Delayed-choice gedanken experiments and their realizations

The wave-particle duality dates back to Einstein's explanation of the photoelectric effect through quanta of light and de Broglie's hypothesis of matter waves. Quantum mechanics uses an abstract description for the behavior of physical systems such as photons, electrons, or atoms. Whether quantum predictions for single systems in an interferometric experiment allow an intuitive understanding in terms of the particle or wave picture, depends on the specific configuration which is being used. In principle, this leaves open the possibility that quantum systems always either behave definitely as a particle or definitely as a wave in every experimental run by a priori adapting to the specific experimental situation. This is precisely what is tried to be excluded by delayed-choice experiments, in which the observer chooses to reveal the particle or wave character -- or even a continuous transformation between the two -- of a quantum system at a late stage of the experiment. We review the history of delayed-choice gedanken experiments, which can be traced back to the early days of quantum mechanics. Then we discuss their experimental realizations, in particular Wheeler's delayed choice in interferometric setups as well as delayed-choice quantum erasure and entanglement swapping. The latter is particularly interesting, because it elevates the wave-particle duality of a single quantum system to an entanglement-separability duality of multiple systems

A Simulation Perspective: Error Analysis in the Distributed Simulation of Continuous System

To construct a corresponding distributed system from a continuous system, the most convenient way is to partition the system into parts according to its topology and deploy the parts on separated nodes directly. However, system error will be introduced during this process because the computing pattern is changed from the sequential to the parallel. In this paper, the mathematical expression of the introduced error is studied. A theorem is proposed to prove that a distributed system preserving the stability property of the continuous system can be found if the system error is limited to be small enough. Then, the compositions of the system error are analyzed one by one and the complete expression is deduced, where the advancing step T in distributed environment is one of the key factors associated. At last, the general steps to determine the step T are given. The significance of this study lies in the fact that the maximum T can be calculated without exceeding the expected error threshold, and a larger T can reduce the simulation cost effectively without causing too much performance degradation compared to the original continuous system

Regularized binormal ROC method in disease classification using microarray data

BACKGROUND: An important application of microarrays is to discover genomic biomarkers, among tens of thousands of genes assayed, for disease diagnosis and prognosis. Thus it is of interest to develop efficient statistical methods that can simultaneously identify important biomarkers from such high-throughput genomic data and construct appropriate classification rules. It is also of interest to develop methods for evaluation of classification performance and ranking of identified biomarkers. RESULTS: The ROC (receiver operating characteristic) technique has been widely used in disease classification with low dimensional biomarkers. Compared with the empirical ROC approach, the binormal ROC is computationally more affordable and robust in small sample size cases. We propose using the binormal AUC (area under the ROC curve) as the objective function for two-sample classification, and the scaled threshold gradient directed regularization method for regularized estimation and biomarker selection. Tuning parameter selection is based on V-fold cross validation. We develop Monte Carlo based methods for evaluating the stability of individual biomarkers and overall prediction performance. Extensive simulation studies show that the proposed approach can generate parsimonious models with excellent classification and prediction performance, under most simulated scenarios including model mis-specification. Application of the method to two cancer studies shows that the identified genes are reasonably stable with satisfactory prediction performance and biologically sound implications. The overall classification performance is satisfactory, with small classification errors and large AUCs. CONCLUSION: In comparison to existing methods, the proposed approach is computationally more affordable without losing the optimality possessed by the standard ROC method

Poly[diaqua­(μ3-1H-benzimidazole-5,6-dicarboxyl­ato-κ4 N 3:O 5,O 6:O 6′)magnesium(II)]

In the title complex, [Mg(C9H4N2O4)(H2O)2]n, the MgII atom is six-coordinated by one N and three O atoms from three different 1H-benzimidazole-5,6-dicarboxyl­ate ligands and two O atoms from two water mol­ecules, forming a slightly distorted octa­hedral geometry. The ligand links the MgII centres into a three-dimensional network. Extensive N—H⋯O and O—H⋯O hydrogen bonds exist between the ligands and water mol­ecules, stabilizing the crystal structure

Experimental quantum teleportation over a high-loss free-space channel

We present a high-fidelity quantum teleportation experiment over a high-loss free-space channel between two laboratories. We teleported six states of three mutually unbiased bases and obtained an average state fidelity of 0.82(1), well beyond the classical limit of 2/3. With the obtained data, we tomographically reconstructed the process matrices of quantum teleportation. The free-space channel attenuation of 31 dB corresponds to the estimated attenuation regime for a down-link from a low-earth-orbit satellite to a ground station. We also discussed various important technical issues for future experiments, including the dark counts of single-photon detectors, coincidence-window width etc. Our experiment tested the limit of performing quantum teleportation with state-of-the-art resources. It is an important step towards future satellite-based quantum teleportation and paves the way for establishing a worldwide quantum communication network

A Case Study on Air Combat Decision Using Approximated Dynamic Programming

As a continuous state space problem, air combat is difficult to be resolved by traditional dynamic programming (DP) with discretized state space. The approximated dynamic programming (ADP) approach is studied in this paper to build a high performance decision model for air combat in 1 versus 1 scenario, in which the iterative process for policy improvement is replaced by mass sampling from history trajectories and utility function approximating, leading to high efficiency on policy improvement eventually. A continuous reward function is also constructed to better guide the plane to find its way to "winner" state from any initial situation. According to our experiments, the plane is more offensive when following policy derived from ADP approach other than the baseline Min-Max policy, in which the "time to win" is reduced greatly but the cumulated probability of being killed by enemy is higher. The reason is analyzed in this paper