Random qubit-states and how best to measure them

We consider the problem of measuring a single qubit, known to have been prepared in either a randomly selected pure state or a randomly selected real pure state. We seek the measurements that provide either the best estimate of the state prepared or maximise the accessible information. Surprisingly, any sensible measurement turns out to be optimal. We discuss the application of these ideas to multiple qubits and higher-dimensional systems

Conformally rescaled spacetimes and Hawking radiation

We study various derivations of Hawking radiation in conformally rescaled metrics. We focus on two important properties, the location of the horizon under a conformal transformation and its associated temperature. We find that the production of Hawking radiation cannot be associated in all cases to the trapping horizon because its location is not invariant under a conformal transformation. We also find evidence that the temperature of the Hawking radiation should transform simply under a conformal transformation, being invariant for asymptotic observers in the limit that the conformal transformation factor is unity at their location.Comment: 22 pages, version submitted to journa

Path Size Logit route choice models: Issues with current models, a new internally consistent approach, and parameter estimation on a large-scale network with GPS data

Path Size Logit route choice models attempt to capture the correlation between routes by including correction terms within the route utility functions. This provides a convenient closed-form solution for implementation in traffic network models. The path size terms measure distinctiveness of routes; a route is penalised based on the number of other routes sharing its links, and the costs of those shared links. Typically, real road networks have many very long routes that should be considered unrealistic. Such unrealistic routes are problematic for the Path Size Logit (PSL) model because they negatively impact the choice probabilities of realistic routes when links are shared. The Generalised Path Size Logit (GPSL) model attempts to address this problem by weighting the contributions of routes to path size terms according to the ratio of route travel costs. However, the GPSL model is not internally consistent in how it defines routes as being unrealistic: the path size terms consider only travel cost, whereas the route choice probability relation considers disutility including the correction term. To solve these challenges, this paper formulates a new internally consistent Adaptive Path Size Logit (APSL) model wherein routes contribute to path size terms according to the ratio of route choice probabilities, ensuring that routes defined as unrealistic by the path size terms, are exactly those with very low choice probabilities. The APSL route choice probability relation is an implicit function, naturally expressed as a fixed-point problem. A proof is provided for the guaranteed existence of solutions, as well as conditions for the uniqueness of solutions. A Maximum Likelihood Estimation procedure is given for estimating the APSL model with tracked route observation data, and this procedure is investigated in a simulation study where it is shown it is generally possible to reproduce assumed true parameters. APSL is then estimated using real tracked route GPS data on a large-scale network, and results are compared with other PSL models

Edge centrality via the Holevo quantity

In the study of complex networks, vertex centrality measures are used to identify the most important vertices within a graph. A related problem is that of measuring the centrality of an edge. In this paper, we propose a novel edge centrality index rooted in quantum information. More specifically, we measure the importance of an edge in terms of the contribution that it gives to the Von Neumann entropy of the graph. We show that this can be computed in terms of the Holevo quantity, a well known quantum information theoretical measure. While computing the Von Neumann entropy and hence the Holevo quantity requires computing the spectrum of the graph Laplacian, we show how to obtain a simplified measure through a quadratic approximation of the Shannon entropy. This in turns shows that the proposed centrality measure is strongly correlated with the negative degree centrality on the line graph. We evaluate our centrality measure through an extensive set of experiments on real-world as well as synthetic networks, and we compare it against commonly used alternative measures

Antipsychotics and Torsadogenic Risk: Signals Emerging from the US FDA Adverse Event Reporting System Database

Background: Drug-induced torsades de pointes (TdP) and related clinical entities represent a current regulatory and clinical burden. Objective: As part of the FP7 ARITMO (Arrhythmogenic Potential of Drugs) project, we explored the publicly available US FDA Adverse Event Reporting System (FAERS) database to detect signals of torsadogenicity for antipsychotics (APs). Methods: Four groups of events in decreasing order of drug-attributable risk were identified: (1) TdP, (2) QT-interval abnormalities, (3) ventricular fibrillation/tachycardia, and (4) sudden cardiac death. The reporting odds ratio (ROR) with 95 % confidence interval (CI) was calculated through a cumulative analysis from group 1 to 4. For groups 1+2, ROR was adjusted for age, gender, and concomitant drugs (e.g., antiarrhythmics) and stratified for AZCERT drugs, lists I and II (http://www.azcert.org, as of June 2011). A potential signal of torsadogenicity was defined if a drug met all the following criteria: (a) four or more cases in group 1+2; (b) significant ROR in group 1+2 that persists through the cumulative approach; (c) significant adjusted ROR for group 1+2 in the stratum without AZCERT drugs; (d) not included in AZCERT lists (as of June 2011). Results: Over the 7-year period, 37 APs were reported in 4,794 cases of arrhythmia: 140 (group 1), 883 (group 2), 1,651 (group 3), and 2,120 (group 4). Based on our criteria, the following potential signals of torsadogenicity were found: amisulpride (25 cases; adjusted ROR in the stratum without AZCERT drugs = 43.94, 95 % CI 22.82-84.60), cyamemazine (11; 15.48, 6.87-34.91), and olanzapine (189; 7.74, 6.45-9.30). Conclusions: This pharmacovigilance analysis on the FAERS found 3 potential signals of torsadogenicity for drugs previously unknown for this risk

Quantum Correlations in NMR systems

In conventional NMR experiments, the Zeeman energy gaps of the nuclear spin ensembles are much lower than their thermal energies, and accordingly exhibit tiny polarizations. Generally such low-purity quantum states are devoid of quantum entanglement. However, there exist certain nonclassical correlations which can be observed even in such systems. In this chapter, we discuss three such quantum correlations, namely, quantum contextuality, Leggett-Garg temporal correlations, and quantum discord. In each case, we provide a brief theoretical background and then describe some results from NMR experiments.Comment: 21 pages, 7 figure

Global and regional brain metabolic scaling and its functional consequences

Background: Information processing in the brain requires large amounts of metabolic energy, the spatial distribution of which is highly heterogeneous reflecting complex activity patterns in the mammalian brain. Results: Here, it is found based on empirical data that, despite this heterogeneity, the volume-specific cerebral glucose metabolic rate of many different brain structures scales with brain volume with almost the same exponent around -0.15. The exception is white matter, the metabolism of which seems to scale with a standard specific exponent -1/4. The scaling exponents for the total oxygen and glucose consumptions in the brain in relation to its volume are identical and equal to $0.86\pm 0.03$, which is significantly larger than the exponents 3/4 and 2/3 suggested for whole body basal metabolism on body mass. Conclusions: These findings show explicitly that in mammals (i) volume-specific scaling exponents of the cerebral energy expenditure in different brain parts are approximately constant (except brain stem structures), and (ii) the total cerebral metabolic exponent against brain volume is greater than the much-cited Kleiber's 3/4 exponent. The neurophysiological factors that might account for the regional uniformity of the exponents and for the excessive scaling of the total brain metabolism are discussed, along with the relationship between brain metabolic scaling and computation.Comment: Brain metabolism scales with its mass well above 3/4 exponen