The pattern regulation process in amphibian limbs has been examined with respect to the presence of discontinuities in the anterior-posterior (a-p) axis. Limbs bearing such discontinuities were surgically created by contralateral exchange of either dorsal or ventral half thighs and these limbs were then amputated immediately after surgery. The results demonstrate that a-p discontinuities lead t...

The textural discontinuity hypothesis (TDH) is based on the observation that animal body mass distributions exhibit discontinuities that may reflect the texture of the landscape available for exploitation. This idea has been extended to other complex systems, hinting that the identification and quantification of discontinuities in the distributions of appropriate variables may provide clues to ...

Physical systems are by nature continuous. Perceived discontinuities in system models are in reality nonlinear behaviors that are linearized to reduce computational complexity and prevent stiffness in system analysis and behavior generation. Discontinuities arise primarily from component parameter simplification and time-scale abstraction. Discontinuities in models are handled by introducing id...

In order to transmit or store three-dimensional (3-D) mesh models efficiently, we need to simplify them. Although the quadric error metric (QEM) provides fast and accurate geometric simplification of 3-D mesh models, it cannot capture discontinuities faithfully. Recently, an enhanced QEM based on subdivided edge classification has been proposed to handle this problem. Although it can capture di...

We study the multi-dimensional re ection map on the spaces D([0; T ];Rk ) and D([0;1);Rk ) of right-continuous Rk -valued functions on [0; T ] or [0;1) with left limits, endowed with variants of the Skorohod(1956) M1 topology. The re ection map was used with the continuous mapping theorem by Harrison and Reiman (1981) and Reiman (1984) to establish heavy-tra c limit theorems with re ected Brown...

We introduce a new texture representation that combines standard bi-linearly interpolated samples, for smoothly varying regions, with customizable discontinuities for sharp boundaries between these regions. It consists in a standard signal texture, plus a second texture we call pinchmap, which encodes discontinuities along generally curved lines; this structure is stored in texture memory as a ...