We propose manifold piecewise constant systems (ab. MPC) and consider basic phenomena: the 2-D, 3-D and 4-D MPCs exhibit limit-cycle, line-expanding chaos and areaexpanding chaos, respectively. The righthand side of the state equation is piecewise-constant, hence the system dynamics can be simplified into a piecewise-linear return map which can be expressed explicitly. In order to analyze the p...

Let P = fp1; : : : ; png and Q = fq1; : : : ; qng be two point sets lying in the interior of rectangles in the plane. We show how to construct a piecewise linear homeomorphism of size O(n2) between the rectangles which maps pi to qi for each i. This bound is optimal in the worst case; i.e., there exist point sets for which any piecewise linear homeomorphism has size (n2). Introduction A homeomo...

The need to reduce the dimensionality of a dataset whilst retaining inherent manifold structure is key in many pattern recognition, machine learning and computer vision tasks. This process is often referred to as manifold learning since the structure is preserved during dimensionality reduction by learning the intrinsic low-dimensional manifold that the data lies on. Since the inception of mani...

This paper presents a minutiae detection procedure based on adaptive tracing the gray-level ridge of the "ngerprint image with piecewise linear lines of di!erent length. The original "ngerprint image is smoothed with an adaptive-oriented smoothing "lter only at some selected points. This will greatly reduce the computational time. Each ridge in the skeleton is labeled with a number so that each...

We study a class of orthonormal exponential bases for the space L2[0, 1] and introduce the concept of spectral sequences. We characterize piecewise linear spectral sequences with the knot at 1/2 and investigate the non-continuity of the piecewise linear spectral sequences. From a special construction of a piecewise constant spectral sequence, the classical Walsh system is recovered.

Diffusion processes are often regarded as among the more abstruse stochastic processes, but diffusion processes are actually relatively elementary, and thus are natural first candidates to consider in queueing applications. To help demonstrate the advantages of diffusion processes, we show that there is a large class of one-dimensional diffusion processes for which it is possible to give conven...

The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is used to establish lattice polynomial representations of piecewise linear functions on R and continuous selectors on linear orders.