• Bulletin of the Korean Mathematical Society
• /
• v.41 no.1
• /
• pp.189-198
• /
• 2004

In this study we consider quantum dynamical semi-group with a normal faithful invariant state. A quantum dynamical semigroup $\alpha\;=\;\{{\alpha}_t\}_{t{\geq}0}$ is a class of linear normal identity-preserving mappings on a von Neumann algebra M with semigroup property and some positivity condition. We investigate the asymptotic behaviors of the semigroup such as ergodicity or mixing properties in terms of their eigenvalues under the assumption that the semigroup satisfies positivity. This extends the result of [13] which is obtained under the assumption that the semi group satisfy 2-positivity.

• Communications for Statistical Applications and Methods
• /
• v.23 no.1
• /
• pp.1-20
• /
• 2016

Causal inference methodologies have been developed for the past decade to estimate the unconfounded effect of an exposure under several key assumptions. These assumptions include, but are not limited to, the stable unit treatment value assumption, the strong ignorability of treatment assignment assumption, and the assumption that propensity scores be bounded away from zero and one (the positivity assumption). Of these assumptions, the first two have received much attention in the literature. Yet the positivity assumption has been recently discussed in only a few papers. Propensity scores of zero or one are indicative of deterministic exposure so that causal effects cannot be defined for these subjects. Therefore, these subjects need to be removed because no comparable comparison groups can be found for such subjects. In this paper, using currently available causal inference methods, we evaluate the effect of arbitrary cutoffs in the distribution of propensity scores and the impact of those decisions on bias and efficiency. We propose a tree-based method that performs well in terms of bias reduction when the definition of positivity is based on a single confounder. This tree-based method can be easily implemented using the statistical software program, R. R code for the studies is available online.

• The Korean Journal of Applied Statistics
• /
• v.34 no.2
• /
• pp.141-152
• /
• 2021

A new statistical model needs additional variables in order to re-evaluate the undecided inference. Then the MNAR assumption is required, since the probabilities for the positivity of the indeterminant and the determinant is calculated differently. In this study, since two statistical models have a hierarchical relationship, we determine the undecided inference under the MNAR assumption using the confidence interval of the difference between two AUCs. Among many methods of estimating the confidence interval of the AUC difference, it is found that four kinds of methods show excellent performance through simulations. And based on these methods, we propose a variable selection method that are useful for the undecided inference using logistic regression models.

• Journal of Korean Philosophical Society
• /
• v.145
• /
• pp.245-270
• /
• 2018

This article aims to examine the possibility of 'philosophy for old age' when humanity begins to reflect on old age in earnest as our country shifts to the aged society. In particular, this article aims to reframe $Ved{\bar{a}}ntic$ philosophy, i.e. a beacon of Hindu philosophy as a model of philosophy for old age, on the assumption that liberation-oriented Hindu philosophies in India can be the most suitable model to frame and apply philosophy for old age mainly at the individual level. First of all, this article identifies that liberation-oriented Hindu philosophies are nothing but a philosophy for the later part of one's life, that is, a philosophy for old age, showing that their common thoughts are very similar to the characteristics of old age. Then, it proves that three points of $Ved{\bar{a}}ntic$ philosophy, i.e. spirit supremacy, the world as an illusion, and freedom from all relations, are fully compatible with philosophy for old age. Finally, it argues that the tradition of Hindu saṃnyāsin (wonderer) embodied to the extreme in $Ved{\bar{a}}ntic$ philosophy is to establish 'old age for philosophy' beyond 'philosophy for old age.' Because $Ved{\bar{a}}ntic$ philosophy establishes saṃnyāsin of old age, which is optimized to strive for the truth as the confident subject of philosophical inquiry, so much that it exists more 'by old age' than 'for old age.' After all, according to $Ved{\bar{a}}ntic$ philosophy, as ontological and practical positivity is maximized in old age, so old age itself can be the best position to overcome not 'negativity of old age', but 'negativity of human condition' or 'negativity of life.'