Threshold Circuits Detecting Global Patterns in Two-dimensional Maps

Threshold Circuits Detecting Global Patterns in Two-dimensional Maps

In this paper, we consider a biologically-inspired Boolean function P D that models a simple task of detecting global spatial patterns on a twodimensional map. We prove that P D is computable by a threshold circuit of size (i.e., number of gates) O( √ n logn), which is an improvement on the previous upper bound O(n), while our circuit has larger depth O( √ n) and total wire length O(n log n). M...

Detecting disparity in two-dimensional patterns

One can measure the disparities between two retinal images in several different ways. Experiments were conducted to identify the measure that is invariant at the threshold for detecting the disparity of two-dimensional patterns. The patterns used were stereo plaids, which permit a partial dissociation between the disparity of the pattern and the disparities of its one-dimensional components. Fo...

Energy-Efficient Threshold Circuits Detecting Global Pattern in 1-Dimentional Arrays

Transport in Two-Dimensional Maps

We study transport in the two-dimensional phase space of C r diffeomorphisms (r ~ 1) of two manifolds between regions of the phase space bounded by pieces of the stable and unstable manifolds of hyperbolic fixed points. The mechanism for the transport is associated with the dynamics of homoclinic and heteroclinic tangles, and the study of this dynamics leads to a general formulation for the tra...

Bifurcations in Two-dimensional Piecewise Smooth Maps | Theory and Applications in Switching Circuits

Recent investigations on the bifurcation behavior of power electronic dc-dc converters has revealed that most of the observed bifurcations do not belong to generic classes like saddle-node, period doubling or Hopf bifurcations. Since these systems yield piecewise smooth maps under stroboscopic sampling, a new class of bifurcations occur in such systems when a xed point crosses the \border" betw...