595 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
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
Scaling-violation phenomena and fractality in the human posture control systems
By analyzing the movements of quiet standing persons by means of wavelet
statistics, we observe multiple scaling regions in the underlying body
dynamics. The use of the wavelet-variance function opens the possibility to
relate scaling violations to different modes of posture control. We show that
scaling behavior becomes close to perfect, when correctional movements are
dominated by the vestibular system.Comment: 12 pages, 4 figures, to appear in Phys. Rev.
Nonextensive aspects of self-organized scale-free gas-like networks
We explore the possibility to interpret as a 'gas' the dynamical
self-organized scale-free network recently introduced by Kim et al (2005). The
role of 'momentum' of individual nodes is played by the degree of the node, the
'configuration space' (metric defining distance between nodes) being determined
by the dynamically evolving adjacency matrix. In a constant-size network
process, 'inelastic' interactions occur between pairs of nodes, which are
realized by the merger of a pair of two nodes into one. The resulting node
possesses the union of all links of the previously separate nodes. We consider
chemostat conditions, i.e., for each merger there will be a newly created node
which is then linked to the existing network randomly. We also introduce an
interaction 'potential' (node-merging probability) which decays with distance
d_ij as 1/d_ij^alpha; alpha >= 0). We numerically exhibit that this system
exhibits nonextensive statistics in the degree distribution, and calculate how
the entropic index q depends on alpha. The particular cases alpha=0 and alpha
to infinity recover the two models introduced by Kim et al.Comment: 7 pages, 5 figure
What is the minimal systemic risk in financial exposure networks?
We quantify how much systemic risk can be eliminated in financial contract networks by rearranging their network topology. By using mixed integer linear programming, financial linkages are optimally organized, whereas the overall economic conditions of banks, such as capital buffers, total interbank assets and liabilities, and average risk-weighted exposure remain unchanged. We apply the new optimization procedure to 10 snapshots of the Austrian interbank market where we focus on the largest 70 banks covering 71% of the market volume. The optimization reduces systemic risk (measured in DebtRank) by about 70%, showing the huge potential that changing the network structure has on the mitigation of financial contagion. Existing capital levels would need to be scaled up by a factor of 3.3 to obtain similar levels of DebtRank. These findings underline the importance of macro-prudential rules that focus on the structure of financial networks. The new optimization procedure allows us to benchmark actual networks to networks with minimal systemic risk. We find that simple topological measures, like link density, degree assortativity, or clustering coefficient, fail to explain the large differences in systemic risk between actual and optimal networks. We find that if the most systemically relevant banks are tightly connected, overall systemic risk is higher than if they are unconnected
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
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