Mass and Angular Momentum in General Relativity

We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without symmetries, we focus on the discussion of energy-momentum for the gravitational field. We illustrate the difficulties rooted in the Equivalence Principle for defining a local energy-momentum density for the gravitational field. This leads to the understanding of gravitational energy-momentum and angular momentum as non-local observables that make sense, at best, for extended domains of spacetime. After introducing Komar quantities associated with spacetime symmetries, it is shown how total energy-momentum can be unambiguously defined for isolated systems, providing fundamental tests for the internal consistency of General Relativity as well as setting the conceptual basis for the understanding of energy loss by gravitational radiation. Finally, several attempts to formulate quasi-local notions of mass and angular momentum associated with extended but finite spacetime domains are presented, together with some illustrations of the relations between total and quasi-local quantities in the particular context of black hole spacetimes. This article is not intended to be a rigorous and exhaustive review of the subject, but rather an invitation to the topic for non-experts. In this sense we follow essentially the expositions in Szabados 2004, Gourgoulhon 2007, Poisson 2004 and Wald 84, and refer the reader interested in further developments to the existing literature, in particular to the excellent and comprehensive review by Szabados (2004).Comment: 41 pages. Notes based on the lecture given at the C.N.R.S. "School on Mass" (June 2008) in Orleans, France. To appear as proceedings in the book "Mass and Motion in General Relativity", eds. L. Blanchet, A. Spallicci and B. Whiting. Some comments and references added

The Moore-Penrose Pseudoinverse. A Tutorial Review of the Theory

In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the solution of linear integral equations, etc. The existence of such applications alone should attract the interest of students and researchers in the Moore-Penrose pseudoinverse and in related sub jects, like the singular values decomposition theorem for matrices. In this note we present a tutorial review of the theory of the Moore-Penrose pseudoinverse. We present the first definitions and some motivations and, after obtaining some basic results, we center our discussion on the Spectral Theorem and present an algorithmically simple expression for the computation of the Moore-Penrose pseudoinverse of a given matrix. We do not claim originality of the results. We rather intend to present a complete and self-contained tutorial review, useful for those more devoted to applications, for those more theoretically oriented and for those who already have some working knowledge of the sub ject.Comment: 23 page

Stationary Black Holes: Uniqueness and Beyond

The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.Comment: Major update of the original version by Markus Heusler from 1998. Piotr T. Chru\'sciel and Jo\~ao Lopes Costa succeeded to this review's authorship. Significantly restructured and updated all sections; changes are too numerous to be usefully described here. The number of references increased from 186 to 32

The Postcranial Skeleton of an Exceptionally Complete Individual of the Plated Dinosaur Stegosaurus stenops (Dinosauria: Thyreophora) from the Upper Jurassic Morrison Formation of Wyoming, U.S.A.

Copyright: © 2015 Maidment et al. This is an open access article distributed under the terms of the Creative Commons Attribution License [4.0], which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The attached file is the published version of the article

In vivo magnetic resonance spectroscopy: basic methodology and clinical applications

The clinical use of in vivo magnetic resonance spectroscopy (MRS) has been limited for a long time, mainly due to its low sensitivity. However, with the advent of clinical MR systems with higher magnetic field strengths such as 3 Tesla, the development of better coils, and the design of optimized radio-frequency pulses, sensitivity has been considerably improved. Therefore, in vivo MRS has become a technique that is routinely used more and more in the clinic. In this review, the basic methodology of in vivo MRS is described—mainly focused on 1H MRS of the brain—with attention to hardware requirements, patient safety, acquisition methods, data post-processing, and quantification. Furthermore, examples of clinical applications of in vivo brain MRS in two interesting fields are described. First, together with a description of the major resonances present in brain MR spectra, several examples are presented of deviations from the normal spectral pattern associated with inborn errors of metabolism. Second, through examples of MR spectra of brain tumors, it is shown that MRS can play an important role in oncology

Burst-Time-Dependent Plasticity Robustly Guides ON/OFF Segregation in the Lateral Geniculate Nucleus

Spontaneous retinal activity (known as “waves”) remodels synaptic connectivity to the lateral geniculate nucleus (LGN) during development. Analysis of retinal waves recorded with multielectrode arrays in mouse suggested that a cue for the segregation of functionally distinct (ON and OFF) retinal ganglion cells (RGCs) in the LGN may be a desynchronization in their firing, where ON cells precede OFF cells by one second. Using the recorded retinal waves as input, with two different modeling approaches we explore timing-based plasticity rules for the evolution of synaptic weights to identify key features underlying ON/OFF segregation. First, we analytically derive a linear model for the evolution of ON and OFF weights, to understand how synaptic plasticity rules extract input firing properties to guide segregation. Second, we simulate postsynaptic activity with a nonlinear integrate-and-fire model to compare findings with the linear model. We find that spike-time-dependent plasticity, which modifies synaptic weights based on millisecond-long timing and order of pre- and postsynaptic spikes, fails to segregate ON and OFF retinal inputs in the absence of normalization. Implementing homeostatic mechanisms results in segregation, but only with carefully-tuned parameters. Furthermore, extending spike integration timescales to match the second-long input correlation timescales always leads to ON segregation because ON cells fire before OFF cells. We show that burst-time-dependent plasticity can robustly guide ON/OFF segregation in the LGN without normalization, by integrating pre- and postsynaptic bursts irrespective of their firing order and over second-long timescales. We predict that an LGN neuron will become ON- or OFF-responsive based on a local competition of the firing patterns of neighboring RGCs connecting to it. Finally, we demonstrate consistency with ON/OFF segregation in ferret, despite differences in the firing properties of retinal waves. Our model suggests that diverse input statistics of retinal waves can be robustly interpreted by a burst-based rule, which underlies retinogeniculate plasticity across different species

Structure of S. aureus HPPK and the Discovery of a New Substrate Site Inhibitor

The first structural and biophysical data on the folate biosynthesis pathway enzyme and drug target, 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (SaHPPK), from the pathogen Staphylococcus aureus is presented. HPPK is the second essential enzyme in the pathway catalysing the pyrophosphoryl transfer from cofactor (ATP) to the substrate (6-hydroxymethyl-7,8-dihydropterin, HMDP). In-silico screening identified 8-mercaptoguanine which was shown to bind with an equilibrium dissociation constant, Kd, of ∼13 µM as measured by isothermal titration calorimetry (ITC) and surface plasmon resonance (SPR). An IC50 of ∼41 µM was determined by means of a luminescent kinase assay. In contrast to the biological substrate, the inhibitor has no requirement for magnesium or the ATP cofactor for competitive binding to the substrate site. The 1.65 Å resolution crystal structure of the inhibited complex showed that it binds in the pterin site and shares many of the key intermolecular interactions of the substrate. Chemical shift and 15N heteronuclear NMR measurements reveal that the fast motion of the pterin-binding loop (L2) is partially dampened in the SaHPPK/HMDP/α,β-methylene adenosine 5′-triphosphate (AMPCPP) ternary complex, but the ATP loop (L3) remains mobile on the µs-ms timescale. In contrast, for the SaHPPK/8-mercaptoguanine/AMPCPP ternary complex, the loop L2 becomes rigid on the fast timescale and the L3 loop also becomes more ordered – an observation that correlates with the large entropic penalty associated with inhibitor binding as revealed by ITC. NMR data, including 15N-1H residual dipolar coupling measurements, indicate that the sulfur atom in the inhibitor is important for stabilizing and restricting important motions of the L2 and L3 catalytic loops in the inhibited ternary complex. This work describes a comprehensive analysis of a new HPPK inhibitor, and may provide a foundation for the development of novel antimicrobials targeting the folate biosynthetic pathway

Arabidopsis Homologs of Retinoblastoma-Associated Protein 46/48 Associate with a Histone Deacetylase to Act Redundantly in Chromatin Silencing

RNA molecules such as small-interfering RNAs (siRNAs) and antisense RNAs (asRNAs) trigger chromatin silencing of target loci. In the model plant Arabidopsis, RNA–triggered chromatin silencing involves repressive histone modifications such as histone deacetylation, histone H3 lysine-9 methylation, and H3 lysine-27 monomethylation. Here, we report that two Arabidopsis homologs of the human histone-binding proteins Retinoblastoma-Associated Protein 46/48 (RbAp46/48), known as MSI4 (or FVE) and MSI5, function in partial redundancy in chromatin silencing of various loci targeted by siRNAs or asRNAs. We show that MSI5 acts in partial redundancy with FVE to silence FLOWERING LOCUS C (FLC), which is a crucial floral repressor subject to asRNA–mediated silencing, FLC homologs, and other loci including transposable and repetitive elements which are targets of siRNA–directed DNA Methylation (RdDM). Both FVE and MSI5 associate with HISTONE DEACETYLASE 6 (HDA6) to form complexes and directly interact with the target loci, leading to histone deacetylation and transcriptional silencing. In addition, these two genes function in de novo CHH (H = A, T, or C) methylation and maintenance of symmetric cytosine methylation (mainly CHG methylation) at endogenous RdDM target loci, and they are also required for establishment of cytosine methylation in the previously unmethylated sequences directed by the RdDM pathway. This reveals an important functional divergence of the plant RbAp46/48 relatives from animal counterparts

Single-copy nuclear genes resolve the phylogeny of the holometabolous insects

Background: Evolutionary relationships among the 11 extant orders of insects that undergo complete metamorphosis, called Holometabola, remain either unresolved or contentious, but are extremely important as a context for accurate comparative biology of insect model organisms. The most phylogenetically enigmatic holometabolan insects are Strepsiptera or twisted wing parasites, whose evolutionary relationship to any other insect order is unconfirmed. They have been controversially proposed as the closest relatives of the flies, based on rDNA, and a possible homeotic transformation in the common ancestor of both groups that would make the reduced forewings of Strepsiptera homologous to the reduced hindwings of Diptera. Here we present evidence from nucleotide sequences of six single-copy nuclear protein coding genes used to reconstruct phylogenetic relationships and estimate evolutionary divergence times for all holometabolan orders. Results: Our results strongly support Hymenoptera as the earliest branching holometabolan lineage, the monophyly of the extant orders, including the fleas, and traditionally recognized groupings of Neuropteroidea and Mecopterida. Most significantly, we find strong support for a close relationship between Coleoptera (beetles) and Strepsiptera, a previously proposed, but analytically controversial relationship. Exploratory analyses reveal that this relationship cannot be explained by long-branch attraction or other systematic biases. Bayesian divergence times analysis, with reference to specific fossil constraints, places the origin of Holometabola in the Carboniferous (355 Ma), a date significantly older than previous paleontological and morphological phylogenetic reconstructions. The origin and diversification of most extant insect orders began in the Triassic, but flourished in the Jurassic, with multiple adaptive radiations producing the astounding diversity of insect species for which these groups are so well known. Conclusion: These findings provide the most complete evolutionary framework for future comparative studies on holometabolous model organisms and contribute strong evidence for the resolution of the 'Strepsiptera problem', a long-standing and hotly debated issue in insect phylogenetics

A New Basal Sauropod Dinosaur from the Middle Jurassic of Niger and the Early Evolution of Sauropoda

The early evolution of sauropod dinosaurs is poorly understood because of a highly incomplete fossil record. New discoveries of Early and Middle Jurassic sauropods have a great potential to lead to a better understanding of early sauropod evolution and to reevaluate the patterns of sauropod diversification.A new sauropod from the Middle Jurassic of Niger, Spinophorosaurus nigerensis n. gen. et sp., is the most complete basal sauropod currently known. The taxon shares many anatomical characters with Middle Jurassic East Asian sauropods, while it is strongly dissimilar to Lower and Middle Jurassic South American and Indian forms. A possible explanation for this pattern is a separation of Laurasian and South Gondwanan Middle Jurassic sauropod faunas by geographic barriers. Integration of phylogenetic analyses and paleogeographic data reveals congruence between early sauropod evolution and hypotheses about Jurassic paleoclimate and phytogeography.Spinophorosaurus demonstrates that many putatively derived characters of Middle Jurassic East Asian sauropods are plesiomorphic for eusauropods, while South Gondwanan eusauropods may represent a specialized line. The anatomy of Spinophorosaurus indicates that key innovations in Jurassic sauropod evolution might have taken place in North Africa, an area close to the equator with summer-wet climate at that time. Jurassic climatic zones and phytogeography possibly controlled early sauropod diversification