We show that, in a parametric model of polymorphism, the type ∀α.((α → α) → α) → (α → α → α) → α is isomorphic to closed de Bruijn terms. That is, the type of closed higher-order abstract syntax terms is isomorphic to a concrete representation. To demonstrate the proof we have constructed a model of parametric polymorphism inside the Coq proof assistant. The proof of the theorem requires parame...

This paper describes a new method to calculate the spatio-temporal correlation efficiently in a parametric eigenspace representation for moving object recognition. A parametric eigenspace compactly represents the temporal change of an image sequence by a trajectory in the eigenspace. This representation reduces the computational cost of correlation-based comparison between image sequences. Expe...

Logarithmic frequency representation plays an important role in many audio and acoustic signal processing applications. This article presents a methodology for frequency-warped signal processing where the frequency representation is logarithmic above a certain limit frequency. It is demonstrated how this approach can be used with FFT or linear prediction to perform non-parametric, or parametric...

Consider linear algebraic systems where the elements of the matrix and the right-hand side vector depend linearly on a number of interval parameters. We prove some sufficient conditions for the united parametric solution set of such a system to have linear boundary. These conditions imply an equivalent representation of the parametric system where each parameter appears once in a diagonal matri...

Weierstrass representation is a classical parameterization of minimal surfaces. However, two functions should be specified to construct the parametric form in Weierestrass representation. In this paper, we propose an explicit parametric form for a class of parametric polynomial minimal surfaces of arbitrary degree. It includes the classical Enneper surface for cubic case. The proposed minimal s...

Generative parametric CSG models, introduced by Snyder in 1992, have many desirable properties. Their functional representation is generally quite compact and resolution independent, since surfaces are represented as piecewise continuous functional programs. However, in practice they have proven impractical for real time rendering because of the difficulty of compactly and exactly representing ...

Traditionally, confounding by continuous variables is controlled by including a linear or categorical term in a regression model. Residual confounding occurs when the effect of the confounder on the outcome is mis-modelled. A continuous representation of a covariate was previously shown to result in a less biased estimate of the adjusted exposure effect than categorization provided the function...

We propose a method to generate a database that contains a parametric representation of F0 contours associated with linguistic and acoustic information, to be used by data-driven Japanese text-to-speech (TTS) systems. The configuration of the database includes recorded speech, F0 contours and their parametric labels, phonetic transcription with durations, and other linguistic information such a...

The parametric or geometric continuity of a rational polynomial curve has often been obtained by requiring the homogeneous polynomial curve associated with the rational curve to possess parametric or geometric continuity, respectively. Recently this approach has been shown overly restrictive. We make use of the necessary and su cient conditions of rational parametric continuity for de ning basi...

Many current geometric modeling systems use the rational parametric form to represent surfaces. Although the parametric representation is useful for tracing, rendering and surface tting, many operations like surface intersection desire one of the surfaces to be represented implicitly. Moreover, the implicit representation can be used for testing whether a point lies on the surface boundary and ...