An explicit height bound for the classical modular polynomial

For a prime m, let Phi_m be the classical modular polynomial, and let h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values is provided for m <= 3607.Comment: Minor correction to the constants in Theorem 1 and Corollary 9. To appear in the Ramanujan Journal. 17 pages

From nodal liquid to nodal Mottness in a frustrated Hubbard model

We investigate the physics of frustrated 3-leg Hubbard ladders in the band limit, when hopping across the ladder's rungs (t$_{\perp}$) is of the same order as hopping along them (t) much greater than the onsite Coulomb repulsion (U). We show that this model exhibits a striking electron-hole asymmetry close to half-filling: the hole-doped system at low temperatures develops a Resonating Valence Bond (RVB)-like d-wave gap (pseudogap close to ($\pi$,0)) coinciding with gapless nodal excitations (nodal liquid); in contrast, the electron-doped system is seen to develop a Mott gap at the nodes, whilst retaining a metallic character of its majority Fermi surface. At lower temperatures in the electron-doped case, d-wave superconducting correlations -- here, coexisting with gapped nodal excitations -- are already seen to arise. Upon further doping the hole-doped case, the RVB-like state yields to d-wave superconductivity. Such physics is reminiscent of that exhibited by the high temperature cuprate superconductors--notably electron-hole asymmetry as noted by Angle Resolved PhotoEmission Spectroscopy (ARPES) and the resistivity exponents observed. This toy model also reinforces the importance of a more thorough experimental investigation of the known 3-leg ladder cuprate systems, and may have some bearing on low dimensional organic superconductors.Comment: 26 pages, 16 figure

Series study of the One-dimensional S-T Spin-Orbital Model

We use perturbative series expansions about a staggered dimerized ground state to compute the ground state energy, triplet excitation spectra and spectral weight for a one-dimensional model in which each site has an S=\case 1/2 spin ${\bf S}_i$ and a pseudospin ${\bf T}_i$, representing a doubly degenerate orbital. An explicit dimerization is introduced to allow study of the confinement of spinon excitations. The elementary triplet represents a bound state of two spinons, and is stable over much of the Brillouine zone. A special line is found in the gapped spin-liquid phase, on which the triplet excitation is dispersionless. The formation of triplet bound states is also investigated.Comment: 9 pages, 9 figure

Determinant representation for some transition probabilities in the TASEP with second class particles

We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an explicit expression of these quantities in terms of the Bethe wave function. In a next step it is proved rigorously that this expression can be written in a compact determinantal form for the case where the order of the first and second class particles does not change in time. An independent geometrical approach provides insight into these results and enables us to generalize the determinantal solution to the multi-class TASEP.Comment: Minor revision; journal reference adde

Mutations in MAP3K7 that Alter the Activity of the TAK1 Signaling Complex Cause Frontometaphyseal Dysplasia.

Frontometaphyseal dysplasia (FMD) is a progressive sclerosing skeletal dysplasia affecting the long bones and skull. The cause of FMD in some individuals is gain-of-function mutations in FLNA, although how these mutations result in a hyperostotic phenotype remains unknown. Approximately one half of individuals with FMD have no identified mutation in FLNA and are phenotypically very similar to individuals with FLNA mutations, except for an increased tendency to form keloid scars. Using whole-exome sequencing and targeted Sanger sequencing in 19 FMD-affected individuals with no identifiable FLNA mutation, we identified mutations in two genes-MAP3K7, encoding transforming growth factor β (TGF-β)-activated kinase (TAK1), and TAB2, encoding TAK1-associated binding protein 2 (TAB2). Four mutations were found in MAP3K7, including one highly recurrent (n = 15) de novo mutation (c.1454C&gt;T [ p.Pro485Leu]) proximal to the coiled-coil domain of TAK1 and three missense mutations affecting the kinase domain (c.208G&gt;C [p.Glu70Gln], c.299T&gt;A [p.Val100Glu], and c.502G&gt;C [p.Gly168Arg]). Notably, the subjects with the latter three mutations had a milder FMD phenotype. An additional de novo mutation was found in TAB2 (c.1705G&gt;A, p.Glu569Lys). The recurrent mutation does not destabilize TAK1, or impair its ability to homodimerize or bind TAB2, but it does increase TAK1 autophosphorylation and alter the activity of more than one signaling pathway regulated by the TAK1 kinase complex. These findings show that dysregulation of the TAK1 complex produces a close phenocopy of FMD caused by FLNA mutations. Furthermore, they suggest that the pathogenesis of some of the filaminopathies caused by FLNA mutations might be mediated by misregulation of signaling coordinated through the TAK1 signaling complex

FUV and X-ray absorption in the Warm-Hot Intergalactic Medium

The Warm-Hot Intergalactic Medium (WHIM) arises from shock-heated gas collapsing in large-scale filaments and probably harbours a substantial fraction of the baryons in the local Universe. Absorption-line measurements in the ultraviolet (UV) and in the X-ray band currently represent the best method to study the WHIM at low redshifts. We here describe the physical properties of the WHIM and the concepts behind WHIM absorption line measurements of H I and high ions such as O VI, O VII, and O VIII in the far-ultraviolet and X-ray band. We review results of recent WHIM absorption line studies carried out with UV and X-ray satellites such as FUSE, HST, Chandra, and XMM-Newton and discuss their implications for our knowledge of the WHIM.Comment: 26 pages, 9 figures, accepted for publication in Space Science Reviews, special issue "Clusters of galaxies: beyond the thermal view", Editor J.S. Kaastra, Chapter 3; work done by an international team at the International Space Science Institute (ISSI), Bern, organised by J.S. Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke

Baryons: What, When and Where?

We review the current state of empirical knowledge of the total budget of baryonic matter in the Universe as observed since the epoch of reionization. Our summary examines on three milestone redshifts since the reionization of H in the IGM, z = 3, 1, and 0, with emphasis on the endpoints. We review the observational techniques used to discover and characterize the phases of baryons. In the spirit of the meeting, the level is aimed at a diverse and non-expert audience and additional attention is given to describe how space missions expected to launch within the next decade will impact this scientific field.Comment: Proceedings Review for "Astrophysics in the Next Decade: JWST and Concurrent Facilities", ed. X. Tielens, 38 pages, 10 color figures. Revised to address comments from the communit