Classification of Generalized Symmetries for the Vacuum Einstein Equations

A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions. To begin, we analyze symmetries that can be built from the metric, curvature, and covariant derivatives of the curvature to any order; these are called natural symmetries and are globally defined on any spacetime manifold. We next classify first-order generalized symmetries, that is, symmetries that depend on the metric and its first derivatives. Finally, using results from the classification of natural symmetries, we reduce the classification of all higher-order generalized symmetries to the first-order case. In each case we find that the generalized symmetries are infinitesimal generalized diffeomorphisms and constant metric scalings. There are no non-trivial conservation laws associated with these symmetries. A novel feature of our analysis is the use of a fundamental set of spinorial coordinates on the infinite jet space of Ricci-flat metrics, which are derived from Penrose's ``exact set of fields'' for the vacuum equations.Comment: 57 pages, plain Te

Results on the Wess-Zumino consistency condition for arbitrary Lie algebras

The so-called covariant Poincare lemma on the induced cohomology of the spacetime exterior derivative in the cohomology of the gauge part of the BRST differential is extended to cover the case of arbitrary, non reductive Lie algebras. As a consequence, the general solution of the Wess-Zumino consistency condition with a non trivial descent can, for arbitrary (super) Lie algebras, be computed in the small algebra of the 1 form potentials, the ghosts and their exterior derivatives. For particular Lie algebras that are the semidirect sum of a semisimple Lie subalgebra with an ideal, a theorem by Hochschild and Serre is used to characterize more precisely the cohomology of the gauge part of the BRST differential in the small algebra. In the case of an abelian ideal, this leads to a complete solution of the Wess-Zumino consistency condition in this space. As an application, the consistent deformations of 2+1 dimensional Chern-Simons theory based on iso(2,1) are rediscussed.Comment: 39 pages Latex file, 1 eps figure, typos and proof of lemma 5 correcte

Potential Conservation Laws

We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially depend on potential variables. This statement provides a significant generalization of results of the recent paper by Bluman, Cheviakov and Ivanova [J. Math. Phys., 2006, V.47, 113505]. Moreover, we present extensions to gauged potential systems, Abelian and general coverings and general foliated systems of differential equations. An example illustrating possible applications of proved statements is considered. A special version of the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are proposed as new tools for the investigation of potential conservation laws.Comment: 36 pages, extended versio

Surface charges and dynamical Killing tensors for higher spin gauge fields in constant curvature spaces

In the context of massless higher spin gauge fields in constant curvature spaces, we compute the surface charges which generalize the electric charge for spin one, the color charges in Yang-Mills theories and the energy-momentum and angular momentum for asymptotically flat gravitational fields. We show that there is a one-to-one map from surface charges onto divergence free Killing tensors. These Killing tensors are computed by relating them to a cohomology group of the first quantized BRST model underlying the Fronsdal action.Comment: 21 pages Latex file, references and comment adde

Asymptotic conservation laws in field theory

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the ADM energy in general relativity.Comment: 13 pages, AMS-TeX, amsppt.sty, revised to give a better exposition (we hope), and to correct some typesetting error

Monoidal closedness of the category of simulations

The category of simulations of nondeterministic dynamical systems is shown to be symmetric monoidal closed category with a subobject classi­fyer. (AMS Classification:18Dl5,68Ql0,03F50

Characteristic cohomology of pp-form gauge theories

The characteristic cohomology $H^k_{char}(d)$ for an arbitrary set of free $p$-form gauge fields is explicitly worked out in all form degrees $k<n-1$, where $n$ is the spacetime dimension. It is shown that this cohomology is finite-dimensional and completely generated by the forms dual to the field strengths. The gauge invariant characteristic cohomology is also computed. The results are extended to interacting $p$-form gauge theories with gauge invariant interactions. Implications for the BRST cohomology are mentioned.Comment: Latex file, no figures, 44 page

Deductive hyperdigraphs - a method of describing diversity of coherences

The main purpose of this paper is to introduce several graphical methods of describing deductive hyperdigraphs and explains its sig­nificance for description of complex systems

MLN64 Transport to the Late Endosome Is Regulated by Binding to 14-3-3 via a Non-canonical Binding Site

MLN64 is an integral membrane protein localized to the late endosome and plasma membrane that is thought to function as a mediator of cholesterol transport from endosomal membranes to the plasma membrane and/or mitochondria. The protein consists of two distinct domains: an N-terminal membrane-spanning domain that shares homology with the MENTHO protein and a C-terminal steroidogenic acute regulatory protein (StAR)-related lipid transfer (START) domain that binds cholesterol. To further characterize the MLN64 protein, full-length and truncated proteins were overexpressed in cells and the effects on MLN64 trafficking and endosomal morphology were observed. To gain insight into MLN64 function, affinity chromatography and mass spectrometric techniques were used to identify potential MLN64 interacting partners. Of the 15 candidate proteins identified, 14-3-3 was chosen for further characterization. We show that MLN64 interacts with 14-3-3 in vitro as well as in vivo and that the strength of the interaction is dependent on the 14-3-3 isoform. Furthermore, blocking the interaction through the use of a 14-3-3 antagonist or MLN64 mutagenesis delays the trafficking of MLN64 to the late endosome and also results in the dispersal of endocytic vesicles to the cell periphery. Taken together, these studies have determined that MLN64 is a novel 14-3-3 binding protein and indicate that 14-3-3 plays a role in the endosomal trafficking of MLN64. Furthermore, these studies suggest that 14-3-3 may be the link by which MLN64 exerts its effects on the actin-mediated endosome dynamics

VASP: A Volumetric Analysis of Surface Properties Yields Insights into Protein-Ligand Binding Specificity

Many algorithms that compare protein structures can reveal similarities that suggest related biological functions, even at great evolutionary distances. Proteins with related function often exhibit differences in binding specificity, but few algorithms identify structural variations that effect specificity. To address this problem, we describe the Volumetric Analysis of Surface Properties (VASP), a novel volumetric analysis tool for the comparison of binding sites in aligned protein structures. VASP uses solid volumes to represent protein shape and the shape of surface cavities, clefts and tunnels that are defined with other methods. Our approach, inspired by techniques from constructive solid geometry, enables the isolation of volumetrically conserved and variable regions within three dimensionally superposed volumes. We applied VASP to compute a comparative volumetric analysis of the ligand binding sites formed by members of the steroidogenic acute regulatory protein (StAR)-related lipid transfer (START) domains and the serine proteases. Within both families, VASP isolated individual amino acids that create structural differences between ligand binding cavities that are known to influence differences in binding specificity. Also, VASP isolated cavity subregions that differ between ligand binding cavities which are essential for differences in binding specificity. As such, VASP should prove a valuable tool in the study of protein-ligand binding specificity