Coloring Mixed and Directional Interval Graphs

A mixed graph has a set of vertices, a set of undirected egdes, and a set ofdirected arcs. A proper coloring of a mixed graph $G$ is a function $c$ thatassigns to each vertex in $G$ a positive integer such that, for each edge $uv$in $G$, $c(u) \ne c(v)$ and, for each arc $uv$ in $G$, $c(u) mixed graph$G$, the chromatic number$\chi(G)$is the smallest number ofcolors in any proper coloring of$G$. A directional interval graph is a mixedgraph whose vertices correspond to intervals on the real line. Such a graph hasan edge between every two intervals where one is contained in the other and anarc between every two overlapping intervals, directed towards the interval thatstarts and ends to the right. Coloring such graphs has applications in routing edges in layered orthogonalgraph drawing according to the Sugiyama framework; the colors correspond to thetracks for routing the edges. We show how to recognize directional intervalgraphs, and how to compute their chromatic number efficiently. On the otherhand, for mixed interval graphs, i.e., graphs where two intersecting intervalscan be connected by an edge or by an arc in either direction arbitrarily, weprove that computing the chromatic number is NP-hard.<br

A molecular nanocap activated by superparamagnetic heating for externally stimulated cargo release

A novel thermoresponsive snaptop for stimulated cargo release from superparamagnetic iron oxide core - mesoporous silica shell nanoparticles based on a [2 + 4] cycloreversion reaction (retro-Diels Alder reaction) is presented. The non-invasive external actuation through alternating magnetic fields makes this material a promising candidate for future applications in externally triggered drug delivery

Unwinding of a cholesteric liquid crystal and bidirectional surface anchoring

We examine the influence of bidirectional anchoring on the unwinding of a planar cholesteric liquid crystal induced by the application of a magnetic field. We consider a liquid crystal layer confined between two plates with the helical axis perpendicular to the substrates. We fixed the director twist on one boundary and allow for bidirectional anchoring on the other by introducing a high-order surface potential. By minimizing the total free energy for the system, we investigate the untwisting of the cholesteric helix as the liquid crystal attempts to align with the magnetic field. The transitions between metastable states occur as a series of pitchjumps as the helix expels quarter or half-turn twists, depending on the relative sizes of the strength of the surface potential and the bidirectional anchoring. We show that secondary easy axis directions can play a significant role in the unwinding of the cholesteric in its transition towards a nematic, especially when the surface anchoring strength is large

Multi-patch methods in general relativistic astrophysics - I. Hydrodynamical flows on fixed backgrounds

Many systems of interest in general relativistic astrophysics, including neutron stars, accreting compact objects in X-ray binaries and active galactic nuclei, core collapse, and collapsars, are assumed to be approximately spherically symmetric or axisymmetric. In Newtonian or fixed-background relativistic approximations it is common practice to use spherical polar coordinates for computational grids; however, these coordinates have singularities and are difficult to use in fully relativistic models. We present, in this series of papers, a numerical technique which is able to use effectively spherical grids by employing multiple patches. We provide detailed instructions on how to implement such a scheme, and present a number of code tests for the fixed background case, including an accretion torus around a black hole.Comment: 26 pages, 20 figures. A high-resolution version is available at http://www.cct.lsu.edu/~bzink/papers/multipatch_1.pd

Enzyme-Responsive Snap-Top Covered Silica Nanocontainers

Mesoporous silica nanoparticles, capable of storing a payload of small molecules and releasing it following specific catalytic activation by an esterase, have been designed and fabricated. The storage and release of the payload is controlled by the presence of [2]rotaxanes, which consist of tri(ethylene glycol) chains threaded by α-cyclodextrin tori, located on the surfaces of the nanoparticles and terminated by a large stoppering group. These modified silica nanoparticles are capable of encapsulating guest molecules when the [2]rotaxanes are present. The bulky stoppers, which serve to hold the tori in place, are stable under physiological conditions but are cleaved by the catalytic action of an enzyme, causing dethreading of the tori and release of the guest molecules from the pores of the nanoparticles. These snap-top covered silica nanocontainers (SCSNs) are prepared by a modular synthetic method, in which the stoppering unit, incorporated in the final step of the synthesis, may be changed at will to target the response of the system to any of a number of hydrolytic enzymes. Here, the design, synthesis, and operation of model SCSNs that open in the presence of porcine liver esterase (PLE) are reported. The empty pores of the silica nanoparticles were loaded with luminescent dye molecules (rhodamine B), and stoppering units that incorporate adamantyl ester moieties were then attached in the presence of α-cyclodextrin using the copper-catalyzed azide−alkyne cycloaddition (CuAAC), closing the SCSNs. The release of rhodamine-B from the pores of the SCSN, following PLE-mediated hydrolysis of the stoppers, was monitored using fluorescence spectroscopy

The Structure of IR Luminous Galaxies at 100 Microns

We have observed twenty two galaxies at 100 microns with the Kuiper Airborne Observatory in order to determine the size of their FIR emitting regions. Most of these galaxies are luminous far-infrared sources, with L_FIR > 10^11 L_sun. This data constitutes the highest spatial resolution ever achieved on luminous galaxies in the far infrared. Our data includes direct measurements of the spatial structure of the sources, in which we look for departures from point source profiles. Additionally, comparison of our small beam 100 micron fluxes with the large beam IRAS fluxes shows how much flux falls beyond our detectors but within the IRAS beam. Several sources with point- like cores show evidence for such a net flux deficit. We clearly resolved six of these galaxies at 100 microns and have some evidence for extension in seven others. Those galaxies which we have resolved can have little of their 100 micron flux directly emitted by a point-like active galactic nucleus (AGN). Dust heated to ~40 K by recent bursts of non-nuclear star formation provides the best explanation for their extreme FIR luminosity. In a few cases, heating of an extended region by a compact central source is also a plausible option. Assuming the FIR emission we see is from dust, we also use the sizes we derive to find the dust temperatures and optical depths at 100 microns which we translate into an effective visual extinction through the galaxy. Our work shows that studies of the far infrared structure of luminous infrared galaxies is clearly within the capabilities of new generation far infrared instrumentation, such as SOFIA and SIRTF.Comment: 8 tables, 23 figure

Prosodic modulation in the babble of cochlear implanted and normally hearing infants: a perceptual study using a visual analogue scale

This study investigates prosodic modulation in the spontaneous canonical babble of congenitally deaf infants with cochlear implants (CI) and normally hearing (NH) infants. Research has shown that the acoustic cues to prominence are less modulated in CI babble. However acoustic measurements of individual cues to prominence give incomplete information about prosodic modulation. In the present study, raters are asked to judge prominence since they simultaneously take into account all prosodic cues. Disyllabic utterances produced by CI and NH infants were presented to naive adult raters who had to indicate the degree and direction of prosodic modulation between syllables on a visual analogue scale. The results show that the babble of infants with CI is rated as having less prosodic modulation. Moreover, segmentally more variegated babble is rated as having more prosodic modulation. Raters do not perceive the babble to be predominantly trochaic, which indicates that the predominant stress pattern of Dutch is not yet apparent in the children’s productions

AMR, stability and higher accuracy

Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes. Here, we argue for the combination, that is a higher order accurate adaptive scheme. This combines the power that adaptive gridding techniques provide to resolve fine scales (in addition to a more efficient use of resources) together with the higher accuracy furnished by higher order schemes when the solution is adequately resolved. To define a convenient higher order adaptive mesh refinement scheme, we discuss a few different modifications of the standard, second order accurate approach of Berger and Oliger. Applying each of these methods to a simple model problem, we find these options have unstable modes. However, a novel approach to dealing with the grid boundaries introduced by the adaptivity appears stable and quite promising for the use of high order operators within an adaptive framework

Enhancement of the electronic contribution to the low temperature specific heat of Fe/Cr magnetic multilayer

We measured the low temperature specific heat of a sputtered $(Fe_{23\AA}/Cr_{12\AA})_{33}$ magnetic multilayer, as well as separate $1000\AA$ thick Fe and Cr films. Magnetoresistance and magnetization measurements on the multilayer demonstrated antiparallel coupling between the Fe layers. Using microcalorimeters made in our group, we measured the specific heat for $4<T<30 K$ and in magnetic fields up to $8 T$ for the multilayer. The low temperature electronic specific heat coefficient of the multilayer in the temperature range $4<T<14 K$ is $\gamma_{ML}=8.4 mJ/K^{2}g-at$. This is significantly larger than that measured for the Fe or Cr films (5.4 and $3.5 mJ/K^{2}mol$ respectively). No magnetic field dependence of $\gamma_{ML}$ was observed up to $8 T$. These results can be explained by a softening of the phonon modes observed in the same data and the presence of an Fe-Cr alloy phase at the interfaces.Comment: 20 pages, 5 figure