Pseudo-Hermiticity and some consequences of a generalized quantum condition

We exploit the hidden symmetry structure of a recently proposed non-Hermitian Hamiltonian and of its Hermitian equivalent one. This sheds new light on the pseudo-Hermitian character of the former and allows access to a generalized quantum condition. Special cases lead to hyperbolic and Morse-like potentials in the framework of a coordinate-dependent mass model.Comment: 10 pages, no figur

A global compilation of dissolved iron measurements: focus on distributions and processes in the Southern Ocean

Due to its importance as a limiting nutrient for phytoplankton growth in large regions of the world's oceans, ocean water column observations of concentration of the trace-metal iron (Fe) have increased markedly over recent decades. Here we compile >13 000 global measurements of dissolved Fe (dFe) and make this available to the community. We then conduct a synthesis study focussed on the Southern Ocean, where dFe plays a fundamental role in governing the carbon cycle, using four regions, six basins and five depth intervals as a framework. Our analysis highlights depth-dependent trends in the properties of dFe between different regions and basins. In general, surface dFe is highest in the Atlantic basin and the Antarctic region. While attributing drivers to these patterns is uncertain, inter-basin patterns in surface dFe might be linked to differing degrees of dFe inputs, while variability in biological consumption between regions covaries with the associated surface dFe differences. Opposite to the surface, dFe concentrations at depth are typically higher in the Indian basin and the Subantarctic region. The inter-region trends can be reconciled with similar ligand variability (although only from one cruise), and the inter-basin difference might be explained by differences in hydrothermal inputs suggested by modelling studies (Tagliabue et al., 2010) that await observational confirmation. We find that even in regions where many dFe measurements exist, the processes governing the seasonal evolution of dFe remain enigmatic, suggesting that, aside from broad Subantarctic - Antarctic trends, biological consumption might not be the major driver of dFe variability. This highlights the apparent importance of other processes such as exogenous inputs, physical transport/mixing or dFe recycling processes. Nevertheless, missing measurements during key seasonal transitions make it difficult to better quantify and understand surface water replenishment processes and the seasonal Fe cycle. Finally, we detail the degree of seasonal coverage by region, basin and depth. By synthesising prior measurements, we suggest a role for different processes and highlight key gaps in understanding, which we hope can help structure future research efforts in the Southern Ocean

Red Panda: A Novel Method for Detecting Variants in Single-Cell RNA Sequencing

BACKGROUND: Single-cell sequencing enables us to better understand genetic diseases, such as cancer or autoimmune disorders, which are often affected by changes in rare cells. Currently, no existing software is aimed at identifying single nucleotide variations or micro (1-50 bp) insertions and deletions in single-cell RNA sequencing (scRNA-seq) data. Generating high-quality variant data is vital to the study of the aforementioned diseases, among others. RESULTS: In this study, we report the design and implementation of Red Panda, a novel method to accurately identify variants in scRNA-seq data. Variants were called on scRNA-seq data from human articular chondrocytes, mouse embryonic fibroblasts (MEFs), and simulated data stemming from the MEF alignments. Red Panda had the highest Positive Predictive Value at 45.0%, while other tools-FreeBayes, GATK HaplotypeCaller, GATK UnifiedGenotyper, Monovar, and Platypus-ranged from 5.8-41.53%. From the simulated data, Red Panda had the highest sensitivity at 72.44%. CONCLUSIONS: We show that our method provides a novel and improved mechanism to identify variants in scRNA-seq as compared to currently existing software. However, methods for identification of genomic variants using scRNA-seq data can be still improved

Amplification Free Detection of SARS-CoV-2 Using Multi-valent Binding

[Image: see text] We present the development of electrochemical impedance spectroscopy (EIS)-based biosensors for sensitive detection of SARS-CoV-2 RNA using multi-valent binding. By increasing the number of probe–target binding events per target molecule, multi-valent binding is a viable strategy for improving the biosensor performance. As EIS can provide sensitive and label-free measurements of nucleic acid targets during probe–target hybridization, we used multi-valent binding to build EIS biosensors for targeting SARS-CoV-2 RNA. For developing the biosensor, we explored two different approaches including probe combinations that individually bind in a single-valent fashion and the probes that bind in a multi-valent manner on their own. While we found excellent biosensor performance using probe combinations, we also discovered unexpected signal suppression. We explained the signal suppression theoretically using inter- and intra-probe hybridizations which confirmed our experimental findings. With our best probe combination, we achieved a LOD of 182 copies/μL (303 aM) of SARS-CoV-2 RNA and used these for successful evaluation of patient samples for COVID-19 diagnostics. We were also able to show the concept of multi-valent binding with shorter probes in the second approach. Here, a 13-nt-long probe has shown the best performance during SARS-CoV-2 RNA binding. Therefore, multi-valent binding approaches using EIS have high utility for direct detection of nucleic acid targets and for point-of-care diagnostics

L2 series solutions of the Dirac equation for power-law potentials at rest mass energy

We obtain solutions of the three dimensional Dirac equation for radial power-law potentials at rest mass energy as an infinite series of square integrable functions. These are written in terms of the confluent hypergeometric function and chosen such that the matrix representation of the Dirac operator is tridiagonal. The "wave equation" results in a three-term recursion relation for the expansion coefficients of the spinor wavefunction which is solved in terms of orthogonal polynomials. These are modified versions of the Meixner-Pollaczek polynomials and of the continuous dual Hahn polynomials. The choice depends on the values of the angular momentum and the power of the potential.Comment: 13 pages, 1 Tabl

A general scheme for the effective-mass Schrodinger equation and the generation of the associated potentials

A systematic procedure to study one-dimensional Schr\"odinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting situation in that, in the presence of a mass background, formation of bound states is signalled. We also discuss coordinate-transformed, constant-mass Schr\"odinger equation, its matching with the PDEM form and the consequent decoupling of the ambiguity parameters. This provides a unified approach to many exact results known in the literature, as well as to a lot of new ones.Comment: 16 pages + 1 figure; minor changes + new "free-particle" problem; version published in Mod. Phys. Lett.

A Microsatellite Guided Insight into the Genetic Status of Adi, an Isolated Hunting-Gathering Tribe of Northeast India

Tibeto-Burman populations of India provide an insight into the peopling of India and aid in understanding their genetic relationship with populations of East, South and Southeast Asia. The study investigates the genetic status of one such Tibeto-Burman group, Adi of Arunachal Pradesh based on 15 autosomal microsatellite markers. Further the study examines, based on 9 common microsatellite loci, the genetic relationship of Adi with 16 other Tibeto-Burman speakers of India and 28 neighboring populations of East and Southeast Asia. Overall, the results support the recent formation of the Adi sub-tribes from a putative ancestral group and reveal that geographic contiguity is a major influencing factor of the genetic affinity among the Tibeto-Burman populations of India