On some Graphs with a Unique Perfect Matching

We show that deciding whether a given graph $G$ of size $m$ has a unique perfect matching as well as finding that matching, if it exists, can be done in time $O(m)$ if $G$ is either a cograph, or a split graph, or an interval graph, or claw-free. Furthermore, we provide a constructive characterization of the claw-free graphs with a unique perfect matching

Searching for the Donor Stars of ULX Pulsars

We report on our search for the optical counterparts of two ultraluminous X-ray pulsars with known orbital periods, M82 X-2 and NGC 5907 X-1, in new and archival HST observations, in an effort to characterize the donor stars in these systems. We detect five near-infrared sources consistent with the position of M82 X-2 that are too bright to be single stars. We also detect seven sources in the WFC3/UVIS F336W image whose photometry matches that of 10-15 M$_\odot$ stars turning off the main sequence. Such stars have densities consistent with the properties of the donor star of M82 X-2 as inferred from X-ray timing analysis, although it is also possible that the donor is a lower mass star below our detection limit or that there is a significant contribution from the accretion disc to the optical emission. We detect three candidate counterparts to NGC 5907 X-1 in the near-infrared. All of these are too bright to be the donor star of the ULX, which based on its orbital period is a red giant. The high background at the location of NGC 5907 X-1 precludes us from detecting this expected donor star. The recently discovered NGC 5907 ULX-2 also falls within the field of view of the near-infrared imaging; we detect four sources in the error circle, with photometry that matches AGB stars. The star suggested to be the counterpart of NGC 5907 ULX-2 by Pintore et al. (2018) falls outside our 2-$\sigma$ error circle.Comment: 10 pages, 3 figures, accepted for publication in Ap

The radio SNR G65.1+0.6 and its associated pulsar J1957+2831

New images of the radio Supernova Remnant (SNR) G65.1+0.6 are presented, based on the 408 MHz and 1420 MHz continuum emission and the HI-line emission data of the Canadian Galactic Plane Survey (CGPS). A large shell-like structure seen in the 2695 MHz Effelsberg map appears to have nonthermal spectral index. HI observations show structures associated with the SNR G65.1+0.6 in the radial velocity range of -20 to -26 km$/$s and suggest a distance of 9.2 kpc for the SNR. The estimated Sedov age for G65.1+0.6 is 4 - 14 x10E4 yr. The pulsar (PSR) J1957+2831 is possibly associated with G65.1+0.6, with consistent distance and kinematic age estimate, but different characteristic age than the SNR. The EGRET source 3EG J1958+2909 and gamma-ray source 2CG 065+00 are also near the eastern edge of the SNR but do not agree in position with the pulsar and are likely not associated with the SNR. The SNR's flux densities at 408 MHz (8.6+-0.8 Jy), 1420 MHz (4.9+-0.5 Jy) and 2695 MHz (3.3+-0.5 Jy) have been corrected for flux densities from compact sources within the SNR. The integrated flux density based spectral index between 1420 MHz and 408 MHz is 0.45+-0.11 and agrees with the T-T plot spectral index of 0.34+-0.20. The nearby SNR DA495 has a T-T plot spectral index of 0.50+-0.01.Comment: 7pages, 5 pictures and tables, will appear in A&

Myogenesis in the mouse embryo: Differential onset of expression of myogenic proteins and the involvement of titin in myofibril assembly.

Antibodies to muscle-specific proteins were used in immunofluorescence to monitor the development of skeletal muscle during mouse embryogenesis. At gestation day (g.d.) 9 a single layer of vimentin filament containing cells in the myotome domain of cervical somites begins to stain positively for myogenic proteins. The muscle-specific proteins are expressed in a specific order between g.d. 9 and 9.5. Desmin is detected first, then titin, then the muscle specific actin and myosin heavy chains, and finally nebulin. At g.d. 9.5 fibrous desmin structures are already present, while for the other myogenic proteins no structure can be detected. Some prefusion myoblasts display at g.d. 11 and 12 tiny and immature myofibrils. These reveal a periodic pattern of myosin, nebulin, and those titin epitopes known to occur at and close to the Z line. In contrast titin epitopes, which are present in mature myofibrils along the A band and at the A-I junction, are still randomly distributed. We propose, that the Z line connected structures and the A bands (myosin filaments) assemble independently, and that the known interaction of the I-Z-I brushes with the A bands occurs at a later developmental stage. After fusion of myoblasts to myotubes at g.d. 13 and 14 all titin epitopes show the myofibrillar banding pattern. The predominantly longitudinal orientation of desmin filaments seen in myoblasts and in early myotubes is transformed at g.d. 17 and 18 to distinct Z line connected striations. Vimentin, still present together with desmin in the myoblasts, is lost from the myotubes. Our results indicate that the putative elastic titin filaments act as integrators during skeletal muscle development. Some developmental aspects of eye and limb muscles are also described

Naturally-phasematched second harmonic generation in a whispering gallery mode resonator

We demonstrate for the first time natural phase matching for optical frequency doubling in a high-Q whispering gallery mode resonator made of Lithium Niobate. A conversion efficiency of 9% is achieved at 30 micro Watt in-coupled continuous wave pump power. The observed saturation pump power of 3.2 mW is almost two orders of magnitude lower than the state-of-the-art. This suggests an application of our frequency doubler as a source of non-classical light requiring only a low-power pump, which easily can be quantum noise limited. Our theoretical analysis of the three-wave mixing in a whispering gallery mode resonator provides the relative conversion efficiencies for frequency doubling in various modes