Optimal Relay Location for Resource-limited Energy-efficient Wireless Communication

In the design of wireless networks, techniques for improving energy efficiency and extending network lifetime have great importance, particularly for defense and civil/rescue applications where resupplying transmitters with new batteries is not feasible. In this paper we study a method for improving the lifetime of wireless networks by minimizing the length of the longest edge in the interconnecting tree by deploying additional relay nodes at specific locations. This optimization problem, known as the Bottleneck Steiner Tree Problem (BSTP), asks to find a Steiner tree for n terminals with at most k Steiner points such that the length of the longest edge in the tree is minimized. We present a ratio- polynomial time approximation algorithm for BSTP, where is an arbitrary positive number.     

Stability of the phase transition of critical-field Ising model on Cayley trees under inhomogeneous external fields

We consider the ferromagnetic Ising model with spatially dependent external fields on a Cayley tree, and we investigate the conditions for the existence of the phase transition for a class of external fields, asymptotically approaching a homogeneous critical external field. Our results extend earlier results by Rozikov and Ganikhodjaev.     

Characterization of polysaccharides purified from Lacquer tree seed cakes and its antioxidant activity

Three polysaccharides, LTPS-1, LTPS-21 and LTPS-31 were isolated and purified from the seed cakes of lacquer tree using DEAE-52 cellulose and Sephadex G-200 column chromatography. The total sugar contents of LTPS-1, LTPS-21 and LTPS-31 were 931.8, 958.2 and 895.1 g kg^?1, respectively. LTPS-1 (3.48 kDa) was mainly composed of rhamnose, arabinose, glucose and galactose in a ratio of 35.36:5.06:1:2. LTPS-21 (11.4 kDa) was mainly composed of rhamnose, arabinose, mannose and galactose in a ratio of 41.93:21.8:1.01:9.24. LTPS-31 (19.49 kDa) was mainly composed of rhamnose, arabinose and mannose in a ratio of 38.31:16.44:1.1. IR analysis suggested they contained lower sulphuric acids, the LTPS-21 and LTPS-31 belonged to β-type polysaccharide. Among the three polysaccharides, LTPS-21 exhibited the strongest reducing power, scavenging activity on ABTS and hydroxyl radicals. These findings suggested that polysaccharides from the seed cakes could be potentially developed as natural functional ingredients in the food and cosmetic industry.     

Mining information from time series in the form of sentences of natural language

The goal of this paper is to provide a more detailed explanation of the principles how special formulas that characterize properties of trend of time series can be formed and how they are interpreted. Then we show how these formulas can be used in a tectogrammatical tree that construes special sentences of natural language, using which information on behavior of time series is provided. We also outline the principles of mining this information. The last part is devoted to application of the theory of intermediate quantifiers to mining summarized information on time series also in sentences of natural language.     

Computational Tools for Evaluating Phylogenetic and Hierarchical Clustering Trees

This article presents an alternative derivation of the generalized approximate crossvalidation (GACV) score of Xiang and Wahba (1996) for smoothing parameter selection in penalized likelihood regression. The new derivation suggests a simple numerical solution that is stable for all sample sizes. Also suggested is a variant of the score that can be computationally more convenient. Simple simulations are presented to illustrate the effectiveness of the scores.     

Patterns in treeshelves

We study the distribution and the popularity of left children on sets of treeshelves avoiding a pattern of size three. (Treeshelves are ordered binary increasing trees where every child is connected to its parent by a left or a right link.) The considered patterns are sub-treeshelves, and for each such a pattern we provide exponential generating function for the corresponding distribution and popularity. Finally, we present constructive bijections between treeshelves avoiding a pattern of size three and some classes of simpler combinatorial objects.     

Comparative analysis of amino acid composition in the active site of nirk gene encoding copper-containing nitrite reductase (CuNiR) in bacterial spp.

The nirk gene encoding the copper-containing nitrite reductase (CuNiR), a key catalytic enzyme in the environmental denitrification process that helps to produce nitric oxide from nitrite. The molecular mechanism of denitrification process is definitely complex and in this case a theoretical investigation has been conducted to know the sequence information and amino acid composition of the active site of CuNiR enzyme using various Bioinformatics tools. 10 Fasta formatted sequences were retrieved from the NCBI database and the domain and disordered regions identification and phylogenetic analyses were done on these sequences. The comparative modeling of protein was performed through Modeller 9v14 program and visualized by PyMOL tools. Validated protein models were deposited in the Protein Model Database (PMDB) (PMDB id: PM0080150 to PM0080159). Active sites of nirk encoding CuNiR enzyme were identified by Castp server. The PROCHECK showed significant scores for four protein models in the most favored regions of the Ramachandran plot. Active sites and cavities prediction exhibited that the amino acid, namely Glycine, Alanine, Histidine, Aspartic acid, Glutamic acid, Threonine, and Glutamine were common in four predicted protein models. The present in silico study anticipates that active site analyses result will pave the way for further research on the complex denitrification mechanism of the selected species in the experimental laboratory.     

Finite element potentials

We present an explicit and efficient way for constructing finite elements with assigned gradient, or curl, or divergence. Some simple notions of homology theory and graph theory applied to the finite element mesh are basic tools for devising the solution algorithms.