Evolving Lorentzian Wormholes

Evolving Lorentzian wormholes with the required matter satisfying the Energy conditions are discussed. Several different scale factors are used and the corresponding consequences derived. The effect of extra, decaying (in time) compact dimensions present in the wormhole metric is also explored and certain interesting conclusions are derived for the cases of exponential and Kaluza--Klein inflation.Comment: 10 pages( RevTex, Twocolumn format), Two figures available on request from the first author. transmission errors corrected

Management of non-visualization following dynamic sentinel lymph node biopsy for squamous cell carcinoma of the penis

Objectives: To review the management and clinical outcomes of uni- or bilateral non-visualization of inguinal lymph nodes during dynamic sentinel lymph node biopsy (DSNB) in patients diagnosed with penile cancer and clinically impalpable inguinal lymph nodes (cN0), and to develop an algorithm for the management of patients in which non-visualization occurs. Patients and Methods: This is a retrospective observational study over a period of 4 years, comprising 166 patients with penile squamous cell carcinoma undergoing DSNB and followed up for a minimum of 6 months. All cases diagnosed with uni- or bilateral non-visualization of sentinel nodes in this cohort were identified from a penile cancer database. The management of the inguinal lymph nodes after non-visualization and the oncological outcomes including local and regional recurrence rates were documented. Results: Out of 166 consecutive patients undergoing DSNB, 20 patients (12%) had unilateral non-visualization after injection of intradermal 99mTc. Of these 20 patients, seven underwent repeat DSNB at a later date, with six having successful visualization. One patient had persistent non-visualization and proceeded to a superficial modified inguinal lymphadenectomy (SML). None of these patients experienced recurrence at follow-up. A further seven patients underwent modified SML with on-table frozen-section analysis of the lymph node packet; none of these patients were found to have micrometastatic disease in the inguinal lymph nodes, although one patient developed metastatic inguinal node disease at a later date. Six patients elected to undergo clinical surveillance and have remained disease-free. Conclusion: Patients with impalpable inguinal lymph nodes undergoing DSNB with ≥G2 T1 disease should ideally have bilateral visualization of the sentinel lymph nodes, reflecting the drainage pattern from the primary tumour. In the present series, 12% of patients were found to have unilateral non-visualization after DSNB. Among patients offered a repeat DSNB at a later date, localizing the sentinel node was successful in 86% of cases. Patients with favourable histological characteristics can be placed on clinical surveillance. Those with high-risk disease can be offered a repeat DSNB procedure on the proviso that SML may be carried out if there is repeated non-visualization. Larger cohorts are required to validate this proposed algorithm

Accelerating Universe from an Evolving Lambda in Higher Dimension

We find exact solutions in five dimensional inhomogeneous matter dominated model with a varying cosmological constant. Adjusting arbitrary constants of integration one can also achieve acceleration in our model. Aside from an initial singularity our spacetime is regular everywhere including the centre of the inhomogeneous distribution. We also study the analogous homogeneous universe in (4+d) dimensions. Here an initially decelerating model is found to give late acceleration in conformity with the current observational demands. We also find that both anisotropy and number of dimensions have a role to play in determining the time of flip, in fact the flip is delayed in multidimensional models. Some astrophysical parameters like the age, luminosity distance etc are also calculated and the influence of extra dimensions is briefly discussed. Interestingly our model yields a larger age of the universe compared to many other quintessential models.Comment: 18 pages, 9 figure

Dilaton Contributions to the Cosmic Gravitational Wave Background

We consider the cosmological amplification of a metric perturbation propagating in a higher-dimensional Brans-Dicke background, including a non trivial dilaton evolution. We discuss the properties of the spectral energy density of the produced gravitons (as well as of the associated squeezing parameter), and we show that the present observational bounds on the graviton spectrum provide significant information on the dynamical evolution of the early universe.Comment: 26 pages, plain tex (to appear in Phys.Rev.D, 1 fig available from the authors upon req.

Heterogeneous response and progression patterns reveal phenotypic heterogeneity of tyrosine kinase inhibitor response in metastatic renal cell carcinoma

SC was funded by fellowships from NIHR and Cancer Research UK. IK was funded by the UCLH Experimental Cancer Centre and UCLH NIHR Biomedical Research Centre. TP was funded by grants from Cancer Research UK (the Experimental Cancer Medicine Centre). MG was funded by grants from Cancer Research UK, Prostate Cancer UK, the Prostate Cancer Foundation, the Schottlander Research Charitable Trust, the Royal Marsden NIHR Biomedical Research Centre for Cancer and the Wellcome Trust (grant number: 105104/Z/14/Z

Metric Perturbations in Dilaton-Driven Inflation

We compute the spectrum of scalar and tensor metric perturbations generated, as amplified vacuum fluctuations, during an epoch of dilaton-driven inflation of the type occurring naturally in string cosmology. In the tensor case the computation is straightforward while, in the scalar case, it is made delicate by the appearance of a growing mode in the familiar longitudinal gauge. In spite of this, a reliable perturbative calculation of perturbations far outside the horizon can be performed by resorting either to appropriate gauge invariant variables, or to a new coordinate system in which the growing mode can be "gauged down". The simple outcome of this complicated analysis is that both scalar and tensor perturbations exhibit nearly Planckian spectra, whose common "temperature" is related to some very basic parameters of the string-cosmology background.Comment: 34 pages, latex, no figure

Scalar and Tensor Inhomogeneities from Dimensional Decoupling

We discuss some perturbative techniques suitable for the gauge-invariant treatment of the scalar and tensor inhomogeneities of an anisotropic and homogeneous background geometry whose spatial section naturally decomposes into the direct product of two maximally symmetric Eucledian manifolds, describing a general situation of dimensional decoupling in which $d$ external dimensions evolve (in conformal time) with scale factor $a(\eta)$ and $n$ internal dimensions evolve with scale factor $b(\eta)$. We analyze the growing mode problem which typically arises in contracting backgrounds and we focus our attention on the situation where the amplitude of the fluctuations not only depends on the external space-time but also on the internal spatial coordinates. In order to illustrate the possible relevance of this analysis we compute the gravity waves spectrum produced in some highly simplified model of cosmological evolution and we find that the spectral amplitude, whose magnitude can be constrained by the usual bounds applied to the stochastic gravity waves backgrounds, depends on the curvature scale at which the compactification occurs and also on the typical frequency of the internal excitations.Comment: 31 pages, Latex, DAMTP 96-92, UCM 96-04, to appear in Phys. Rev. D 55 (1997

Integration of D-dimensional 2-factor spaces cosmological models by reducing to the generalized Emden-Fowler equation

The D-dimensional cosmological model on the manifold $M = R \times M_{1} \times M_{2}$ describing the evolution of 2 Einsteinian factor spaces, $M_1$ and $M_2$, in the presence of multicomponent perfect fluid source is considered. The barotropic equation of state for mass-energy densities and the pressures of the components is assumed in each space. When the number of the non Ricci-flat factor spaces and the number of the perfect fluid components are both equal to 2, the Einstein equations for the model are reduced to the generalized Emden-Fowler (second-order ordinary differential) equation, which has been recently investigated by Zaitsev and Polyanin within discrete-group analysis. Using the integrable classes of this equation one generates the integrable cosmological models. The corresponding metrics are presented. The method is demonstrated for the special model with Ricci-flat spaces $M_1,M_2$ and the 2-component perfect fluid source.Comment: LaTeX file, no figure

The trace left by signature-change-induced compactification

Recently, it has been shown that an infinite succession of classical signature changes (''signature oscillations'') can compactify and stabilize internal dimensions, and simultaneously leads, after a coarse graining type of average procedure, to an effective (''physical'') space-time geometry displaying the usual Lorentzian metric signature. Here, we consider a minimally coupled scalar field on such an oscillating background and study its effective dynamics. It turns out that the resulting field equation in four dimensions contains a coupling to some non-metric structure, the imprint of the ''microscopic'' signature oscillations on the effective properties of matter. In a multidimensional FRW model, this structure is identical to a massive scalar field evolving in its homogeneous mode.Comment: 15 pages, LaTeX, no figure

Toda chains with type A_m Lie algebra for multidimensional m-component perfect fluid cosmology

We consider a D-dimensional cosmological model describing an evolution of Ricci-flat factor spaces, M_1,...M_n (n > 2), in the presence of an m-component perfect fluid source (n > m > 1). We find characteristic vectors, related to the matter constants in the barotropic equations of state for fluid components of all factor spaces. We show that, in the case where we can interpret these vectors as the root vectors of a Lie algebra of Cartan type A_m=sl(m+1,C), the model reduces to the classical open m-body Toda chain. Using an elegant technique by Anderson (J. Math. Phys. 37 (1996) 1349) for solving this system, we integrate the Einstein equations for the model and present the metric in a Kasner-like form.Comment: LaTeX, 2 ps figure