Characters of solvable groups, Hilbert-Schmidt stability and dense periodic measures

We study the character theory of metabelian and polycyclic groups. It is used to investigate Hilbert-Schmidt stability via the character-theoretic criterion of Hadwin and Shulman. There is a close connection between stability and dynamics of automorphisms of compact abelian groups. Relying on this, we deduce that finitely generated virtually nilpotent groups, free metabelian groups, lamplighter groups as well as upper triangular groups over certain rings of algebraic integers are Hilbert-Schmidt stable.Comment: To appear in the Mathematische Annalen. Very few minor changes from v

On the Complexity of Two Dimensional Commuting Local Hamiltonians

The complexity of the commuting local Hamiltonians (CLH) problem still remains a mystery after two decades of research of quantum Hamiltonian complexity; it is only known to be contained in NP for few low parameters. Of particular interest is the tightly related question of understanding whether groundstates of CLHs can be generated by efficient quantum circuits. The two problems touch upon conceptual, physical and computational questions, including the centrality of non-commutation in quantum mechanics, quantum PCP and the area law. It is natural to try to address first the more physical case of CLHs embedded on a 2D lattice, but this problem too remained open apart from some very specific cases [Aharonov and Eldar, 2011; Hastings, 2012; Schuch, 2011]. Here we consider a wide class of two dimensional CLH instances; these are k-local CLHs, for any constant k; they are defined on qubits set on the edges of any surface complex, where we require that this surface complex is not too far from being "Euclidean". Each vertex and each face can be associated with an arbitrary term (as long as the terms commute). We show that this class is in NP, and moreover that the groundstates have an efficient quantum circuit that prepares them. This result subsumes that of Schuch [Schuch, 2011] which regarded the special case of 4-local Hamiltonians on a grid with qubits, and by that it removes the mysterious feature of Schuch\u27s proof which showed containment in NP without providing a quantum circuit for the groundstate and considerably generalizes it. We believe this work and the tools we develop make a significant step towards showing that 2D CLHs are in NP

The Space of Traces of the Free Group and Free Products of Matrix Algebras

We show that the space of traces of the free group is a Poulsen simplex, i.e., every trace is a pointwise limit of extremal traces. We prove that this fails for many virtually free groups. Using a similar strategy, we show that the space of traces of the free product of matrix algebras $\mathbf{M}_n(\mathbb{C}) * \mathbf{M}_n(\mathbb{C})$ is a Poulsen simplex as well, answering a question of Musat and R{\o}rdam for $n \geq 4$. Similar results are shown for certain faces of the simplices above, most notably, for the face of finite-dimensional traces

Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region

The purpose of this paper is to establish the admitted region for five simultaneous, functionally independent invariants of the strain rate tensor S and rotation rate tensor Ω and calculate some simultaneous invariants of these tensors which are encountered in the theory of constitutive relations for turbulent flows. Such a problem, as far as we know, has not yet been considered, though it is obviously an integral part of any problem in which scalar functions of the tensors S and Ω are studied. The theory provided inside this paper is the building block for a derivation of new algebraic constitutive relations for three-dimensional turbulent flows in the form of expansions of the Reynolds-stress tensor in a tensorial basis formed by the tensors S and Ω, in which the scalar coefficients depend on simultaneous invariants of these tensors

Vaccination with SARS-CoV-2 variants of concern protects mice from challenge with wild-type virus.

Funder: open philanthropy projectFunder: jpb foundationVaccines against Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) have been highly efficient in protecting against Coronavirus Disease 2019 (COVID-19). However, the emergence of viral variants that are more transmissible and, in some cases, escape from neutralizing antibody responses has raised concerns. Here, we evaluated recombinant protein spike antigens derived from wild-type SARS-CoV-2 and from variants B.1.1.7, B.1.351, and P.1 for their immunogenicity and protective effect in vivo against challenge with wild-type SARS-CoV-2 in the mouse model. All proteins induced high neutralizing antibodies against the respective viruses but also induced high cross-neutralizing antibody responses. The decline in neutralizing titers between variants was moderate, with B.1.1.7-vaccinated animals having a maximum fold reduction of 4.8 against B.1.351 virus. P.1 induced the most cross-reactive antibody responses but was also the least immunogenic in terms of homologous neutralization titers. However, all antigens protected from challenge with wild-type SARS-CoV-2 in a mouse model

A Tandem Mass Spectrometry Sequence Database Search Method for Identification of O-Fucosylated Proteins by Mass Spectrometry.

Thrombospondin type 1 repeats (TSRs), small adhesive protein domains with a wide range of functions, are usually modified with O-linked fucose, which may be extended to O-fucose-β1,3-glucose. Collision-induced dissociation (CID) spectra of O-fucosylated peptides cannot be sequenced by standard tandem mass spectrometry (MS/MS) sequence database search engines because O-linked glycans are highly labile in the gas phase and are effectively absent from the CID peptide fragment spectra, resulting in a large mass error. Electron transfer dissociation (ETD) preserves O-linked glycans on peptide fragments, but only a subset of tryptic peptides with low m/ z can be reliably sequenced from ETD spectra compared to CID. Accordingly, studies to date that have used MS to identify O-fucosylated TSRs have required manual interpretation of CID mass spectra even when ETD was also employed. In order to facilitate high-throughput, automatic identification of O-fucosylated peptides from CID spectra, we re-engineered the MS/MS sequence database search engine Comet and the MS data analysis suite Trans-Proteomic Pipeline to enable automated sequencing of peptides exhibiting the neutral losses characteristic of labile O-linked glycans. We used our approach to reanalyze published proteomics data from Plasmodium parasites and identified multiple glycoforms of TSR-containing proteins

The inactivated NDV-HXP-S COVID-19 vaccine induces a significantly higher ratio of neutralizing to non-neutralizing antibodies in humans as compared to mRNA vaccines

NDV-HXP-S is a recombinant Newcastle disease virus based-vaccine against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which expresses an optimized (HexaPro) spike protein on its surface. The vaccine can be produced in embryonated chicken eggs using the same process as that employed for the production of influenza virus vaccines. Here we performed a secondary analysis of the antibody responses after vaccination with inactivated NDV-HXP-S in a Phase I clinical study in Thailand. Please click Download on the upper right corner to see the full abstract

Emerging roles for hyaluronidase in cancer metastasis and therapy

Hyaluronidases are a family of five human enzymes that have been differentially implicated in the progression of many solid tumor types, both clinically and in functional studies. Advances in the past five years have clarified many apparent contradictions, (1) by demonstrating that specific hyaluronidases have alternative substrates to hyaluronan (HA) or do not exhibit any enzymatic activity, (2) that high molecular weight HA polymers elicit signaling effects that are opposite those of the hyaluronidase-digested HA oligomers, and (3) that it is actually the combined overexpression of HA synthesizing enzymes with hyaluronidases that confers tumorigenic potential. This review examines the literature supporting these conclusions and discusses novel mechanisms by which hyaluronidases impact invasive tumor cell processes. In addition, a detailed structural and functional comparison of the hyaluronidases is presented with insights into substrate selectivity and potential for therapeutic targeting. Finally, technological advances in targeting hyaluronidase for tumor imaging and cancer therapy are summarized