Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra

The purpose of this paper is to generalize Zhu's theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights. To recover SL_2(Z)-invariance of the characters it turns out to be necessary to consider twisted modules alongside ordinary ones. It also turns out to be necessary, in describing the space of conformal blocks in the supersymmetric case, to include certain `odd traces' on modules alongside traces and supertraces. We prove that the set of supertrace functions, thus supplemented, spans a finite dimensional SL_2(Z)-invariant space. We close the paper with several examples.Comment: 42 pages. Published versio

Logarithmic intertwining operators and vertex operators

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra $M(1)_a$, of central charge $1-12a^2$. We classify these operators in terms of {\em depth} and provide explicit constructions in all cases. Furthermore, for $a=0$ we focus on the vertex operator subalgebra L(1,0) of $M(1)_0$ and obtain logarithmic intertwining operators among indecomposable Virasoro algebra modules. In particular, we construct explicitly a family of {\em hidden} logarithmic intertwining operators, i.e., those that operate among two ordinary and one genuine logarithmic L(1,0)-module.Comment: 32 pages. To appear in CM

A novel minimal in vitro system for analyzing HIV-1 Gag mediated budding

A biomimetic minimalist model membrane was used to study the mechanism and kinetics of cell-free in vitro HIV-1 Gag budding from a giant unilamellar vesicle (GUV). Real time interaction of Gag, RNA and lipid leading to the formation of mini-vesicles was measured using confocal microscopy. Gag forms resolution limited punctae on the GUV lipid membrane. Introduction of the Gag and urea to a GUV solution containing RNA led to the budding of mini-vesicles on the inside surface of the GUV. The GUV diameter showed a linear decrease in time due to bud formation. Both bud formation and decrease in GUV size were proportional to Gag concentration. In the absence of RNA, addition of urea to GUVs incubated with Gag also resulted in subvesicle formation but exterior to the surface. These observations suggest the possibility that clustering of GAG proteins leads to membrane invagination even in the absence of host cell proteins. The method presented here is promising, and allows for systematic study of the dynamics of assembly of immature HIV and help classify the hierarchy of factors that impact the Gag protein initiated assembly of retroviruses such as HIV.Comment: 27 pages, 9 Figures and 0 Table

Aligning Manifolds of Double Pendulum Dynamics Under the Influence of Noise

This study presents the results of a series of simulation experiments that evaluate and compare four different manifold alignment methods under the influence of noise. The data was created by simulating the dynamics of two slightly different double pendulums in three-dimensional space. The method of semi-supervised feature-level manifold alignment using global distance resulted in the most convincing visualisations. However, the semi-supervised feature-level local alignment methods resulted in smaller alignment errors. These local alignment methods were also more robust to noise and faster than the other methods.Comment: The final version will appear in ICONIP 2018. A DOI identifier to the final version will be added to the preprint, as soon as it is availabl

Dirac cohomology, elliptic representations and endoscopy

The first part (Sections 1-6) of this paper is a survey of some of the recent developments in the theory of Dirac cohomology, especially the relationship of Dirac cohomology with (g,K)-cohomology and nilpotent Lie algebra cohomology; the second part (Sections 7-12) is devoted to understanding the unitary elliptic representations and endoscopic transfer by using the techniques in Dirac cohomology. A few problems and conjectures are proposed for further investigations.Comment: This paper will appear in `Representations of Reductive Groups, in Honor of 60th Birthday of David Vogan', edited by M. Nervins and P. Trapa, published by Springe

Residue codes of extremal Type II Z_4-codes and the moonshine vertex operator algebra

In this paper, we study the residue codes of extremal Type II Z_4-codes of length 24 and their relations to the famous moonshine vertex operator algebra. The main result is a complete classification of all residue codes of extremal Type II Z_4-codes of length 24. Some corresponding results associated to the moonshine vertex operator algebra are also discussed.Comment: 21 pages, shortened from v

Decoding co-/post-transcriptional complexities of plant transcriptomes and epitranscriptome using next-generation sequencing technologies

Next-generation sequencing (NGS) technologies – Illumina RNA-seq, Pacific Biosciences isoform sequencing (PacBio Iso-seq), and Oxford Nanopore direct RNA sequencing (DRS) - have revealed the complexity of plant transcriptomes and their regulation at the co-/posttranscriptional level. Global analysis of mature mRNAs, transcripts from nuclear run-on assays, and nascent chromatin-bound mRNAs using short as well as full-length and single-molecule DRS reads have uncovered potential roles of different forms of RNA polymerase II during the transcription process, and the extent of co-transcriptional pre-mRNA splicing and polyadenylation. These tools have also allowed mapping of transcriptome-wide start sites in cap-containing RNAs, poly(A) site choice, poly(A) tail length, and RNA base modifications. Analysis of a large number of plant transcriptomes using high-throughput short and long reads under different conditions has established that diverse abiotic and biotic stresses and environmental cues such as light, which regulates many aspects of plant growth and development, have a profound impact on gene expression at the co-/post-transcriptional level. The emerging theme from these studies is that reprogramming of gene expression in response to developmental cues and stresses at the co-/post transcriptional level likely plays a crucial role in eliciting appropriate responses for optimal growth and plant survival under adverse conditions. Although the mechanisms by which developmental cues and different stresses regulate co-/posttranscriptional splicing are largely unknown, a few recent studies are beginning to provide some insights into these mechanisms. These studies indicate that the external cues target spliceosomal and splicing regulatory proteins to modulate alternative splicing. In this review, we provide an overview of recent discoveries on the dynamics and complexities of plant transcriptomes, mechanistic insights into splicing regulation, and discuss critical gaps in co-/post-transcriptional research that need to be addressed using diverse genomic and biochemical approaches

A zebrafish model of conditional targeted podocyte ablation and regeneration

Podocytes are specialized cells that contribute critically to the normal structure and function of the glomerular filtration barrier. Their depletion plays an important role in the pathogenesis of glomerulosclerosis. Here, we report generation of a genetic model of conditional podocyte ablation and regeneration in zebrafish using a bacterial nitroreductase strategy to convert a prodrug, Metronidazole, into a cytotoxic metabolite. A transgenic zebrafish line was generated that expresses a green fluorescence protein (GFP) and the nitroreductase fusion protein under the control of the podocin promoter Tg(podocin:nitroreductase-GFP). Treatment of these transgenic zebrafish with Metronidazole results in podocyte apoptosis, a loss of nephrin and podocin expression, foot process effacement, and a leaky glomerular filtration barrier. Following Metronidazole washout, proliferating cells were detected in the glomeruli of recovering transgenic fish with a restoration of nitroreductase-GFP fluorescence, nephrin and podocin expression, a reestablishment of normal foot process architecture and glomerular barrier function. Thus, our studies show that zebrafish podocytes are capable of regenerating following depletion and establish the Tg(podocin:NTR-GFP) fish as a new model to study podocyte injury and repair

Power spectra of TASEPs with a localized slow site

The totally asymmetric simple exclusion process (TASEP) with a localized defect is revisited in this article with attention paid to the power spectra of the particle occupancy N(t). Intrigued by the oscillatory behaviors in the power spectra of an ordinary TASEP in high/low density phase(HD/LD) observed by Adams et al. (2007 Phys. Rev. Lett. 99 020601), we introduce a single slow site with hopping rate q<1 to the system. As the power spectrum contains time-correlation information of the particle occupancy of the system, we are particularly interested in how the defect affects fluctuation in particle number of the left and right subsystems as well as that of the entire system. Exploiting Monte Carlo simulations, we observe the disappearance of oscillations when the defect is located at the center of the system. When the defect is off center, oscillations are restored. To explore the origin of such phenomenon, we use a linearized Langevin equation to calculate the power spectrum for the sublattices and the whole lattice. We provide insights into the interactions between the sublattices coupled through the defect site for both simulation and analytical results.Comment: 16 pages, 6 figures; v2: Minor revision