The tetralogy of Birkhoff theorems

We classify the existent Birkhoff-type theorems into four classes: First, in field theory, the theorem states the absence of helicity 0- and spin 0-parts of the gravitational field. Second, in relativistic astrophysics, it is the statement that the gravitational far-field of a spherically symmetric star carries, apart from its mass, no information about the star; therefore, a radially oscillating star has a static gravitational far-field. Third, in mathematical physics, Birkhoff's theorem reads: up to singular exceptions of measure zero, the spherically symmetric solutions of Einstein's vacuum field equation with Lambda = 0 can be expressed by the Schwarzschild metric; for Lambda unequal 0, it is the Schwarzschild-de Sitter metric instead. Fourth, in differential geometry, any statement of the type: every member of a family of pseudo-Riemannian space-times has more isometries than expected from the original metric ansatz, carries the name Birkhoff-type theorem. Within the fourth of these classes we present some new results with further values of dimension and signature of the related spaces; including them are some counterexamples: families of space-times where no Birkhoff-type theorem is valid. These counterexamples further confirm the conjecture, that the Birkhoff-type theorems have their origin in the property, that the two eigenvalues of the Ricci tensor of two-dimensional pseudo-Riemannian spaces always coincide, a property not having an analogy in higher dimensions. Hence, Birkhoff-type theorems exist only for those physical situations which are reducible to two dimensions.Comment: 26 pages, updated references, minor text changes, accepted by Gen. Relat. Gra

Connectivity independent protein-structure alignment: a hierarchical approach

BACKGROUND: Protein-structure alignment is a fundamental tool to study protein function, evolution and model building. In the last decade several methods for structure alignment were introduced, but most of them ignore that structurally similar proteins can share the same spatial arrangement of secondary structure elements (SSE) but differ in the underlying polypeptide chain connectivity (non-sequential SSE connectivity). RESULTS: We perform protein-structure alignment using a two-level hierarchical approach implemented in the program GANGSTA. On the first level, pair contacts and relative orientations between SSEs (i.e. α-helices and β-strands) are maximized with a genetic algorithm (GA). On the second level residue pair contacts from the best SSE alignments are optimized. We have tested the method on visually optimized structure alignments of protein pairs (pairwise mode) and for database scans. For a given protein structure, our method is able to detect significant structural similarity of functionally important folds with non-sequential SSE connectivity. The performance for structure alignments with strictly sequential SSE connectivity is comparable to that of other structure alignment methods. CONCLUSION: As demonstrated for several applications, GANGSTA finds meaningful protein-structure alignments independent of the SSE connectivity. GANGSTA is able to detect structural similarity of protein folds that are assigned to different superfamilies but nevertheless possess similar structures and perform related functions, even if these proteins differ in SSE connectivity

Homothetic perfect fluid space-times

A brief summary of results on homotheties in General Relativity is given, including general information about space-times admitting an r-parameter group of homothetic transformations for r>2, as well as some specific results on perfect fluids. Attention is then focussed on inhomogeneous models, in particular on those with a homothetic group $H_4$ (acting multiply transitively) and $H_3$. A classification of all possible Lie algebra structures along with (local) coordinate expressions for the metric and homothetic vectors is then provided (irrespectively of the matter content), and some new perfect fluid solutions are given and briefly discussed.Comment: 27 pages, Latex file, Submitted to Class. Quantum Gra

A transposase strategy for creating libraries of circularly permuted proteins

A simple approach for creating libraries of circularly permuted proteins is described that is called PERMutation Using Transposase Engineering (PERMUTE). In PERMUTE, the transposase MuA is used to randomly insert a minitransposon that can function as a protein expression vector into a plasmid that contains the open reading frame (ORF) being permuted. A library of vectors that express different permuted variants of the ORF-encoded protein is created by: (i) using bacteria to select for target vectors that acquire an integrated minitransposon; (ii) excising the ensemble of ORFs that contain an integrated minitransposon from the selected vectors; and (iii) circularizing the ensemble of ORFs containing integrated minitransposons using intramolecular ligation. Construction of a Thermotoga neapolitana adenylate kinase (AK) library using PERMUTE revealed that this approach produces vectors that express circularly permuted proteins with distinct sequence diversity from existing methods. In addition, selection of this library for variants that complement the growth of Escherichia coli with a temperature-sensitive AK identified functional proteins with novel architectures, suggesting that PERMUTE will be useful for the directed evolution of proteins with new functions

Circular Permutation in Proteins

This is a ‘‘Topic Page’ ’ article for PLoS Computational Biology. Circular permutation describes a type of relationship between proteins, whereby the proteins have a changed order of amino acids in their protein sequence, such that the sequence of the first portion of one protein (adjacent to the N-terminus) is related to that of the second portion of the other protein (near its C-terminus), and vice versa (see Figure 1). This is directly analogous to the mathematical notion of a cyclic permutation over the set of residues in a protein. Circular permutation can be the result of evolutionary events, post-translational modifications, or artificially engineered mutations. The result is a protein structure with different connectivity, but overall similar three-dimensional (3D) shape. The homology between portions of the proteins can be established by observing similar sequences between N- and C-terminal portions of the tw

Gravitational-wave research as an emerging field in the Max Planck Society. The long roots of GEO600 and of the Albert Einstein Institute

On the occasion of the 50th anniversary since the beginning of the search for gravitational waves at the Max Planck Society, and in coincidence with the 25th anniversary of the foundation of the Albert Einstein Institute, we explore the interplay between the renaissance of general relativity and the advent of relativistic astrophysics following the German early involvement in gravitational-wave research, to the point when gravitational-wave detection became established by the appearance of full-scale detectors and international collaborations. On the background of the spectacular astrophysical discoveries of the 1960s and the growing role of relativistic astrophysics, Ludwig Biermann and his collaborators at the Max Planck Institute for Astrophysics in Munich became deeply involved in research related to such new horizons. At the end of the 1960s, Joseph Weber's announcements claiming detection of gravitational waves sparked the decisive entry of this group into the field, in parallel with the appointment of the renowned relativist Juergen Ehlers. The Munich area group of Max Planck institutes provided the fertile ground for acquiring a leading position in the 1970s, facilitating the experimental transition from resonant bars towards laser interferometry and its innovation at increasingly large scales, eventually moving to a dedicated site in Hannover in the early 1990s. The Hannover group emphasized perfecting experimental systems at pilot scales, and never developed a full-sized detector, rather joining the LIGO Scientific Collaboration at the end of the century. In parallel, the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) had been founded in Potsdam, and both sites, in Hannover and Potsdam, became a unified entity in the early 2000s and were central contributors to the first detection of gravitational waves in 2015.Comment: 94 pages. Enlarged version including new results from further archival research. A previous version appears as a chapter in the volume The Renaissance of General Relativity in Context, edited by A. Blum, R. Lalli and J. Renn (Boston: Birkhauser, 2020

Wirklichkeitsnahe Behandlung des Torsionsproblems von Stahlbeton- und Spannbetonbauteilen Abschlussbericht zum Forschungsvorhaben

TIB: RN 3064 (48) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman