Using Gray Sirens to Resolve the Hubble-Lema\^{i}tre Tension

The measurement of the Hubble-Lema\^{i}tre constant $(H_0)$ from the cosmic microwave background and the Type IA supernovae are at odds with each other. One way to resolve this tension is to use an independent way to measure $H_0$. This can be accomplished by using gravitational-wave (GW) observations. Previous works have shown that with the onset of the next-generation of GW detector networks, it will be possible to constrain $H_0$ better than $2\%$ (which is enough to resolve the tension) with binary black hole systems, also called dark sirens. Bright sirens like binary neutron star systems can also help resolve the tension if both the GW and the following electromagnetic counterpart are detected. In this work, we assess the potential of using neutron star-black hole (NSBH) mergers to measure the Hubble-Lema\^{i}tre constant, both as dark sirens as well as bright sirens, thus, assigning them the term gray sirens. We find that the Voyager network might be able to resolve the tension using NSBH mergers in an observation span of 5 years, whereas next-generation networks which include the Cosmic Explorer detectors and the Einstein Telescope will be able to measure the $H_0$ to sub-percent level.Comment: 22 pages, 10 figures, 9 table

An Interesting Case of Sebaceous Gland Carcinoma of Upper Eyelid with Tubercular Lymphadenitis

Sebaceous gland carcinoma (SGC) is a rare, potentially aggressive tumor and the third most common malignancy of the eyelid.We present a case of SGC (confirmed by histopathology) of right upper eyelid in a 48-year-old female, which was managed by excision of mass with 5 mm clear margin with lid reconstruction using Cutler Beard technique and three cycles of cryotherapy. A positive uptake on PET scan of left cervical lymph node followed by FNAC of the same showed tubercular lymphadenitis rather than metastasis. Coming across this case raises a possibility of association of SGC with TB but having said that further research is needed for the same

Masking of obstructive sleep apnoea by drug induced central sleep apnoea

Benzodiazepines are widely prescribed hypnotic agents which have multiple proven neurological and respiratory side effects. However, literature is sparse with regards to the incidence and occurrence of new onset central sleep apnoea in individuals being treated with benzodiazepines for insomnia. We present a case report of a patient presenting with new onset central sleep apnoea secondary to long term usage of benzodiazepines, with resultant masking of his pre-existing obstructive sleep apnoea