In this report, which is an extended version of that appearing in the Proceedings of GR16, I will give a summary of the main topics covered in Session A.3. on mathematical relativity at GR16, Durban. The summary is mainly based on extended abstracts submitted by the speakers. I would like to thank all participants for their contributions and help with this summary. According to a conjecture by ...

Paid Search (PS) ads are one of the main revenue sources of online advertising companies where the goal is returning a set of relevant ads for a searched query in search engine websites such as Bing. Typical PS algorithms, return the ads which their Bided

AIMS This study examined the prevalence of alcohol ads, the spatial relationship between alcohol ads and schools, churches and playgrounds, and area-level determinants of alcohol ad density in Central Harlem, New York City. METHODS Alcohol advertising was quantified using street observation. Data on city demographics and infrastructure were obtained from the census and municipal databases. ...

We calculate the difference of one-loop vacuum energies for massive scalar field in five-dimensional AdS black hole. (The same is done in five-dimensional deSitter space). In each case this difference is specified by the boundary conditions corresponding to the double-trace operator (massive term) and it describes RG flow in the manner discussed by Gubser-Mitra for pure AdS space. For AdS black...

We formulate the variational problem for AdS gravity with Dirichlet boundary conditions and demonstrate that the covariant counterterms are necessary to make the variational problem well-posed. The holographic charges associated with asymptotic symmetries are then rederived via Noether’s theorem and ‘covariant phase space’ techniques. This allows us to prove the first law of black hole mechanic...

This representative study of German search engine users (N=1,000) focuses on the ability of users to distinguish between organic results and advertisements on Google results pages. We combine questions about Google’s business with task-based studies in which users were asked to distinguish between ads and organic results in screenshots of results pages. We find that only a small percentage of u...

I present further analytic time symmetric initial data for five dimensions describing “bubbles of nothing” which have no Kaluza-Klein circle asymptotically. The new solutions consist of a large family of single bubbles in both asymptotically flat and asymptotically AdS space. I also numerically construct gravitational solitons in AdS where the usual boundary conditions are modified geometricall...

The isometries of AdS 5 space and supersymmetric AdS 5 ⊗ S 1 space are non-linearly realized on four dimensional Minkowski space. The resultant effective actions in terms of the Nambu-Goldstone modes are constructed. The dilatonic mode governing the motion of the Minkowski space probe brane into the co-volume of supersymmetric AdS 5 space is found to be unstable and the bulk of the AdS 5 space ...

The Poisson kernels and relations between them for a massive scalar field in a unit ball B with Hua’s metric and conformal flat metric are obtained by describing the B as a submanifold of an (n+1)-dimensional embedding space. Global geometric properties of the AdS space are discussed. We show that the (n+1)-dimensional AdS space AdSn+1 is isomorphic to RP 1 ×Bn and boundary of the AdS is isomor...