We prove a general theorem which includes most notions of “exact completion” as special cases. The theorem is that “κ-ary exact categories” are a reflective sub-2-category of “κ-ary sites”, for any regular cardinal κ. A κ-ary exact category is an exact category with disjoint and universal κ-small coproducts, and a κ-ary site is a site whose covering sieves are generated by κ-small families and ...

Two utility models are classically used to represent interaction among criteria: the Choquet integral and the Generalized Additive Independence (GAI) model. We propose a comparison of these models. Looking at their mathematical expression, it seems that the second one is much more general than the first one. The GAI model has been mostly studied in the case where attributes are discrete. We pro...

This paper proposes a model of placing a liaison which forms relations to two members of different levels in a pyramid organization structure such that the communication of information between every member in the organization becomes the most efficient. For the model of adding a node of liaison which gets adjacent to a node with a depth M and its descendant with a depth N in a complete K-ary tr...

In this paper, we present a real-time faulttolerant design for an l-level k-ary tree multiprocessor with two modes of operations and examine its reconfigurability. The k-ary tree is augmented by spare nodes at stages one and two. We consider two modes of operations, one under heavy computation or hard deadline and the other under light computation or soft deadline. By utilizing the capabilities...

Dimensionality reduction aims at providing low-dimensional representations of high-dimensional data sets. Many new nonlinear methods have been proposed for the last years, yet the question of their assessment and comparison remains open. This paper first reviews some of the existing quality measures that are based on distance ranking and K-ary neighborhoods. Next, the definition of the corankin...

Our weighted-tree similarity algorithm matches buyers and sellers in e-Business environments. We use arc-labeled, arc-weighted trees to represent the products (or services) sought/offered by buyers/sellers. Partial product descriptions can be represented via subtrees missing in either or both of the trees. In order to take into account the effect of a missing subtree on the similarity between t...

Given a simple graph G = (V,E), a subset S of the vertices is called a global defensive alliance if S is a dominating set and for every vertex v in S at least half of the vertices in the closed neighborhood of v are in S. Similarly, a subset S is called a global offensive alliance if S is a dominating set and for every vertex v not in S at least half of the vertices in the closed neighborhood o...

which reduce to (n + 1) for a = b = c = 1. We refine Cayley’s formula by showing that Pn(a, b, c) counts rooted forests by the number of trees and the number of proper vertices, which are vertices that are less than all of their proper descendants. Moreover, other evaluations of Pn(a, b, c) have similar interpretations for other types of trees and forests: k-ary trees, forests of ordered trees,...

Gossiping is the process of information diiusion in which each node of a network holds a packet that must be communicated to all other nodes in the network. We consider the problem of gossiping in communication networks under the restriction that communicating nodes can exchange up to a xed number p of packets at each round. In the rst part of the paper we study the extremal case p = 1 and we e...

This study considers the addition of relation to an organization structure such that the communication of information between every member in the organization becomes the most efficient. This paper proposes a model of adding relation to a linking pin organization structure where every pair of siblings in a complete K-ary tree of height H is adjacent. When a new edge between the root and a node ...