Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv admin note: text overlap with arXiv:1409.060

Generalized iterated wreath products of cyclic groups and rooted trees correspondence

Consider the generalized iterated wreath product $\mathbb{Z}_{r_1}\wr \mathbb{Z}_{r_2}\wr \ldots \wr \mathbb{Z}_{r_k}$ where $r_i \in \mathbb{N}$. We prove that the irreducible representations for this class of groups are indexed by a certain type of rooted trees. This provides a Bratteli diagram for the generalized iterated wreath product, a simple recursion formula for the number of irreducible representations, and a strategy to calculate the dimension of each irreducible representation. We calculate explicitly fast Fourier transforms (FFT) for this class of groups, giving literature's fastest FFT upper bound estimate.Comment: 15 pages, to appear in Advances in the Mathematical Science

Sequences in the cytoplasmic tail of SARS-CoV-2 Spike facilitate expression at the cell surface and syncytia formation.

The Spike (S) protein of SARS-CoV-2 binds ACE2 to direct fusion with host cells. S comprises a large external domain, a transmembrane domain, and a short cytoplasmic tail. Understanding the intracellular trafficking of S is relevant to SARS-CoV-2 infection, and to vaccines expressing full-length S from mRNA or adenovirus vectors. Here we report a proteomic screen for cellular factors that interact with the cytoplasmic tail of S. We confirm interactions with the COPI and COPII vesicle coats, ERM family actin regulators, and the WIPI3 autophagy component. The COPII binding site promotes exit from the endoplasmic reticulum, and although binding to COPI should retain S in the early Golgi where viral budding occurs, there is a suboptimal histidine residue in the recognition motif. As a result, S leaks to the surface where it accumulates and can direct the formation of multinucleate syncytia. Thus, the trafficking signals in the tail of S indicate that syncytia play a role in the SARS-CoV-2 lifecycle

Phase diagram of the su(8) quantum spin tube

We calculate the phase diagram of an integrable anisotropic 3-leg quantum spin tube connected to the su(8) algebra. We find several quantum phase transitions for antiferromagnetic rung couplings. Their locations are calculated exactly from the Bethe Ansatz solution and we discuss the nature of each of the different phases.Comment: 10 pages, RevTeX, 1 postscript figur

Arsenite sorption and co-precipitation with calcite

Sorption of As(III) by calcite was investigated as a function of As(III) concentration, time and pH. The sorption isotherm, i.e. the log As(III) vs. log [As(OH)3 degrees / Assat] plot is S-shaped and has been modelled on an extended version of the surface precipitation model. At low concentrations, As(OH)3 degrees is adsorbed by complexation to surface Ca surface sites, as previously described by the X-ray standing wave technique. The inflexion point of the isotherm, where As(OH)3 degrees is limited by the amount of surface sites (ST), yields 6 sites nm-2 in good agreement with crystallographic data. Beyond this value, the amount of sorbed arsenic increases linearly with solution concentration, up to the saturation of arsenic with respect to the precipitation of CaHAsO3(s). The solid solutions formed in this concentration range were examined by X-ray and neutron diffraction. The doped calcite lattice parameters increase with arsenic content while c/a ratio remains constant. Our results made on bulk calcite on the atomic displacement of As atoms along [0001] direction extend those published by Cheng et al., (1999) on calcite surface. This study provides a molecular-level explanation for why As(III) is trapped by calcite in industrial treatments.Comment: 9 page

Multidimensional Dynamics of the Proteome in the Neurodegenerative and Aging Mammalian Brain

Neurodegenerative diseases are characterized by the abnormal accumulation of aggregated proteins in the brain. Using in vivo pulse isotope labeling, we screened the proteome for changes in protein turnover and abundance in multiple mouse models of neurodegeneration. These data suggest that the disease state of pathologically affected tissue is characterized by a proteome-wide increase in protein turnover and repair. In contrast, in healthy wild-type mice, aging in the mammalian brain is associated with a global slowdown in protein turnover.Peer reviewe

An evaluation of GO annotation retrieval for BioCreAtIvE and GOA

from A critical assessment of text mining methods in molecular biolog

SnoopCGH: software for visualizing comparative genomic hybridization data

Summary: Array-based comparative genomic hybridization (CGH) technology is used to discover and validate genomic structural variation, including copy number variants, insertions, deletions and other structural variants (SVs). The visualization and summarization of the array CGH data outputs, potentially across many samples, is an important process in the identification and analysis of SVs. We have developed a software tool for SV analysis using data from array CGH technologies, which is also amenable to short-read sequence data

Note on the thermodynamic Bethe Ansatz approach to the quantum phase diagram of the strong coupling ladder compounds

We investigate the low-temperature phase diagram of the exactly solved su(4) two-leg spin ladder as a function of the rung coupling $J_{\perp}$ and magnetic field $H$ by means of the thermodynamic Bethe Ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases, while in the presence of a strong magnetic field there is no singlet ground state for ferromagnetic rung coupling. For antiferromagnetic rung coupling, there is a gapped phase in the regime H H_{c2} and a Luttinger liquid magnetic phase in the regime H_{c1} < H < H_{c2}. The critical behaviour derived using the TBA is consistent with the existing experimental, numerical and perturbative results for the strong coupling ladder compounds. This includes the spin excitation gap and the critical fields H_{c1} and H_{c2}, which are in excellent agreement with the experimental values for the known strong coupling ladder compounds (5IAP)_2CuBr_4 2H_2 O, Cu_2(C_5 H_{12} N_2)_2 Cl_4 and (C_5 H_{12} N)_2 CuBr_4. In addition we predict the spin gap $\Delta \approx J_{\perp}-{1/2}J_{\parallel}$ for the weak coupling compounds with $J_{\perp} \sim J_{\parallel}$, such as (VO)_2 P_2 O_7, and also show that the gap opens for arbitrary $J_{\perp}/ J_{\parallel}$.Comment: 10 pages, 3 figure

Structural Organization and Dynamics of Homodimeric Cytohesin Family Arf GTPase Exchange Factors in Solution and on Membranes

Membrane dynamic processes require Arf GTPase activation by guanine nucleotide exchange factors (GEFs) with a Sec7 domain. Cytohesin family Arf GEFs function in signaling and cell migration through Arf GTPase activation on the plasma membrane and endosomes. In this study, the structural organization of two cytohesins (Grp1 and ARNO) was investigated in solution by size exclusion-small angle X-ray scattering and negative stain-electron microscopy and on membranes by dynamic light scattering, hydrogen-deuterium exchange-mass spectrometry and guanosine diphosphate (GDP)/guanosine triphosphate (GTP) exchange assays. The results suggest that cytohesins form elongated dimers with a central coiled coil and membrane-binding pleckstrin-homology (PH) domains at opposite ends. The dimers display significant conformational heterogeneity, with a preference for compact to intermediate conformations. Phosphoinositide-dependent membrane recruitment is mediated by one PH domain at a time and alters the conformational dynamics to prime allosteric activation by Arf-GTP. A structural model for membrane targeting and allosteric activation of full-length cytohesin dimers is discussed