Magnetic Surfaces in Stationary Axisymmetric General Relativity

In this paper a new method is derived for constructing electromagnetic surface sources for stationary axisymmetric electrovac spacetimes endowed with non-smooth or even discontinuous Ernst potentials. This can be viewed as a generalization of some classical potential theory results, since lack of continuity of the potential is related to dipole density and lack of smoothness, to monopole density. In particular this approach is useful for constructing the dipole source for the magnetic field. This formalism involves solving a linear elliptic differential equation with boundary conditions at infinity. As an example, two different models of surface densities for the Kerr-Newman electrovac spacetime are derived.Comment: 15 page

Color My World: Deterministic Tagging for Memory Safety

Hardware-assisted memory protection features are increasingly being deployed in COTS processors. ARMv8.5 Memory Tagging Extensions (MTE) is a recent example, which has been used to provide probabilistic checks for memory safety. This use of MTE is not secure against the standard adversary with arbitrary read/write access to memory. Consequently MTE is used as a software development tool. In this paper we present the first design for deterministic memory protection using MTE that can resist the standard adversary, and hence is suitable for post-deployment memory safety. We describe our compiler extensions for LLVM Clang implementing static analysis and subsequent MTE instrumentation. Via a comprehensive evaluation we show that our scheme is effective

New Techniques for Analysing Axisymmetric Gravitational Systems. 1. Vacuum Fields

A new framework for analysing the gravitational fields in a stationary, axisymmetric configuration is introduced. The method is used to construct a complete set of field equations for the vacuum region outside a rotating source. These equations are under-determined. Restricting the Weyl tensor to type D produces a set of equations which can be solved, and a range of new techniques are introduced to simplify the problem. Imposing the further condition that the solution is asymptotically flat yields the Kerr solution uniquely. The implications of this result for the no-hair theorem are discussed. The techniques developed here have many other applications, which are described in the conclusions.Comment: 30 pages, no figure

On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories

The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between k-symplectic field theories and the so-called autonomous k-cosymplectic field theories, extending in this way the description of the symplectic formalism of autonomous systems as a particular case of the cosymplectic formalism in non-autonomous mechanics. Furthermore, we clarify some aspects of the geometric character of the solutions to the Hamilton-de Donder-Weyl and the Euler-Lagrange equations in these formalisms. Second, we study the equivalence between k-cosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangian field theories (those where the configuration bundle of the theory is trivial).Comment: 25 page

T-Duality and Penrose limits of spatially homogeneous and inhomogeneous cosmologies

Penrose limits of inhomogeneous cosmologies admitting two abelian Killing vectors and their abelian T-duals are found in general. The wave profiles of the resulting plane waves are given for particular solutions. Abelian and non-abelian T-duality are used as solution generating techniques. Furthermore, it is found that unlike in the case of abelian T-duality, non-abelian T-duality and taking the Penrose limit are not commutative procedures.Comment: 16 pages, 4 figures. Discussion on non-abelian T-duality expande

Singularity free dilaton-driven cosmologies and pre-little-bang

There are no reasons why the singularity in the growth of the dilaton coupling should not be regularised, in a string cosmological context, by the presence of classical inhomogeneities. We discuss a class of inhomogeneous dilaton-driven models whose curvature invariants are all bounded and regular in time and space. We prove that the non-space-like geodesics of these models are all complete in the sense that none of them reaches infinity for a finite value of the affine parameter. We conclude that our examples represent truly singularity-free solutions of the low energy beta functions. We discuss some symmetries of the obtained solutions and we clarify their physical interpretation. We also give examples of solutions with spherical symmetry. In our scenario each physical quantity is everywhere defined in time and space, the big-bang singularity is replaced by a maximal curvature phase where the dilaton kinetic energy reaches its maximum. The maximal curvature is always smaller than one (in string units) and the coupling constant is also smaller than one and it grows between two regimes of constant dilaton, implying, together with the symmetries of the solutions, that higher genus and higher curvature corrections are negligible. We argue that our examples describe, in a string cosmological context, the occurrence of ``little bangs''(i.e. high curvature phases which never develop physical singularities). They also suggest the possibility of an unexplored ``pre-little-bang'' phase.Comment: 25 pages in LaTex style, 3 encapsulated figure

Lower-order ODEs to determine new twisting type N Einstein spaces via CR geometry

In the search for vacuum solutions, with or without a cosmological constant, of the Einstein field equations of Petrov type N with twisting principal null directions, the CR structures to describe the parameter space for a congruence of such null vectors provide a very useful tool. A work of Hill, Lewandowski and Nurowski has given a good foundation for this, reducing the field equations to a set of differential equations for two functions, one real, one complex, of three variables. Under the assumption of the existence of one Killing vector, the (infinite-dimensional) classical symmetries of those equations are determined and group-invariant solutions are considered. This results in a single ODE of the third order which may easily be reduced to one of the second order. A one-parameter class of power series solutions, g(w), of this second-order equation is realized, holomorphic in a neighborhood of the origin and behaving asymptotically as a simple quadratic function plus lower-order terms for large values of w, which constitutes new solutions of the twisting type N problem. The solution found by Leroy, and also by Nurowski, is shown to be a special case in this class. Cartan's method for determining equivalence of CR manifolds is used to show that this class is indeed much more general. In addition, for a special choice of a parameter, this ODE may be integrated once, to provide a first-order Abel equation. It can also determine new solutions to the field equations although no general solution has yet been found for it.Comment: 28 page

Programmable in situ amplification for multiplexed imaging of mRNA expression

In situ hybridization methods enable the mapping of mRNA expression within intact biological samples. With current approaches, it is challenging to simultaneously map multiple target mRNAs within whole-mount vertebrate embryos, representing a significant limitation in attempting to study interacting regulatory elements in systems most relevant to human development and disease. Here, we report a multiplexed fluorescent in situ hybridization method based on orthogonal amplification with hybridization chain reactions (HCR). With this approach, RNA probes complementary to mRNA targets trigger chain reactions in which fluorophore-labeled RNA hairpins self-assemble into tethered fluorescent amplification polymers. The programmability and sequence specificity of these amplification cascades enable multiple HCR amplifiers to operate orthogonally at the same time in the same sample. Robust performance is achieved when imaging five target mRNAs simultaneously in fixed whole-mount and sectioned zebrafish embryos. HCR amplifiers exhibit deep sample penetration, high signal-to-background ratios and sharp signal localization

Effects of Subthalamic Nucleus Lesions and Stimulation upon Corticostriatal Afferents in the 6-Hydroxydopamine-Lesioned Rat

Abnormalities of striatal glutamate neurotransmission may play a role in the pathophysiology of Parkinson's disease and may respond to neurosurgical interventions, specifically stimulation or lesioning of the subthalamic nucleus (STN). The major glutamatergic afferent pathways to the striatum are from the cortex and thalamus, and are thus likely to be sources of striatal neuronally-released glutamate. Corticostriatal terminals can be distinguished within the striatum at the electron microscopic level as their synaptic vesicles contain the vesicular glutamate transporter, VGLUT1. The majority of terminals which are immunolabeled for glutamate but are not VGLUT1 positive are likely to be thalamostriatal afferents. We compared the effects of short term, high frequency, STN stimulation and lesioning in 6-hydroxydopamine (6OHDA)-lesioned rats upon striatal terminals immunolabeled for both presynaptic glutamate and VGLUT1. 6OHDA lesions resulted in a small but significant increase in the proportions of VGLUT1-labeled terminals making synapses on dendritic shafts rather than spines. STN stimulation for one hour, but not STN lesions, increased the proportion of synapses upon spines. The density of presynaptic glutamate immuno-gold labeling was unchanged in both VGLUT1-labeled and -unlabeled terminals in 6OHDA-lesioned rats compared to controls. Rats with 6OHDA lesions+STN stimulation showed a decrease in nerve terminal glutamate immuno-gold labeling in both VGLUT1-labeled and -unlabeled terminals. STN lesions resulted in a significant decrease in the density of presynaptic immuno-gold-labeled glutamate only in VGLUT1-labeled terminals. STN interventions may achieve at least part of their therapeutic effect in PD by normalizing the location of corticostriatal glutamatergic terminals and by altering striatal glutamatergic neurotransmission