Unlike most artificial systems, the brain is able to face situations that it has not learned or even encountered before. This ability is not in general echoed by the properties of most neural networks. Here, we show that neural computation based on least-square error learning between populations of intensity-coded neurons can explain interpolation and extrapolation capacities of the nervous sys...

We extend lemmas by Bourgain-Brezis-Mironescu (2001), and Maz’ya-Shaposhnikova (2002), on limits of Sobolev spaces, to the setting of interpolation scales. This is achieved by means of establishing the continuity of real and complex interpolation scales at the end points. A connection to extrapolation theory is developed, and a new application to limits of Sobolev scales is obtained. We also gi...

The E{algorithm is the most general extrapolation algorithm actually known. The aim of this paper is to provide a new approach to this algorithm. This approach gives a deeper insight into the E{algorithm, allows to obtain new properties and to relate it to other algorithms. Some extensions of the procedure are discussed. The E{algorithm is the most general extrapolation algorithm actually known...

This paper presents an interpolation/extrapolation technique for sequence partitions. It consists of four steps: region parametrization, region interpolation, region ordering and partition creation. The evolution of each region is divided into two types: regular motion and random deformations. Both types of evolution are parametrized by means of the Fourier descriptors of the regions and they a...

In this paper, we present a new approach to obtain the asymptotic expansion and superconvergence for the linear element on Union Jack mesh. First, we construct a generalized interpolation function and its discrete harmonic extension by using the energy embedding method and the method of separation of variables. Then, we present elaborate estimates for the generalized interpolation function and ...

We developed a melody-morphing method in which we input melodies A and B and not only interpolate but also extrapolate other melodies between those two melodies. This is done in a systematic order according to a certain numerical measure, based on the parameters which reflect the influential features of two input melodies. The main advantage of our method is that a time-span tree is used, which...

Fuzzy Rule Interpolation and Extrapolation Techniques: Criteria and Evaluation Guidelines Domonkos Tikk∗1, Zsolt Csaba Johanyák∗2, Szilveszter Kovács∗3, and Kok Wai Wong∗4 ∗1Dep. of Telecommunications and Media Informatics, Budapest University of Technology and Economics Magyar tudósok krt. 2, H-1117 Budapest, Hungary E-mail: [email protected] ∗2Institute of Information Technology, Kecskemét Col...

A common problem in optical motion capture is the so-called missing marker problem. The occlusion of markers can lead to significant loss of tracking accuracy unless continuous data flow is guaranteed by computationally demanding interpolation or extrapolation schemes. Since interpolation algorithms require data sampled before and after an occlusion, they cannot be used for real-time applicatio...