Spectra of complex networks

We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the case of networks with correlations between neighboring vertices. The tail of the density of eigenvalues $\rho(\lambda)$ at large $|\lambda|$ is related to the behavior of the vertex degree distribution $P(k)$ at large $k$. In particular, as $P(k) \sim k^{-\gamma}$, $\rho(\lambda) \sim |\lambda|^{1-2\gamma}$. We propose a simple approximation, which enables us to calculate spectra of various graphs analytically. We analyse spectra of various complex networks and discuss the role of vertices of low degree. We show that spectra of locally tree-like random graphs may serve as a starting point in the analysis of spectral properties of real-world networks, e.g., of the Internet.Comment: 10 pages, 4 figure

A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade

We provide a framework for analyzing the problem of interacting electrons in a ballistic quantum dot with chaotic boundary conditions within an energy $E_T$ (the Thouless energy) of the Fermi energy. Within this window we show that the interactions can be characterized by Landau Fermi liquid parameters. When $g$, the dimensionless conductance of the dot, is large, we find that the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as $g\to\infty$ (as in a large-N theory). The infinite $g$ theory shows a transition to a strong-coupling phase characterized by the same order parameter as in the Pomeranchuk transition in clean systems (a spontaneous interaction-induced Fermi surface distortion), but smeared and pinned by disorder. At finite $g$, the two phases and critical point evolve into three regimes in the $u_m-1/g$ plane -- weak- and strong-coupling regimes separated by crossover lines from a quantum-critical regime controlled by the quantum critical point. In the strong-coupling and quantum-critical regions, the quasiparticle acquires a width of the same order as the level spacing $\Delta$ within a few $\Delta$'s of the Fermi energy due to coupling to collective excitations. In the strong coupling regime if $m$ is odd, the dot will (if isolated) cross over from the orthogonal to unitary ensemble for an exponentially small external flux, or will (if strongly coupled to leads) break time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we are treating charge-channel instabilities in spinful systems, leaving spin-channel instabilities for future work. No substantive results are change

The state of the Martian climate

60°N was +2.0°C, relative to the 1981–2010 average value (Fig. 5.1). This marks a new high for the record. The average annual surface air temperature (SAT) anomaly for 2016 for land stations north of starting in 1900, and is a significant increase over the previous highest value of +1.2°C, which was observed in 2007, 2011, and 2015. Average global annual temperatures also showed record values in 2015 and 2016. Currently, the Arctic is warming at more than twice the rate of lower latitudes

The Theory of Brown Dwarfs and Extrasolar Giant Planets

Straddling the traditional realms of the planets and the stars, objects below the edge of the main sequence have such unique properties, and are being discovered in such quantities, that one can rightly claim that a new field at the interface of planetary science and and astronomy is being born. In this review, we explore the essential elements of the theory of brown dwarfs and giant planets, as well as of the new spectroscopic classes L and T. To this end, we describe their evolution, spectra, atmospheric compositions, chemistry, physics, and nuclear phases and explain the basic systematics of substellar-mass objects across three orders of magnitude in both mass and age and a factor of 30 in effective temperature. Moreover, we discuss the distinctive features of those extrasolar giant planets that are irradiated by a central primary, in particular their reflection spectra, albedos, and transits. Aspects of the latest theory of Jupiter and Saturn are also presented. Throughout, we highlight the effects of condensates, clouds, molecular abundances, and molecular/atomic opacities in brown dwarf and giant planet atmospheres and summarize the resulting spectral diagnostics. Where possible, the theory is put in its current observational context.Comment: 67 pages (including 36 figures), RMP RevTeX LaTeX, accepted for publication in the Reviews of Modern Physics. 30 figures are color. Most of the figures are in GIF format to reduce the overall size. The full version with figures can also be found at: http://jupiter.as.arizona.edu/~burrows/papers/rm

Genome-wide association study in frontal fibrosing alopecia identifies four susceptibility loci including HLA-B*07:02

Frontal fibrosing alopecia (FFA) is a recently described inflammatory and scarring type of hair loss affecting almost exclusively women. Despite a dramatic recent increase in incidence the aetiopathogenesis of FFA remains unknown. We undertake genome-wide association studies in females from a UK cohort, comprising 844 cases and 3,760 controls, a Spanish cohort of 172 cases and 385 controls, and perform statistical meta-analysis. We observe genome-wide significant association with FFA at four genomic loci: 2p22.2, 6p21.1, 8q24.22 and 15q2.1. Within the 6p21.1 locus, fine-mapping indicates that the association is driven by the HLA-B*07:02 allele. At 2p22.1, we implicate a putative causal missense variant in CYP1B1, encoding the homonymous xenobiotic- and hormone-processing enzyme. Transcriptomic analysis of affected scalp tissue highlights overrepresentation of transcripts encoding components of innate and adaptive immune response pathways. These findings provide insight into disease pathogenesis and characterise FFA as a genetically predisposed immuno-inflammatory disorder driven by HLA-B*07:02

Knockout mouse model for Fxr2: a model for mental retardation

Fragile X syndrome is a common form of mental retardation caused by the absence of the FMR1 protein, FMRP. Fmr1 knockout mice exhibit a phenotype with some similarities to humans, such as macro-orchidism and behavioral abnormalities. Two homologs of FMRP have been identified, FXR1P and FXR2P. These proteins show high sequence similarity, including all functional domains identified in FMRP, such as RNA binding domains. They have an overlap in tissue distribution to that of FMRP. Interactions between the three FXR proteins have also been described. FXR2P shows high expression in brain and testis, like FMRP. To study the function of FXR2P, we generated an Fxr2 knockout mouse model. No pathological differences between knockout and wild-type mice were found in brain or testis. Given the behavioral phenotype in fragile X patients and the phenotype previously reported for the Fmr1 knockout mouse, we performed a thorough evaluation of the Fxr2 knockout phenotype using a behavioral test battery. Fxr2 knockout mice were hyperactive (i.e. traveled a greater distance, spent more time moving and moved faster) in the open-field test, impaired on the rotarod test, had reduced levels of prepulse inhibition, displayed less contextual conditioned fear, impaired at locating the hidden platform in the Morris water task and were less sensitive to a heat stimulus. Interestingly, there are some behavioral phenotypes in Fxr2 knockout mice which are similar to those observed in Fmr1 knockout mice, but there are also some different behavioral abnormalities that are only observed in the Fxr2 mutant mice. The findings implicate a role for Fxr2 in central nervous system function