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 $\beta$ can be described by a superposition of several statistics, a "super statistics". We consider first, the Gamma, log-normal and $F$-distributions of $\beta$. It is assumed that they depend only on $p_l$, the probability associated with the microscopic configuration of the system. For each of the three $\beta-$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 $p_l$, and to obtain then an equation relating $p_l$ with $\beta E_l$. 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 $q$ but on $p_l$. For the $p_l$-Gamma distribution and its corresponding $B_{p_l}(E)$ 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