Box representations of embedded graphs

A $d$-box is the cartesian product of $d$ intervals of $\mathbb{R}$ and a $d$-box representation of a graph $G$ is a representation of $G$ as the intersection graph of a set of $d$-boxes in $\mathbb{R}^d$. It was proved by Thomassen in 1986 that every planar graph has a 3-box representation. In this paper we prove that every graph embedded in a fixed orientable surface, without short non-contractible cycles, has a 5-box representation. This directly implies that there is a function $f$, such that in every graph of genus $g$, a set of at most $f(g)$ vertices can be removed so that the resulting graph has a 5-box representation. We show that such a function $f$ can be made linear in $g$. Finally, we prove that for any proper minor-closed class $\mathcal{F}$, there is a constant $c(\mathcal{F})$ such that every graph of $\mathcal{F}$ without cycles of length less than $c(\mathcal{F})$ has a 3-box representation, which is best possible.Comment: 16 pages, 6 figures - revised versio

A 10-hour period revealed in optical spectra of the highly variable WN8 Wolf-Rayet star WR 123

Aims. What is the origin of the large-amplitude variability in Wolf-Rayet WN8 stars in general and WR123 in particular? A dedicated spectroscopic campaign targets the ten-hour period previously found in the high-precision photometric data obtained by the MOST satellite. Methods. In June-August 2003 we obtained a series of high signal-to-noise, mid-resolution spectra from several sites in the {\lambda}{\lambda} 4000 - 6940 A^{\circ} domain. We also followed the star with occasional broadband (Johnson V) photometry. The acquired spectroscopy allowed a detailed study of spectral variability on timescales from \sim 5 minutes to months. Results. We find that all observed spectral lines of a given chemical element tend to show similar variations and that there is a good correlation between the lines of different elements, without any significant time delays, save the strong absorption components of the Hei lines, which tend to vary differently from the emission parts. We find a single sustained periodicity, P \sim 9.8 h, which is likely related to the relatively stable pulsations found in MOST photometry obtained one year later. In addition, seemingly stochastic, large-amplitude variations are also seen in all spectral lines on timescales of several hours to several days.Comment: 6 pages, 4 figures, 2 tables, data available on-line, accepted in A&A Research Note

Boxicity of graphs on surfaces

The boxicity of a graph $G=(V,E)$ is the least integer $k$ for which there exist $k$ interval graphs $G_i=(V,E_i)$, $1 \le i \le k$, such that $E=E_1 \cap ... \cap E_k$. Scheinerman proved in 1984 that outerplanar graphs have boxicity at most two and Thomassen proved in 1986 that planar graphs have boxicity at most three. In this note we prove that the boxicity of toroidal graphs is at most 7, and that the boxicity of graphs embeddable in a surface $\Sigma$ of genus $g$ is at most $5g+3$. This result yields improved bounds on the dimension of the adjacency poset of graphs on surfaces.Comment: 9 pages, 2 figure

Spherical gravitational collapse: tangential pressure and related equations of state

We derive an equation for the acceleration of a fluid element in the spherical gravitational collapse of a bounded compact object made up of an imperfect fluid. We show that non-singular as well as singular solutions arise in the collapse of a fluid initially at rest and having only a tangential pressure. We obtain an exact solution of Einstein equations, in the form of an infinite series, for collapse under tangential pressure with a linear equation of state. We show that if a singularity forms in the tangential pressure model, the conditions for the singularity to be naked are exactly the same as in the model of dust collapse.Comment: Latex, 26 page

Unification of couplings and soft supersymmetry breaking terms in 4D superstring models

We consider the predictions for the hierarchy of mass scales, the fine structure constant, the radii of compactification and the soft SUSY breaking terms which follow if SUSY breaking is triggered by a gaugino condensate.Comment: 16 pages (LaTeX) Oxford preprint OUTP-93-32

Mutations in Arabidopsis \u3ci\u3eYellow Stripe-Like1\u3c/i\u3e and \u3ci\u3eYellow Stripe-Like3\u3c/i\u3e Reveal Their Roles in Metal Ion Homeostasis and Loading of Metal Ions in Seeds

Here, we describe two members of the Arabidopsis (Arabidopsis thaliana) Yellow Stripe-Like (YSL) family, AtYSL1 and AtYSL3. The YSL1 and YSL3 proteins are members of the oligopeptide transporter family and are predicted to be integral membrane proteins. YSL1 and YSL3 are similar to the maize (Zea mays) YS1 phytosiderophore transporter (ZmYS1) and the AtYSL2 iron (Fe)-nicotianamine transporter, and are predicted to transport metal-nicotianamine complexes into cells. YSL1 and YSL3 mRNAs are expressed in both root and shoot tissues, and both are regulated in response to the Fe status of the plant. β-Glucuronidase reporter expression, driven by YSL1 and YSL3 promoters, reveals expression patterns of the genes in roots, leaves, and flowers. Expression was highest in senescing rosette leaves and cauline leaves. Whereas the single mutants ysl1 and ysl3 had no visible phenotypes, the ysl1ysl3 double mutant exhibited Fe deficiency symptoms, such as interveinal chlorosis. Leaf Fe concentrations are decreased in the double mutant, whereas manganese, zinc, and especially copper concentrations are elevated. In seeds of double-mutant plants, the concentrations of Fe, zinc, and copper are low. Mobilization of metals from leaves during senescence is impaired in the double mutant. In addition, the double mutant has reduced fertility due to defective anther and embryo development. The proposed physiological roles for YSL1 and YSL3 are in delivery of metal micronutrients to and from vascular tissues

Modulated Amplitude Waves in Bose-Einstein Condensates

We analyze spatio-temporal structures in the Gross-Pitaevskii equation to study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs) with mean-field interactions. A coherent structure ansatz yields a parametrically forced nonlinear oscillator, to which we apply Lindstedt's method and multiple-scale perturbation theory to determine the dependence of the intensity of periodic orbits (``modulated amplitude waves'') on their wave number. We explore BEC band structure in detail using Hamiltonian perturbation theory and supporting numerical simulations.Comment: 5 pages, 4 figs, revtex, final form of paper, to appear in PRE (forgot to include \bibliography command in last update, so this is a correction of that; the bibliography is hence present again

Effects of end-stage osteoarthritis on markers of skeletal muscle Long INterspersed Element-1 activity

Objective: Long INterspersed Element-1 (L1) is an autonomous transposable element in the genome. L1 transcripts that are not reverse transcribed back into the genome can accumulate in the cytoplasm and activate an inflammatory response via the cyclic GMP-AMP (cGAS)-STING pathway. We examined skeletal muscle L1 markers as well as STING protein levels in 10 older individuals (63 ± 11 y, BMI= 30.2 ± 6.8 kg/m2) with end-stage osteoarthritis (OA) undergoing total hip (THA, n= 4) or knee (TKA, n= 6) arthroplasty versus 10 young, healthy comparators (Y, 22 ± 2 y, BMI= 23.2 ± 2.5 kg/m2). For OA, muscle was collected from surgical (SX) and contralateral (CTL) sides whereas single vastus lateralis samples were collected from Y. Results: L1 mRNA was higher in CTL and SX compared to Y (p \u3c 0.001 and p= 0.001, respectively). Protein expression was higher in SX versus Y for ORF1p (p= 0.002) and STING (p= 0.022). While these data are preliminary due to limited n-sizes and the lack of a BMI-matched younger control group, higher L1 mRNA expression, ORF1p and STING protein are evident in older versus younger adults. More research is needed to determine whether cGAS-STING signaling contributes to heightened muscle inflammation during aging and/or OA

A Spectroscopic Survey of WNL Stars in the LMC: General Properties and Binary Status

We report the results of an intense, spectroscopic survey of all 41 late-type, nitrogen-rich Wolf-Rayet (WR) stars in the Large Magellanic Cloud (LMC) observable with ground-based telescopes. This survey concludes the decade-long effort of the Montr\'eal Massive Star Group to monitor every known WR star in the Magellanic Clouds except for the 6 crowded WNL stars in R136, which will be discussed elsewhere. The focus of our survey was to monitor the so-called WNL stars for radial-velocity (RV) variability in order to identify the short- to intermediate-period (P \la 200 days) binaries among them. Our results are in line with results of previous studies of other WR subtypes, and show that the binary frequency among LMC WNL stars is statistically consistent with that of WNL stars in the Milky Way. We have identified four previously unknown binaries, bringing the total number of known WNL binaries in the LMC to nine. Since it is very likely that none but one of the binaries are classical, helium-burning WNL stars, but rather superluminous, hence extremely massive, hydrogen-burning objects, our study has dramatically increased the number of known binaries harbouring such objects, and thus paved the way to determine their masses through model-independent, Keplerian orbits. It is expected that some of the stars in our binaries will be among the most massive known. With the binary status of each WR star now known, we also studied the photometric and X-ray properties of our program stars using archival MACHO photometry as well as Chandra and ROSAT data. We find that one of our presumably single WNL stars is among the X-ray brightest WR sources known. We also identify a binary candidate from its RV variability and X-ray luminosity which harbours the most luminous WR star known in the Local Group.Comment: 25 pages, 11 figures; accepted for MNRA

Unification Scale in String Theory

We study the unification scale and gauge coupling constant in 4D string theory. We show that the fine structure constant is determined by the dimension of the hidden gauge group and only $SU(6)$ and $SO(9)$ are consistent with minimal string unification while the unification scale can be of order of $10^{16}\,GeV$.Comment: 12 pages (LaTeX