Qudit versions of the qubit "pi-over-eight" gate

When visualised as an operation on the Bloch sphere, the qubit "pi-over-eight" gate corresponds to one-eighth of a complete rotation about the vertical axis. This simple gate often plays an important role in quantum information theory, typically in situations for which Pauli and Clifford gates are insufficient. Most notably, when it supplements the set of Clifford gates then universal quantum computation can be achieved. The "pi-over-eight" gate is the simplest example of an operation from the third level of the Clifford hierarchy (i.e., it maps Pauli operations to Clifford operations under conjugation). Here we derive explicit expressions for all qudit (d-level, where d is prime) versions of this gate and analyze the resulting group structure that is generated by these diagonal gates. This group structure differs depending on whether the dimensionality of the qudit is two, three or greater than three. We then discuss the geometrical relationship of these gates (and associated states) with respect to Clifford gates and stabilizer states. We present evidence that these gates are maximally robust to depolarizing and phase damping noise, in complete analogy with the qubit case. Motivated by this and other similarities we conjecture that these gates could be useful for the task of qudit magic-state distillation and, by extension, fault-tolerant quantum computing. Very recent, independent work by Campbell, Anwar and Browne confirms the correctness of this intuition, and we build upon their work to characterize noise regimes for which noisy implementations of these gates can (or provably cannot) supplement Clifford gates to enable universal quantum computation.Comment: Version 2 changed to reflect improved distillation routines in arXiv:1205.3104v2. Minor typos fixed. 12 Pages,2 Figures,3 Table

Percolative shunting on electrified surface

The surface discharge of electrified dielectrics at high humidity is considered. The percolative nature of charge transport in electrets is established. Particular attention is given to the phenomena of adsorption and nucleation of electrically conducting phase in the cause of percolation cluster growth on electrified surface. The critical index of the correlation lenght for percolation cluster is found, and its value is in good agreement with the known theoretical estimations.Comment: 4 pages with 1 figure, revtex, published in Tech. Phys. Lett. 25 (1999) 877-879 with one additional figur

Equivalence of operator-splitting schemes for the integration of the Langevin equation

We investigate the equivalence of different operator-splitting schemes for the integration of the Langevin equation. We consider a specific problem, so called the directed percolation process, which can be extended to a wider class of problems. We first give a compact mathematical description of the operator-splitting method and introduce two typical splitting schemes that will be useful in numerical studies. We show that the two schemes are essentially equivalent through the map that turns out to be an automorphism. An associated equivalent class of operator-splitting integrations is also defined by generalizing the specified equivalence.Comment: 4 page

Optimizing prediction of binge eating episodes : a comparison approach to test alternative conceptualizations of the affect regulation model

Background : Although a wealth of studies have tested the link between negative mood states and likelihood of a subsequent binge eating episode, the assumption that this relationship follows a typical linear dose&ndash;response pattern (i.e., that risk of a binge episode increases in proportion to level of negative mood) has not been challenged. The present study demonstrates the applicability of an alternative, non-linear conceptualization of this relationship, in which the strength of association between negative mood and probability of a binge episode increases above a threshold value for the mood variable relative to the slope below this threshold value (threshold dose response model). Methods : A sample of 93 women aged 18 to 40 completed an online survey at random intervals seven times per day for a period of one week. Participants self-reported their current mood state and whether they had recently engaged in an eating episode symptomatic of a binge. Results : As hypothesized, the threshold approach was a better predictor than the linear dose&ndash;response modeling of likelihood of a binge episode. The superiority of the threshold approach was found even at low levels of negative mood (3 out of 10, with higher scores reflecting more&nbsp; negative mood). Additionally, severity of negative mood beyond this threshold value appears to be useful for predicting time to onset of a binge episode. Conclusions : Present findings suggest that simple dose&ndash;response formulations for the association between&nbsp; negative mood and onset of binge episodes miss vital aspects of this relationship. Most&nbsp; notably, the impact of mood on binge eating appears to depend on whether a threshold value&nbsp; of negative mood has been breached, and elevation in mood beyond this point may be useful&nbsp; for clinicians and researchers to identify time to onset. <br /

Unboundedness and downward closures of higher-order pushdown automata

We show the diagonal problem for higher-order pushdown automata (HOPDA), and hence the simultaneous unboundedness problem, is decidable. From recent work by Zetzsche this means that we can construct the downward closure of the set of words accepted by a given HOPDA. This also means we can construct the downward closure of the Parikh image of a HOPDA. Both of these consequences play an important role in verifying concurrent higher-order programs expressed as HOPDA or safe higher-order recursion schemes

Transport on Directed Percolation Clusters

We study random lattice networks consisting of resistor like and diode like bonds. For investigating the transport properties of these random resistor diode networks we introduce a field theoretic Hamiltonian amenable to renormalization group analysis. We focus on the average two-port resistance at the transition from the nonpercolating to the directed percolating phase and calculate the corresponding resistance exponent $\phi$ to two-loop order. Moreover, we determine the backbone dimension $D_B$ of directed percolation clusters to two-loop order. We obtain a scaling relation for $D_B$ that is in agreement with well known scaling arguments.Comment: 4 page

Lunar navigation study, sections 1 through 7 Final report, Jun. 1964 - May 1965

Lunar navigation analysis using passive nongyro, inertial navigation, and radio frequency technolog

Lunar navigation study, summary volume Final report, Jun. 1964 - May 1965

Lunar surface navigation and guidance study to implement lunar surface vehicle exploration mission

Risk assessment and suicide by patients with schizophrenia in secondary mental healthcare: a case-control study

Objectives: To investigate the role of risk assessment in predicting suicide in patients with schizophrenia spectrum disorders (SSDs) receiving secondary mental healthcare. We postulated that risk assessment plays a limited role in predicting suicide in these patients. Design: Retrospective case–control study. Setting: Anonymised electronic mental health record data from the South London and Maudsley National Health Service (NHS) Foundation Trust (SLaM) (London, UK) linked with national mortality data. Participants: In 242 227 SLaM service users up to 31 December 2013, 635 suicides were identified. 96 (15.1%) had a SSD diagnosis. Those who died before 1 January 2007 (n=25) were removed from the analyses. Thus, 71 participants with SSD who died from suicide over the study period (cases) were compared with 355 controls. Main outcome measure: Risk of suicide in relation to risk assessment ratings. Results: Cases were younger at first contact with services (mean±SD 34.5±12.6 vs 39.2±15.2) and with a higher preponderance of males (OR=2.07, 95% CI 1.18 to 3.65, p=0.01) than controls. Also, suicide occurred within 10 days after last contact with services in half of cases, with the most common suicide methods being hanging (14) and jumping (13). Cases were more likely to have the following ‘risk assessment’ items previously recorded: suicidal history (OR=4.42, 95% CI 2.01 to 9.65, p<0.001), use of violent method (OR=3.37, 95% CI 1.47 to 7.74, p=0.01), suicidal ideation (OR=3.57, 95% CI 1.40 to 9.07, p=0.01) and recent hospital discharge (OR=2.71, 95% CI 1.17 to 6.28, p=0.04). Multiple regression models predicted only 21.5% of the suicide outcome variance. Conclusions: Predicting suicide in schizophrenia is highly challenging due to the high prevalence of risk factors within this diagnostic group irrespective of outcome, including suicide. Nevertheless, older age at first contact with mental health services and lack of suicidal history and suicidal ideation are useful protective markers indicative of those less likely to end their own lives

The relationships between internal and external threat and right-wing attitudes: A three-wave longitudinal study

The interplay between threat and right-wing attitudes has received much research attention, but its longitudinal relationship has hardly been investigated. In this study, we investigated the longitudinal relationships between internal and external threat and right-wing attitudes using a cross-lagged design at three different time points in a large nationally representative sample (N = 800). We found evidence for bidirectional relationships. Higher levels of external threat were related to higher levels of Right-Wing Authoritarianism and to both the egalitarianism and dominance dimensions of Social Dominance Orientation at a later point in time. Conversely, higher levels of RWA were also related to increased perception of external threat later in time. Internal threat did not yield significant direct or indirect longitudinal relationships with right-wing attitudes. Theoretical and practical implications of these longitudinal effects are discussed