Ideally embedded space-times

Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we extend the notion of ideal embeddings from Riemannian geometry to the indefinite case. Ideal embeddings are such that the embedded manifold receives the least amount of tension from the surrounding space. Then it is shown that the de Sitter spaces, a Robertson-Walker space-time and some anisotropic perfect fluid metrics can be ideally embedded in a five-dimensional pseudo-Euclidean space.Comment: layout changed and typos corrected; uses revtex

On the embedding of branes in five-dimensional spaces

We investigate the embedding of four-dimensional branes in five-dimensional spaces. We firstly consider the case when the embedding space is a vacuum bulk whose energy-momentum tensor consists of a Dirac delta function with support in the brane. We then consider the embedding in the context of Randall-Sundrum-type models, taking into account $Z_{2}$ symmetry and a cosmological constant. We employ the Campbell-Magaard theorem to construct the embeddings and are led to the conclusion that the content of energy-matter of the brane does not necessarily determine its curvature. Finally, as an application to illustrate our results, we construct the embedding of Minkowski spacetime filled with dust.Comment: 12 pages - REVTEX To appear in Classical and Quantum Gravit

Embeddings in Spacetimes Sourced by Scalar Fields

The extension of the Campbell-Magaard embedding theorem to general relativity with minimally-coupled scalar fields is formulated and proven. The result is applied to the case of a self-interacting scalar field for which new embeddings are found, and to Brans-Dicke theory. The relationship between Campbell-Magaard theorem and the general relativity, Cauchy and initial value problems is outlined.Comment: RevTEX (11 pages)/ To appear in the Journal of Mathematical Physic

Effective Field Equations of Brane-Induced Electromagnetism

Using a covariant embedding formalism, we find the effective field equations for the Electromagnetism that emerge on branes in the context of Dvali-Gabadadze-Porrati (DGP) braneworld scenario. Our treatment is essentially geometrical. We start with Maxwell equations in five-dimensions and project them into an arbitrary brane. The formalism is quite general and allows us to consider curved bulk spaces and curved branes whose tension is not necessarily null. The kinetic electromagnetic term induced on the world volume of the brane, proper of DGP models, is incorporated in this formulation by means of an appropriate match condition. We also give an estimate of each term of the effective field equations and determine the domain in which the four-dimensional Maxwell equations can be recovered in the brane

Understanding signaling cascades in melanoma

Understanding regulatory pathways involved in melanoma development and progression has advanced significantly in recent years. It is now appreciated that melanoma is the result of complex changes in multiple signaling pathways that affect growth control, metabolism, motility and the ability to escape cell death programs. Here we review the major signaling pathways currently known to be deregulated in melanoma with an implication to its development and progression. Among these pathways are Ras, B-Raf, MEK, PTEN, phosphatidylinositol-3 kinase (PI3Ks) and Akt which are constitutively activated in a significant number of melanoma tumors, in most cases due to genomic change. Other pathways discussed in this review include the [Janus kinase/signal transducer and activator of transcription (JAK/STAT), transforming growth factor-beta pathways which are also activated in melanoma, although the underlying mechanism is not yet clear. As a paradigm for remodeled signaling pathways, melanoma also offers a unique opportunity for targeted drug development.Fil: Lopez Bergami, Pablo Roberto. Sanford-burnham Medical Research Institute; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Fitchmann, B. Sanford-burnham Medical Research Institute; Estados UnidosFil: Ronai, Ze´ev. Sanford-burnham Medical Research Institute; Estados Unido

Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces

We study the classical geodesic motions of nonzero rest mass test particles and photons in (3+1+n)- dimensional warped product spaces. An important feature of these spaces is that they allow a natural decoupling between the motions in the (3+1)-dimensional spacetime and those in the extra n dimensions. Using this decoupling and employing phase space analysis we investigate the conditions for confinement of particles and photons to the (3+1)- spacetime submanifold. In addition to providing information regarding the motion of photons, we also show that these motions are not constrained by the value of the extrinsic curvature. We obtain the general conditions for the confinement of geodesics in the case of pseudo-Riemannian manifolds as well as establishing the conditions for the stability of such confinement. These results also generalise a recent result of the authors concerning the embeddings of hypersurfaces with codimension one.Comment: 8 pages, 1 figure. To appear in General Relativity and Gravitation as a contributed paper to Mashhoon Festschrif

Recent advances in understanding Cushing disease: resistance to glucocorticoid negative feedback and somatic USP8 mutations

Cushing’s disease is a rare disease with a characteristic phenotype due to significant hypercortisolism driven by over-secretion of adrenocorticotropic hormone and to high morbidity and mortality if untreated. It is caused by a corticotroph adenoma of the pituitary, but the exact mechanisms leading to tumorigenesis are not clear. Recent advances in molecular biology such as the discovery of somatic mutations of the ubiquitin-specific peptidase 8 (USP8) gene allow new insights into the pathogenesis, which could be translated into exciting and much-needed therapeutic applications

Relativistic quantum clocks

The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories. The results obtained with this clock model in flat spacetime are reviewed, and the problem of generalizing the model to curved spacetime is discussed, before briefly describing an experimental setup which could be used to test of the model. Taking an operationalist view, where time is that which is measured by a clock, we discuss the conclusions that can be drawn from these results, and what clues they contain for a full quantum relativistic theory of time.Comment: 12 pages, 4 figures. Invited contribution for the proceedings for "Workshop on Time in Physics" Zurich 201

The Akt inhibitor KP372-1 suppresses Akt activity and cell proliferation and induces apoptosis in thyroid cancer cells

The phosphatidylinositol 3′ kinase (PI3K)/phosphatase and tensin homologue deleted on chromosome ten/Akt pathway, which is a critical regulator of cell proliferation and survival, is mutated or activated in a wide variety of cancers. Akt appears to be a key central node in this pathway and thus is an attractive target for targeted molecular therapy. We demonstrated that Akt is highly phosphorylated in thyroid cancer cell lines and human thyroid cancer specimens, and hypothesised that KP372-1, an Akt inhibitor, would block signalling through the PI3K pathway and inhibit cell proliferation while inducing apoptosis of thyroid cancer cells. KP372-1 blocked signalling downstream of Akt in thyroid tumour cells, leading to inhibition of cell proliferation and increased apoptosis. As thyroid cancer consistently expresses phosphorylated Akt and KP372-1 effectively blocks Akt signalling, further preclinical evaluation of this compound for treatment of thyroid cancer is warranted