Characterization of graphs with hall number 2

Hall's condition is a simple requirement that a graph G and list assignment L must satisfy if G is to have a proper L‐colouring. The Hall number of G is the smallest integer m such that whenever the lists on the vertices each has size at least m and Hall's condition is satisfied a proper L‐colouring exists. Hilton and P.D. Johnson introduced the parameter and showed that a graph has Hall number 1 if and only if every block is a clique. In this paper we give a forbidden‐induced‐subgraph characterization of graphs with Hall number 2. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 81–100, 2004     

Inhibitor effect of sodium benzoate on the corrosion behavior of nanocrystalline pure iron metal in near-neutral aqueous solutions

Nanocrystalline iron coating was produced on carbon steel surface by pulse electrodeposition using citric acid bath. The grain size of a nanocrystalline surface was analyzed by X-ray diffractometry and scanning electron microscopy. The electrochemical behavior of nanocrystalline iron coating in the presence of sodium benzoate was evaluated in 30 mg l^-1 NaCl + 70 mg l^-1 Na₂SO₄ aqueous solution using potentiodynamic polarization curves and electrochemical impedance spectroscopy. The results were compared with that of the coarse-grained iron surface. The thermodynamic properties of the inhibitor adsorption were also determined. The results indicated that corrosion inhibition of sodium benzoate in near-neutral aqueous solution was increased as the grain size of iron was decreased from micro- to nanocrystalline surface. This was reported in terms of excess free energy of nanocrystalline surface.     

Importance of RNA secondary structure information for yeast donor and acceptor splice site predictions by neural networks

Previously, Patterson et al. showed that mRNA structure information aids splice site prediction in human genes [Patterson, D.J., Yasuhara, K., Ruzzo, W.L., 2002. Pre-mRNA secondary structure prediction aids splice site prediction. Pac. Symp. Biocomput. 7, 223-234]. Here, we have attempted to predict splice sites in selected genes of Saccharomyces cerevisiae using the information obtained from the secondary structures of corresponding mRNAs. From Ares database, 154 genes were selected and their structures were predicted by Mfold. We selected a 20-nucleotide window around each site, each containing 4 nucleotides in the exon region. Based on whether the nucleotide is in a stem or not, the conventional four-letter nucleotide alphabet was translated into an eight-letter alphabet. Two different three-layer-based perceptron neural networks were devised to predict the 5' and 3' splice sites. In case of 5' site determination, a network with 3 neurons at the hidden layer was chosen, while in case of 3' site 20 neurons acted more efficiently. Both neural nets were trained applying Levenberg-Marquardt backpropagation method, using half of the available genes as training inputs and the other half for testing and cross-validations. Sequences with GUs and AGs non-sites were used as negative controls. The correlation coefficients in the predictions of 5' and 3' splice sites using eight-letter alphabet were 98.0% and 69.6%, respectively, while these values were 89.3% and 57.1% when four-letter alphabet is applied. Our results suggest that considering the secondary structure of mRNA molecules positively affects both donor and acceptor site predictions by increasing the capacity of neural networks in learning the patterns.     

Theoretical Analysis of the Underwater Incremental Adaptive Network Performance Based on the VLC Technology

In this paper, the underwater implementation of the incremental adaptive networks is proposed based on the visible light communication technology. The underwater distance between transmitter and receiver nodes and the salinity and temperature levels of the considered water determines the stochastical properties of the underwater link that is modeled with the Log-normal distribution. The incremental network performance can be expressed with the excess mean square error and mean square deviation values and we used them in this paper for our theoretical analysis. Our findings showed that the distances between the nodes must not be more than 10 m or the incremental network will diverge from its estimation goal. The network performance is analyzed through multiple link distances and the results are presented with several simulations. The simulation results are devised in order to elaborate the effects of the underwater turbulent links on the performances of estimating adaptive network. Also, the impacts of different salinity and temperature levels are analyzed theoretically and the results are compared with the simulation results.