Union types allow to capture the possibility of a term to be of several possibly unrelated types. Traditional static approaches to union types are untagged and tagged unions, which present dual advantages in their use. Inspired by recent work on using abstract interpretation to understand gradual typing, we present a novel design for union types, called gradual union types. Gradual union types ...

In this paper, we deal with special generalization of measures by considering their values in the set of gradual numbers. Firstly, the concept of gradual number-valued measures is introduced and some of its properties are investigated. And then, Lebesgue type decomposition theorem for this kind of measure is obtained. Mathematics Subject Classification: 28E10, 03E72

Interrupted Time Series (ITS) analysis represents a powerful quasi-experime-ntal design in which a discontinuity is enforced at a specific intervention point in a time series, and separate regression functions are fitted before and after the intervention point. Segmented linear/quantile regression can be used in ITS designs to isolate intervention effects by estimating the sudden/level change (...

Few clinical studies have evaluated physiotherapeutic interventions for patients with degenerative cerebellar disease. In particular, evidence for long-term effects and transfer to activities of daily life is rare. We have recently shown that coordinative training leads to short-term improvements in motor performance. To evaluate long-term benefits and translation to real world function, we her...

Gradual Abstract Proof Search (GAPS) is a new 2-player search technique. It has been used to prove that 11x11 Phutball is a win for the first player in 25 plies or less, that 6x6 Atari-Go with a crosscut in the center is a win for the first player in 15 plies or less. I give domain dependent optimizations for the two games. I also describe theoretical and experimental comparisons with other rel...

Gradual typing combines static and dynamic typing in the same program. One would hope that the performance in a gradually typed language would range between that of a dynamically typed language and a statically typed language. Existing implementations of gradually typed languages have not achieved this goal due to overheads associated with runtime casts. Takikawa et al. (2016) report up to 100×...

This paper presents an approach to the approximate description of univariate real-valued functions in terms of precise or imprecise reference points and interpolation between these points. It is achieved by means of gradual rules which express that the closer the variable to the abscissa of a reference point, the closer the value of the function to the ordinate of this reference point. Gradual ...

To index, search, browse and retrieve relevant material, indexes describing the video content are required. Here, a new and fast strategy which allows detecting abrupt and gradual transitions is proposed. A pixel-based analysis is applied to detect abrupt transitions and, in parallel, an edge-based analysis is used to detect gradual transitions. Both analysis are reinforced with a motion analys...