Mathematical Morphology, partially ordered sets, complete semilattices, signal processing, image processing In this paper, we prove that several key signal processing tasks (linear filtering, quantization, decimation, JPEG coding, and others) are particular cases of morphological operators. This is obtained as a consequence of the recent extension of MM's framework, from complete lattices to co...

A bipartite tournament is a directed graph T := (A ∪ B,E) such that every pair of vertices (a, b), a ∈ A, b ∈ B are connected by an arc, and no arc connects two vertices of A or two vertices of B. A feedback vertex set is a set S of vertices in T such that T − S is acyclic. In this article we consider the Feedback Vertex Set problem in bipartite tournaments. Here the input is a bipartite tourna...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii PRELIMINARIES AND NOTATION . . . . . . . . . . . . . . . . . . . . . ix CHAPTER 1. OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 The Graph Ramsey Number . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Arrow Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 The Dir...

The handling of partially ordered degrees of preference can be important for constraint-based languages, especially when there is more than one criterion that we are interested in optimising. This paper describes branch and bound algorithms for a very general class of soft constraint optimisation problems. At each node of the search tree, a propagation mechanism is applied which generates an up...

We consider a stochastic directed graph on the integers whereby a directed edge between i and a larger integer j exists with probability pj−i depending solely on the distance between the two integers. Under broad conditions, we identify a regenerative structure that enables us to prove limit theorems for the maximal path length in a long chunk of the graph. The model is an extension of a specia...

The notation "" for OR is bad and misleading. Just think that in the context of boolean functions, the author uses  instead of ∨.The integers modulo 2, that is Z2  0,1, have an addition where 1  1  0 while 1 ∨ 1  1. A set A is partially ordered by a binary relation ≤, if this relation is reflexive, that is a ≤ a holds for every element a ∈ S, it is transitive, that is if a ≤ b and b ≤ c...

the notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. the extensionproperty for (fuzzy) absorbent orderedfilters is established. conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...

We introduce partially ordered two-way Büchi automata and characterize their expressive power in terms of fragments of first-order logic FO[<]. Partially ordered two-way Büchi automata are Büchi automata which can change the direction in which the input is processed with the constraint that whenever a state is left, it is never re-entered again. Nondeterministic partially ordered two-way Büchi ...

In this paper, we show that if a partially ordered set has 2n elements and has dimension n, then it is isosnorphic to the set of n-l element subsets and lelement subsets of a sef, ordered by inclusion, or else it has six elements and is isomorphic to a partially ordered b;i we call the chevron or to its dual.