Let P2n be a point set in the plane with n red and n blue points. Let CR and CB (SR and SB) respectively be red and blue colored and disjoint disks (axisparallel squares). In this paper we prove the following results. Finding the positions for CR and CB that maximizes the number of red points covered by CR plus the number of blue points covered by CB can be done in O(n log n) time. Finding two ...

Let F be a graph and let G, H denote nonempty families of graphs. We write F → (G,H) if in any 2-coloring of edges of F with red and blue, there is a red subgraph isomorphic to some graph from G or a blue subgraph isomorphic to some graph from H. The graph F without isolated vertices is said to be a (G,H)-minimal graph if F → (G,H) and F − e 6→ (G,H) for every e ∈ E(F ). We present a technique ...

1.1. Jigsaw puzzles reimagined. I will describe jigsaw puzzles that are somewhat different to the familiar kind. A box, shown in Figure 1, contains an infinite supply of the three types of pieces pictured on its side: one five–sided and two four–sided, their edges coloured green, blue and red and directed by arrows. It also holds an infinite supply of red, green and blue rods, again directed by...

Leukocyte segmentation is one of the essential steps in an automatic leukocyte recognition system. Due to the complexity of the overlapping cell images, methods for leukocyte segmentation are still needed. In this paper, we first construct a combined image by saturation and green channels to extract the nucleus and in turn locate a cursory circular region of the leukocyte. Then the boundary of ...

A red tide rolls ashore in Puget Sound, Washington. Environmental changes, heightened awareness, and improved detection have increased the number of HABs reported each year.

the value of good X (x-axis) and such that the response is menu dependent (red when X is offered against Y, blue when X is offered against Z). Transitivity violations (i.e., cases where x-axis orderings are not conserved on the y-axis) are possible, as for X1, X2, X3. However, if the representation is menu invariant (i.e., if red and blue lines coincide), transitivity violations cannot occur. I...