30 research outputs found
Do extremists impose the structure of social networks?
The structure and the properties of complex networks essentially depend on
the way how nodes get connected to each other. We assume here that each node
has a feature which attracts the others. We model the situation by assigning
two numbers to each node, \omega and \alpha, where \omega indicates some
property of the node and \alpha the affinity towards that property. A node A is
more likely to establish a connection with a node B if B has a high value of
\omega and A has a high value of \alpha. Simple computer simulations show that
networks built according to this principle have a degree distribution with a
power law tail, whose exponent is determined only by the nodes with the largest
value of the affinity \alpha (the "extremists"). This means that the extremists
lead the formation process of the network and manage to shape the final
topology of the system. The latter phenomenon may have implications in the
study of social networks and in epidemiology.Comment: 4 pages, 3 figure
Risk attitude, beliefs, and information in a corruption game: An experimental analysis
For our experiment on corruption we designed a coordination game to model the influence of risk attitudes, beliefs, and information on behavioral choices and determined the equilibria. We observed that the participants' risk attitudes failed to explain their choices between corrupt and non-corrupt behavior. Instead, beliefs appeared to be a better predictor of whether or not they would opt for the corrupt alternative. Furthermore, varying the quantity of information available to players (modeled by changing the degree of uncertainty) provided additional insight into the players' propensity to engage in corrupt behavior. The experimental results show that a higher degree of uncertainty in the informational setting reduces corruption. --Corruption,game theory,experiment,risk attitude,beliefs
A quantum version of Sanov's theorem
We present a quantum extension of a version of Sanov's theorem focussing on a
hypothesis testing aspect of the theorem: There exists a sequence of typical
subspaces for a given set of stationary quantum product states
asymptotically separating them from another fixed stationary product state.
Analogously to the classical case, the exponential separating rate is equal to
the infimum of the quantum relative entropy with respect to the quantum
reference state over the set . However, while in the classical case the
separating subsets can be chosen universal, in the sense that they depend only
on the chosen set of i.i.d. processes, in the quantum case the choice of the
separating subspaces depends additionally on the reference state.Comment: 15 page
Quantisations of piecewise affine maps on the torus and their quantum limits
For general quantum systems the semiclassical behaviour of eigenfunctions in
relation to the ergodic properties of the underlying classical system is quite
difficult to understand. The Wignerfunctions of eigenstates converge weakly to
invariant measures of the classical system, the so called quantum limits, and
one would like to understand which invariant measures can occur that way,
thereby classifying the semiclassical behaviour of eigenfunctions. We introduce
a class of maps on the torus for whose quantisations we can understand the set
of quantum limits in great detail. In particular we can construct examples of
ergodic maps which have singular ergodic measures as quantum limits, and
examples of non-ergodic maps where arbitrary convex combinations of absolutely
continuous ergodic measures can occur as quantum limits. The maps we quantise
are obtained by cutting and stacking
Typical support and Sanov large deviations of correlated states
Discrete stationary classical processes as well as quantum lattice states are
asymptotically confined to their respective typical support, the exponential
growth rate of which is given by the (maximal ergodic) entropy. In the iid case
the distinguishability of typical supports can be asymptotically specified by
means of the relative entropy, according to Sanov's theorem. We give an
extension to the correlated case, referring to the newly introduced class of
HP-states.Comment: 29 pages, no figures, references adde
Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem
In classical information theory, entropy rate and Kolmogorov complexity per
symbol are related by a theorem of Brudno. In this paper, we prove a quantum
version of this theorem, connecting the von Neumann entropy rate and two
notions of quantum Kolmogorov complexity, both based on the shortest qubit
descriptions of qubit strings that, run by a universal quantum Turing machine,
reproduce them as outputs.Comment: 26 pages, no figures. Reference to publication added: published in
the Communications in Mathematical Physics
(http://www.springerlink.com/content/1432-0916/
A look into the future of the COVID-19 pandemic in Europe: an expert consultation.
How will the coronavirus disease 2019 (COVID-19) pandemic develop in the coming months and years? Based on an expert survey, we examine key aspects that are likely to influence the COVID-19 pandemic in Europe. The challenges and developments will strongly depend on the progress of national and global vaccination programs, the emergence and spread of variants of concern (VOCs), and public responses to non-pharmaceutical interventions (NPIs). In the short term, many people remain unvaccinated, VOCs continue to emerge and spread, and mobility and population mixing are expected to increase. Therefore, lifting restrictions too much and too early risk another damaging wave. This challenge remains despite the reduced opportunities for transmission given vaccination progress and reduced indoor mixing in summer 2021. In autumn 2021, increased indoor activity might accelerate the spread again, whilst a necessary reintroduction of NPIs might be too slow. The incidence may strongly rise again, possibly filling intensive care units, if vaccination levels are not high enough. A moderate, adaptive level of NPIs will thus remain necessary. These epidemiological aspects combined with economic, social, and health-related consequences provide a more holistic perspective on the future of the COVID-19 pandemic