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

When do generalized entropies apply? How phase space volume determines entropy

We show how the dependence of phase space volume $\Omega(N)$ of a classical system on its size $N$ 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

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

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 q-exponential family in statistical physics

The notion of generalised exponential family is considered in the restricted context of nonextensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown that the configurational probability distributions of the microcanonical ensemble belong to the q-exponential family.Comment: 18 pages, 4 figures, proceedings of SigmaPhi 200

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

Peer-review in a world with rational scientists: Toward selection of the average

One of the virtues of peer review is that it provides a self-regulating selection mechanism for scientific work, papers and projects. Peer review as a selection mechanism is hard to evaluate in terms of its efficiency. Serious efforts to understand its strengths and weaknesses have not yet lead to clear answers. In theory peer review works if the involved parties (editors and referees) conform to a set of requirements, such as love for high quality science, objectiveness, and absence of biases, nepotism, friend and clique networks, selfishness, etc. If these requirements are violated, what is the effect on the selection of high quality work? We study this question with a simple agent based model. In particular we are interested in the effects of rational referees, who might not have any incentive to see high quality work other than their own published or promoted. We find that a small fraction of incorrect (selfish or rational) referees can drastically reduce the quality of the published (accepted) scientific standard. We quantify the fraction for which peer review will no longer select better than pure chance. Decline of quality of accepted scientific work is shown as a function of the fraction of rational and unqualified referees. We show how a simple quality-increasing policy of e.g. a journal can lead to a loss in overall scientific quality, and how mutual support-networks of authors and referees deteriorate the system.Comment: 5 pages 4 figure

The Nimbus 4 Infrared Spectroscopy Experiment, IRIS-D. Part 1: Calibrated Thermal Emission Spectra

Calibrated infrared emission spectra of earth and atmosphere using high resolution interferometer spectrophotometer on Nimbus 4 satellit

Spectrometry: Report of panel

Spectroscopic measurements are required to define the spectral background and provide the detailed spectral information that is essential for the design of species-specific systems and the analysis of data obtained from them. This function of spectroscopic measurements is expected to be an important part of any tropospheric remote-sensing program, and both emission and absorption spectroscopy are relevant in this context. The data from such observations are of value to tropospheric science in their own right, during the initial phases while species-specific techniques and instruments are under development. In addition, there are a number of unresolved problems in tropospheric radiative transfer and spectroscopy which presently limit the accuracy and reliability of all remote sensing methods. Only through a supporting program of spectroscopic measurements can progress be made in improving the understanding of these aspects of radiative transfer and ultimately reaching the desired confidence in the accuracy to species-specific monitoring techniques