The performance of medical image classification has been enhanced by deep convolutional neural networks (CNNs), which are typically trained with cross-entropy (CE) loss. However, when the label presents an intrinsic ordinal property in nature, e.g., development from benign to malignant tumor, CE loss cannot take into account such information allow for better generalization. To improve model gen...

Combinatorics coding is a new data coding method based on combinatorics. Ordinal computing is the core technology of in the combinatorics coding. Ordinal properties of combinatorics coding is studied in this paper. Firstly, the combinatorics coding theory and the correlative basic concepts are described. Then, the properties of the ordinal are revealed. The study indicates that the value of ord...

Recently, Schlicht and Stephan lifted the notion of automatic-structures to the notion of (finite-word) ordinal-automatic structures. These are structures whose domain and relations can be represented by automata reading finite words whose shape is some fixed ordinal α. We lift Delhommé’s relative-growth-technique from the automatic and tree-automatic setting to the ordinal-automatic setting. T...

How do we compare the complexities of various classes of structures? The Turing ordinal of a class of structures, introduced by Jockusch and Soare, is defined in terms of the number of jumps required for coding to be possible. The back-and-forth ordinal, introduced by Montalbán, is defined in terms of Σα-types. The back-and-forth ordinal is (roughly) bounded by the Turing ordinal. In this paper...

Article history: Received 25 October 2010 Accepted 31 March 2011 Available online 8 April 2011

Several observations suggest that overlearned ordinal categories (e.g., letters, numbers, weekdays, months) are processed differently than non-ordinal categories in the brain. In synesthesia, for example, anomalous perceptual experiences are most often triggered by members of ordinal categories (Rich et al., 2005; Eagleman, 2009). In semantic dementia (SD), the processing of ordinal stimuli app...

Many applied studies collect one or more ordered categorical predictors, which do not fit neatly within classic regression frameworks. In most cases, ordinal predictors are treated as either nominal (unordered) variables or metric (continuous) variables in regression models, which is theoretically and/or computationally undesirable. In this paper, we discuss the benefit of taking a smoothing sp...