S. P. Franklin and G. V. Krishnarao have defined a point x in a topological space (X, 9~) to be a strong cut point if the set X — {x} has two components. They then show that " a connected and locally connected separable and regular space, in which every point is a strong cut point, is homeomorphic to the real line " [1]. We will show that a separable Hausdorjf space (X, ST) is homeomorphic to t...

This paper presents a novel approach to separate connected digits in handwritten numerals by employing two agents in the process. The first agent decides on candidate cut-point as the closest feature-point to the center of the deepest top-valley, if any. The second agent argues candidate cut-point as the closest feature-point to the center of the highest bottom-hill, if any. Then the actual cut...

Assume that 2m red points and 2n blue points are given on the lattice Z2 in the plane R2. We show that if they are in general position, that is, if at most one point lies on each vertical line and horizontal line, then there exists a rectangular cut that bisects both red points and blue points. Moreover, if they are not in general position, namely if some vertical and horizontal lines may conta...

We consider various decision problems for probabilistic finite automata (PFA)s with isolated cut-points. Recall that a cut-point x is said to be isolated for a PFA if the acceptance probability of all finite strings is bounded away from x. First we establish the exact level of undecidability of the problem of determining if a cut-point is isolated; we show this problem to be Σ2-complete. Next w...

We propose and test several computational methods to automatically determine possible saliency cut-off points in Sketch Engine (Kilgarriff and Tugwell, 2001). Sketch Engine currently displays collocations in descending importance, as well as according to grammatical relations. However, Sketch Engine does not provide suggestions for a cut-off point such that any items above this cut-off point ma...

with different baseline characteristics and different therapy approaches. Similarly, a cut point defined in one chemotherapy trial might be different in a second chemotherapy trial with different treatment and response rate. From our point of view, this shows that a data-derived cut point optimization is not possible. However, this does not imply that Ki67—and other proliferation markers—are no...