On two-qubit states ordering with quantum discords

The counterintuitive effect of non-unique ordering of two-qubit states with quantum entanglement measures was discovered over ten years ago. More precisely, it was shown by Monte Carlo simulations that there exist states for which the entanglement of formation and the negativity do not impose the same ordering of states, i.e. $E_{F}(\rho_{AB}) \leq (\geq) E_{F}(\rho_{AB}^{\prime})$ is not equivalent to $N(\rho_{AB}) \leq (\geq) N(\rho_{AB}^{\prime})$. Recently, it was discovered that quantum discord and the geometric quantum discord do not necessarily imply the same ordering of two-qubit $X$-states, which means that the lack of the unique ordering of states with quantum entanglement measures goes beyond entanglement. Inspired by this observation, we study the problem of the states ordering with quantum discords, considering two-qubit Bell-diagonal states for analytical simplicity. In particular, we identify some classes of states for which the states ordering with quantum discords is preserved as long as the states belong to the same class and give a few illustrative examples.Comment: 6 pages, 4 figure

A generalized matrix profile framework with support for contextual series analysis

The Matrix Profile is a state-of-the-art time series analysis technique that can be used for motif discovery, anomaly detection, segmentation and others, in various domains such as healthcare, robotics, and audio. Where recent techniques use the Matrix Profile as a preprocessing or modeling step, we believe there is unexplored potential in generalizing the approach. We derived a framework that focuses on the implicit distance matrix calculation. We present this framework as the Series Distance Matrix (SDM). In this framework, distance measures (SDM-generators) and distance processors (SDM-consumers) can be freely combined, allowing for more flexibility and easier experimentation. In SDM, the Matrix Profile is but one specific configuration. We also introduce the Contextual Matrix Profile (CMP) as a new SDM-consumer capable of discovering repeating patterns. The CMP provides intuitive visualizations for data analysis and can find anomalies that are not discords. We demonstrate this using two real world cases. The CMP is the first of a wide variety of new techniques for series analysis that fits within SDM and can complement the Matrix Profile

Kant’s Antinomy of Teleology: In Defense of a Traditional Interpretation

Kant’s Antinomy of Teleological Judgment is unique in offering two pairs of oppositions, one of regulative maxims, and the other of constitutive principles. Here I defend a traditional interpretation of the antinomy— as proposed, for example, by Stadler (1874), Adickes (1925), and Cassirer (1921)—that the antinomy consists in an opposition between constitutive principles, and is resolved by pointing out their legitimate status as merely regulative maxims. I argue against recent interpretations—for example, in McLaughlin (1990), Allison (1991), and Watkins (2009)—which treat the regulative pair as itself antinomial. I then address several textual worries having to do with reconciling the traditional interpretation within the overall structure of the Dialectic of Teleological Judgment that have led these scholars to espouse the new view. Throughout the paper, I emphasize hitherto neglected parallels with Kant’s treatment of the antinomy of taste, which sheds light on understanding the antinomy of teleology