Mapping of shape invariant potentials by the point canonical transformation

In this paper by using the method of point canonical transformation we find that the Coulomb and Kratzer potentials can be mapped to the Morse potential. Then we show that the P\"{o}schl-Teller potential type I belongs to the same subclass of shape invariant potentials as Hulth\'{e}n potential. Also we show that the shape-invariant algebra for Coulomb, Kratzer, and Morse potentials is SU(1,1), while the shape-invariant algebra for P\"{o}schl-Teller type I and Hulth\'{e}n is SU(2)

Algebraic Approach to Shape Invariance

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as strength and range. Shape-invariance algebras, in general, are shown to be infinite-dimensional. The conditions under which they become finite-dimensional are explored.Comment: Submitted to Physical Review A. Latex file, 9 pages. Manuscript is also available at http://nucth.physics.wisc.edu/preprints

A Caenorhabditis elegans assay of seizure-like activity optimised for identifying antiepileptic drugs and their mechanisms of action

BACKGROUND: Epilepsy affects around 1% of people, but existing antiepileptic drugs (AEDs) only offer symptomatic relief and are ineffective in approximately 30% of patients. Hence, new AEDs are sorely needed. However, a major bottleneck is the low-throughput nature of early-stage AED screens in conventional rodent models. This process could potentially be expedited by using simpler invertebrate systems, such as the nematode Caenorhabditis elegans. NEW METHOD: Head-bobbing convulsions were previously reported to be inducible by pentylenetetrazol (PTZ) in C. elegans with loss-of-function mutations in unc-49, which encodes a GABAA receptor. Given that epilepsy-linked mutations in human GABAA receptors are well documented, this could represent a clinically-relevant system for early-stage AED screens. However, the original agar plate-based assay is unsuited to large-scale screening and has not been validated for identifying AEDs. Therefore, we established an alternative streamlined, higher-throughput approach whereby mutants were treated with PTZ and AEDs via liquid-based incubation. RESULTS: Convulsions induced within minutes of PTZ exposure in unc-49 mutants were strongly inhibited by the established AED ethosuximide. This protective activity was independent of ethosuximide's suggested target, the T-type calcium channel, as a null mutation in the worm cca-1 ortholog did not affect ethosuximide's anticonvulsant action. COMPARISON WITH EXISTING METHOD: Our streamlined assay is AED-validated, feasible for higher throughput compound screens, and can facilitate insights into AED mechanisms of action. CONCLUSIONS: Based on an epilepsy-associated genetic background, this C. elegans unc-49 model of seizure-like activity presents an ethical, higher throughput alternative to conventional rodent seizure models for initial AED screens

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society

Erratum: "A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo" (2021, ApJ, 909, 218)

[no abstract available