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Equivalence, Indicators, Quasi-indicators and Optimal Steiner Topologies on Four Points in Space

100%

Weng J. F. , Smith J. M. , Brazil M. , Thomas D. A.

2008

tom Vol. 84, nr 1

135-149

The Steiner tree problem is an intractable optimization problem, which asks for a network, in fact a tree, interconnecting a given point set V in a metric space and minimizing the total length of the network. The tree topology t of the network is called a Steiner topology and a tree T with minimum length with respect to its Steiner topology is called a Steiner tree. As a combinatorial optimization problem, the Steiner tree problem asks for a Steiner tree T with minimum length over all possible topologies t on V. It has been proved that if T is in E3 then the length of T cannot be expressed by radicals even when T spans just 4 points. For such optimization problems in which the objective functions do not have closed form solutions the traditional approach is approximation. In this paper we propose a new approach by introducing some new concepts: equivalence, indicators and quasi-indicators, and then we apply these concepts to the Steiner tree problem. Roughly speaking, a quasi-indicator is a function that is simple to compute but indicates with high probability the optimal solution to the original optimisation problem. For a specific optimisation problem - finding the optimal Steiner topologies on 4 points in space, we demonstrate how to find good quasi-indicators. The extensive computational experiments over 5000 random 4-point sets show that the best quasi-indicator for finding optimal Steiner topologies on 4 points in space is not only easy to compute but also extremely successful with less than 1.5% failures in indicating optimal topologies even if degeneracy of Steiner minimal trees exists. Moreover, within the 1.5% cases of failure, the maximum and the average relative error are 1.5% and 0.2% respectively. Therefore, the performance of the proposed Q-indicator is very good and could be applied to the four vertices surrounding any pair of adjacent Steiner points in a Steiner tree on n ( > 4) points in space to make local improvements to the topology of the Steiner minimal tree in space.

Application of culture dependent methods and culture-independent methods (DGGE analysis) to study Lactic acid bacteria ecology of Ivorian fermented fish Adjuevan

88%

Clementine K. A. , Nguessan K. F. , Thomas D. A. , Dje M. K. , Montet D.

Challenges of Modern Technology

2012

tom Vol. 3, no. 1

51--56

The occurrence of lactic acid bacteria flora (LAB) was investigated on Ivorian fermented fish Adjuevan products produced with sea fish at different salt concentration (10, 15, 20, 25, 30%) according two traditional methods. LAB biodiversity was investigated using traditional culture-dependent method and culture-independent method (DGGE). LAB isolates were Lactobacillus fermentum 54%, Leuconostoc lactis subsp lactis 27%, Pediococcus pentosaceus 19% according method 1 and Pediococcus pentosaceus 61%, Lactococcus garviae 32%, Streptococcus diffi cilis 7% for method 2. The results of culture-independent method using DGGE patterns and sequencing of DNA bands revealed a higher number of lactic acid bacteria species even if the identification of several lactic acid bacteria species were not possible by traditional microbiological procedures. LAB were Lactobacillus delbrueckii subsp bulgaricus, Lactobacillus helveticus, Leuconostoc lactis, Lactococcus raffi nolactis. Microflora was influence by salt percentage and more by the method of fermentation used. The molecular method DGGE which used three primers Lac1, Lac2GC and Lac3 to study LAB biodiversity directly in the fermented fish matrix, have allowed us to get a more complete picture of the dominant lactic acid bacteria diversity in these fermented product Adjuevan.