Transition from small to large world in growing networks

We examine the global organization of growing networks in which a new vertex is attached to already existing ones with a probability depending on their age. We find that the network is infinite- or finite-dimensional depending on whether the attachment probability decays slower or faster than $(age)^{-1}$. The network becomes one-dimensional when the attachment probability decays faster than $(age)^{-2}$. We describe structural characteristics of these phases and transitions between them.Comment: 5 page

Flexible construction of hierarchical scale-free networks with general exponent

Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model which reproduces the main experimental properties observed in real networks: scale-free of degree distribution $P(k)$ (frequency of the nodes that are connected to $k$ other nodes decays as a power-law $P(k)\sim k^{-\gamma}$) and power-law scaling of the clustering coefficient $C(k)\sim k^{-1}$. The major novelties of our model can be summarized as follows: {\it (a)} The model generates networks with scale-free distribution for the degree of nodes with general exponent $\gamma > 2$, and arbitrarily close to any specified value, being able to reproduce most of the observed hierarchical scale-free topologies. In contrast, previous models can not obtain values of $\gamma > 2.58$. {\it (b)} Our model has structural flexibility because {\it (i)} it can incorporate various types of basic building blocks (e.g., triangles, tetrahedrons and, in general, fully connected clusters of $n$ nodes) and {\it (ii)} it allows a large variety of configurations (i.e., the model can use more than $n-1$ copies of basic blocks of $n$ nodes). The structural features of our proposed model might lead to a better understanding of architectures of biological and non-biological networks.Comment: RevTeX, 5 pages, 4 figure

Normocalcemic versus Hypercalcemic Primary Hyperparathyroidism: More Stone than Bone?

Introduction. Normocalcemic primary hyperparathyroidism (NPHPT) is considered a variant of the more frequent form of the disease characterized by normal serum calcium levels with high PTH. The higher prevalence of renal stones in patients with HPTP and the well established association with bone disorders show the importance of studies on how to manage asymptomatic patients. Objective. To compare the clinical and laboratory data between the normocalcemic and mild hypercalcemic forms of PHPT. Methods. We retrospectively evaluated 70 patients with PHPT, 33 normocalcemic and 37 mild hypercalcemic. Results. The frequency of nephrolithiasis was 18.2% in normocalcemic patients and 18.9% in the hypercalcemic ones (P = 0.937). Fifteen percent of normocalcemic patients had a previous history of fractures compared to 10.8% of hypercalcemic patients, although there was no statistically significant difference (P = 0.726). Conclusion. Our data confirms a high prevalence of urolithiasis in normocalcemic primary hyperparathyroidism, but with the preservation of cortical bone. This finding supports the hypothesis that this disease is not an idle condition and needs treatment

Diluted antiferromagnet in a ferromagnetic enviroment

The question of robustness of a network under random ``attacks'' is treated in the framework of critical phenomena. The persistence of spontaneous magnetization of a ferromagnetic system to the random inclusion of antiferromagnetic interactions is investigated. After examing the static properties of the quenched version (in respect to the random antiferromagnetic interactions) of the model, the persistence of the magnetization is analysed also in the annealed approximation, and the difference in the results are discussed

Infrared properties of propagators in Landau-gauge pure Yang-Mills theory at finite temperature

The finite-temperature behavior of gluon and of Faddeev-Popov-ghost propagators is investigated for pure SU(2) Yang-Mills theory in Landau gauge. We present nonperturbative results, obtained using lattice simulations and Dyson-Schwinger equations. Possible limitations of these two approaches, such as finite-volume effects and truncation artifacts, are extensively discussed. Both methods suggest a very different temperature dependence for the magnetic sector when compared to the electric one. In particular, a clear thermodynamic transition seems to affect only the electric sector. These results imply in particular the confinement of transverse gluons at all temperatures and they can be understood inside the framework of the so-called Gribov-Zwanziger scenario of confinement.Comment: 25 pages, 14 figures, 2 tables, minor changes of typographical and design character, some minor errors corrected, version to appear in PR

Preferential attachment of communities: the same principle, but a higher level

The graph of communities is a network emerging above the level of individual nodes in the hierarchical organisation of a complex system. In this graph the nodes correspond to communities (highly interconnected subgraphs, also called modules or clusters), and the links refer to members shared by two communities. Our analysis indicates that the development of this modular structure is driven by preferential attachment, in complete analogy with the growth of the underlying network of nodes. We study how the links between communities are born in a growing co-authorship network, and introduce a simple model for the dynamics of overlapping communities.Comment: 7 pages, 3 figure

Spectral transitions in networks

We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdos-Renyi (E-R) random graph is determined by the average degree , and p(s) undergoes a dramatic change when is varied around the critical point of the percolation transition, =1. When > 1, the p(s) is described by the statistics of the Gaussian Orthogonal Ensemble (GOE), one of the major statistical ensembles in Random Matrix Theory, whereas at =1 it follows the Poisson level spacing distribution. Closely above the critical point, p(s) can be described in terms of an intermediate distribution between Poisson and the GOE, the Brody-distribution. Furthermore, below the critical point p(s) can be given with the help of the regularised Gamma-function. Motivated by these results, we analyse the behaviour of p(s) in real networks such as the Internet, a word association network and a protein protein interaction network as well. When the giant component of these networks is destroyed in a node deletion process simulating the networks subjected to intentional attack, their level spacing distribution undergoes a similar transition to that of the E-R graph.Comment: 11 pages, 5 figure

COMPARATIVE ANALYSIS OF THE EFFICIENCY OF THERMAL SYSTEMS BUILT WITH REFLECTIVE INSULATORS WITH AND WITHOUT VACUUM

The use of reflective surfaces functioning as thermal insulators has grown significantly over the years. Reflective thermal insulators are materials that have several characteristics such as low emissivity, low absorptivity and high reflectivity in the infrared spectrum. The use of these materials has grown very much lately, since they contain several important radioactive properties that minimize the heat loss of thermal systems and cooling systems that are used to block the heat on the roof of buildings. A system made of three surfaces of 430 stainless steel mirror was built to analyze the influence of reflective surfaces as a way to reduce the heat loss and thereby conserve the energy of a thermal system. The system was analyzed both with and without the presence of vacuum, and then compared with a system that contained glass wool between the stainless steel mirror walls, since this insulator is considered resistive and also broadly used around the world in thermal systems. The reflectivity and emissivity of the surfaces used were also measured in this experiment. A type K thermocouple was fixed on the wall of the system to obtain the temperature of the stainless steel mirror surfaces and to analyze the thermal behavior of each configuration used. The results showed an efficiency of 13% when the reflective surfaces were used to minimize the heat loss of the thermal system. However, the system with vacuum had the best outcome, a 60% efficiency. Both of these were compared to the system made of glass wool as a thermal insulator