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

W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1,p)

We construct new Yang-Baxter integrable boundary conditions in the lattice approach to the logarithmic minimal model WLM(1,p) giving rise to reducible yet indecomposable representations of rank 1 in the continuum scaling limit. We interpret these W-extended Kac representations as finitely-generated W-extended Feigin-Fuchs modules over the triplet W-algebra W(p). The W-extended fusion rules of these representations are inferred from the recently conjectured Virasoro fusion rules of the Kac representations in the underlying logarithmic minimal model LM(1,p). We also introduce the modules contragredient to the W-extended Kac modules and work out the correspondingly-extended fusion algebra. Our results are in accordance with the Kazhdan-Lusztig dual of tensor products of modules over the restricted quantum universal enveloping algebra $\bar{U}_q(sl_2)$ at $q=e^{\pi i/p}$. Finally, polynomial fusion rings isomorphic with the various fusion algebras are determined, and the corresponding Grothendieck ring of characters is identified.Comment: 28 page

An automated Raman-based platform for the sorting of live cells by functional properties

Stable-isotope probing is widely used to study the function of microbial taxa in their natural environment, but sorting of isotopically labelled microbial cells from complex samples for subsequent genomic analysis or cultivation is still in its early infancy. Here, we introduce an optofluidic platform for automated sorting of stable-isotope-probing-labelled microbial cells, combining microfluidics, optical tweezing and Raman microspectroscopy, which yields live cells suitable for subsequent single-cell genomics, mini-metagenomics or cultivation. We describe the design and optimization of this Raman-activated cell-sorting approach, illustrate its operation with four model bacteria (two intestinal, one soil and one marine) and demonstrate its high sorting accuracy (98.3 ± 1.7%), throughput (200-500 cells h-1; 3.3-8.3 cells min-1) and compatibility with cultivation. Application of this sorting approach for the metagenomic characterization of bacteria involved in mucin degradation in the mouse colon revealed a diverse consortium of bacteria, including several members of the underexplored family Muribaculaceae, highlighting both the complexity of this niche and the potential of Raman-activated cell sorting for identifying key players in targeted processes.</p

The Role of Purported Mucoprotectants in Dealing with Irritable Bowel Syndrome, Functional Diarrhea, and Other Chronic Diarrheal Disorders in Adults

Chronic diarrhea is a frequent presenting symptom, both in primary care medicine and in specialized gastroenterology units. It is estimated that more than 5% of the global population suffers from chronic diarrhea. and that about 40% of these subjects are older than 60 years. The clinician is frequently faced with the need to decide which is the best therapeutic approach for these patients. While the origin of chronic diarrhea is diverse, impairment of intestinal barrier function, dysbiosis. and mucosal micro-inflammation are being increasingly recognized as underlying phenomena characterizing a variety of chronic diarrheal diseases. In addition to current pharmacological therapies, there is growing interest in alternative products such as mucoprotectants, which form a mucoadhesive film over the epithelium to reduce and protect against the development of altered intestinal permeability, dysbiosis, and mucosal micro-inflammation. This manuscript focuses on chronic diarrhea in adults, and we will review recent evidence on the ability of these natural compounds to improve symptoms associated with chronic diarrhea and to exert protective effects for the intestinal barrier

Vertex operator algebras with central charges 164/5 and 236/7

This paper completes the classification problem which was proposed in the previous paper [1] in which we attempted to characterize the minimal models and families obtained by the tensor products and the simple current extensions of minimal models under the condition that the characters of simple modules satisfy modular differential equations of the third order, and a mild condition on vertex operator algebras. In the previous work, several vertex operator algebras which are not the minimal models appeared. Five elevenths of them are identified to well-known vertex operator algebras which are all vertex operator algebras related with orbifold models of lattice vertex operator algebras. However, we were not able to deny the existence of simple, rational vertex operator algebras of CFT and finite type with central charges either 164/5 or 236/7 under the condition on which we worked in [1]. The characterization of minimal models with at most two simple modules was achieved in the same paper. The numbers 164/5 and 236/7 were already appeared in the paper of Tuite and Van ([17]) in the different context. However, they were out of reach of our conclusion. Moreover, we solve the conjecture, which was proposed by Hampapura and Mukhi [8], that the j‑function is expressed by characters of the minimal models

Vertex operator algebras, minimal models, and modular linear differential equations of order 4

In this paper we classify vertex operator algebras with three conditions which arise from Virasoro minimal models: (A) the central charge and conformal weights are rational numbers, (B) the space spanned by characters of all simple modules of a vertex operator algebra coincides with the space of solutions of a modular linear differential equation of order 4 and (C) the dimensions of first three weight subspaces of a VOA are 1, 0 and 1, respectively. It is shown that vertex operator algebras which we concern have central charges c= −46/3, −3/5, −114/7, 4/5, and are isomorphic to minimal models for c= −46/3, −3/5 and $Z_2$ -graded simple current extensions of minimal models for c= −114/7, 4/5

Trans-Golgi protein TVP23B regulates host-microbe interactions via Paneth cell homeostasis and Goblet cell glycosylation

Abstract A key feature in intestinal immunity is the dynamic intestinal barrier, which separates the host from resident and pathogenic microbiota through a mucus gel impregnated with antimicrobial peptides. Using a forward genetic screen, we have found a mutation in Tvp23b, which conferred susceptibility to chemically induced and infectious colitis. Trans-Golgi apparatus membrane protein TVP23 homolog B (TVP23B) is a transmembrane protein conserved from yeast to humans. We found that TVP23B controls the homeostasis of Paneth cells and function of goblet cells, leading to a decrease in antimicrobial peptides and more penetrable mucus layer. TVP23B binds with another Golgi protein, YIPF6, which is similarly critical for intestinal homeostasis. The Golgi proteomes of YIPF6 and TVP23B-deficient colonocytes have a common deficiency of several critical glycosylation enzymes. TVP23B is necessary for the formation of the sterile mucin layer of the intestine and its absence disturbs the balance of host and microbe in vivo