The Contribution of the First Stars to the Cosmic Infrared Background

We calculate the contribution to the cosmic infrared background from very massive metal-free stars at high redshift. We explore two plausible star-formation models and two limiting cases for the reprocessing of the ionizing stellar emission. We find that Population III stars may contribute significantly to the cosmic near-infrared background if the following conditions are met: (i) The first stars were massive, with M > ~100 M_sun. (ii) Molecular hydrogen can cool baryons in low-mass haloes. (iii) Pop III star formation is ongoing, and not shut off through negative feedback effects. (iv) Virialized haloes form stars at about 40 per cent efficiency up to the redshift of reionization, z~7. (v) The escape fraction of the ionizing radiation into the intergalactic medium is small. (vi) Nearly all of the stars end up in massive black holes without contributing to the metal enrichment of the Universe.Comment: 11 pages, 6 figures, expanded discussion, added mid-IR to Fig 6, MNRAS in pres

Percolation Critical Exponents in Scale-Free Networks

We study the behavior of scale-free networks, having connectivity distribution P(k) k^-a, close to the percolation threshold. We show that for networks with 3<a<4, known to undergo a transition at a finite threshold of dilution, the critical exponents are different than the expected mean-field values of regular percolation in infinite dimensions. Networks with 2<a<3 possess only a percolative phase. Nevertheless, we show that in this case percolation critical exponents are well defined, near the limit of extreme dilution (where all sites are removed), and that also then the exponents bear a strong a-dependence. The regular mean-field values are recovered only for a>4.Comment: Latex, 4 page

Competition and Facilitation: a Synthetic Approach to Interactions in Plant Communities

Interactions among organisms take place within a complex milieu of abiotic and biotic processes, but we generally study them as solitary phenomena. Complex combinations of negative and positive interactions have been identified in a number of plant communities. The importance of these two processes in structuring plant communities can best be understood by comparing them along gradients of abiotic stress, consumer pressure, and among different life stages, sizes, and densities of the interacting species. Here, we discuss the roles of life stage, physiology, indirect interactions, and the physical environment on the balance of competition and facilitation in plant communities

Retrograde Tracing with Recombinant Rabies Virus Reveals Correlations Between Projection Targets and Dendritic Architecture in Layer 5 of Mouse Barrel Cortex

A recombinant rabies virus was used as a retrograde tracer to allow complete filling of the axonal and dendritic arbors of identified projection neurons in layer 5 of mouse primary somatosensory cortex (S1) in vivo. Previous studies have distinguished three types of layer 5 pyramids in S1: tall-tufted, tall-simple, and short. Layer 5 pyramidal neurons were retrogradely labeled from several known targets: contralateral S1, superior colliculus, and thalamus. The complete dendritic arbors of labeled cells were reconstructed to allow for unambiguous classification of cell type. We confirmed that the tall-tufted pyramids project to the superior colliculus and thalamus and that short layer 5 pyramidal neurons project to contralateral cortex, as previously described. We found that tall-simple pyramidal neurons contribute to corticocortical connections. Axonal reconstructions show that corticocortical projection neurons have a large superficial axonal arborization locally, while the subcortically projecting neurons limit axonal arbors to the deep layers. Furthermore, reconstructions of local axons suggest that tall-simple cell axons have extensive lateral spread while those of the short pyramids are more columnar. These differences were revealed by the ability to completely label dendritic and axonal arbors in vivo and have not been apparent in previous studies using labeling in brain slices

Evaluation of the optical conductivity tensor in terms of contour integrations

For the case of finite life-time broadening the standard Kubo-formula for the optical conductivity tensor is rederived in terms of Green's functions by using contour integrations, whereby finite temperatures are accounted for by using the Fermi-Dirac distribution function. For zero life-time broadening, the present formalism is related to expressions well-known in the literature. Numerical aspects of how to calculate the corresponding contour integrals are also outlined.Comment: 8 pages, Latex + 2 figure (Encapsulated Postscript

The architecture of complex weighted networks

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity. Along with a complex topological structure, real networks display a large heterogeneity in the capacity and intensity of the connections. These features, however, have mainly not been considered in past studies where links are usually represented as binary states, i.e. either present or absent. Here, we study the scientific collaboration network and the world-wide air-transportation network, which are representative examples of social and large infrastructure systems, respectively. In both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network. We define new appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices. This information allows us to investigate for the first time the correlations among weighted quantities and the underlying topological structure of the network. These results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

Computational complexity arising from degree correlations in networks

We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the NP-hard optimization problem of finding minimal vertex covers on these graphs, we show that such correlations may lead to a qualitatively different solution structure as compared to uncorrelated networks. This results in a higher complexity of the network in a computational sense: Simple heuristic algorithms fail to find a minimal vertex cover in the highly correlated case, whereas uncorrelated networks seem to be simple from the point of view of combinatorial optimization.Comment: 4 pages, 1 figure, accepted in Phys. Rev.

Ising Model on Networks with an Arbitrary Distribution of Connections

We find the exact critical temperature $T_c$ of the nearest-neighbor ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary degree distribution $P(k)$. We observe an anomalous behavior of the magnetization, magnetic susceptibility and specific heat, when $P(k)$ is fat-tailed, or, loosely speaking, when the fourth moment of the distribution diverges in infinite networks. When the second moment becomes divergent, $T_c$ approaches infinity, the phase transition is of infinite order, and size effect is anomalously strong.Comment: 5 page

Matching conditions and Higgs mass upper bounds revisited

Matching conditions relate couplings to particle masses. We discuss the importance of one-loop matching conditions in Higgs and top-quark sector as well as the choice of the matching scale. We argue for matching scales $\mu_{0,t} \simeq m_t$ and $\mu_{0,H} \simeq max[ m_t, M_H ]$. Using these results, the two-loop Higgs mass upper bounds are reanalyzed. Previous results for $\Lambda\approx$ few TeV are found to be too stringent. For $\Lambda=10^{19}$ GeV we find $M_H < 180 \pm 4\pm 5$ GeV, the first error indicating the theoretical uncertainty, the second error reflecting the experimental uncertainty due to $m_t=175\pm6$ GeV.Comment: 20 pages, 6 figures; uses epsf and rotate macro

Are randomly grown graphs really random?

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time steps. In the limit of large t, the resulting graph displays surprisingly rich characteristics. In particular, a giant component emerges in an infinite-order phase transition at delta = 1/8. At the transition, the average component size jumps discontinuously but remains finite. In contrast, a static random graph with the same degree distribution exhibits a second-order phase transition at delta = 1/4, and the average component size diverges there. These dramatic differences between grown and static random graphs stem from a positive correlation between the degrees of connected vertices in the grown graph--older vertices tend to have higher degree, and to link with other high-degree vertices, merely by virtue of their age. We conclude that grown graphs, however randomly they are constructed, are fundamentally different from their static random graph counterparts.Comment: 8 pages, 5 figure