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

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

Cross-Section Dependence and the Monetary Exchange Rate Model: A Panel Analysis

This paper tackles the issue of cross-section dependence for the monetary exchange rate model in the presence of unobserved common factors using panel data from 1973 until 2007 for 19 OECD countries. Applying a principal component analysis we distinguish between common factors and idiosyncratic components and determine whether non-stationarity stems from international or national stochastic trends. We find evidence for a cross-section cointegration relationship between the exchange rates and fundamentals which is driven by those common international trends. In addition, the estimated coefficients of income and money are in line with the suggestions of the monetary model

Energy Consumption and Economic Growth - New Insights into the Cointegration Relationship

This paper examines the long-run relationship between energy consumption and real GDP, including energy prices, for 25 OECD countries from 1981 to 2007. The distinction between common factors and idiosyncratic components using principal component analysis allows to distinguish between developments on an international and a national level as drivers of the long-run relationship. Indeed, cointegration between the common components of the underlying variables indicates that international developments dominate the long-run relationship between energy consumption and real GDP. Furthermore, the results suggest that energy consumption is price-inelastic. Causality tests indicate the presence of a bi-directional causal relationship between energy consumption and economic growth.Dieses Papier untersucht unter Einbeziehung von Energiepreisen die langfristige Beziehung zwischen Energieverbrauch und realen BIP für 25 OECD Länder von 1981 bis 2007. Durch die Unterscheidung von gemeinsamen und idiosynkratischen Komponenten mit Hilfe einer Faktoranalyse kann zwischen Entwicklungen auf internationaler und nationaler Ebene als Treiber der Langfristbeziehung differenziert werden. In der Tat deutet Kointegration zwischen den gemeinsamen Faktoren der zugrundeliegenden Variablen darauf hin, dass internationale Entwicklungen die langfristige Beziehung zwischen Energieverbrauch und realem BIP dominieren. Des Weiteren suggerieren die ökonometrischen Ergebnisse, dass der Energieverbrauch relativ preisunelastisch ist. Kausalitätstests ergeben eine bidirektionale kausale Beziehung zwischen Energieverbrauch und Wirtschaftswachstum

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

Publisher Connection: Export-Led Growth in the UAE: Multivariate Causality Between Primary Exports, Manufactured Exports and Economic Growth

The principal question that this research addresses is the validity of the Export-Led Growth hypothesis (ELG) in the United Arab Emirates (UAE) over the period 1981–2012, focusing on the causality between primary exports, manufactured exports and economic growth. Unit root tests are applied to examine the time-series properties of the variables, while the Johansen cointegration test is performed to confirm or not the existence of a long-run relationship between the variables. Moreover, the multivariate Granger causality test and a modified version of Wald test are applied to examine the direction of the short-run and long-run causality respectively. The cointegration analysis reveals that manufactured exports contribute more to economic growth than primary exports in the long-run. In addition, this research provides evidence to support a bi-directional causality between manufactured exports and economic growth in the short-run, while the Growth-Led Exports (GLE) hypothesis is valid in the long-run for UAE