Like it or not, attempts to evaluate and monitor the quality of academic research have become increasingly prevalent worldwide. Performance reviews range from at the level of individuals, through research groups and departments, to entire universitie
s. Many of these are informed by, or functions of, simple scientometric indicators and the results of such exercises impact onto careers, funding and prestige. However, there is sometimes a failure to appreciate that scientometrics are, at best, very blunt instruments and their incorrect usage can be misleading. Rather than accepting the rise and fall of individuals and institutions on the basis of such imprecise measures, calls have been made for indicators be regularly scrutinised and for improvements to the evidence base in this area. It is thus incumbent upon the scientific community, especially the physics, complexity-science and scientometrics communities, to scrutinise metric indicators. Here, we review recent attempts to do this and show that some metrics in widespread use cannot be used as reliable indicators research quality.
The Ising model on annealed complex networks with degree distribution decaying algebraically as $p(K)sim K^{-lambda}$ has a second-order phase transition at finite temperature if $lambda> 3$. In the absence of space dimensionality, $lambda$ controls
the transition strength; mean-field theory applies for $lambda >5$ but critical exponents are $lambda$-dependent if $lambda < 5$. Here we show that, as for regular lattices, the celebrated Lee-Yang circle theorem is obeyed for the former case. However, unlike on regular lattices where it is independent of dimensionality, the circle theorem fails on complex networks when $lambda < 5$. We discuss the importance of this result for both theory and experiments on phase transitions and critical phenomena. We also investigate the finite-size scaling of Lee-Yang zeros in both regimes as well as the multiplicative logarithmic corrections which occur at $lambda=5$.
The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described by the top
ology of a network. We consider the q-state Potts model on an uncorrelated scale-free network for which the node-degree distribution manifests a power-law decay governed by the exponent lambda. We work within the mean-field approximation, since for systems on random uncorrelated scale-free networks this method is known to often give asymptotically exact results. Depending on particular values of q and lambda one observes either a first-order or a second-order phase transition or the system is ordered at any finite temperature. In a case study, we consider the limit q=1 (percolation) and find a correspondence between the magnetic exponents and those describing percolation on a scale-free network. Interestingly, logarithmic corrections to scaling appear at lambda=4 in this case.
This paper analyses the impact of random failure or attack on the public transit networks of London and Paris in a comparative study. In particular we analyze how the dysfunction or removal of sets of stations or links (rails, roads, etc.) affects th
e connectivity properties within these networks. We show how accumulating dysfunction leads to emergent phenomena that cause the transportation system to break down as a whole. Simulating different directed attack strategies, we find minimal strategies with high impact and identify a-priory criteria that correlate with the resilience of these networks. To demonstrate our approach, we choose the London and Paris public transit networks. Our quantitative analysis is performed in the frames of the complex network theory - a methodological tool that has emerged recently as an interdisciplinary approach joining methods and concepts of the theory of random graphs, percolation, and statistical physics. In conclusion we demonstrate that taking into account cascading effects the network integrity is controlled for both networks by less than 0.5 % of the stations i.e. 19 for Paris and 34 for London.
The goals of this paper are to present criteria, that allow to a priori quantify the attack stability of real world correlated networks of finite size and to check how these criteria correspond to analytic results available for infinite uncorrelated
networks. As a case study, we consider public transportation networks (PTN) of several major cities of the world. To analyze their resilience against attacks either the network nodes or edges are removed in specific sequences (attack scenarios). During each scenario the size S(c) of the largest remaining network component is observed as function of the removed share c of nodes or edges. To quantify the PTN stability with respect to different attack scenarios we use the area below the curve described by S(c) for c in [0,1] recently introduced (Schneider, C. M, et al., PNAS 108 (2011) 3838) as a numerical measure of network robustness. This measure captures the network reaction over the whole attack sequence. We present results of the analysis of PTN stability against node and link-targeted attacks.
We analyze a controversial question about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both analytical and numerical studies performed so far support an extended Harris criterion (A. Weinrib
, B. I. Halperin, Phys. Rev. B 27 (1983) 413) and bring about the new universality class, the numerical values of the critical exponents found so far differ essentially. To resolve this discrepancy we perform extensive Monte Carlo simulations of a 3d Ising magnet with non-magnetic impurities arranged as lines with random orientation. We apply Wolff cluster algorithm accompanied by a histogram reweighting technique and make use of the finite-size scaling to extract the values of critical exponents governing the magnetic phase transition. Our estimates for the exponents differ from the results of the two numerical simulations performed so far and are in favour of a non-trivial dependency of the critical exponents on the peculiarities of long-range correlations decay.
We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well as to the
Swendsen-Wang and Wolff cluster algorithms. The lattice sizes of L=10-96 are analysed by a finite-size-scaling technique. The site dilution concentration p=0.85 was chosen to minimize the correction-to-scaling effects. We calculate numerical values of the dynamical critical exponents for the integrated and exponential autocorrelation times for energy and magnetization. As expected, cluster algorithms are characterized by lower values of dynamical critical exponent than the local one: also in the case of dilution critical slowing down is more pronounced for the Metropolis algorithm. However, the striking feature of our estimates is that they suggest that dilution leads to decrease of the dynamical critical exponent for the cluster algorithms. This phenomenon is quite opposite to the local dynamics, where dilution enhances critical slowing down.
The influence of a layered aperiodic modulation of the couplings on the critical behaviour of the two-dimensional Ising model is studied in the case of marginal perturbations. The aperiodicity is found to induce anisotropic scaling. The anisotropy ex
ponent z, given by the sum of the surface magnetization scaling dimensions, depends continuously on the modulation amplitude. Thus these systems are scale invariant but not conformally invariant at the critical point.
