Xk-Digraphs

AbstractLet G be a directed graph on n vertices (single loops allowed) such that there are λ directed paths of length k from P to Q for any distinct pair of vertices (P, Q). We prove that if n > 2 and k > 2, G is regular. The regular case is also discussed

On the rational spectra of graphs with abelian singer groups

AbstractLet G be a finite abelian group. We investigate those graphs G admitting G as a sharply 1-transitive automorphism group and all of whose eigenvalues are rational. The study is made via the rational algebra P(G) of rational matrices with rational eigenvalues commuting with the regular matrix representation of G. In comparing the spectra obtainable for graphs in P(G) for various G's, we relate subschemes of a related association scheme, subalgebras of P(G), and the lattice of subgroups of G. One conclusion is that if the order of G is fifth-power-free, any graph with rational eigenvalues admitting G has a cospectral mate admitting the abelian group of the same order with prime-order elementary divisors

Characteristics of pebble- and cobble-sized clasts along the Curiosity rover traverse from Bradbury Landing to Rocknest

We have assessed the characteristics of clasts along Curiosity's traverse to shed light on the processes important in the genesis, modification, and transportation of surface materials. Pebble- to cobble-sized clasts at Bradbury Landing, and subsequentl

Spectral stability of noncharacteristic isentropic Navier-Stokes boundary layers

Building on work of Barker, Humpherys, Lafitte, Rudd, and Zumbrun in the shock wave case, we study stability of compressive, or "shock-like", boundary layers of the isentropic compressible Navier-Stokes equations with gamma-law pressure by a combination of asymptotic ODE estimates and numerical Evans function computations. Our results indicate stability for gamma in the interval [1, 3] for all compressive boundary-layers, independent of amplitude, save for inflow layers in the characteristic limit (not treated). Expansive inflow boundary-layers have been shown to be stable for all amplitudes by Matsumura and Nishihara using energy estimates. Besides the parameter of amplitude appearing in the shock case, the boundary-layer case features an additional parameter measuring displacement of the background profile, which greatly complicates the resulting case structure. Moreover, inflow boundary layers turn out to have quite delicate stability in both large-displacement and large-amplitude limits, necessitating the additional use of a mod-two stability index studied earlier by Serre and Zumbrun in order to decide stability

Reconstruction of the Dark Energy equation of state

One of the main challenges of modern cosmology is to investigate the nature of dark energy in our Universe. The properties of such a component are normally summarised as a perfect fluid with a (potentially) time-dependent equation-of-state parameter $w(z)$. We investigate the evolution of this parameter with redshift by performing a Bayesian analysis of current cosmological observations. We model the temporal evolution as piecewise linear in redshift between `nodes', whose $w$-values and redshifts are allowed to vary. The optimal number of nodes is chosen by the Bayesian evidence. In this way, we can both determine the complexity supported by current data and locate any features present in $w(z)$. We compare this node-based reconstruction with some previously well-studied parameterisations: the Chevallier-Polarski-Linder (CPL), the Jassal-Bagla-Padmanabhan (JBP) and the Felice-Nesseris-Tsujikawa (FNT). By comparing the Bayesian evidence for all of these models we find an indication towards possible time-dependence in the dark energy equation-of-state. It is also worth noting that the CPL and JBP models are strongly disfavoured, whilst the FNT is just significantly disfavoured, when compared to a simple cosmological constant $w=-1$. We find that our node-based reconstruction model is slightly disfavoured with respect to the $\Lambda$CDM model.Comment: 17 pages, 5 figures, minor correction

Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic

Neutron scattering search for static magnetism in oxygen ordered YBa2Cu3O6.5

We present elastic and inelastic neutron scattering results on highly oxygen ordered YBa2Cu3O6.5 ortho-II. We find no evidence for the presence of ordered magnetic moments to a sensitivity of 0.003 Bohr magnetons, an order of magnitude smaller than has been suggested in theories of orbital or d-density-wave (DDW) currents. The absence of sharp elastic peaks, shows that the d-density-wave phase is not present, at least for the superconductor with the doping of 6.5 and the ordered ortho-II structure. We cannot exclude the possibility that a broad peak may exist with extremely short-range DDW correlations. For less ordered or more doped crystals it is possible that disorder may lead to static magnetism. We have also searched for the large normal state spin gap that is predicted to exist in an ordered DDW phase. Instead of a gap we find that the Q-correlated spin susceptibility persists to the lowest energies studied, 6 meV. Our results are compatible with the coexistence of superconductivity with orbital currents, but only if they are dynamic, and exclude a sharp phase transition to an ordered d-density-wave phase.Comment: 6 pages 4 figures RevTex Submitted to Phys Rev B January 23, 200

Observational constraints on conformal time symmetry, missing matter and double dark energy

The current concordance model of cosmology is dominated by two mysterious ingredients: dark matter and dark energy. In this paper, we explore the possibility that, in fact, there exist two dark-energy components: the cosmological constant $\Lambda$, with equation-of-state parameter $w_\Lambda=-1$, and a `missing matter' component $X$ with $w_X=-2/3$, which we introduce here to allow the evolution of the universal scale factor as a function of conformal time to exhibit a symmetry that relates the big bang to the future conformal singularity, such as in Penrose's conformal cyclic cosmology. Using recent cosmological observations, we constrain the present-day energy density of missing matter to be $\Omega_{X,0}=-0.034 \pm 0.075$. This is consistent with the standard $\Lambda$CDM model, but constraints on the energy densities of all the components are considerably broadened by the introduction of missing matter; significant relative probability exists even for $\Omega_{X,0} \sim 0.1$, and so the presence of a missing matter component cannot be ruled out. As a result, a Bayesian model selection analysis only slightly disfavours its introduction by 1.1 log-units of evidence. Foregoing our symmetry requirement on the conformal time evolution of the universe, we extend our analysis by allowing $w_X$ to be a free parameter. For this more generic `double dark energy' model, we find $w_X = -1.01 \pm 0.16$ and $\Omega_{X,0} = -0.10 \pm 0.56$, which is again consistent with the standard $\Lambda$CDM model, although once more the posterior distributions are sufficiently broad that the existence of a second dark-energy component cannot be ruled out. The model including the second dark energy component also has an equivalent Bayesian evidence to $\Lambda$CDM, within the estimation error, and is indistinguishable according to the Jeffreys guideline.Comment: Revised version emphasising a different version of the underlying symmetry, as published in JCA

The choroid plexus as a sex hormone target: Functional implications

The choroid plexuses (CPs) are highly vascularized branched structures that protrude into the ventricles of the brain, and form a unique interface between the blood and the cerebrospinal fluid (CSF). In recent years, novel functions have been attributed to this tissue such as in immune and chemical surveillance of the central nervous system, brain development, adult neurogenesis and circadian rhythm regulation. Sex hormones (SH) are widely recognized as modulators in several neurodegenerative diseases, and there is evidence that estrogens and androgens regulate several fundamental biological functions in the CPs. Therefore, SH are likely to affect the composition of the CSF impacting on brain homeostasis. This review will look at implications of the CPs' sex-related specificities.Portuguese Foundation for Science and Technology (FCT, Portugal – http://www.fct.pt) project grants (PTDC/SAU-NEU/114800/2009); and by FEDER funds through the POCI – COMPETE 2020 – Operational Programme Competitiveness and Internationalisation in Axis I – Strengthening research, technological development and innovation (Project No. 007491) and National Funds by FCT – Foundation for Science and Technology (Project UID/Multi/00709). Joana Tomás was supported by a grant from CENTRO-07-ST24-FEDER-002015. Telma Quintela is a recipient of a FCT fellowship (SFRH/BPD/70781/2010). The work at ICVS/3B’s has the support of Portuguese North Regional Operational Program (ON.2 – O Novo Norte) under the National Strategic Reference Framework (QREN), through the European Regional Development Fund (FEDER). Fernanda Marques is a recipient of a FCT Investigator award (IF/00231/2013) of the Fundação para a Ciência e Tecnologia (FCT, Portugal)info:eu-repo/semantics/publishedVersio