By applying the matroid partition theorem of J. Edmonds [1] to a hypergraphic generalization of graphic matroids, due to M. Lorea [3], we obtain a generalization of Tutte’s disjoint trees theorem for hypergraphs. As a corollary, we prove for positive integers k and q that every (kq)-edge-connected hypergraph of rank q can be decomposed into k connected sub-hypergraphs, a well-known result for q...

The role of the normalized modularity matrix in finding homogeneous cuts will be presented. We also discuss the testability of the structural eigenvalues and that of the subspace spanned by the corresponding eigenvectors of this matrix. In the presence of a spectral gap between the k− 1 largest absolute value eigenvalues and the remainder of the spectrum, this in turn implies the testability of...

We consider the problem of determining, given x, y ∈ Z and a finite set F of affine functions on Z, whether y is reachable from x by applying the functions F . We also consider the analogous problem over N. These problems are known to be undecidable for k ≥ 2. We give 2-EXPTIME algorithms for both problems in the remaining case k = 1. The exact complexities remain open, although we show a simpl...

The shortest hyperpath problem is an extension of the classical shortest path problem and has applications in many different areas. Recently, algorithms for finding the K shortest hyperpaths in a directed hypergraph have been developed by Andersen, Nielsen and Pretolani. In this paper we improve the worst-case computational complexity of an algorithm for finding the K shortest hyperpaths in an ...

We present here a new formalization of beliefs, which has a simpler semantics than the previous formalizations, and develop an inference method for it by generalizing the resolution method. The usual prepositional formulas are embedded in our logic as a special type of belief formulas. One can obtain a non-monotonic logic of beliefs by applying, say, circumscription to the basic belieflogic dev...

In this article I consider the convergence of the Eilenberg– Moore spectral sequence for Morava K-theory. This spectral sequence can be constructed by applying Morava K-theory to D. L. Rector’s geometric cobar construction of the Eilenberg–Moore spectral sequence. I have shown that the Eilenberg–Moore spectral sequence for Morava Ktheory converges if the Eilenberg–Moore spectral sequence for or...

In this paper, the idea of applying the k-harmonic means (KHM) technique in biomedical colour image segmentation is presented. The k-means (KM) technique establishes a background for the comparison of clustering techniques. Two original initialization methods for both clustering techniques and two evaluation functions are described. The proposed method of colour image segmentation is completed ...

In this note, we describe a method of simulated annealing for producing k-anonymity. For analytic purposes, there is no reason to expect that the method will be superior or worse than the method of applying genetic algorithms used by Iyengar (2002). The main appeal of simulated annealing is the amount of control it allows of the microaggregation process. The k-anonymity problem is known to be N...

We propose broadcasting algorithms for line digraphs in the telephone model. The new protocols use a broadcasting protocol for a graph G to obtain a broadcasting protocol for the graph L k (G), the graph obtained by applying k times, the line digraph operation to G. As a consequence improved bounds for the broadcasting time in De Bruijn, Kautz and Wrapped Butterry digraphs are obtained.

economic growth is the most important purpose of developing countries. each country can improve social welfare and access to international markets by increasing production potential. production can increase by two ways: the first one, using more inputs that raising production cost and the second one, improving efficiency that can produce more output with certain inputs or the same output with l...