On Gravitational Waves in Spacetimes with a Nonvanishing Cosmological Constant

We study the effect of a cosmological constant $\Lambda$ on the propagation and detection of gravitational waves. To this purpose we investigate the linearised Einstein's equations with terms up to linear order in $\Lambda$ in a de Sitter and an anti-de Sitter background spacetime. In this framework the cosmological term does not induce changes in the polarization states of the waves, whereas the amplitude gets modified with terms depending on $\Lambda$. Moreover, if a source emits a periodic waveform, its periodicity as measured by a distant observer gets modified. These effects are, however, extremely tiny and thus well below the detectability by some twenty orders of magnitude within present gravitational wave detectors such as LIGO or future planned ones such as LISA.Comment: 8 pages, 4 figures, accepted for publication in Physical Review

Experimental Designs for Binary Data in Switching Measurements on Superconducting Josephson Junctions

We study the optimal design of switching measurements of small Josephson junction circuits which operate in the macroscopic quantum tunnelling regime. Starting from the D-optimality criterion we derive the optimal design for the estimation of the unknown parameters of the underlying Gumbel type distribution. As a practical method for the measurements, we propose a sequential design that combines heuristic search for initial estimates and maximum likelihood estimation. The presented design has immediate applications in the area of superconducting electronics implying faster data acquisition. The presented experimental results confirm the usefulness of the method. KEY WORDS: optimal design, D-optimality, logistic regression, complementary log-log link, quantum physics, escape measurement

A Testable Solution of the Cosmological Constant and Coincidence Problems

We present a new solution to the cosmological constant (CC) and coincidence problems in which the observed value of the CC, $\Lambda$, is linked to other observable properties of the universe. This is achieved by promoting the CC from a parameter which must to specified, to a field which can take many possible values. The observed value of Lambda ~ 1/(9.3 Gyrs)^2$(approximately 10^(-120) in Planck units) is determined by a new constraint equation which follows from the application of a causally restricted variation principle. When applied to our visible universe, the model makes a testable prediction for the dimensionless spatial curvature of Omega_k0 = -0.0056 s_b/0.5; where s_b ~ 1/2 is a QCD parameter. Requiring that a classical history exist, our model determines the probability of observing a given Lambda. The observed CC value, which we successfully predict, is typical within our model even before the effects of anthropic selection are included. When anthropic selection effects are accounted for, we find that the observed coincidence between t_Lambda = Lambda^(-1/2) and the age of the universe, t_U, is a typical occurrence in our model. In contrast to multiverse explanations of the CC problems, our solution is independent of the choice of a prior weighting of different$\Lambda$-values and does not rely on anthropic selection effects. Our model includes no unnatural small parameters and does not require the introduction of new dynamical scalar fields or modifications to general relativity, and it can be tested by astronomical observations in the near future.Comment: 31 pages, 4 figures; v2: version accepted by Phys. Rev.

Agreement of MSmetrix with established methods for measuring cross-sectional and longitudinal brain atrophy

Introduction Despite the recognized importance of atrophy in multiple sclerosis (MS), methods for its quantification have been mostly restricted to the research domain. Recently, a CE labelled and FDA approved MS-specific atrophy quantification method, MSmetrix, has become commercially available. Here we perform a validation of MSmetrix against established methods in simulated and in vivo MRI data. Methods Whole-brain and gray matter (GM) volume were measured with the cross-sectional pipeline of MSmetrix and compared to the outcomes of FreeSurfer (cross-sectional pipeline), SIENAX and SPM. For this comparison we investigated 20 simulated brain images, as well as in vivo data from 100 MS patients and 20 matched healthy controls. In fifty of the MS patients a second time point was available. In this subgroup, we additionally analyzed the whole-brain and GM volume change using the longitudinal pipeline of MSmetrix and compared the results with those of FreeSurfer (longitudinal pipeline) and SIENA. Results In the simulated data, SIENAX displayed the smallest average deviation compared with the reference whole-brain volume (+ 19.56 ± 10.34 mL), followed by MSmetrix (− 38.15 ± 17.77 mL), SPM (− 42.99 ± 17.12 mL) and FreeSurfer (− 78.51 ± 12.68 mL). A similar pattern was seen in vivo. Among the cross-sectional methods, Deming regression analyses revealed proportional errors particularly in MSmetrix and SPM. The mean difference percentage brain volume change (PBVC) was lowest between longitudinal MSmetrix and SIENA (+ 0.16 ± 0.91%). A strong proportional error was present between longitudinal percentage gray matter volume change (PGVC) measures of MSmetrix and FreeSurfer (slope = 2.48). All longitudinal methods were sensitive to the MRI hardware upgrade that occurred during the time of the study. Conclusion MSmetrix, FreeSurfer, FSL and SPM show differences in atrophy measurements, even at the whole-brain level, that are large compared to typical atrophy rates observed in MS. Especially striking are the proportional errors between methods. Cross-sectional MSmetrix behaved similarly to SPM, both in terms of mean volume difference as well as proportional error. Longitudinal MSmetrix behaved most similar to SIENA. Our results indicate that brain volume measurement and normalization from T1-weighted images remains an unsolved problem that requires much more attention

Deforming the Maxwell-Sim Algebra

The Maxwell alegbra is a non-central extension of the Poincar\'e algebra, in which the momentum generators no longer commute, but satisfy $[P_\mu,P_\nu]=Z_{\mu\nu}$. The charges $Z_{\mu\nu}$ commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincar\'e, this being the symmetry algebra of Very Special Relativity. It admits an analogous non-central extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to DISim$_b$, where $b$ is a non-trivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding Maxwell-DISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force.Comment: Appendix on Lifshitz and Schrodinger algebras adde

Proper Size of the Visible Universe in FRW Metrics with Constant Spacetime Curvature

In this paper, we continue to examine the fundamental basis for the Friedmann-Robertson-Walker (FRW) metric and its application to cosmology, specifically addressing the question: What is the proper size of the visible universe? There are several ways of answering the question of size, though often with an incomplete understanding of how far light has actually traveled in reaching us today from the most remote sources. The difficulty usually arises from an inconsistent use of the coordinates, or an over-interpretation of the physical meaning of quantities such as the so-called proper distance R(t)=a(t)r, written in terms of the (unchanging) co-moving radius r and the universal expansion factor a(t). In this paper, we use the five non-trivial FRW metrics with constant spacetime curvature (i.e., the static FRW metrics, but excluding Minkowski) to prove that in static FRW spacetimes in which expansion began from an initial signularity, the visible universe today has a proper size equal to R_h(t_0/2), i.e., the gravitational horizon at half its current age. The exceptions are de Sitter and Lanczos, whose contents had pre-existing positions away from the origin. In so doing, we confirm earlier results showing the same phenomenon in a broad range of cosmologies, including LCDM, based on the numerical integration of null geodesic equations through an FRW metric.Comment: Accepted for publication in Classical and Quantum Gravit

Classification of multifluid CP world models

Various classification schemes exist for homogeneous and isotropic (CP) world models, which include pressureless matter (so-called dust) and Einstein's cosmological constant Lambda. We here classify the solutions of more general world models consisting of up to four non-interacting fluids, each with pressure P, energy density epsilon and an equation of state P = (gamma - 1) epsilon with 0 <= gamma <= 2. In addition to repulsive fluids with negative pressure and positive energy density, which generalize the classical repulsive (positive) Lambda component, we consider fluids with negative energy density as well. The latter generalize a negative Lambda component. This renders possible new types of models that do not occur among the classical classifications of world models. Singularity-free periodic solutions as well as further `hill-type', `hollow-type' and `shifting-type' models are feasible. However, if one only allows for three components (dust, radiation and one repulsive component) in a spatially flat universe the repulsive classical Lambda fluid (with Lambda > 0) tends to yield the smoothest fits of the Supernova Ia data from Perlmutter et al. (1999). Adopting the SN Ia constraints, exotic negative energy density components can be fittingly included only if the universe consists of four or more fluids.Comment: 12 pages, 11 figures, latex, A&A in pres

Can metabolomics in addition to genomics add to prognostic and predictive information in breast cancer?

Genomic data from breast cancers provide additional prognostic and predictive information that is beginning to be used for patient management. The question arises whether additional information derived from other 'omic' approaches such as metabolomics can provide additional information. In an article published this month in BMC Cancer, Borgan et al. add metabolomic information to genomic measures in breast tumours and demonstrate, for the first time, that it may be possible to further define subgroups of patients which could be of value clinically

Revisiting Weyl's calculation of the gravitational pull in Bach's two-body solution

When the mass of one of the two bodies tends to zero, Weyl's definition of the gravitational force in an axially symmetric, static two-body solution can be given an invariant formulation in terms of a force four-vector. The norm of this force is calculated for Bach's two-body solution, that is known to be in one-to-one correspondence with Schwarzschild's original solution when one of the two masses l, l' is made to vanish. In the limit when, say, l' goes to zero, the norm of the force divided by l' and calculated at the position of the vanishing mass is found to coincide with the norm of the acceleration of a test body kept at rest in Schwarzschild's field. Both norms happen thus to grow without limit when the test body (respectively the vanishing mass l') is kept at rest in a position closer and closer to Schwarzschild's two-surface.Comment: 11 pages, 2 figures. Text to appear in Classical and Quantum Gravit

Neoplastic Meningitis: How MRI and CSF Cytology Are Influenced by CSF Cell Count and Tumor Type

Background. Although CSF cytology and MRI are standard methods to diagnose neoplastic meningitis (NM), this complication of neoplastic disease remains difficult to detect. We therefore reevaluated the sensitivity of gadolinium (GD)-enhanced MRI and cerebrospinal-fluid (CSF)-cytology and the relevance of tumor type and CSF cell count. Methods. We retrospectively identified 111 cases of NM diagnosed in our CSF laboratory since 1990 with complete documentation of both MRI and CSF cytology. 37 had haematological and 74 solid neoplasms. CSF cell counts were increased in 74 and normal in 37 patients. Results. In hematological neoplasms, MRI was positive in 49% and CSF cytology in 97%. In solid tumors, the sensitivity of MRI was 80% and of cytology 78%. With normal CSF cell counts, MRI was positive in 59% (50% hematological, 72% solid malignancies) and CSF cytology in 76% (92% in hematological, 68% in solid neoplasms). In cases of elevated cell counts, the sensitivity of MRI was 72% (50% for hematological, 83% for solid malignancies) and of CSF cytology 91% (100% for haematological and 85% for solid neoplasms). 91% of cytologically positive cases were diagnosed at first and another 7% at second lumbar puncture. Routine protein analyses had a low sensitivity in detecting NM. Conclusions. The high overall sensitivity of MRI was only confirmed for NM from solid tumors and for elevated CSF cell counts. With normal cell counts and haematological neoplasms, CSF-cytology was superior to MRI. None of the analysed routine CSF proteins had an acceptable sensitivity and specificity in detecting leptomeningeal disease