure
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