A simple formula for the average gate fidelity of a quantum dynamical operation

This Letter presents a simple formula for the average fidelity between a unitary quantum gate and a general quantum operation on a qudit, generalizing the formula for qubits found by Bowdrey et al. [Phys. Lett. A 294 (2002) 258]. This formula may be useful for experimental determination of average gate fidelity. We also give a simplified proof of a formula due to Horodecki et al. [Phys. Rev. A 60 (1999) 1888], connecting average gate fidelity to entanglement fidelity. (C) 2002 Elsevier Science B.V. All rights reserved.

Application of the maximum entropy method to the (2 + 1)D four-fermion model

We investigate spectral functions extracted using the maximum entropy method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma, and massive pseudoscalar meson; our results confirm the Goldstone nature of the π and permit an estimate of the meson binding energy. We have, however, seen no signal of σ→ππ decay as the chiral limit is approached. In the symmetric phase we observe a resonance of nonzero width in qualitative agreement with analytic expectations; in addition the ultraviolet behavior of the spectral functions is consistent with the large nonperturbative anomalous dimension for fermion composite operators expected in this model.

Cholesterol-lowering therapy with pravastatin in patients with average cholesterol levels and established ischaemic heart disease: is it cost-effective?

Objective: To measure the cost-effectiveness of cholesterol-lowering therapy with pravastatin in patients with established ischaemic heart disease and average baseline cholesterol levels. Design: Prospective economic evaluation within a double-blind randomised trial (Long-Term Intervention with Pravastatin in Ischaemic Disease [LIPID]), in which patients with a history of unstable angina or previous myocardial infarction were randomised to receive 40 mg of pravastatin daily or matching placebo. Patients and setting: 9014 patients aged 35-75 years from 85 centres in Australia and New Zealand, recruited from June 1990 to December 1992. Main outcome measures: Cost per death averted, cost per life-year gained, and cost per quality-adjusted life-year gained, calculated from measures of hospitalisations, medication use, outpatient visits, and quality of life. Results: The LIPID trial showed a 22% relative reduction in all-cause mortality (P < 0.001). Over a mean follow-up of 6 years, hospital admissions for coronary heart disease and coronary revascularisation were reduced by about 20%. Over this period, pravastatin cost $A4913 per patient, but reduced total hospitalisation costs by $A1385 per patient and other long-term medication costs by $A360 per patient. In a subsample of patients, average quality of life was 0.98 (where 0 = dead and 1 = normal good health); the treatment groups were not significantly different. The absolute reduction in all-cause mortality was 3.0% (95% CI, 1.6%-4.4%), and the incremental cost was $3246 per patient, resulting in a cost per life saved of $107730 (95% Cl, $68626-$209881) within the study period. Extrapolating long-term survival from the placebo group, the undiscounted cost per life-year saved was $7695 (and $10 938 with costs and life-years discounted at an annual rate of 5%). Conclusions: Pravastatin therapy for patients with a history of myocardial infarction or unstable angina and average cholesterol levels reduces all-cause mortality and appears cost effective compared with accepted treatments in high-income countries.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Fiber average size and distribution dependence on the electrospinning parameters of poly(vinylidene fluoride trifluoroethylene)) membranes for biomedical applications

Poly(vinylidene fluoride-trifluoethylene) electrospun membranes were obtained from a blend of dimethylformamide (DMF) and methylethylketone (MEK) solvents. The inclusion of the MEK to the solvent system promotes a faster solvent evaporation allowing complete polymer crystallization during the jet travelling between the tip and the grounded collector. Several processing parameters were systematically changed to study their influence on fiber dimensions. Applied voltage and inner needle diameter do not have large influence on the electrospun fiber average diameter but in the fiber diameter distribution. On the other hand, the increase of the distance between the needle tip to collector results in fibers with larger average diameter. Independently on the processing conditions, all mats are produced in the electroactive phase of the polymer. Further, MC-3T3-E1cell adhesion was not inhibited by the fiber mats preparation, indicating their potential use for biomedical applications.

Contradiction between the average age of retirement at the time of death and the average pension time for men and women in public employment in Portugal

The short article attempts to make some very brief reflections on the effects a lack of public policies positively discriminatory in terms of public employment retirement. In particular, the observation of the absurd contradiction between the average age of retirement at the time of death (for men and women) and the average pension time for men and women in public employment in Portugal.

Toplological Entropy in the Syncronization of Piecewise Linear and Monotone Maps. Coupled Duffing Oscillators

In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupled identical chaotic Duffing equations is given. We discuss the complete synchronization of two identical double-well Duffing oscillators, from the point of view of symbolic dynamics. Working with Poincare cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized.

Stabilization constraints from different-average public debt levels in a Monetary Union with country-size asymmetry

In the sequence of the recent financial and economic crisis, the recent public debt accumulation is expected to hamper considerably business cycle stabilization, by enlarging the budgetary consequences of the shocks. This paper analyses how the average level of public debt in a monetary union shapes optimal discretionary fiscal and monetary stabilization policies and affects stabilization welfare. We use a two-country micro-founded New-Keynesian model, where a benevolent central bank and the fiscal authorities play discretionary policy games under different union-average debt-constrained scenarios. We find that high debt levels shift monetary policy assignment from inflation to debt stabilization, making cooperation welfare superior to noncooperation. Moreover, when average debt is too high, welfare moves directly (inversely) with debt-to-output ratios for the union and the large country (small country) under cooperation. However, under non-cooperation, higher average debt levels benefit only the large country.

Entropy analysis of DNA code dynamics in human chromosomes

Deoxyribonucleic acid, or DNA, is the most fundamental aspect of life but present day scientific knowledge has merely scratched the surface of the problem posed by its decoding. While experimental methods provide insightful clues, the adoption of analysis tools supported by the formalism of mathematics will lead to a systematic and solid build-up of knowledge. This paper studies human DNA from the perspective of system dynamics. By associating entropy and the Fourier transform, several global properties of the code are revealed. The fractional order characteristics emerge as a natural consequence of the information content. These properties constitute a small piece of scientific knowledge that will support further efforts towards the final aim of establishing a comprehensive theory of the phenomena involved in life.

Shannon, rényie and tsallis entropy analysis of DNA using phase plane

This paper analyzes DNA information using entropy and phase plane concepts. First, the DNA code is converted into a numerical format by means of histograms that capture DNA sequence length ranging from one up to ten bases. This strategy measures dynamical evolutions from 4 up to 410 signal states. The resulting histograms are analyzed using three distinct entropy formulations namely the Shannon, Rényie and Tsallis definitions. Charts of entropy versus sequence length are applied to a set of twenty four species, characterizing 486 chromosomes. The information is synthesized and visualized by adapting phase plane concepts leading to a categorical representation of chromosomes and species.

A multidimensional scaling analysis of musical sounds based on pseudo phase plane

This paper studies musical opus from the point of view of three mathematical tools: entropy, pseudo phase plane (PPP), and multidimensional scaling (MDS). The experiments analyze ten sets of different musical styles. First, for each musical composition, the PPP is produced using the time series lags captured by the average mutual information. Second, to unravel hidden relationships between the musical styles the MDS technique is used. The MDS is calculated based on two alternative metrics obtained from the PPP, namely, the average mutual information and the fractal dimension. The results reveal significant differences in the musical styles, demonstrating the feasibility of the proposed strategy and motivating further developments towards a dynamical analysis of musical sounds.

Contradiction between the average age of retirement at the time of death and the average pension time for men and women in public employment in Portugal

The short article attempts to make some very brief reflections on the effects a lack of public policies positively discriminatory in terms of public employment retirement. In particular, the observation of the absurd contradiction between the average age of retirement at the time of death (for men and women) and the average pension time for men and women in public employment in Portugal.

Entropy diversity in multi-objective particle swarm optimization

Multi-objective particle swarm optimization (MOPSO) is a search algorithm based on social behavior. Most of the existing multi-objective particle swarm optimization schemes are based on Pareto optimality and aim to obtain a representative non-dominated Pareto front for a given problem. Several approaches have been proposed to study the convergence and performance of the algorithm, particularly by accessing the final results. In the present paper, a different approach is proposed, by using Shannon entropy to analyzethe MOPSO dynamics along the algorithm execution. The results indicate that Shannon entropy can be used as an indicator of diversity and convergence for MOPSO problems.

Power law and entropy analysis of catastrophic phenomena

Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, tsunamis, floods and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties has separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the statistical distributions of the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data sets are better approximated by two PLs instead of a single one. We plot the PL parameters, corresponding to several events, and observe an interesting pattern in the charts, where the lines that connect each pair of points defining the double PLs are almost parallel to each other. A complementary data analysis is performed by means of the computation of the entropy. The results reveal relationships hidden in the data that may trigger a future comprehensive explanation of this type of phenomena.