Isotropic singularities in shear-free perfect fluid cosmologies

We investigate barotropic perfect fluid cosmologies which admit an isotropic singularity. From the General Vorticity Result of Scott, it is known that these cosmologies must be irrotational. In this paper we prove, using two different methods, that if we make the additional assumption that the perfect fluid is shear-free, then the fluid flow must be geodesic. This then implies that the only shear-free, barotropic, perfect fluid cosmologies which admit an isotropic singularity are the FRW models.

Intraspecific co-variation between egg and body size affects fertilisation kinetics of free-spawning marine invertebrates

Fertilisation of eggs of free-spawning marine invertebrates depends on factors affecting sperm concentration in the field and also on gamete characteristics such as egg size. In the free-spawning intertidal ascidian Pyura stolonifera mean egg size increased with maternal size in 2 separate populations. The largest ascidian produced eggs that were, on average, 50% greater in volume than the eggs produced by the smallest individual studied. There was no evidence to suggest that egg density varied with adult size and egg dry organic weight increased with maternal size. The fertilisation kinetics of this species were strongly affected by the variation in egg size, with the eggs of large individuals requiring much less concentrated sperm to achieve maximal levels of fertilisation success than the eggs of small individuals. We suggest that variation in egg size between individuals of different sizes and ages may be an important factor in determining fertilisation success for ascidians of this species.

The interaction between the equity premium and the risk-free rate

The equity premium arises from the interaction between the atemporal risk premium for equity, the risk-free rate of intertemporal substitution and the impact of risk on the precautionary motive for saving. Depending on parameter values, the equity premium may either be increased or reduced by the presence of undiversifiable background risk. (C) 2000 Elsevier Science S.A. All rights reserved.

Inactive free : total prostate specific antigen ratios in ejaculate from men with suspected and known prostate cancer, compared with young control men

Objective To measure free:total prostate specific antigen (PSA) ratios in ejaculate from men with suspected and known prostate cancer, and in young control men, to determine if this ratio might be useful in discriminating benign from malignant prostatic conditions. Patients, subjects and methods Forty-seven men with prostate cancer (positive biopsies), 52 men with suspected prostate cancer but who had negative biopsies and 28 young men (< 30 years old) and with no family history of cancer, provided either a single ejaculate specimen (total 59) or multiple specimens (total 193) on subsequent occasions. Free and total PSA were measured using appropriate assays. All specimens were diluted in a PSA-negative female serum pool. Results The median free:total PSA ratios were 0.76-0.81 among the patient groups and control men, and there was no statistical difference between the groups. These data presumably only reflect the inactive component of free PSA, given that any alpha(2)-macroglobulin or alpha(1)-antichymotrypsin in the assay serum diluent was likely to have bound the active free PSA component in these samples. Similar results were obtained from those providing single and multiple samples, suggesting that a single specimen is sufficient to reflect the seminal plasma free:total PSA ratio over that period. There was no relationship between seminal plasma free:total PSA ratio and age for the controls or the positive biopsy group, although there was a negative relationship (i.e. a decline with age) that almost reached significance in those with negative biopsies (P = 0.058, R-2 = 0.07). Conclusions This is the first report of free:total PSA ratios in the ejaculate of men with suspected and known prostate cancer compared with young control men. Although no significant changes were detected in the free:total PSA ratios in ejaculate, these results may be confounded by differences in ratios with age, as is the case for serum PSA or different molecular forms of PSA. Indeed, these data suggest that a large proportion of free PSA in seminal plasma may be inactive. Further studies are needed to determine the potential utility of measuring free:total PSA, or other candidate markers, in ejaculate to better discriminate benign from malignant prostate disease.

Quantification of free mycophenolic acid by high-performance liquid chromatography-atmospheric pressure chemical ionisation tandem mass spectrometry

To facilitate the investigation of free mycophenolic acid concentrations we developed a high-performance liquid chromatography tandem mass spectrometry method using indomethacin as an internal standard. Free drug was isolated from plasma samples (500 mul) using ultrafiltration, The analytes were extracted from the ultrafiltrate (200 mul) using C-18 solid-phase extraction. Detection was by selected reactant monitoring of mycophenolic acid (m/z 318.9-->190.9) and the internal standard (m/z 356.0-->297.1) with an atmospheric pressure chemical ionisation interface. The total chromatographic analysis time was 12 min. The method was found to be linear over the range investigated, 2.5-200 mug/l (r>0.990, n=6). The relative recovery of the method for the control samples studied (7.5, 40.0 and 150 mug/l) ranged from 95 to 104%. The imprecision of the method, expressed in terms of intra- and inter-day coefficients of variation, was

Context-free and context-sensitive dynamics in recurrent neural networks

Continuous-valued recurrent neural networks can learn mechanisms for processing context-free languages. The dynamics of such networks is usually based on damped oscillation around fixed points in state space and requires that the dynamical components are arranged in certain ways. It is shown that qualitatively similar dynamics with similar constraints hold for a(n)b(n)c(n), a context-sensitive language. The additional difficulty with a(n)b(n)c(n), compared with the context-free language a(n)b(n), consists of 'counting up' and 'counting down' letters simultaneously. The network solution is to oscillate in two principal dimensions, one for counting up and one for counting down. This study focuses on the dynamics employed by the sequential cascaded network, in contrast to the simple recurrent network, and the use of backpropagation through time. Found solutions generalize well beyond training data, however, learning is not reliable. The contribution of this study lies in demonstrating how the dynamics in recurrent neural networks that process context-free languages can also be employed in processing some context-sensitive languages (traditionally thought of as requiring additional computation resources). This continuity of mechanism between language classes contributes to our understanding of neural networks in modelling language learning and processing.

Free energy approximations in simple lattice proteins

This work addresses the question of whether it is possible to define simple pairwise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how reliable it could possibly be. In a two-dimensional, infinite lattice model system one can calculate exact free energies by exhaustive enumeration. A series of approximations were fitted to exact results to assess the feasibility and utility of pairwise free energy terms. Approximating the true free energy with pairwise interactions gives a poor fit with little transferability between systems of different size. Adding extra artificial terms to the approximation yields better fits, but does not improve the ability to generalize from one system size to another. Furthermore, one cannot distinguish folding from nonfolding sequences via the approximated free energies. Most usefully, the methodology shows how one can assess the utility of various terms in lattice protein/polymer models. (C) 2001 American Institute of Physics.

Analytical solution to the zero-inertia problem for surge flow phenomena in nonprismatic channels

Surge flow phenomena. e.g.. as a consequence of a dam failure or a flash flood, represent free boundary problems. ne extending computational domain together with the discontinuities involved renders their numerical solution a cumbersome procedure. This contribution proposes an analytical solution to the problem, It is based on the slightly modified zero-inertia (ZI) differential equations for nonprismatic channels and uses exclusively physical parameters. Employing the concept of a momentum-representative cross section of the moving water body together with a specific relationship for describing the cross sectional geometry leads, after considerable mathematical calculus. to the analytical solution. The hydrodynamic analytical model is free of numerical troubles, easy to run, computationally efficient. and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model compares very favorably with a full hydrodynamic numerical model in respect to published results of surge flow simulations in different types of prismatic channels. In order to extend these considerations to natural rivers, the accuracy of the analytical model in describing an irregular cross section is investigated and tested successfully. A sensitivity and error analysis reveals the important impact of the hydraulic radius on the velocity of the surge, and this underlines the importance of an adequate description of the topography, The new approach is finally applied to simulate a surge propagating down the irregularly shaped Isar Valley in the Bavarian Alps after a hypothetical dam failure. The straightforward and fully stable computation of the flood hydrograph along the Isar Valley clearly reflects the impact of the strongly varying topographic characteristics on the How phenomenon. Apart from treating surge flow phenomena as a whole, the analytical solution also offers a rigorous alternative to both (a) the approximate Whitham solution, for generating initial values, and (b) the rough volume balance techniques used to model the wave tip in numerical surge flow computations.

In situ measures of spawning synchrony and fertilization success in an intertidal, free-spawning invertebrate

The rocky intertidal zone has the potential to be one of the harshest environments for free-spawning organisms, but empirical data on fertilization success are scarce. Here, I report on an intertidal, solitary ascidian, Pyura stolonifera, which was observed to spawn at low tide. At a scale likely to be most important to gametes (metres, duration of tide), approximately 30% of individuals in the population were spawning synchronously. Spawned gametes remained in a viscous matrix and this appeared to minimise their dilution. Fertilization success varied greatly among individuals (0 to 92%) and was related to the distance to the nearest neighbouring spawner. Occasional wave wash facilitated the movement of sperm between spawners. Fertilization success in some individuals was limited by the scarcity of sperm whilst the experimental addition of sperm did not increase success in others.

On entanglement and Lorentz transformations

We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin 1/2 particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed.

Superhyperfine interactions in inhomogeneously broadened paramagnetic centers observed via a hole-burned free induction decay

Superhyperfine interactions in inhomogeneously broadened paramagnetic centers are observed using a single high-turn-angle microwave pulse. The free induction signal that follows the hole-burning pulse exhibits oscillations that are distinct from the oscillatory free induction decay observable in some inhomogeneously broadened systems. It contains frequencies characteristic of the superhyperfine splittings, together with a zero frequency component. Experimental examples of the effect in both orientationally disordered (powdered) and structurally disordered (glassy) systems are presented and compared with the conceptually similar Fourier transform electron paramagnetic resonance detected nuclear magnetic resonance experiment, together with numerical simulations. (C) 2003 American Institute of Physics.

Quantum error correction for continuously detected errors

We show that quantum feedback control can be used as a quantum-error-correction process for errors induced by a weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per physical qubit, quantum feedback can act to perfectly protect a stabilizer codespace. Using the stabilizer formalism we derive an explicit scheme, involving feedback and an additional constant Hamiltonian, to protect an (n-1)-qubit logical state encoded in n physical qubits. This works for both Poisson (jump) and white-noise (diffusion) measurement processes. Universal quantum computation is also possible in this scheme. As an example, we show that detected-spontaneous emission error correction with a driving Hamiltonian can greatly reduce the amount of redundancy required to protect a state from that which has been previously postulated [e.g., Alber , Phys. Rev. Lett. 86, 4402 (2001)].

Sources of variation in larval quality for free-spawning marine invertebrates: Egg size and the local sperm environment

There has been growing interest in the effects of variation in larval quality on the post-larval performance of adult marine invertebrates. Variation in egg/larval size is an obvious source of variation in larval quality but sources of variation have received little attention. For broadcast spawners, larval size may vary according to the local sperm environment but the generality of this result is unclear. Here, we show that, for a solitary ascidian, a polychaete and an echinoid, larval size is affected by the concentration of sperm present during fertilization. Larvae that are produced at high sperm concentrations are smaller than larvae that are produced from eggs exposed to low sperm concentrations. We also show that for three ascidians and an asteroid, egg size increases with maternal body size. These differences in larval size are likely to affect larval and subsequent adult performance in the field. Given that sperm concentrations in the field can fluctuate widely, it is likely that larval quality in free-spawning marine invertebrates will also vary widely.

The early sperm gets the good egg: mating order effects in free spawners

Mating order can have important consequences for the fertilization success of males whose ejaculates compete to fertilize a clutch of eggs. Despite an excellent body of literature on mating-order effects in many animals, they have rarely been considered in marine free-spawning invertebrates, where both sexes release gametes into the water column. In this study, we show that in such organisms, mating order can have profound repercussions for male reproductive success. Using in vitro fertilization for two species of sea urchin we found that the 'fertilization history' of a clutch of eggs strongly influenced the size distribution of unfertilized eggs, and consequently the likelihood that they will be fertilized. Males that had first access to a batch of eggs enjoyed elevated fertilization success because they had privileged access to the largest and therefore most readily fertilizable eggs within a clutch. By contrast, when a male's sperm were exposed to a batch of unfertilized eggs left over from a previous mating event, fertilization rates were reduced, owing to smaller eggs remaining in egg clutches previously exposed to sperm. Because of this size-dependent fertilization, the fertilization history of eggs also strongly influenced the size distribution of offspring, with first-spawning males producing larger, and therefore fitter, offspring. These findings suggest that when there is variation in egg size, mating order will influence not only the quantity but also the quality of offspring sired by competing males.