Rank penalized estimation of a quantum system

We introduce a new method to reconstruct the density matrix $\rho$ of a system of $n$-qubits and estimate its rank $d$ from data obtained by quantum state tomography measurements repeated $m$ times. The procedure consists in minimizing the risk of a linear estimator $\hat{\rho}$ of $\rho$ penalized by given rank (from 1 to $2^n$), where $\hat{\rho}$ is previously obtained by the moment method. We obtain simultaneously an estimator of the rank and the resulting density matrix associated to this rank. We establish an upper bound for the error of penalized estimator, evaluated with the Frobenius norm, which is of order $dn(4/3)^n /m$ and consistency for the estimator of the rank. The proposed methodology is computationaly efficient and is illustrated with some example states and real experimental data sets

Directed network of substorms using SuperMAG ground‐based magnetometer data

We quantify the spatio‐temporal evolution of the substorm ionospheric current system utilizing the SuperMAG 100+ magnetometers. We construct dynamical directed networks from this data for the first time. If the canonical cross‐correlation (CCC) between vector magnetic field perturbations observed at two magnetometer stations exceeds a threshold, they form a network connection. The time lag at which CCC is maximal determines the direction of propagation or expansion of the structure captured by the network connection. If spatial correlation reflects ionospheric current patterns, network properties can test different models for the evolving substorm current system. We select 86 isolated substorms based on nightside ground station coverage. We find, and obtain the timings for, a consistent picture in which the classic substorm current wedge (SCW) forms. A current system is seen pre‐midnight following the SCW westward expansion. Later, there is a weaker signal of eastward expansion. Finally, there is evidence of substorm‐enhanced convection

On the statistical modeling of persistence in total ozone anomalies

Geophysical time series sometimes exhibit serial correlations that are stronger than can be captured by the commonly used first‐order autoregressive model. In this study we demonstrate that a power law statistical model serves as a useful upper bound for the persistence of total ozone anomalies on monthly to interannual timescales. Such a model is usually characterized by the Hurst exponent. We show that the estimation of the Hurst exponent in time series of total ozone is sensitive to various choices made in the statistical analysis, especially whether and how the deterministic (including periodic) signals are filtered from the time series, and the frequency range over which the estimation is made. In particular, care must be taken to ensure that the estimate of the Hurst exponent accurately represents the low‐frequency limit of the spectrum, which is the part that is relevant to long‐term correlations and the uncertainty of estimated trends. Otherwise, spurious results can be obtained. Based on this analysis, and using an updated equivalent effective stratospheric chlorine (EESC) function, we predict that an increase in total ozone attributable to EESC should be detectable at the 95% confidence level by 2015 at the latest in southern midlatitudes, and by 2020–2025 at the latest over 30°–45°N, with the time to detection increasing rapidly with latitude north of this range

Seasonal persistence of northern low- and middle-latitude anomalies of ozone and other trace gases in the upper stratosphere

Analysis of observed ozone profiles in Northern Hemisphere low and middle latitudes reveals the seasonal persistence of ozone anomalies in both the lower and upper stratosphere. Principal component analysis is used to detect that above 16 hPa the persistence is strongest in the latitude band 15–45°N, while below 16 hPa the strongest persistence is found over 45–60°N. In both cases, ozone anomalies persist through the entire year from November to October. The persistence of ozone anomalies in the lower stratosphere is presumably related to the wintertime ozone buildup with subsequent photochemical relaxation through summer, as previously found for total ozone. The persistence in the upper stratosphere is more surprising, given the short lifetime of Ox at these altitudes. It is hypothesized that this “seasonal memory” in the upper stratospheric ozone anomalies arises from the seasonal persistence of transport-induced wintertime NOy anomalies, which then perturb the ozone chemistry throughout the rest of the year. This hypothesis is confirmed by analysis of observations of NO2, NOx, and various long-lived trace gases in the upper stratosphere, which are found to exhibit the same seasonal persistence. Previous studies have attributed much of the year-to-year variability in wintertime extratropical upper stratospheric ozone to the Quasi-Biennial Oscillation (QBO) through transport-induced NOy (and hence NO2) anomalies but have not identified any statistical connection between the QBO and summertime ozone variability. Our results imply that through this “seasonal memory,” the QBO has an asynchronous effect on ozone in the low to midlatitude upper stratosphere during summer and early autumn

Impact of long-range correlations on trend detection in total ozone

Total ozone trends are typically studied using linear regression models that assume a first-order autoregression of the residuals [so-called AR(1) models]. We consider total ozone time series over 60°S–60°N from 1979 to 2005 and show that most latitude bands exhibit long-range correlated (LRC) behavior, meaning that ozone autocorrelation functions decay by a power law rather than exponentially as in AR(1). At such latitudes the uncertainties of total ozone trends are greater than those obtained from AR(1) models and the expected time required to detect ozone recovery correspondingly longer. We find no evidence of LRC behavior in southern middle-and high-subpolar latitudes (45°–60°S), where the long-term ozone decline attributable to anthropogenic chlorine is the greatest. We thus confirm an earlier prediction based on an AR(1) analysis that this region (especially the highest latitudes, and especially the South Atlantic) is the optimal location for the detection of ozone recovery, with a statistically significant ozone increase attributable to chlorine likely to be detectable by the end of the next decade. In northern middle and high latitudes, on the other hand, there is clear evidence of LRC behavior. This increases the uncertainties on the long-term trend attributable to anthropogenic chlorine by about a factor of 1.5 and lengthens the expected time to detect ozone recovery by a similar amount (from ∼2030 to ∼2045). If the long-term changes in ozone are instead fit by a piecewise-linear trend rather than by stratospheric chlorine loading, then the strong decrease of northern middle- and high-latitude ozone during the first half of the 1990s and its subsequent increase in the second half of the 1990s projects more strongly on the trend and makes a smaller contribution to the noise. This both increases the trend and weakens the LRC behavior at these latitudes, to the extent that ozone recovery (according to this model, and in the sense of a statistically significant ozone increase) is already on the verge of being detected. The implications of this rather controversial interpretation are discussed

Predicting Worst-Case Execution Time Trends in Long-Lived Real-Time Systems

In some long-lived real-time systems, it is not uncommon to see that the execution times of some tasks may exhibit trends. For hard and firm real-time systems, it is important to ensure these trends will not jeopardize the system. In this paper, we first introduce the notion of dynamic worst-case execution time (dWCET), which forms a new perspective that could help a system to predict potential timing failures and optimize resource allocations. We then have a comprehensive review of trend prediction methods. In the evaluation, we make a comparative study of dWCET trend prediction. Four prediction methods, combined with three data selection processes, are applied in an evaluation framework. The result shows the importance of applying data preprocessing and suggests that non-parametric estimators perform better than parametric methods

Complex-valued wavelet lifting and applications

Signals with irregular sampling structures arise naturally in many fields. In applications such as spectral decomposition and nonparametric regression, classical methods often assume a regular sampling pattern, thus cannot be applied without prior data processing. This work proposes new complex-valued analysis techniques based on the wavelet lifting scheme that removes ‘one coefficient at a time’. Our proposed lifting transform can be applied directly to irregularly sampled data and is able to adapt to the signal(s)’ characteristics. As our new lifting scheme produces complex-valued wavelet coefficients, it provides an alternative to the Fourier transform for irregular designs, allowing phase or directional information to be represented. We discuss applications in bivariate time series analysis, where the complex-valued lifting construction allows for coherence and phase quantification. We also demonstrate the potential of this flexible methodology over real-valued analysis in the nonparametric regression context

The Role of Macroeconomic Fundamentals in Malaysian Post Recession Growth

This study aims to find out the role of macroeconomic fundamentals in Malaysian post recession growth. The selected macroeconomic variables are exports, imports, price level, money supply, interest rate, exchange rate and government expenditure. The technique of cointegration was employed to assess the long run equilibrium relationships among the variables. Then, this study performs the Granger causality tests based on VECM to establish the short run causality among the variables. The long-run cointegrating relationship shown that an increase in exports, government expenditure or depreciation of exchange rate will promote long-term economic growth while increase in inflation, interest rate and imports will tamper the Malaysian economic growth. The results of short-run Granger-causality indicated that price level and government spending Granger-caused economic growth in the short-run. In conclusion, based on the results of long-run and short run analysis, the fiscal policy is probably the most appropriate tool in promoting economic growth in Malaysia during the post recession period