We propose to accelerate the rate of convergence of the pattern recognition task by directly minimizing the variance diameters of certain hypothesis spaces, which are critical quantities in fast-convergence results. We show that the variance diameters can be controlled by dividing hypothesis spaces into metric balls based on a new order metric. This order metric can be minimized as an ordinal r...

How can we grasp the temporal structure of events? A few studies have indicated that representations of temporal structure are acquired when there is an intention to learn, but not when learning is incidental. Response-to-stimulus intervals, uncorrelated temporal structures, unpredictable ordinal information, and lack of metrical organization have been pointed out as key obstacles to incidental...

In some statistical process monitoring applications, quality of a process or product is described by more than one ordinal factors called ordinal multivariate process. To show the relationship between these factors, an ordinal contingency table is used and modeled with ordinal log-linear model. In this paper, a new control charts based on ordinal-normal statistic is developed to monitor the ord...

Statistical complexity measures are used to quantify the degree of complexity of the delayed logistic map, with linear and nonlinear feedback. We employ two methods for calculating the complexity measures, one with the 'histogram-based' probability distribution function and the other one with ordinal patterns. We show that these methods provide complementary information about the complexity of ...

We expose a pattern for establishing Friedman-Weiermann style independence results according to which there are thresholds of provability of some parameterized variants of well-partial-ordering. For this purpose, we investigate an ordinal notation system for θΩω , the small Veblen ordinal, which is the proof-theoretic ordinal of the theory (Π2-BI)0. We also show that it sometimes suffices to pr...

INTRODUCTION A functional activation (i.e., ordinal trend) pattern was previously identified in both young and older adults during task-switching performance, the expression of which correlated with reaction time. The current study aimed to (1) replicate this functional activation pattern in a new group of fMRI activation data, and (2) extend the previous study by specifically examining whether...