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

PFTAIRE Kinase L63 Interactor 1A (Pif1A Protein) Is Required for Actin Cone Movement during Spermatid Individualization in Drosophila melanogaster

A useful model for determining the mechanisms by which actin and actin binding proteins control cellular architecture is the Drosophila melanogaster process of spermatogenesis. During the final step of spermatogenesis, 64 syncytial spermatids individualized as stable actin cones move synchronously down the axonemes and remodel the membranes. To identify new genes involved in spermatid individualization, we screened a collection of Drosophila male-sterile mutants and found that, in the line Z3-5009, actin cones formed near to the spermatid nuclei but failed to move, resulting in failed spermatid individualization. However, we show by phalloidin actin staining, electron microscopy and immunocytochemical localization of several actin binding proteins that the early cones had normal structure. We sequenced the genome of the Z3-5009 line and identified mutations in the PFTAIRE kinase L63 interactor 1A (Pif1A) gene. Quantitative real-time PCR showed that Pif1A transcript abundance was decreased in the mutant, and a transgene expressing Pif1A fused to green fluorescent protein (GFP) was able to fully rescue spermatid individualization and male fertility. Pif1A-GFP localized to the front of actin cones before initiation of movement. We propose that Pif1A plays a pivotal role in directing actin cone movement

Graded extension of SO(2,1) Lie algebra and the search for exact solutions of Dirac equation by point canonical transformations

SO(2,1) is the symmetry algebra for a class of three-parameter problems that includes the oscillator, Coulomb and Morse potentials as well as other problems at zero energy. All of the potentials in this class can be mapped into the oscillator potential by point canonical transformations. We call this class the "oscillator class". A nontrivial graded extension of SO(2,1) is defined and its realization by two-dimensional matrices of differential operators acting in spinor space is given. It turns out that this graded algebra is the supersymmetry algebra for a class of relativistic potentials that includes the Dirac-Oscillator, Dirac-Coulomb and Dirac-Morse potentials. This class is, in fact, the relativistic extension of the oscillator class. A new point canonical transformation, which is compatible with the relativistic problem, is formulated. It maps all of these relativistic potentials into the Dirac-Oscillator potential.Comment: Replaced with a more potrable PDF versio

Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry

We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $\cal PT$ symmetry may facilitate reconciling our approach to the requirement that the rationally-extended potentials be singularity free. Some examples are shown.Comment: 13 pages, no figure, some additions to introduction and conclusion, 4 more references; to be published in Special issue of Pramana - J. Phy

Reanalysis of single-cell RNA sequencing data does not support herpes simplex virus 1 latency in non-neuronal ganglionic cells in mice

Most individuals are latently infected with herpes simplex virus type 1 (HSV-1), and it is well-established that HSV-1 establishes latency in sensory neurons of peripheral ganglia. However, it was recently proposed that latent HSV-1 is also present in immune cells recovered from the ganglia of experimentally infected mice. Here, we reanalyzed the single-cell RNA sequencing (scRNA-Seq) data that formed the basis for that conclusion. Unexpectedly, off-target priming in 3’ scRNA-Seq experiments enabled the detection of non-polyadenylated HSV-1 latency-associated transcript (LAT) intronic RNAs. However, LAT reads were near-exclusively detected in mixed populations of cells undergoing cell death. Specific loss of HSV-1 LAT and neuronal transcripts during quality control filtering indicated widespread destruction of neurons, supporting the presence of contaminating cell-free RNA in other cells following tissue processing. In conclusion, the reported detection of latent HSV-1 in non-neuronal cells is best explained using compromised scRNA-Seq datasets. IMPORTANCE Most people are infected with herpes simplex virus type 1 (HSV-1) during their life. Once infected, the virus generally remains in a latent (silent) state, hiding within the neurons of peripheral ganglia. Periodic reactivation (reawakening) of the virus may cause fresh diseases such as cold sores. A recent study using single-cell RNA sequencing (scRNA-Seq) proposed that HSV-1 can also establish latency in the immune cells of mice, challenging existing dogma. We reanalyzed the data from that study and identified several flaws in the methodologies and analyses performed that invalidate the published conclusions. Specifically, we showed that the methodologies used resulted in widespread destruction of neurons which resulted in the presence of contaminants that confound the data analysis. We thus conclude that there remains little to no evidence for HSV-1 latency in immune cells.</p

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.

Resolving the backbone tilt of crystalline poly(3-hexylthiophene) with resonant tender X-ray diffraction

The way in which conjugated polymers pack in the solid state strongly affects the performance of polymer-based optoelectronic devices. However, even for the most crystalline conjugated polymers the precise packing of chains within the unit cell is not well established. Here we show that by performing resonant X-ray diffraction experiments at the sulfur K-edge we are able to resolve the tilting of the planar backbones of crystalline poly(3-hexylthiophene) (P3HT) within the unit cell. This approach exploits the anisotropic nature of the X-ray optical properties of conjugated polymers, enabling us to discern between different proposed crystal structures. By comparing our data with simulations based on different orientations, a tilting of the planar conjugated backbone with respect to the side chain stacking direction of 30 ± 5° is determined

Inference of population splits and mixtures from genome-wide allele frequency data

Many aspects of the historical relationships between populations in a species are reflected in genetic data. Inferring these relationships from genetic data, however, remains a challenging task. In this paper, we present a statistical model for inferring the patterns of population splits and mixtures in multiple populations. In this model, the sampled populations in a species are related to their common ancestor through a graph of ancestral populations. Using genome-wide allele frequency data and a Gaussian approximation to genetic drift, we infer the structure of this graph. We applied this method to a set of 55 human populations and a set of 82 dog breeds and wild canids. In both species, we show that a simple bifurcating tree does not fully describe the data; in contrast, we infer many migration events. While some of the migration events that we find have been detected previously, many have not. For example, in the human data we infer that Cambodians trace approximately 16% of their ancestry to a population ancestral to other extant East Asian populations. In the dog data, we infer that both the boxer and basenji trace a considerable fraction of their ancestry (9% and 25%, respectively) to wolves subsequent to domestication, and that East Asian toy breeds (the Shih Tzu and the Pekingese) result from admixture between modern toy breeds and "ancient" Asian breeds. Software implementing the model described here, called TreeMix, is available at http://treemix.googlecode.comComment: 28 pages, 6 figures in main text. Attached supplement is 22 pages, 15 figures. This is an updated version of the preprint available at http://precedings.nature.com/documents/6956/version/

Evolutionary history of endogenous Human Herpesvirus 6 reflects human migration out of Africa

Human herpesvirus 6A and 6B (HHV-6) can integrate into the germline, and as a result, ∼70 million people harbor the genome of one of these viruses in every cell of their body. Until now, it has been largely unknown if 1) these integrations are ancient, 2) if they still occur, and 3) whether circulating virus strains differ from integrated ones. Here, we used next-generation sequencing and mining of public human genome data sets to generate the largest and most diverse collection of circulating and integrated HHV-6 genomes studied to date. In genomes of geographically dispersed, only distantly related people, we identified clades of integrated viruses that originated from a single ancestral event, confirming this with fluorescent in situ hybridization to directly observe the integration locus. In contrast to HHV-6B, circulating and integrated HHV-6A sequences form distinct clades, arguing against ongoing integration of circulating HHV-6A or “reactivation” of integrated HHV-6A. Taken together, our study provides the first comprehensive picture of the evolution of HHV-6, and reveals that integration of heritable HHV-6 has occurred since the time of, if not before, human migrations out of Africa