We proposed a simple formula to assess the statistical significance of homologous segments found in comparison of two nucleic acid sequences (Goad and Kanehisa, Nucleic Acids Res. 10, 247-263, 1982). This paper clarifies the basic assumptions of the formula and its reliability is examined by Monte Carlo calculations. The results were satisfactory for random sequences. The formula is a useful me...

A (finite) sequence of nonnegative integers is graphic if it is the degree sequence of some simple graph G. Given graphs G1 and G2, we consider the smallest integer n such that for every n-term graphic sequence π, there is some graph G with degree sequence π with G1 ⊆ G or with G2 ⊆ G. When the phrase “some graph” in the prior sentence is replaced with “all graphs” the smallest such integer n i...

A bisection of a graph G is a balanced bipartite spanning subgraph of G. Given a graphic sequence π, we show that π has a realization G containing a bisection H where degH(v) ≥ b(degG(v)− 1)/2c for all vertices v. This bound is very close to best possible. We use this result to provide evidence for a conjecture of Busch et. al. [1] that if π and π − k are graphic sequences, then π has a realiza...

At the 16th British Combinatorial Conference (1997), Cameron introduced a new concept called 2-simultaneous edge-coloring and conjectured that every bipartite graphic sequence, with all degrees at least 2, has a 2-simultaneous edge-colorable realization. In fact, this conjecture is a reformulation of a conjecture of Keedwell (Graph Theory, Combinatorics, Algorithms and Applications, Proceedings...

in this paper, we introduce and study the concepts of $mathcal{i}_2$-convergence, $mathcal{i}_2^{*}$-convergence for double sequences of fuzzy real numbers, where $mathcal{i}_2$ denotes the ideal of subsets of $mathbb n times mathbb n$. also, we study some properties and relations of them.

A (finite) sequence of nonnegative integers is graphic if it is the degree sequence of some simple graph G. Given graphs G1 and G2, we consider the smallest integer n such that for every n-term graphic sequence π, there is some graph G with degree sequence π with G1 ⊆ G or with G2 ⊆ G. When the phrase “some graph” in the prior sentence is replaced with “all graphs” the smallest such integer n i...

UNLABELLED The correct post-transcriptional RNA processing is finely regulated by RNA-binding proteins. Unfortunately, there is little experimental information on target RNA sequences of RNA-binding proteins and moreover such experimentally derived target sequences are annotated in a compact form by the score matrices that overestimate the number of possible recognized sequences. We carried out...

AMILab is an image processing environment with a graphic window interface which runs on Unix workstations or Linux machines. It contains specific features for reading, saving and visualizing 2D and 3D images. Most of the standard image formats can be read and saved (GIF, JPEG, TGA, TIFF, etc ...). Images can be zoomed and intensity can be adjusted in real time. Furthermore, it can also work wit...

Petri nets are a graphic and mathematic modeling tool which is applicable to several systems and to all those systems presenting particular characteristics such as concurrency, distribution, parallelism, non-determinism and/or stochastically. In this paper, a wheel Petri net whose reachability tree contains all the binary ntuples or sequences as marking vectors has been defined. The result is p...