Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks

In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral equation, a systematic way to determine the ensemble averaged eigenvalue spectrum for a general type of tree-like networks. Close to the percolation threshold we find characteristic scaling functions for the density of states rho(lambda) of scale-free networks. rho(lambda) shows characteristic power laws rho(lambda) ~ lambda^alpha_1 or rho(lambda) ~ lambda^alpha_2 for small lambda, where alpha_1 holds below and alpha_2 at the percolation threshold. In the range where the spectra are accessible from a numerical diagonalization procedure the two methods lead to very similar results.Comment: 9 pages, 6 figure

Scaling Properties of Random Walks on Small-World Networks

Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These properties include the average number of distinct sites visited by the random walker, the mean-square displacement of the walker, and the distribution of first-return times. The scaling form has three characteristic time regimes. At short times, the walker does not see the small-world shortcuts and effectively probes an ordinary Euclidean network in $d$-dimensions. At intermediate times, the properties of the walker shows scaling behavior characteristic of an infinite small-world network. Finally, at long times, the finite size of the network becomes important, and many of the properties of the walker saturate. We propose general analytical forms for the scaling properties in all three regimes, and show that these analytical forms are consistent with our numerical simulations.Comment: 7 pages, 8 figures, two-column format. Submitted to PR

Critical Exponents from Five-Loop Strong-Coupling phi^4-Theory in 4- epsilon Dimensions

With the help of strong-coupling theory, we calculate the critical exponents of O(N)-symmetric phi^4-theories in 4- epsilon dimensions up to five loops with an accuracy comparable to that achieved by Borel-type resummation methods.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/29

Self-avoiding walks and connective constants in small-world networks

Long-distance characteristics of small-world networks have been studied by means of self-avoiding walks (SAW's). We consider networks generated by rewiring links in one- and two-dimensional regular lattices. The number of SAW's $u_n$ was obtained from numerical simulations as a function of the number of steps $n$ on the considered networks. The so-called connective constant, $\mu = \lim_{n \to \infty} u_n/u_{n-1}$, which characterizes the long-distance behavior of the walks, increases continuously with disorder strength (or rewiring probability, $p$). For small $p$, one has a linear relation $\mu = \mu_0 + a p$, $\mu_0$ and $a$ being constants dependent on the underlying lattice. Close to $p = 1$ one finds the behavior expected for random graphs. An analytical approach is given to account for the results derived from numerical simulations. Both methods yield results agreeing with each other for small $p$, and differ for $p$ close to 1, because of the different connectivity distributions resulting in both cases.Comment: 7 pages, 5 figure

Invaded cluster simulations of the XY model in two and three dimensions

The invaded cluster algorithm is used to study the XY model in two and three dimensions up to sizes 2000^2 and 120^3 respectively. A soft spin O(2) model, in the same universality class as the 3D XY model, is also studied. The static critical properties of the model and the dynamical properties of the algorithm are reported. The results are K_c=0.45412(2) for the 3D XY model and eta=0.037(2) for the 3D XY universality class. For the 2D XY model the results are K_c=1.120(1) and eta=0.251(5). The invaded cluster algorithm does not show any critical slowing for the magnetization or critical temperature estimator for the 2D or 3D XY models.Comment: 30 pages, 11 figures, problem viewing figures corrected in v

Practitioner’s Section: Integrated Resource Efficiency Analysis for Reducing Climate Impacts in the Chemical Industry

Reducing greenhouse gas emissions of the material-intensive chemical industry requires an integrated analysis and optimization of the complex production systems including raw material and energy use, resulting costs and environmental and climate impacts. To meet this challenge, the research project InReff (Integrated Resource Efficiency Analysis for Reducing Climate Impacts in the Chemical Industry) has been established. It aims at the development of an IT-supported modeling and evaluation framework which is able to comprehensively address issues of resource efficiency and climate change within the chemical industry, e.g. the minimization of material and energy intensity and consequently greenhouse gas emissions, without compromising on production performance. The paper presents background information on resource efficiency and the research project, an ideal-typical decision model for resource efficiency analysis, the conceptual approach for an IT-based integration platform as well as the case study design at the industrial project partners’ sites. These first results are linked to future activities and further research questions are highlighted in the concluding section

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions concerning the critical crossover functions, finding a good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal lscrossover behavior of our data for any finite range.Comment: 43 pages, revte

Efficacy and Toxicity of Different Chemotherapy Protocols for Concurrent Chemoradiation in Non-Small Cell Lung Cancer—A Secondary Analysis of the PET Plan Trial

(1) Background: The optimal chemotherapy (CHT) regimen for concurrent chemoradiation (cCRT) is not well defined. In this secondary analysis of the international randomized PET-Plan trial, we evaluate the efficacy of different CHT. (2) Methods: Patients with inoperable NSCLC were randomized at a 1:1 ratio regarding the target volume definition and received isotoxically dose-escalated cCRT using cisplatin 80 mg/m2 (day 1, 22) and vinorelbin 15 mg/m2 (day 1, 8, 22, 29) (P1) or cisplatin 20 mg/m2 (day 1–5, 29–33) and vinorelbin 12.5 mg/m2 (day 1, 8, 15, 29, 36, 43) (P2) or carboplatin AUC1 (day 1–5, 29–33) and vinorelbin 12.5 mg/m2 (day 1, 8, 15, 29, 36, 43) (P3) or other CHT at the treating physician’s discretion. (3) Results: Between 05/2009 and 11/2016, 205 patients were randomized and 172 included in the per-protocol analysis. Patients treated in P1 or P2 had a better overall survival (OS) compared to P3 (p = 0.015, p = 0.01, respectively). Patients treated with carboplatin had a worse OS compared to cisplatin (HR 1.78, p = 0.03), but the difference did not remain significant after adjusting for age, ECOG, cardiac function creatinine and completeness of CHT. (4) Conclusions: Carboplatin doublets show no significant difference compared to cisplatin, after adjusting for possibly relevant factors, probably due to existing selection bias

Critical behavior of the three-dimensional XY universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class. We find alpha=-0.0146(8), gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and delta=4.780(2). We observe a discrepancy with the most recent experimental estimate of alpha; this discrepancy calls for further theoretical and experimental investigations. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions. Two improved models (with suppressed leading scaling corrections) are selected by Monte Carlo computation. The critical exponents are computed from high-temperature expansions specialized to these improved models. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine the specific-heat amplitude ratio.Comment: 61 pages, 3 figures, RevTe