Supersymmetric Reciprocal Transformation and Its Applications

The supersymmetric analog of the reciprocal transformation is introduced. This is used to establish a transformation between one of the supersymmetric Harry Dym equations and the supersymmetric modified Korteweg-de Vries equation. The reciprocal transformation, as a B\"{a}cklund-type transformation between these two equations, is adopted to construct a recursion operator of the supersymmetric Harry Dym equation. By proper factorization of the recursion operator, a bi-Hamiltonian structure is found for the supersymmetric Harry Dym equation. Furthermore, a supersymmetric Kawamoto equation is proposed and is associated to the supersymmetric Sawada-Kotera equation. The recursion operator and odd bi-Hamiltonian structure of the supersymmetric Kawamoto equation are also constructed.Comment: 31 pages, expande

On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach

A gradient-holonomic approach for the Lax type integrability analysis of differentialdiscrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied, the related gradient identity is stated. The integrability of a discrete nonlinear Schredinger type dynamical system is treated in detail.Comment: 20 page

Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.Comment: 11 page

Studying the photometric and spectroscopic variability of the magnetic hot supergiant ζ\zeta Orionis Aa

Massive stars play a significant role in the chemical and dynamical evolution of galaxies. However, much of their variability, particularly during their evolved supergiant stage, is poorly understood. To understand the variability of evolved massive stars in more detail, we present a study of the O9.2Ib supergiant $\zeta$ Ori Aa, the only currently confirmed supergiant to host a magnetic field. We have obtained two-color space-based BRIght Target Explorer photometry (BRITE) for $\zeta$ Ori Aa during two observing campaigns, as well as simultaneous ground-based, high-resolution optical CHIRON spectroscopy. We perform a detailed frequency analysis to detect and characterize the star's periodic variability. We detect two significant, independent frequencies, their higher harmonics, and combination frequencies: the stellar rotation period $P_{\mathrm{rot}} = 6.82\pm0.18$ d, most likely related to the presence of the stable magnetic poles, and a variation with a period of $10.0\pm0.3$ d attributed to circumstellar environment, also detected in the H$\alpha$ and several He I lines, yet absent in the purely photospheric lines. We confirm the variability with $P_{\mathrm{rot}}$/4, likely caused by surface inhomogeneities, being the possible photospheric drivers of the discrete absorption components. No stellar pulsations were detected in the data. The level of circumstellar activity clearly differs between the two BRITE observing campaigns. We demonstrate that $\zeta$ Ori Aa is a highly variable star with both periodic and non-periodic variations, as well as episodic events. The rotation period we determined agrees well with the spectropolarimetric value from the literature. The changing activity level observed with BRITE could explain why the rotational modulation of the magnetic measurements was not clearly detected at all epochs.Comment: 20 pages, 5 tables, 12 figures, accepted for publication in A&

Enabling large-scale design, synthesis and validation of small molecule protein-protein antagonists

Although there is no shortage of potential drug targets, there are only a handful known low-molecular-weight inhibitors of protein-protein interactions (PPIs). One problem is that current efforts are dominated by low-yield high-throughput screening, whose rigid framework is not suitable for the diverse chemotypes present in PPIs. Here, we developed a novel pharmacophore-based interactive screening technology that builds on the role anchor residues, or deeply buried hot spots, have in PPIs, and redesigns these entry points with anchor-biased virtual multicomponent reactions, delivering tens of millions of readily synthesizable novel compounds. Application of this approach to the MDM2/p53 cancer target led to high hit rates, resulting in a large and diverse set of confirmed inhibitors, and co-crystal structures validate the designed compounds. Our unique open-access technology promises to expand chemical space and the exploration of the human interactome by leveraging in-house small-scale assays and user-friendly chemistry to rationally design ligands for PPIs with known structure. © 2012 Koes et al

Characterization of SARS-CoV-2 replication complex elongation and proofreading activity

The replication complex (RC) of SARS-CoV-2 was recently shown to be one of the fastest RNA-dependent RNA polymerases of any known coronavirus. With this rapid elongation, the RC is more prone to incorporate mismatches during elongation, resulting in a highly variable genomic sequence. Such mutations render the design of viral protein targets difficult, as drugs optimized for a given viral protein sequence can quickly become inefficient as the genomic sequence evolves. Here, we use biochemical experiments to characterize features of RNA template recognition and elongation fidelity of the SARS-CoV-2 RdRp, and the role of the exonuclease, nsp14. Our study highlights the 2′OH group of the RNA ribose as a critical component for RdRp template recognition and elongation. We show that RdRp fidelity is reduced in the presence of the 3′ deoxy-terminator nucleotide 3′dATP, which promotes the incorporation of mismatched nucleotides (leading to U:C, U:G, U:U, C:U, and A:C base pairs). We find that the nsp10–nsp14 heterodimer is unable to degrade RNA products lacking free 2′OH or 3′OH ribose groups. Our results suggest the potential use of 3′ deoxy-terminator nucleotides in RNA-derived oligonucleotide inhibitors as antivirals against SARS-CoV-2

Supersymmetric Moyal-Lax Representations

The super Moyal-Lax representation and the super Moyal momentum algebra are introduced and the properties of simple and extended supersymmetric integrable models are systematically investigated. It is shown that, much like in the bosonic cases, the super Moyal-Lax equation can be interpreted as a Hamiltonian equation and can be derived from an action. Similarly, we show that the parameter of non-commutativity, in this case, is related to the central charge of the second Hamiltonian structure of the system. The super Moyal-Lax description allows us to go to the dispersionless limit of these models in a singular limit and we discuss some of the properties of such systems.Comment: 16 page

Catalogue of BRITE-Constellation targets I. Fields 1 to 14 (November 2013 - April 2016)

The BRIght Target Explorer (BRITE) mission collects photometric time series in two passbands aiming to investigate stellar structure and evolution. Since their launches in the years 2013 and 2014, the constellation of five BRITE nano-satellites has observed a total of more than 700 individual bright stars in 64 fields. Some targets have been observed multiple times. Thus, the total time base of the data sets acquired for those stars can be as long as nine years. Our aim is to provide a complete description of ready-to-use BRITE data, to show the scientific potential of the BRITE-Constellation data by identifying the most interesting targets, and to demonstrate and encourage how scientists can use these data in their research. We apply a decorrelation process to the automatically reduced BRITE-Constellation data to correct for instrumental effects. We perform a statistical analysis of the light curves obtained for the 300 stars observed in the first 14 fields during the first ~2.5 years of the mission. We also perform cross-identification with the International Variable Star Index. We present the data obtained by the BRITE-Constellation mission in the first 14 fields it observed from November 2013 to April 2016. We also describe the properties of the data for these fields and the 300 stars observed in them. Using these data, we detected variability in 64% of the presented sample of stars. Sixty-four stars or 21.3% of the sample have not yet been identified as variable in the literature and their data have not been analysed in detail. They can therefore provide valuable scientific material for further research. All data are made publicly available through the BRITE Public Data Archive and the Canadian Astronomy Data Centre.Comment: accepted by Astronomy & Astrophysics, 13 pages main text, 22 pages of appendi

The c-Myc Target Glycoprotein1bα Links Cytokinesis Failure to Oncogenic Signal Transduction Pathways in Cultured Human Cells

An increase in chromosome number, or polyploidization, is associated with a variety of biological changes including breeding of cereal crops and flowers, terminal differentiation of specialized cells such as megakaryocytes, cellular stress and oncogenic transformation. Yet it remains unclear how cells tolerate the major changes in gene expression, chromatin organization and chromosome segregation that invariably accompany polyploidization. We show here that cancer cells can initiate increases in chromosome number by inhibiting cell division through activation of glycoprotein1b alpha (GpIbα), a component of the c-Myc signaling pathway. We are able to recapitulate cytokinesis failure in primary cells by overexpression of GpIbα in a p53-deficient background. GpIbα was found to localize to the cleavage furrow by microscopy analysis and, when overexpressed, to interfere with assembly of the cellular cortical contraction apparatus and normal division. These results indicate that cytokinesis failure and tetraploidy in cancer cells are directly linked to cellular hyperproliferation via c-Myc induced overexpression of GpIbα