Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we provide a fast and reliable algorithm for maximum likelihood reconstruction that avoids this slow convergence. Our method utilizes the state-of-the-art convex optimization scheme-an accelerated projected-gradient method-that allows one to accommodate the quantum nature of the problem in a different way than in the standard methods. We demonstrate the power of our approach by comparing its performance with other algorithms for n-qubit state tomography. In particular, an 8-qubit situation that purportedly took weeks of computation time in 2005 can now be completed in under a minute for a single set of data, with far higher accuracy than previously possible. This refutes the common claim that MLE reconstruction is slow, and reduces the need for alternative methods that often come with difficult-to-verify assumptions. In fact, recent methods assuming Gaussian statistics or relying on compressed sensing ideas are demonstrably inapplicable for the situation under consideration here. Our algorithm can be applied to general optimization problems over the quantum state space; the philosophy of projected gradients can further be utilized for optimization contexts with general constraints. PACS numbers: 03.65.Wj, 03.67.-a, 02.60.PnIntroduction.-Efficient and reliable characterization of properties of a quantum system, e.g., its state or the process it is undergoing, is needed for any quantum information processing task. Such are the goals of quantum tomography [1], broadly classified into state tomography and process tomography. Process tomography can be recast as state tomography via the Choi-Jamiolkowski isomorphism [2, 3]; we hence restrict our attention to state tomography. Tomography is a two-step process: the first is data gathering from measurements of the quantum system; the second is the estimation of the state from the gathered data. This second step is the focus of this article.A popular estimation strategy is that of the maximumlikelihood estimator (MLE) [4] from standard statistics. Computing the MLE for quantum tomography is, however, not straightforward due to the constraints imposed by quantum mechanics. While general-purpose convex optimization toolboxes (e.g., CVX [5,6]) are available for small-sized problems, specially adapted MLE algorithms are needed for tackling useful system sizes. Past MLE algorithms [7,8] incorporate the quantum constraints by going to the factored space (see definition later) where the constraints are satisfied by an appropriate parameterization. Gradient methods are then straightforwardly employed in the now-unconstrained factored space. These algorithms can be slow in practice, with an extreme
Our results suggest that overexpressed miR-191 is associated with ICC progression through the miR-191/TET1/p53 pathway. (Hepatology 2017;66:136-151).
BackgroundStudies investigating the association between hepatitis C virus (HCV) infections and the occurrence of cholangiocarcinoma (CCA), especially intrahepatic cholangiocarcinoma (ICC), have shown inconsistent findings. Although previous meta-analyses referred to HCV and CCA, they mainly focused on ICC rather than CCA or extrahepatic cholangiocarcinoma (ECC). Since then, relevant new studies have been published on the association between HCV and ICC. Since the different anatomic locations of CCA have distinct epidemiologic features and different risk factors, it is necessary to evaluate the relationship between HCV infection and ICC, ECC, and CCA.MethodsRelevant studies were identified by searching PUBMED, EMBASE, and MEDLINE databases prior to 1 August 2013. Pooled risk estimates were calculated with random-effects models using STATA 11.0.ResultsA total of 16 case-control studies were included in the final analysis. Pooled risk estimates showed a statistically significant increasing risk of CCA (odds ratio (OR) = 5.44, 95% CI, 2.72 to 10.89). The pooled risk estimate of ICC (OR = 3.38, 95% CI, 2.72 to 4.21) was higher than that of ECC (OR = 1.75, 95% CI, 1.00 to 3.05). In a subgroup analysis, the pooled risk estimate of ICC in studies from North America was obviously higher than in Asia (6.48 versus 2.01). The Begg funnel plot and Egger test showed no evidence of publication bias.ConclusionsHCV infection is associated with the increasing risk of CCA, especially ICC.
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