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

The Missouri farm real estate situation for 1930-1931

Publication authorized July 12, 1932."The text of this bulletin represents a revision of a manuscript with the same title submitted originally by Mr. Callaway to the Graduate School of the University of Missouri in partial fulfillment of the requirements for the Degree of Master of Arts"--P. [5].Digitized 2007 AES.Includes bibliographical references

Comment on "Breakdown of the Internet under Intentional Attack"

We obtain the exact position of the percolation threshold in intentionally damaged scale-free networks.Comment: 1 page, to appear in Phys. Rev. Let

Local softness, softness dipole and polarizabilities of functional groups: application to the side chains of the twenty amino acids

The values of molecular polarizabilities and softnesses of the twenty amino acids were computed ab initio (MP2). By using the iterative Hirshfeld scheme to partition the molecular electronic properties, we demonstrate that the values of the softness of the side chain of the twenty amino acid are clustered in groups reflecting their biochemical classification, namely: aliphatic, basic, acidic, sulfur containing, and aromatic amino acids . The present findings are in agreement with previous results using different approximations and partitioning schemes [P. Senet and F. Aparicio, J. Chem. Phys. 126,145105 (2007)]. In addition, we show that the polarizability of the side chain of an amino acid depends mainly on its number of electrons (reflecting its size) and consequently cannot be used to cluster the amino acids in different biochemical groups, in contrast to the local softness. Our results also demonstrate that the global softness is not simply proportional to the global polarizability in disagreement with the intuition that "a softer moiety is also more polarizable". Amino acids with the same softness may have a polarizability differing by a factor as large as 1.7. This discrepancy can be understood from first principles as we show that the molecular polarizability depends on a "softness dipole vector" and not simply on the global softness

Penalized Orthogonal-Components Regression for Large p Small n Data

We propose a penalized orthogonal-components regression (POCRE) for large p small n data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlation to the response residuals. A new penalization framework, implemented via empirical Bayes thresholding, is presented to effectively identify sparse predictors of each component. POCRE is computationally efficient owing to its sequential construction of leading sparse principal components. In addition, such construction offers other properties such as grouping highly correlated predictors and allowing for collinear or nearly collinear predictors. With multivariate responses, POCRE can construct common components and thus build up latent-variable models for large p small n data.Comment: 12 page

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

A priori Wannier functions from modified Hartree-Fock and Kohn-Sham equations

The Hartree-Fock equations are modified to directly yield Wannier functions following a proposal of Shukla et al. [Chem. Phys. Lett. 262, 213-218 (1996)]. This approach circumvents the a posteriori application of the Wannier transformation to Bloch functions. I give a novel and rigorous derivation of the relevant equations by introducing an orthogonalizing potential to ensure the orthogonality among the resulting functions. The properties of these, so-called a priori Wannier functions, are analyzed and the relation of the modified Hartree-Fock equations to the conventional, Bloch-function-based equations is elucidated. It is pointed out that the modified equations offer a different route to maximally localized Wannier functions. Their computational solution is found to involve an effort that is comparable to the effort for the solution of the conventional equations. Above all, I show how a priori Wannier functions can be obtained by a modification of the Kohn-Sham equations of density-functional theory.Comment: 7 pages, RevTeX4, revise

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

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