Time-reversal of rank-one quantum strategy functions

The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a class of linear functions, defined on quantum strategy representations within this framework, that corresponds to the set of rank-one positive semidefinite operators on a certain space. This time-reversal property states that the maximum value obtained by such a function over all valid quantum strategies is also obtained when the direction of time for the function is reversed, despite the fact that the strategies themselves are generally not time reversible. An application of this fact is an alternative proof of a known relationship between the conditional min- and max-entropy of bipartite quantum states, along with generalizations of this relationship.Comment: 17 page

The Hawking-Page phase transitions in the extended phase space in the Gauss-Bonnet gravity

In this paper, the Hawking-Page phase transitions between the black holes and thermal anti-de Sitter (AdS) space are studied with the Gauss-Bonnet term in the extended phase space, in which the varying cosmological constant plays the role of an effective thermodynamic pressure. The Gauss-Bonnet term exhibits its effects via introducing the corrections to the black hole entropy and Gibbs free energy. The global phase structures, especially the phase transition temperature $T_{\rm HP}$ and the Gibbs free energy $G$, are systematically investigated, first for the Schwarzschild-AdS black holes and then for the charged and rotating AdS black holes in the grand canonical ensembles, with both analytical and numerical methods. It is found that there are terminal points in the coexistence lines, and $T_{\rm HP}$ decreases at large electric potentials and angular velocities and also decreases with the Gauss-Bonnet coupling constant $\alpha$.Comment: 13 pages, 13 figure

Feel Safe to Take More Risks? Insecure Attachment Increases Consumer Risk-Taking Behavior

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Threshold-free Evaluation of Medical Tests for Classification and Prediction: Average Precision versus Area Under the ROC Curve

When evaluating medical tests or biomarkers for disease classification, the area under the receiver-operating characteristic (ROC) curve is a widely used performance metric that does not require us to commit to a specific decision threshold. For the same type of evaluations, a different metric known as the average precision (AP) is used much more widely in the information retrieval literature. We study both metrics in some depths in order to elucidate their difference and relationship. More specifically, we explain mathematically why the AP may be more appropriate if the earlier part of the ROC curve is of interest. We also address practical matters, deriving an expression for the asymptotic variance of the AP, as well as providing real-world examples concerning the evaluation of protein biomarkers for prostate cancer and the assessment of digital versus film mammography for breast cancer screening.Comment: The first two authors contributed equally to this paper, and should be regarded as co-first author

Preparation and properties of novel dental adhesives based upon pentaerythritol

Urethane methacrylates were synthesized from Pentaerythritol, TDI, HEMA and four phenolic blocking agents or from hydroxypropyl methacrylatel TDI and two phenolic blocking agents. All the products were characterized by melting pointy infrared spectroscopy, NMR spectra, and elemental analysis. The bonding of these materials to dentin slices was also investigated. Such materials are supposed to not only react with the organic constituent of dentin but also polymerized with restorative resin. It was found that bond strength was enhanced by the use of the urethane methacrylates, resulting in best mean bonding strengths of 2400 psi