The use of statistical measures to constrain generalisa-tion in learning systems has proved successful in many domains, but can only be applied where large numbers of examples exist. In domains where few training examples are available, other mechanisms for constraining gener-alisation are required. In this paper, we propose a representation of background knowledge based on arguments for and ag...

The objective of this paper is to describe a new approach for locating the centromere of each chromosome displayed in the digitalized photomicrography of fish cells. To detect the centromere position, the authors propose methods for both image segmentation and split touching chromosomes based on the fuzzy sets theory and a method for the rotation of chromosomes. These methods were applied to tw...

Data-extrapolating (extension) technique has important applications in image processing on implicit surfaces and in level set methods. The existing data-extrapolating techniques are inefficient because they are designed without concerning the specialities of the extrapolating equations. Besides, there exists little work on locating the narrow band after data extrapolating—a very important probl...

A set D of vertices in a graph G is a locating-dominating set if for every two vertices u, v of G \ D the sets N(u) ∩ D and N(v) ∩ D are non-empty and different. In this paper, we characterize vertices that are in all or in no minimum locating dominating sets in trees. The characterization guarantees that the γL-excellent tree can be recognized in a polynomial time.

The network design problem with relays (NDPR) is defined on an undirected graph G = (V,E,K), where V = {1, . . . ,n} is a vertex set, E = {(i, j) : i, j 2 V, i < j} is an edge set. The set K = {(o(k),d(k))} is a set of communication pairs (or commodities): o(k) 2 V and d(k) 2 V denote the origin and the destination of the kth commodity, respectively. With each edge (i, j) are associated a cost ...

A locating-dominating set D of a graph G = (V (G), E(G)) is a set D ⊆ V (G) such that every vertex of V (G) − D is adjacent to a vertex of D and for every pair of distinct vertices u, v in V (G) − D, N(u) ∩ D = N(v) ∩ D. The minimum cardinality of a locating-dominating set is denoted by γL(G). A graph G is said to be a locating domination edge removal critical graph, or just γ L -ER-critical gr...

A total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. A locating-total dominating set of G is a total dominating set D of G with the additional property that every two distinct vertices outside D have distinct neighbors in D; that is, for distinct vertices u and v outside D, N(u) ∩D 6= N(v) ∩D where N(u) denotes the open neighborhood of...

For a graph G = (V,E) without isolated vertices, a subset D of vertices of V is a total dominating set (TDS) of G if every vertex in V is adjacent to a vertex in D. The total domination number γt(G) is the minimum cardinality of a TDS of G. A subset D of V which is a total dominating set, is a locating-total dominating set, or just a LTDS of G, if for any two distinct vertices u and v of V (G) ...

Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its neighbourhood within the dominating set. In this paper, we study the size of a smallest locating-dominating set or identifying code for graphs of girth at least 5 and o...