Discrete Formulation for the dynamics of rods deforming in space

We describe the main ingredients needed to create, from the smooth lagrangian density, a variational principle for discrete motions of a discrete rod, with corresponding conserved Noether currents. We describe all geometrical objects in terms of elements on the linear Atiyah bundle, using a reduced forward difference operator. We show how this introduces a discrete lagrangian density that models the discrete dynamics of a discrete rod. The presented tools are general enough to represent a discretization of any variational theory in principal bundles, and its simplicity allows to perform an iterative integration algorithm to compute the discrete rod evolution in time, starting from any predefined configurations of all discrete rod elements at initial times

Emitter-site selective photoelectron circular dichroism of trifluoromethyloxirane

The angle-resolved inner-shell photoionization of R-trifluoromethyloxirane, C3H3F3O, is studied experimentally and theoretically. Thereby, we investigate the photoelectron circular dichroism (PECD) for nearly-symmetric O 1s and F 1s electronic orbitals, which are localized on different molecular sites. The respective dichroic $\beta_{1}$ and angular distribution $\beta_{2}$ parameters are measured at the photoelectron kinetic energies from 1 to 16 eV by using variably polarized synchrotron radiation and velocity map imaging spectroscopy. The present experimental results are in good agreement with the outcome of ab initio electronic structure calculations. We report a sizable chiral asymmetry $\beta_{1}$ of up to about 9% for the K-shell photoionization of oxygen atom. For the individual fluorine atoms, the present calculations predict asymmetries of similar size. However, being averaged over all fluorine atoms, it drops down to about 2%, as also observed in the present experiment. Our study demonstrates a strong emitter- and site-sensitivity of PECD in the one-photon inner-shell ionization of this chiral molecule

A New Biology: A Modern Perspective on the Challenge of Closing the Gap between the Islands of Knowledge

This paper discusses the rebirth of the old quest for the principles of biology along the discourse line of machine-organism disanalogy and within the context of biocomputation from a modern perspective. It reviews some new attempts to revise the existing body of research and enhance it with new developments in some promising fields of mathematics and computation. The major challenge is that the latter are expected to also answer the need for a new framework, a new language and a new methodology capable of closing the existing gap between the different levels of complex system organization

MacDowell-Mansouri gravity and Cartan geometry

The geometric content of the MacDowell-Mansouri formulation of general relativity is best understood in terms of Cartan geometry. In particular, Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick of combining the Levi-Civita connection and coframe field, or soldering form, into a single physical field. The Cartan perspective allows us to view physical spacetime as tangentially approximated by an arbitrary homogeneous "model spacetime", including not only the flat Minkowski model, as is implicitly used in standard general relativity, but also de Sitter, anti de Sitter, or other models. A "Cartan connection" gives a prescription for parallel transport from one "tangent model spacetime" to another, along any path, giving a natural interpretation of the MacDowell-Mansouri connection as "rolling" the model spacetime along physical spacetime. I explain Cartan geometry, and "Cartan gauge theory", in which the gauge field is replaced by a Cartan connection. In particular, I discuss MacDowell-Mansouri gravity, as well as its more recent reformulation in terms of BF theory, in the context of Cartan geometry.Comment: 34 pages, 5 figures. v2: many clarifications, typos correcte

Author Correction: CHD3 helicase domain mutations cause a neurodevelopmental syndrome with macrocephaly and impaired speech and language.

© 2019, The Author(s). The original version of this Article contained an error in the spelling of the author Laurence Faivre, which was incorrectly given as Laurence Faive. This has now been corrected in both the PDF and HTML versions of the Article

Isolation, crystallization, and investigation of ribosomal protein S8 complexed with specific fragments of rRNA of bacterial or archaeal origin. Biochemistry 66

Study of the nature of protein-rRNA complexes is a topical problem of modern molecular biology. Structural studies of rRNA-protein complexes are the most direct and precise method of analysis of these interactions. Because ribosomal proteins are most conservative during evolution, their complexes with specific RNA fragments provide an interesting model for studying RNA-protein interactions. Ribosomal protein S8 from E. coli plays a key role in assembling the small ribosomal subunit The major region of protein S8 binding on 16S rRNA was determined by partial hydrolysis with restric tion endonucleases The binding sites of protein S8 on 16S rRNA are similar in E. coli and T. thermophilus. It was shown that ACCELERATED PUBLICATION 0006 2979/01/6609 0948$25.00 ©2001 MAIK "Nauka / Interperiodica" * To whom correspondence should be addressed. Vol. 66, No. 9, 2001, pp. 948 953. Translated from Biokhimiya, Vol. 66, No. 9, 2001, pp. 1165 1171. Original Russian Text Copyright © 2001 Abstract-The core ribosomal protein S8 binds to the central domain of 16S rRNA independently of other ribosomal proteins and is required for assembling the 30S subunit. It has been shown with E. coli ribosomes that a short rRNA fragment restrict ed by nucleotides 588 602 and 636 651 is sufficient for strong and specific protein S8 binding. In this work, we studied the complexes formed by ribosomal protein S8 from Thermus thermophilus and Methanococcus jannaschii with short rRNA frag ments isolated from the same organisms. The dissociation constants of the complexes of protein S8 with rRNA fragments were determined. Based on the results of binding experiments, rRNA fragments of different length were designed and syn thesized in preparative amounts in vitro using T7 RNA polymerase. Stable S8-RNA complexes were crystallized. Crystals were obtained both for homologous bacterial and archaeal complexes and for hybrid complexes of archaeal protein with bac terial rRNA. Crystals of the complex of protein S8 from M. jannaschii with the 37 nucleotide rRNA fragment from the same organism suitable for X ray analysis were obtained

Interatomic and Intermolecular Coulombic Decay

Interatomic or intermolecular Coulombic decay (ICD) is a nonlocal electronic decay mechanism occurring in weakly bound matter. In an ICD process, energy released by electronic relaxation of an excited atom or molecule leads to ionization of a neighboring one via Coulombic electron interactions. ICD has been predicted theoretically in the mid nineties of the last century, and its existence has been confirmed experimentally approximately ten years later. Since then, a number of fundamental and applied aspects have been studied in this quickly growing field of research. This review provides an introduction to ICD and draws the connection to related energy transfer and ionization processes. The theoretical approaches for the description of ICD as well as the experimental techniques developed and employed for its investigation are described. The existing body of literature on experimental and theoretical studies of ICD processes in different atomic and molecular systems is reviewed. © 2020 American Chemical Societ

On the affine group of a normal homogeneous manifold

A very important class of homogeneous Riemannian manifolds are the so-called normal homogeneous spaces, which have associated a canonical connection. In this work we obtain geometrically the (connected component of the) group of affine transformations with respect to the canonical connection for a normal homogeneous space. The naturally reductive case is also treated. This completes the geometric calculation of the isometry group of naturally reductive spaces. In addition, we prove that for normal homogeneous spaces the set of fixed points of the full isotropy is a torus. As an application of our results it follows that the holonomy group of a homogeneous fibration is contained in the group of (canonically) affine transformations of the fibers, in particular this holonomy group is a Lie group (this is a result of Guijarro and Walschap).Comment: Final version to appear in Ann. Global Anal. Geom

Mutation Symmetries in BPS Quiver Theories: Building the BPS Spectra

We study the basic features of BPS quiver mutations in 4D $\mathcal{N}=2$ supersymmetric quantum field theory with $G=ADE$ gauge symmetries.\ We show, for these gauge symmetries, that there is an isotropy group $\mathcal{G}_{Mut}^{G}$ associated to a set of quiver mutations capturing information about the BPS spectra. In the strong coupling limit, it is shown that BPS chambers correspond to finite and closed groupoid orbits with an isotropy symmetry group $\mathcal{G}_{strong}^{G}$ isomorphic to the discrete dihedral groups $Dih_{2h_{G}}$ contained in Coxeter$(G)$ with $$ the Coxeter number of G. These isotropy symmetries allow to determine the BPS spectrum of the strong coupling chamber; and give another way to count the total number of BPS and anti-BPS states of $\mathcal{N}=2$ gauge theories. We also build the matrix realization of these mutation groups $\mathcal{G}_{strong}^{G}$ from which we read directly the electric-magnetic charges of the BPS and anti-BPS states of $\mathcal{N}=2$ QFT$_{4}$ as well as their matrix intersections. We study as well the quiver mutation symmetries in the weak coupling limit and give their links with infinite Coxeter groups. We show amongst others that $\mathcal{G}_{weak}^{su_{2}}$ is contained in ${GL}({2,}\mathbb{Z})$; and isomorphic to the infinite Coxeter ${I_{2}^{\infty}}$. Other issues such as building $\mathcal{G}$ and $\mathcal{G}_{weak}^{su_{3}}$ are also studied.Comment: LaTeX, 98 pages, 18 figures, Appendix I on groupoids adde