All Maximally Entangled Four Qubits States

We find an operational interpretation for the 4-tangle as a type of residual entanglement, somewhat similar to the interpretation of the 3-tangle. Using this remarkable interpretation, we are able to find the class of maximally entangled four-qubits states which is characterized by four real parameters. The states in the class are maximally entangled in the sense that their average bipartite entanglement with respect to all possible bi-partite cuts is maximal. We show that while all the states in the class maximize the average tangle, there are only few states in the class that maximize the average Tsillas or Renyi $\alpha$-entropy of entanglement. Quite remarkably, we find that up to local unitaries, there exists two unique states, one maximizing the average $\alpha$-Tsallis entropy of entanglement for all $\alpha\geq 2$, while the other maximizing it for all $0<\alpha\leq 2$ (including the von-Neumann case of $\alpha=1$). Furthermore, among the maximally entangled four qubits states, there are only 3 maximally entangled states that have the property that for 2, out of the 3 bipartite cuts consisting of 2-qubits verses 2-qubits, the entanglement is 2 ebits and for the remaining bipartite cut the entanglement between the two groups of two qubits is 1ebit. The unique 3 maximally entangled states are the 3 cluster states that are related by a swap operator. We also show that the cluster states are the only states (up to local unitaries) that maximize the average $\alpha$-Renyi entropy of entanglement for all $\alpha\geq 2$.Comment: 15 pages, 2 figures, Revised Version: many references added, an appendix added with a statement of the Kempf-Ness theore

The incidence of sudden unexpected death in epilepsy (sudep) in south dublin and wicklow

Patients with epilepsy have a mortality rate higher than that of the general population. Some of this excess mortality is attributable to sudden unexpected death (SUDEP). We examined the incidence of this phenomenon both retrospectively and prospectively in the population of South Dublin and Wicklow over the period May 1992–1995. Cases were ascertained by examination of post-mortem registers of hospitals serving the area studied. Information on cases was sought from hospital records, general practitioners and families. Fifteen cases (10 male, five female) were identified resulting in an overall incidence rate of SUDEP of 1:680/year for the 3 years of the study. This is the only study of incidence of SUDEP conducted in Ireland and our results are in keeping with incidence rates elsewhere in Europe and the USA

Bulk and surface energetics of lithium hydride crystal: benchmarks from quantum Monte Carlo and quantum chemistry

We show how accurate benchmark values of the surface formation energy of crystalline lithium hydride can be computed by the complementary techniques of quantum Monte Carlo (QMC) and wavefunction-based molecular quantum chemistry. To demonstrate the high accuracy of the QMC techniques, we present a detailed study of the energetics of the bulk LiH crystal, using both pseudopotential and all-electron approaches. We show that the equilibrium lattice parameter agrees with experiment to within 0.03 %, which is around the experimental uncertainty, and the cohesive energy agrees to within around 10 meV per formula unit. QMC in periodic slab geometry is used to compute the formation energy of the LiH (001) surface, and we show that the value can be accurately converged with respect to slab thickness and other technical parameters. The quantum chemistry calculations build on the recently developed hierarchical scheme for computing the correlation energy of a crystal to high precision. We show that the hierarchical scheme allows the accurate calculation of the surface formation energy, and we present results that are well converged with respect to basis set and with respect to the level of correlation treatment. The QMC and hierarchical results for the surface formation energy agree to within about 1 %.Comment: 16 pages, 4 figure

Polymorphisms in the circadian expressed genes PER3 and ARNTL2 are associated with diurnal preference and GNβ3 with sleep measures

Sleep and circadian rhythms are intrinsically linked, with several sleep traits, including sleep timing and duration, influenced by both sleep homeostasis and the circadian phase. Genetic variation in several circadian genes has been associated with diurnal preference (preference in timing of sleep), although there has been limited research on whether they are associated with other sleep measurements. We investigated whether these genetic variations were associated with diurnal preference (Morningness-Eveningness Questionnaire) and various sleep measures, including: the global Pittsburgh Sleep Quality index score; sleep duration; and sleep latency and sleep quality. We genotyped 10 polymorphisms in genes with circadian expression in participants from the G1219 sample (n = 966), a British longitudinal population sample of young adults. We conducted linear regressions using dominant, additive and recessive models of inheritance to test for associations between these polymorphisms and the sleep measures. We found a significant association between diurnal preference and a polymorphism in period homologue 3 (PER3) (P < 0.005, recessive model) and a novel nominally significant association between diurnal preference and a polymorphism in aryl hydrocarbon receptor nuclear translocator-like 2 (ARNTL2) (P < 0.05, additive model). We found that a polymorphism in guanine nucleotide binding protein beta 3 (GNβ3) was associated significantly with global sleep quality (P < 0.005, recessive model), and that a rare polymorphism in period homologue 2 (PER2) was associated significantly with both sleep duration and quality (P < 0.0005, recessive model). These findings suggest that genes with circadian expression may play a role in regulating both the circadian clock and sleep homeostasis, and highlight the importance of further studies aimed at dissecting the specific roles that circadian genes play in these two interrelated but unique behaviours

A Characterisation of Strong Wave Tails in Curved Space-Times

A characterisation of when wave tails are strong is proposed. The existence of a curvature induced tail (i.e. a Green's function term whose support includes the interior of the light-cone) is commonly understood to cause backscattering of the field governed by the relevant wave equation. Strong tails are characterised as those for which the purely radiative part of the field is backscattered. With this definition, it is shown that electromagnetic waves in asymptotically flat space-times and fields governed by tail-free propagation have weak tails, but minimally coupled scalar fields in a cosmological scenario have strong tails.Comment: 17 pages, Revtex, to appear in Classical and Quantum Gravit

Goodness-of-Fit Tests for Symmetric Stable Distributions -- Empirical Characteristic Function Approach

We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard symmetric stable distribution with the characteristic exponent $\alpha$ estimated from the data. We treat $\alpha$ as an unknown parameter, but for theoretical simplicity we also consider the case that $\alpha$ is fixed. For estimation of parameters and the standardization of data we use maximum likelihood estimator (MLE) and an equivariant integrated squared error estimator (EISE) which minimizes the weighted integral. We derive the asymptotic covariance function of the characteristic function process with parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of the covariance function are numerically evaluated and asymptotic distribution of the test statistic is obtained using complex integration. Simulation studies show that the asymptotic distribution of the test statistics is very accurate. We also present a formula of the asymptotic covariance function of the characteristic function process with parameters estimated by an efficient estimator for general distributions

Two new species of Prosorhynchoides (Digenea: Bucephalidae) from Tylosurus crocodilus (Belonidae) from the great barrier reef and French Polynesia

We surveyed 14 individuals of Tylosurus crocodilus Péron & Lesueur 1821 (Belonidae) collected from the waters around Lizard Island and Heron Island, Great Barrier Reef, Queensland, Australia, and the waters around Moorea, French Polynesia. We describe two new species of bucephaline trematodes from them, Prosorhynchoides galaktionovi n. sp. and P. kohnae n. sp. They are morphologically distinct from existing Prosorhynchoides spp., with molecular data from 28S and ITS-2 ribosomal DNA, as well as cox1 mitochondrial DNA, further supporting our morphological findings. Neither species has been observed in other belonid fishes. The new species fall into the clade of species of Prosorhynchoides from belonids previously identified in Australian waters. These findings strengthen the observation that groups of bucephaline species have radiated, at least in part, in tight association with host taxa. There are now five species of Prosorhynchoides known from two belonid species in Australian waters. We, therefore, predict further richness in the nine other belonid species present

Rubidium Rydberg macrodimers

We explore long-range interactions between two atoms excited into high principal quantum number n Rydberg states, and present calculated potential energy surfaces (PES) for various symmetries of doubly excited ns and np rubidium atoms. We show that the PES for these symmetries exhibit deep (~GHz) potential wells, which can support very extended (~micrometers) bound vibrational states (macrodimers). We present n-scaling relations for both the depth De of the wells and the equilibrium separations Re of these macrodimers, and explore their response to small electric fields and stability with respect to predissociation. Finally, we present a scheme to form and study these macrodimers via photoassociation, and show how one can probe the various \ell-character of the potential wells

The Central Singularity in Spherical Collapse

The gravitational strength of the central singularity in spherically symmetric space-times is investigated. Necessary conditions for the singularity to be gravitationally weak are derived and it is shown that these are violated in a wide variety of circumstances. These conditions allow conclusions to be drawn about the nature of the singularity without having to integrate the geodesic equations. In particular, any geodesic with a non-zero amount of angular momentum which impinges on the singularity terminates in a strong curvature singularity.Comment: 17 pages; revised and corrected with improved result