Sustainable growth in complex networks

Based on the empirical analysis of the dependency network in 18 Java projects, we develop a novel model of network growth which considers both: an attachment mechanism and the addition of new nodes with a heterogeneous distribution of their initial degree, $k_0$. Empirically we find that the cumulative degree distributions of initial degrees and of the final network, follow power-law behaviors: $P(k_{0}) \propto k_{0}^{1-\alpha}$, and $P(k)\propto k^{1-\gamma}$, respectively. For the total number of links as a function of the network size, we find empirically $K(N)\propto N^{\beta}$, where $\beta$ is (at the beginning of the network evolution) between 1.25 and 2, while converging to $\sim 1$ for large $N$. This indicates a transition from a growth regime with increasing network density towards a sustainable regime, which revents a collapse because of ever increasing dependencies. Our theoretical framework is able to predict relations between the exponents $\alpha$, $\beta$, $\gamma$, which also link issues of software engineering and developer activity. These relations are verified by means of computer simulations and empirical investigations. They indicate that the growth of real Open Source Software networks occurs on the edge between two regimes, which are either dominated by the initial degree distribution of added nodes, or by the preferential attachment mechanism. Hence, the heterogeneous degree distribution of newly added nodes, found empirically, is essential to describe the laws of sustainable growth in networks.Comment: 5 pages, 2 figures, 1 tabl

A complementary view on the growth of directory trees

Trees are a special sub-class of networks with unique properties, such as the level distribution which has often been overlooked. We analyse a general tree growth model proposed by Klemm {\em et. al.} (2005) to explain the growth of user-generated directory structures in computers. The model has a single parameter $q$ which interpolates between preferential attachment and random growth. Our analysis results in three contributions: First, we propose a more efficient estimation method for $q$ based on the degree distribution, which is one specific representation of the model. Next, we introduce the concept of a level distribution and analytically solve the model for this representation. This allows for an alternative and independent measure of $q$. We argue that, to capture real growth processes, the $q$ estimations from the degree and the level distributions should coincide. Thus, we finally apply both representations to validate the model with synthetically generated tree structures, as well as with collected data of user directories. In the case of real directory structures, we show that $q$ measured from the level distribution are incompatible with $q$ measured from the degree distribution. In contrast to this, we find perfect agreement in the case of simulated data. Thus, we conclude that the model is an incomplete description of the growth of real directory structures as it fails to reproduce the level distribution. This insight can be generalised to point out the importance of the level distribution for modeling tree growth.Comment: 16 pages, 7 figure

Interpolating self-energy of the infinite-dimensional Hubbard model: Modifying the iterative perturbation theory

We develop an analytical expression for the self-energy of the infinite-dimensional Hubbard model that is correct in a number of different limits. The approach represents a generalization of the iterative perturbation theory to arbitrary fillings. In the weak-coupling regime perturbation theory to second order in the interaction U is recovered. The theory is exact in the atomic limit. The high-energy behavior of the self-energy up to order (1/E)**2 and thereby the first four moments of the spectral density are reproduced correctly. Referring to a standard strong-coupling moment method, we analyze the limit of strong U. Different modifications of the approach are discussed and tested by comparing with the results of an exact diagonalization study.Comment: LaTeX, 14 pages, 5 ps figures included, title changed, references updated, minor change

Superconductivity in the two dimensional Hubbard Model.

Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (pi,0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. Singlet d_{x^2-y^2}-wave pairing is strongly favoured and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest neighbour antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favouring superconductivity. However the mechanism for superconductivity is a local one, in contrast to spin fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature T_c is in the range 10-100K. The optimum doping delta_c lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and (2*Delta_{max})/(kT_c) ~ 4.Comment: REVTeX, 35 pages, including 19 PostScript figures numbered 1a to 11. Uses epsf.sty (included). Everything in uuencoded gz-compressed .tar file, (self-unpacking, see header). Submitted to Phys. Rev. B (24-2-95

Anomalous low doping phase of the Hubbard model

We present results of a systematic Quantum-Monte-Carlo study for the single-band Hubbard model. Thereby we evaluated single-particle spectra (PES & IPES), two-particle spectra (spin & density correlation functions), and the dynamical correlation function of suitably defined diagnostic operators, all as a function of temperature and hole doping. The results allow to identify different physical regimes. Near half-filling we find an anomalous `Hubbard-I phase', where the band structure is, up to some minor modifications, consistent with the Hubbard-I predictions. At lower temperatures, where the spin response becomes sharp, additional dispersionless `bands' emerge due to the dressing of electrons/holes with spin excitatons. We present a simple phenomenological fit which reproduces the band structure of the insulator quantitatively. The Fermi surface volume in the low doping phase, as derived from the single-particle spectral function, is not consistent with the Luttinger theorem, but qualitatively in agreement with the predictions of the Hubbard-I approximation. The anomalous phase extends up to a hole concentration of 15%, i.e. the underdoped region in the phase diagram of high-T_c superconductors. We also investigate the nature of the magnetic ordering transition in the single particle spectra. We show that the transition to an SDW-like band structure is not accomplished by the formation of any resolvable `precursor bands', but rather by a (spectroscopically invisible) band of spin 3/2 quasiparticles. We discuss implications for the `remnant Fermi surface' in insulating cuprate compounds and the shadow bands in the doped materials.Comment: RevTex-file, 20 PRB pages, 16 figures included partially as gif. A full ps-version including ps-figures can be found at http://theorie.physik.uni-wuerzburg.de/~eder/condmat.ps.gz Hardcopies of figures (or the entire manuscript) can also be obtained by e-mail request to: [email protected]

The Hubbard model within the equations of motion approach

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference

Self-bias and the emotionality of foreign languages

Article first published online: June 13, 2018Foreign language contexts impose a relative psychological and emotional distance in bilinguals. In our previous studies, we demonstrated that the use of a foreign language changes the strength of the seemingly automatic emotional responses in the self-paradigm, showing a robust asymmetry in the self-bias effect in a native and a foreign language context. Namely, larger effects were found in the native language, suggesting an emotional blunting in the foreign language context. In the present study, we investigated the source of these effects by directly comparing whether they stem from a language’s foreignness versus its non-nativeness. We employed the same self-paradigm (a simple perceptual matching task of associating simple geometric shapes with the labels “you,” “friend,” and “other”), testing unbalanced Spanish–Basque–English trilinguals. We applied the paradigm to three language contexts: native, non-native but contextually present (i.e., non-native local), and non-native foreign. Results showed a smaller self-bias only in the foreign language pointing to the foreign-language-induced psychological/emotional distance as the necessary prerequisite for foreign language effects. Furthermore, we explored whether perceived emotional distance towards foreign languages in Spanish–English bilinguals modulates foreign language effects. Results suggest that none of the different indices of emotional distance towards the foreign language obtained via questionnaires modulated the self-biases in the foreign language contexts. Our results further elucidate the deeply rooted and automatic nature of foreign-language-driven differential emotional processing.This research has been partially funded by grants PSI2015-65689-P and SEV-2015-0490 from the Spanish Government, AThEME-613465 from the European Union, and a 2016 BBVA Foundation Grant for Researchers and Cultural Creators awarded to the last author (J.A.D.)

Effects of place attachment on home return travel: a spatial perspective

Recent studies on place-mobility relationships suggest an increasing possibility that people can have multiple place attachments at varied spatial scales. Yet our understanding of how place attachment in different spatial scales affects mobility remains limited. This study investigates home return visits by Chinese diaspora tourists from North America who have made multiple trips to China. A total of 27 in-depth interviews with repeat home return travellers was conducted. Four different types of return movements were identified: local; dispersed; local & dispersed; and second-migration locale focused. A relationship was found between the participants’ sense of place, place identity and home return travel. The findings suggest that home return travel is more complex than previously thought. More focused sense of place and strong personal connection to ancestral homes may lead to more localized return, while a more generic sense of place (i.e. to ‘China’) and collective personal identity would result in a more dispersed travel pattern. Family migration history and strong attachment to family’s first migration destination also leads to focused return to the place. The study highlights the fact that place and place attachment are deeply personal and can evolve over time and space

Modelling Hot Spots of Soil Loss by Wind Erosion (SoLoWind) in Western Saxony, Germany

Land Degradation and Development published by John Wiley & Sons, Ltd. While it needs yet to be assessed whether or not wind erosion in Western Saxony is a major point of concern regarding land degradation and fertility, it has already been recognized that considerable off-site effects of wind erosion in the adjacent regions of Saxony-Anhalt and Brandenburg are connected to the spread of herbicides, pesticides and dust. So far, no wind erosion assessment for Western Saxony, Germany, exists. The wind erosion model previously applied for Germany (DIN standard 19706) is considering neither changes in wind direction over time nor influences of field size. This study aims to provide a first assessment of wind erosion for Western Saxony by extending the existing DIN model to a multidirectional model on soil loss by wind (SoLoWind) with new controlling factors (changing wind directions, soil cover, mean field length and mean protection zone) combined by fuzzy logic. SoLoWind is used for a local off-site effect evaluation in combination with high-resolution wind speed and wind direction data at a section of the highway A72. The model attributes 3·6% of the arable fields in Western Saxony to the very-high-wind erosion risk class. A relationship between larger fields (greater than 116 ha) and higher proportions (51·7%) of very-high-wind erosion risk can be observed. Sections of the highway A72 might be under high risk according to the modelled off-site effects of wind erosion. The presented applications showed the potential of SoLoWind to support and consult management for protection measures on a regional scale. © 2016 The Authors. Land Degradation and Development published by John Wiley & Sons, Ltd.The authors would like to thank Jürgen Heinrich and Gudrun Mayer for the technical revision of the model conception and the German Weather Service, the Saxon State Office for the Environment, Agriculture and Geology, the Saxon State Office for Road Construction and Traffic, the Saxon State Ministry of the Environment and Agriculture, the Saxon State Spatial Data and Land Survey Corporation, the Saxon Road Maintenance Depots, OpenStreetMap and the National Aeronautics and Space Administration for providing the datasets. We would also like to thank three anonymous reviewers for helpful comments.info:eu-repo/semantics/publishedVersio