Limit curve theorems in Lorentzian geometry

The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the beginning are one, two or at most denumerable. Some applications are considered. It is proved that in chronological spacetimes, strong causality is either everywhere verified or everywhere violated on maximizing lightlike segments with open domain. As a consequence, if in a chronological spacetime two distinct lightlike lines intersect each other then strong causality holds at their points. Finally, it is proved that two distinct components of the chronology violating set have disjoint closures or there is a lightlike line passing through each point of the intersection of the corresponding boundaries.Comment: 25 pages, 1 figure. v2: Misprints fixed, matches published versio

Mean curvature flow and quasilocal mass for two-surfaces in Hamiltonian General Relativity

A family of quasilocal mass definitions that includes as special cases the Hawking mass and the Brown-York ``rest mass'' energy is derived for spacelike 2-surfaces in spacetime. The definitions involve an integral of powers of the norm of the spacetime mean curvature vector of the 2-surface, whose properties are connected with apparent horizons. In particular, for any spacelike 2-surface, the direction of mean curvature is orthogonal (dual in the normal space) to a unique normal direction in which the 2-surface has vanishing expansion in spacetime. The quasilocal mass definitions are obtained by an analysis of boundary terms arising in the gravitational ADM Hamiltonian on hypersurfaces with a spacelike 2-surface boundary, using a geometric time-flow chosen proportional to the dualized mean curvature vector field at the boundary surface. A similar analysis is made choosing a geometric rotational flow given in terms of the twist covector of the dual pair of mean curvature vector fields, which leads to a family of quasilocal angular momentum definitions involving the squared norm of the twist. The large sphere limit of these definitions is shown to yield the ADM mass and angular momentum in asymptotically flat spacetimes, while at apparent horizons a quasilocal version of the Gibbons-Penrose inequality is derived. Finally, some results concerning positivity are proved for the quasilocal masses, motivated by consideration of spacelike mean curvature flow of 2-surfaces in spacetime.Comment: Revised version, includes an analysis of null flows with applications to mass and angular momentum for apparent horizon

Magnification relations for Kerr lensing and testing Cosmic Censorship

A Kerr black hole with mass parameter m and angular momentum parameter a acting as a gravitational lens gives rise to two images in the weak field limit. We study the corresponding magnification relations, namely the signed and absolute magnification sums and the centroid up to post-Newtonian order. We show that there are post-Newtonian corrections to the total absolute magnification and centroid proportional to a/m, which is in contrast to the spherically symmetric case where such corrections vanish. Hence we also propose a new set of lensing observables for the two images involving these corrections, which should allow measuring a/m with gravitational lensing. In fact, the resolution capabilities needed to observe this for the Galactic black hole should in principle be accessible to current and near-future instrumentation. Since a/m >1 indicates a naked singularity, a most interesting application would be a test of the Cosmic Censorship conjecture. The technique used to derive the image properties is based on the degeneracy of the Kerr lens and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple physical explanation for this degeneracy is also given.Comment: 13 pages, version 2: references added, minor changes. To appear in Phys. Rev.

Wave-number Selection by Target Patterns and Side Walls in Rayleigh-Benard Convection

We present experimental results for Rayleigh-Benard convection patterns in a cylindrical container with static side-wall forcing induced by a heater. This forcing stabilized a pattern of concentric rolls (a target pattern) with the central roll (the umbilicus) at the center of the cell after a jump from the conduction to the convection state. A quasi-static increase of the control parameter (epsilon) beyond 0.8 caused the umbilicus of the pattern to move off center. As observed by others, a further quasi-static increase of epsilon up to 15.6 caused a sequence of transitions. Each transition began with the displacement of the umbilicus and then proceeded with the loss of one convection roll at the umbilicus and the return of the umbilicus to a location near the center of the cell. Alternatively, with decreasing epsilon new rolls formed at the umbilicus but large umbilicus displacements did not occur. In addition to quantitative measurements of the umbilicus displacement, we determined and analyzed the entire wave-director field of each image. The wave numbers varied in the axial direction, with minima at the umbilicus and at the cell wall and a maximum at a radial position close to 2/3 Gamma. The wave numbers at the maximum showed hysteretic jumps at the transitions, but on average agreed well with the theoretical predictions for the wave numbers selected in the far field of an infinitely extended target pattern.Comment: ReVTeX, 11 pages, 16 eps figures include

A Semantic Hierarchy for Erasure Policies

We consider the problem of logical data erasure, contrasting with physical erasure in the same way that end-to-end information flow control contrasts with access control. We present a semantic hierarchy for erasure policies, using a possibilistic knowledge-based semantics to define policy satisfaction such that there is an intuitively clear upper bound on what information an erasure policy permits to be retained. Our hierarchy allows a rich class of erasure policies to be expressed, taking account of the power of the attacker, how much information may be retained, and under what conditions it may be retained. While our main aim is to specify erasure policies, the semantic framework allows quite general information-flow policies to be formulated for a variety of semantic notions of secrecy.Comment: 18 pages, ICISS 201

Normal Levels of Sox9 Expression in the Developing Mouse Testis Depend on the TES/TESCO Enhancer, but This Does Not Act Alone

During mouse sex determination, transient expression of the Y-linked gene Sry up-regulates its direct target gene Sox9, via a 3.2 kb testis specific enhancer of Sox9 (TES), which includes a core 1.4 kb element, TESCO. SOX9 activity leads to differentiation of Sertoli cells, rather than granulosa cells from the bipotential supporting cell precursor lineage. Here, we present functional analysis of TES/TESCO, using CRISPR/Cas9 genome editing in mice. Deletion of TESCO or TES reduced Sox9 expression levels in XY fetal gonads to 60 or 45% respectively relative to wild type gonads, and reduced expression of the SOX9 target Amh. Although human patients heterozygous for null mutations in SOX9, which are assumed to have 50% of normal expression, often show XY female sex reversal, mice deleted for one copy of Sox9 do not. Consistent with this, we did not observe sex reversal in either TESCO-/- or TES-/- XY embryos or adult mice. However, embryos carrying both a conditional Sox9 null allele and the TES deletion developed ovotestes. Quantitative analysis of these revealed levels of 23% expression of Sox9 compared to wild type, and a significant increase in the expression of the granulosa cell marker Foxl2. This indicates that the threshold in mice where sex reversal begins to be seen is about half that of the ~50% levels predicted in humans. Our results demonstrate that TES/TESCO is a crucial enhancer regulating Sox9 expression in the gonad, but point to the existence of additional enhancers that act redundantly

Deriving genetic programming fitness properties by static analysis

Deriving Genetic Programming Fitness Properties by Static Analysis Colin G. Johnson The aim of this paper is to introduce the idea of using static analysis of computer programs as a way of measuring fitness in genetic programming. Such techniques extract information about the programs without explicitly running them, and in particular they infer properties which hold across the whole of the input space of a program. This can be applied to measure fitness, and has a number of advantages over measuring fitness by running members of the population on test cases. The most important advantage is that if a solution is found then it is possible to formally trust that solution to be correct across all inputs. This paper introduces these ideas, discusses various ways in which they could be applied, discusses the type of problems for which they are appropriate, and ends by giving a simple test example and some questions for future research

Demography and disorders of the French Bulldog population under primary veterinary care in the UK in 2013

Abstract Background Despite its Gallic name, the French Bulldog is a breed of both British and French origin that was first recognised by The Kennel Club in 1906. The French Bulldog has demonstrated recent rapid rises in Kennel Club registrations and is now (2017) the second most commonly registered pedigree breed in the UK. However, the breed has been reported to be predisposed to several disorders including ocular, respiratory, neurological and dermatological problems. The VetCompass™ Programme collates de-identified clinical data from primary-care veterinary practices in the UK for epidemiological research. Using VetCompass™ clinical data, this study aimed to characterise the demography and common disorders of the general population of French Bulldogs under veterinary care in the UK. Results French Bulldogs comprised 2228 (0.49%) of 445,557 study dogs under veterinary care during 2013. Annual proportional birth rates showed that the proportional ownership of French Bulldog puppies rose steeply from 0.02% of the annual birth cohort attending VetCompass™ practices in 2003 to 1.46% in 2013. The median age of the French Bulldogs overall was 1.3 years (IQR 0.6–2.5, range 0.0–13.0). The most common colours of French Bulldogs were brindle (solid or main) (32.36%) and fawn (solid or main) (29.9%). Of the 2228 French Bulldogs under veterinary care during 2013, 1612 (72.4%) had at least one disorder recorded. The most prevalent fine-level precision disorders recorded were otitis externa (14.0%, 95% CI: 12.6–15.5), diarrhoea (7.5%, 95% CI: 6.4–8.7), conjunctivitis (3.2%, 95% CI: 2.5–4.0), nails overlong (3.1%, 95% CI% 2.4–3.9) and skin fold dermatitis (3.0%, 95% CI% 2.3–3.8). The most prevalent disorder groups were cutaneous (17.9%, 95% CI: 16.3–19.6), enteropathy (16.7%, 95% CI: 15.2–18.3), aural (16.3%, 95% CI: 14.8–17.9), upper respiratory tract (12.7%, 95% CI: 11.3–14.1) and ophthalmological (10.5%, 95% CI: 9.3–11.9). Conclusions Ownership of French Bulldogs in the UK is rising steeply. This means that the disorder profiles reported in this study reflect a current young UK population and are likely to shift as this cohort ages. Otitis externa, diarrhoea and conjunctivitis were the most common disorders in French Bulldogs. Identification of health priorities based on VetCompass™ data can support evidence–based reforms to improve health and welfare within the breed

Integration of the Friedmann equation for universes of arbitrary complexity

An explicit and complete set of constants of the motion are constructed algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models consisting of an arbitrary number of non-interacting species. The inheritance of constants of the motion from simpler models as more species are added is stressed. It is then argued that all FLRW models admit what amounts to a unique candidate for a gravitational epoch function (a dimensionless scalar invariant derivable from the Riemann tensor without differentiation which is monotone throughout the evolution of the universe). The same relations that lead to the construction of constants of the motion allow an explicit evaluation of this function. In the simplest of all models, the $\Lambda$CDM model, it is shown that the epoch function exists for all models with $\Lambda > 0$, but for almost no models with $\Lambda \leq 0$.Comment: Final form to appear in Physical Review D1

Painleve-Gullstrand Coordinates for the Kerr Solution

We construct a coordinate system for the Kerr solution, based on the zero angular momentum observers dropped from infinity, which generalizes the Painleve-Gullstrand coordinate system for the Schwarzschild solution. The Kerr metric can then be interpreted as describing space flowing on a (curved) Riemannian 3-manifold. The stationary limit arises as the set of points on this manifold where the speed of the flow equals the speed of light, and the horizons as the set of points where the radial speed equals the speed of light. A deeper analysis of what is meant by the flow of space reveals that the acceleration of free-falling objects is generally not in the direction of this flow. Finally, we compare the new coordinate system with the closely related Doran coordinate system.Comment: 6 pages; v2: new section, matches final published version; v3: sign error in the expression of the function delta correcte