Topological Mechanics from Supersymmetry

In topological mechanics, the identification of a mechanical system's rigidity matrix with an electronic tight-binding model allows to infer topological properties of the mechanical system, such as the occurrence of `floppy' boundary modes, from the associated electronic band structure. Here we introduce an approach to systematically construct topological mechanical systems by an exact supersymmetry (SUSY) that relates the bosonic (mechanical) and fermionic (e.g. electronic) degrees of freedom. As examples we discuss mechanical analogues of the Kitaev honeycomb model and of a second-order topological insulator with floppy corner modes. Our SUSY construction naturally defines hitherto unexplored topological invariants for bosonic (mechanical) systems, such as bosonic Wilson loop operators that are formulated in terms of a SUSY-related fermionic Berry curvature.Comment: 8 pages, 6 figure

Genomic Accumulation of Retrotransposons Was Facilitated by Repressive RNA-Binding Proteins: A Hypothesis

Retrotransposon-derived elements (RDEs) can disrupt gene expression, but are nevertheless widespread in metazoan genomes. This review presents a hypothesis that repressive RNA-binding proteins (RBPs) facilitated the large-scale accumulation of RDEs. Many RBPs bind RDEs in pre-mRNAs to repress the effects of RDEs on RNA processing, or the formation of inverted repeat RNA structures. RDE-binding RBPs often assemble on extended, multivalent binding sites across the RDE, which ensures repression of cryptic splice or polyA sites. RBPs thereby minimize the effects of RDEs on gene expression, which likely reduces the negative selection against RDEs. While mutations that change splice sites in RDEs act as an off-on switch in exon formation, mutations that decrease the multivalency of RBP binding sites resemble a rheostat that enables a more gradual evolution of new RDE-derived exons. RBPs might also repress aberrant processing of active retrotransposons, thus increasing the chance that full-length copies are made. Taken together, in this review, it is proposed that RBPs facilitate the widespread accumulation of intronic RDEs by repressing RNA processing while chaperoning their potential to gradually evolve into new exons

Supersymmetry on the lattice: Geometry, Topology, and Spin Liquids

In quantum mechanics, supersymmetry (SUSY) posits an equivalence between two elementary degrees of freedom, bosons and fermions. Here we show how this fundamental concept can be applied to connect bosonic and fermionic lattice models in the realm of condensed matter physics, e.g., to identify a variety of (bosonic) phonon and magnon lattice models which admit topologically nontrivial free fermion models as superpartners. At the single-particle level, the bosonic and the fermionic models that are generated by the SUSY are isospectral except for zero modes, such as flat bands, whose existence is undergirded by the Witten index of the SUSY theory. We develop a unifying framework to formulate these SUSY connections in terms of general lattice graph correspondences and discuss further ramifications such as the definition of supersymmetric topological invariants for generic bosonic systems. Notably, a Hermitian form of the supercharge operator, the generator of the SUSY, can itself be interpreted as a hopping Hamiltonian on a bipartite lattice. This allows us to identify a wide class of interconnected lattices whose tight-binding Hamiltonians are superpartners of one another or can be derived via squaring or square-rooting their energy spectra all the while preserving band topology features. We introduce a five-fold way symmetry classification scheme of these SUSY lattice correspondences, including cases with a non-zero Witten index, based on a topological classification of the underlying Hermitian supercharge operator. These concepts are illustrated for various explicit examples including frustrated magnets, Kitaev spin liquids, and topological superconductors.Comment: 37 pages, 27 figure

Asymptotic Behavior of the Correlator for Polyakov Loops

The asymptotic behavior of the correlator for Polyakov loop operators separated by a large distance $R$ is determined for high temperature QCD. It is dominated by nonperturbative effects related to the exchange of magnetostatic gluons. To analyze the asymptotic behavior, the problem is formulated in terms of the effective field theory of QCD in 3 space dimensions. The Polyakov loop operator is expanded in terms of local gauge-invariant operators constructed out of the magnetostatic gauge field, with coefficients that can be calculated using resummed perturbation theory. The asymptotic behavior of the correlator is $\exp(-MR)/R$, where $M$ is the mass of the lowest-lying glueball in $(2+1)$-dimensional QCD. This result implies that existing lattice calculations of the Polyakov loop correlator at the highest temperatures available do not probe the true asymptotic region in $R$.Comment: 10 pages, NUHEP-TH-94-2

On the equivalence between 2D Yukawa and Gross-Neveu models

We study numerically on the lattice the 2D Yukawa model with the U(1) chiral symmetry and $N_F$ = 16 at infinite scalar field self-coupling. The scaling behaviour of the fermion mass, as the Yukawa coupling approaches zero, is analysed using the mean field method. It is found to agree with that of the Gross-Neveu model with the same symmetry and $N_F$. The results suggest that the 2D Yukawa models belong to the universality class of the Gross-Neveu models not only at weak scalar field self-coupling but also for a broad range of the bare parameters which is not accessible to the $1/N_F$ expansion. New universality classes might arise at the crossover to the spin model universality class, however.Comment: 18 pages, Juelich HLRZ 111/9

Functional interactions between polypyrimidine tract binding protein and PRI peptide ligand containing proteins.

Polypyrimidine tract binding protein (PTBP1) is a heterogeneous nuclear ribonucleoprotein (hnRNP) that plays roles in most stages of the life-cycle of pre-mRNA and mRNAs in the nucleus and cytoplasm. PTBP1 has four RNA binding domains of the RNA recognition motif (RRM) family, each of which can bind to pyrimidine motifs. In addition, RRM2 can interact via its dorsal surface with proteins containing short peptide ligands known as PTB RRM2 interacting (PRI) motifs, originally found in the protein Raver1. Here we review our recent progress in understanding the interactions of PTB with RNA and with various proteins containing PRI ligands.This work was supported by the Biotechnology and Biological Sciences Research Council [grant number BB/H004203/1 (to C.W.J.S.)]; the Wellcome Trust [grant number 092900 (to C.W.J.S.)]; the Boehringer Ingelheim Fond (to J.A.); the Medical Research Council [grant number MR/M026302/1 (to D.B.A. and D.E.V.P.)]; the Fundação de Amparo à Pesquisa do Estado de Minas Gerais [grant number MR/M026302/1 (to D.B.A. and D.E.V.P.)]; and the National Health and Medical Research Council CJ Martin Fellowship [grant number APP1072476 (to D.B.A.)]

The transcriptional landscape of endogenous retroelements delineates esophageal adenocarcinoma subtypes

Most cancer types exhibit aberrant transcriptional activity, including derepression of retrotransposable elements (RTEs). However, the degree, specificity and potential consequences of RTE transcriptional activation may differ substantially among cancer types and subtypes. Representing one extreme of the spectrum, we characterize the transcriptional activity of RTEs in cohorts of esophageal adenocarcinoma (EAC) and its precursor Barrett's esophagus (BE) from the OCCAMS (Oesophageal Cancer Clinical and Molecular Stratification) consortium, and from TCGA (The Cancer Genome Atlas). We found exceptionally high RTE inclusion in the EAC transcriptome, driven primarily by transcription of genes incorporating intronic or adjacent RTEs, rather than by autonomous RTE transcription. Nevertheless, numerous chimeric transcripts straddling RTEs and genes, and transcripts from stand-alone RTEs, particularly KLF5- and SOX9-controlled HERVH proviruses, were overexpressed specifically in EAC. Notably, incomplete mRNA splicing and EAC-characteristic intronic RTE inclusion was mirrored by relative loss of the respective fully-spliced, functional mRNA isoforms, consistent with compromised cellular fitness. Defective RNA splicing was linked with strong transcriptional activation of a HERVH provirus on Chr Xp22.32 and defined EAC subtypes with distinct molecular features and prognosis. Our study defines distinguishable RTE transcriptional profiles of EAC, reflecting distinct underlying processes and prognosis, thus providing a framework for targeted studies

Heavy Quark Free Energies and Screening in SU(2) Gauge Theory

We investigate the singlet, triplet and colour average heavy quark free energies in SU(2) pure gauge theory at various temperatures T. We focus on the long distance behaviour of the free energies, studying in particular the temperature dependence of the string tension and the screening masses. The results are qualitatively similar to the SU(3) scenario, except near the critical temperature Tc of the deconfining transition. Finally we test a recently proposed method to renormalize the Polyakov loop.Comment: 5 pages, 4 figures, contribution to the Proceedings of SEWM 2002 (Heidelberg

Linking the chiral and deconfinement phase transitions

We show that the electric glueball becomes critical at the end-point of the deconfinement phase transition in finite temperature QCD. Based on this observation and existing lattice data, we argue that the chiral phase transition at a zero quark mass and the deconfinement phase transition at an infinite quark mass are continuously connected by the glueball-sigma mixing.Comment: 4 pages, terminology corrected. To appear in Phys. Rev.