On the threshold-width of graphs

The GG-width of a class of graphs GG is defined as follows. A graph G has GG-width k if there are k independent sets N1,...,Nk in G such that G can be embedded into a graph H in GG such that for every edge e in H which is not an edge in G, there exists an i such that both endpoints of e are in Ni. For the class TH of threshold graphs we show that TH-width is NP-complete and we present fixed-parameter algorithms. We also show that for each k, graphs of TH-width at most k are characterized by a finite collection of forbidden induced subgraphs

Coherent spin mixing dynamics in a spin-1 atomic condensate

We study the coherent off-equilibrium spin mixing inside an atomic condensate. Using mean field theory and adopting the single spatial mode approximation (SMA), the condensate spin dynamics is found to be well described by that of a nonrigid pendulum, and displays a variety of periodic oscillations in an external magnetic field. Our results illuminate several recent experimental observations and provide critical insights into the observation of coherent interaction-driven oscillations in a spin-1 condensate.Comment: 6 pages, 5 eps figures, update the discussion of the experimental result

A flowing plasma model to describe drift waves in a cylindrical helicon discharge

A two-fluid model developed originally to describe wave oscillations in the vacuum arc centrifuge, a cylindrical, rapidly rotating, low temperature and confined plasma column, is applied to interpret plasma oscillations in a RF generated linear magnetised plasma (WOMBAT), with similar density and field strength. Compared to typical centrifuge plasmas, WOMBAT plasmas have slower normalised rotation frequency, lower temperature and lower axial velocity. Despite these differences, the two-fluid model provides a consistent description of the WOMBAT plasma configuration and yields qualitative agreement between measured and predicted wave oscillation frequencies with axial field strength. In addition, the radial profile of the density perturbation predicted by this model is consistent with the data. Parameter scans show that the dispersion curve is sensitive to the axial field strength and the electron temperature, and the dependence of oscillation frequency with electron temperature matches the experiment. These results consolidate earlier claims that the density and floating potential oscillations are a resistive drift mode, driven by the density gradient. To our knowledge, this is the first detailed physics model of flowing plasmas in the diffusion region away from the RF source. Possible extensions to the model, including temperature non-uniformity and magnetic field oscillations, are also discussed

Mechanistic target of rapamycin (mTOR) signaling genes in decapod crustaceans: cloning and tissue expression of mTOR, Akt, Rheb, and S6 kinase in the green crab, Carcinus maenas, and blackback land crab, Gecarcinus lateralis

Mechanistic target of rapamycin (mTOR) controls global translation of mRNA into protein by phosphorylating p70 S6 kinase (S6K) and eIF4E-binding protein-1. Akt and Rheb, a GTP-binding protein, regulate mTOR protein kinase activity. Molting in crustaceans is regulated by ecdysteroids synthesized by a pair of molting glands, or Y-organs (YOs), located in the cephalothorax. During premolt, the YOs hypertrophy and increase production of ecdysteroids. Rapamycin (1 μM) inhibited ecdysteroid secretion in Carcinus maenas and Gecarcinus lateralis YOs in vitro, indicating that ecdysteroidogenesis requires mTOR-dependent protein synthesis. The effects of molting on the expression of four key mTOR signaling genes (mTOR, Akt, Rheb, and S6K) in the YO was investigated. Partial cDNAs encoding green crab (C. maenas) mTOR (4031 bp), Akt (855 bp), and S6K (918 bp) were obtained from expressed sequence tags. Identity/similarity of the deduced amino acid sequence of the C. maenas cDNAs to human orthologs were 72%/81% for Cm-mTOR, 58%/73% for Cm-Akt, and 77%/88% for Cm-S6K. mTOR, Akt, S6K, and elongation factor 2 (EF2) in C. maenas and blackback land crab (G. lateralis) were expressed in all tissues examined. The two species differed in the effects of molting on gene expression in the YO. In G. lateralis, Gl-mTOR, Gl-Akt, and Gl-EF2 mRNA levels were increased during premolt. By contrast, molting had no effect on the expression of Cm-mTOR, Cm-Akt, Cm-S6K, Cm-Rheb, and Cm-EF2. These data suggest that YO activation during premolt involves up regulation of mTOR signaling genes in G. lateralis, but is not required in C. maenas

Roles of mechanistic target of rapamycin and transforming growth factor-B signaling in the molting gland (Y-organ) of the blackback land crab, Gecarcinus lateralis

Molting in decapod crustaceans is controlled by molt-inhibiting hormone (MIH), an eyestalk neuropeptide that suppresses production of ecdysteroids by a pair of molting glands (Y-organs or YOs). Eyestalk ablation (ESA) activates the YOs, which hypertrophy and increase ecdysteroid secretion. At mid premolt, which occurs 7–14 days post-ESA, the YO transitions to the committed state; hemolymph ecdysteroid titers increase further and the animal reaches ecdysis ~ 3 weeks post-ESA. Two conserved signaling pathways, mechanistic target of rapamycin (mTOR) and transforming growth factor-β (TGF-β), are expressed in the Gecarcinus lateralis YO. Rapamycin, an mTOR antagonist, inhibits YO ecdysteroidogenesis in vitro. In this study, rapamycin lowered hemolymph ecdysteroid titer in ESA G. lateralis in vivo; levels were significantly lower than in control animals at all intervals (1–14 days post-ESA). Injection of SB431542, an activin TGF-β receptor antagonist, lowered hemolymph ecdysteroid titers 7 and 14 days post-ESA, but had no effect on ecdysteroid titers at 1 and 3 days post-ESA. mRNA levels of mTOR signaling genes Gl-mTOR, Gl-Akt, and Gl-S6k were increased by 3 days post-ESA; the increases in Gl-mTOR and Gl-Akt mRNA levels were blocked by SB431542. Gl-elongation factor 2 and Gl-Rheb mRNA levels were not affected by ESA, but SB431542 lowered mRNA levels at Days 3 and 7 post-ESA. The mRNA level of an activin TGF-β peptide, Gl-myostatin-like factor (Mstn), increased 5.5-fold from 0 to 3 days post-ESA, followed by a 50-fold decrease from 3 to 7 days post-ESA. These data suggest that (1) YO activation involves an up regulation of the mTOR signaling pathway; (2) mTOR is required for YO commitment; and (3) a Mstn-like factor mediates the transition of the YO from the activated to the committed state

Dynamical instability and domain formation in a spin-1 Bose condensate

We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.Comment: RevTex4, 4 pages with 3 color eps figure, to appear in Phys. Rev. Let

A three-dimensional algebraic grid generation scheme for gas turbine combustors with inclined slots

A 3D algebraic grid generation scheme is presented for generating the grid points inside gas turbine combustors with inclined slots. The scheme is based on the 2D transfinite interpolation method. Since the scheme is a 2D approach, it is very efficient and can easily be extended to gas turbine combustors with either dilution hole or slot configurations. To demonstrate the feasibility and the usefulness of the technique, a numerical study of the quick-quench/lean-combustion (QQ/LC) zones of a staged turbine combustor is given. Preliminary results illustrate some of the major features of the flow and temperature fields in the QQ/LC zones. Formation of co- and counter-rotating bulk flow and shape temperature fields can be observed clearly, and the resulting patterns are consistent with experimental observations typical of the confined slanted jet-in-cross flow. Numerical solutions show the method to be an efficient and reliable tool for generating computational grids for analyzing gas turbine combustors with slanted slots