1,058 research outputs found
On the robustness of q-expectation values and Renyi entropy
We study the robustness of functionals of probability distributions such as
the R\'enyi and nonadditive S_q entropies, as well as the q-expectation values
under small variations of the distributions. We focus on three important types
of distribution functions, namely (i) continuous bounded (ii) discrete with
finite number of states, and (iii) discrete with infinite number of states. The
physical concept of robustness is contrasted with the mathematically stronger
condition of stability and Lesche-stability for functionals. We explicitly
demonstrate that, in the case of continuous distributions, once unbounded
distributions and those leading to negative entropy are excluded, both Renyi
and nonadditive S_q entropies as well as the q-expectation values are robust.
For the discrete finite case, the Renyi and nonadditive S_q entropies and the
q-expectation values are robust. For the infinite discrete case, where both
Renyi entropy and q-expectations are known to violate Lesche-stability and
stability respectively, we show that one can nevertheless state conditions
which guarantee physical robustness.Comment: 6 pages, to appear in Euro Phys Let
Parkinson's Law Quantified: Three Investigations on Bureaucratic Inefficiency
We formulate three famous, descriptive essays of C.N. Parkinson on
bureaucratic inefficiency in a quantifiable and dynamical socio-physical
framework. In the first model we show how the use of recent opinion formation
models for small groups can be used to understand Parkinson's observation that
decision making bodies such as cabinets or boards become highly inefficient
once their size exceeds a critical 'Coefficient of Inefficiency', typically
around 20. A second observation of Parkinson - which is sometimes referred to
as Parkinson's Law - is that the growth of bureaucratic or administrative
bodies usually goes hand in hand with a drastic decrease of its overall
efficiency. In our second model we view a bureaucratic body as a system of a
flow of workers, which enter, become promoted to various internal levels within
the system over time, and leave the system after having served for a certain
time. Promotion usually is associated with an increase of subordinates. Within
the proposed model it becomes possible to work out the phase diagram under
which conditions bureaucratic growth can be confined. In our last model we
assign individual efficiency curves to workers throughout their life in
administration, and compute the optimum time to send them to old age pension,
in order to ensure a maximum of efficiency within the body - in Parkinson's
words we compute the 'Pension Point'.Comment: 15 pages, 5 figure
Is the Tsallis entropy stable?
The question of whether the Tsallis entropy is Lesche-stable is revisited. It
is argued that when physical averages are computed with the escort
probabilities, the correct application of the concept of Lesche-stability
requires use of the escort probabilities. As a consequence, as shown here, the
Tsallis entropy is unstable but the thermodynamic averages are stable. We
further show that Lesche stability as well as thermodynamic stability can be
obtained if the homogeneous entropy is used as the basis of the formulation of
non-extensive thermodynamics. In this approach, the escort distribution arises
naturally as a secondary structure.Comment: 6 page
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
Mars: Mariner 9 spectroscopic evidence for H2O ice clouds
Spectral features observed with the Mariner 9 Interferometer Spectrometer are identified as those of water ice. Measured spectra are compared with theoretical calulations for the transfer of radiation through clouds of ice particles with variations in size distribution and integrated cloud mass. Comparisons with an observed spectrum from the Tharsis Ridge region indicate water ice clouds composed of particles with mean radius 2.0 microns and integrated cloud mass 0.00005 g/sq cm
The phase transition in random catalytic sets
The notion of (auto) catalytic networks has become a cornerstone in
understanding the possibility of a sudden dramatic increase of diversity in
biological evolution as well as in the evolution of social and economical
systems. Here we study catalytic random networks with respect to the final
outcome diversity of products. We show that an analytical treatment of this
longstanding problem is possible by mapping the problem onto a set of
non-linear recurrence equations. The solution of these equations show a crucial
dependence of the final number of products on the initial number of products
and the density of catalytic production rules. For a fixed density of rules we
can demonstrate the existence of a phase transition from a practically
unpopulated regime to a fully populated and diverse one. The order parameter is
the number of final products. We are able to further understand the origin of
this phase transition as a crossover from one set of solutions from a quadratic
equation to the other.Comment: 7 pages, ugly eps files due to arxiv restriction
Generalized information entropies depending only on the probability distribution
Systems with a long-term stationary state that possess as a spatio-temporally
fluctuation quantity can be described by a superposition of several
statistics, a "super statistics". We consider first, the Gamma, log-normal and
-distributions of . It is assumed that they depend only on , the
probability associated with the microscopic configuration of the system. For
each of the three distributions we calculate the Boltzmann factors and
show that they coincide for small variance of the fluctuations. For the Gamma
distribution it is possible to calculate the entropy in a closed form,
depending on , and to obtain then an equation relating with . We also propose, as other examples, new entropies close related with the
Kaniadakis and two possible Sharma-Mittal entropies. The entropies presented in
this work do not depend on a constant parameter but on . For the
-Gamma distribution and its corresponding Boltzmann factor
and the associated entropy, we show the validity of the saddle-point
approximation. We also briefly discuss the generalization of one of the four
Khinchin axioms to get this proposed entropy.Comment: 13 pages, 3 figure
The freshwater crayfish Austropotamobius pallipes in South Tyrol. Heritage species and bioindicator
Rapid decline of crayfish in European freshwaters and continuing threat necessitate integrated actions in conservation and management of native crayfish populations. Besides biological reasons (diseases, plague), the impact of toxic and harmful substances (fertilisers, herbicides) or wastewater effluents, habitat alteration or fragmentation have been responsible for their decline in some regions. The same is true for the region of South Tyrol, where compared to previous investigations, only 10 of a former total of 15 crayfish locations in the water bodies could be affirmed. Although two new populations of the non-indigenous Astacus astacus were detected, the native Austropotamobius pallipes continues to decline. While many investigations have focused accurately on causal coherences for the decline of native populations, the properties of crayfish facilitate to reverse the situation. In a few examples, the potential of Austropotamobius pallipes, the native crayfish in South Tyrol, as “surrogate species” for effective biological conservation is discussed. Given the various adequate attributes of freshwater crayfish as surrogate species (including indicator species, umbrella species and flagship species qualities), they may help to advance not only the crayfish situation itself but also freshwater ecosystem properties in general
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
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