PERCOLATION ON THE INFORMATION-THEORETICALLY SECURE SIGNAL TO INTERFERENCE RATIO GRAPH

We consider a continuum percolation model consisting of two types of nodes, namely legitimate and eavesdropper nodes, distributed according to independent Poisson point processes in R-2 of intensities lambda and lambda(E), respectively. A directed edge from one legitimate node A to another legitimate node B exists provided that the strength of the signal transmitted from node A that is received at node B is higher than that received at any eavesdropper node. The strength of the signal received at a node from a legitimate node depends not only on the distance between these nodes, but also on the location of the other legitimate nodes and an interference suppression parameter gamma. The graph is said to percolate when there exists an infinitely connected component. We show that for any finite intensity lambda(E) of eavesdropper nodes, there exists a critical intensity lambda(c) < infinity such that for all lambda > lambda(c) the graph percolates for sufficiently small values of the interference parameter. Furthermore, for the subcritical regime, we show that there exists a lambda(0) such that for all lambda < lambda(0) <= lambda(c) a suitable graph defined over eavesdropper node connections percolates that precludes percolation in the graphs formed by the legitimate nodes.

Study on QSPR of alcohols with a novel edge connectivity index F-m

A novel edge degree f(i) for heteroatom and multiple bonds in molecular graph is derived on the basis of the edge degree delta(e(r)). A novel edge connectivity index F-m is introduced. The multiple linear regression by using the edge connectivity index F-m and alcohol-type parameter delta, alcohol-distance parameter L can provide high-quality QSPR models for the normal boiling points (BPs), molar volumes (MVs), molar refraction (MRs), water solubility(log(1/S)) and octanol/water partition (logP) of alcohols with up to 17 non-hydrogen atoms. The results imply that these physical properties may be expressed as a liner combination of the edge connectivity index and alcohol-type parameter, 6, alcohol-distance parameter, L. For the models of the five properties, the correlation coefficient r and the standard errors are 0.9969,3.022; 0.9993, 1.504; 0.9992, 0.446; 0.9924,0.129 and 0.9973,0.123 for BPs, MVs, MRs, log(1/S) and logP, respectively. The cross-validation by using the leave-one-out method demonstrates the models to be highly reliable from the point of view of statistics.

Edge-preserving self-healing: Keeping network backbones densely connected

Healing algorithms play a crucial part in distributed peer-to-peer networks where failures occur continuously and frequently. Whereas there are approaches for robustness that rely largely on built-in redundancy, we adopt a responsive approach that is more akin to that of biological networks e.g. the brain. The general goal of self-healing distributed graphs is to maintain certain network properties while recovering from failure quickly and making bounded alterations locally. Several self-healing algorithms have been suggested in the recent literature [IPDPS'08, PODC'08, PODC'09, PODC'11]; they heal various network properties while fulfilling competing requirements such as having low degree increase while maintaining connectivity, expansion and low stretch of the network. In this work, we augment the previous algorithms by adding the notion of edge-preserving self-healing which requires the healing algorithm to not delete any edges originally present or adversarialy inserted. This reflects the cost of adding additional edges but more importantly it immediately follows that edge preservation helps maintain any subgraph induced property that is monotonic, in particular important properties such as graph and subgraph densities. Density is an important network property and in certain distributed networks, maintaining it preserves high connectivity among certain subgraphs and backbones. We introduce a general model of self-healing, and introduce xheal+, an edge-preserving version of xheal[PODC'11]. © 2012 IEEE.

Memory-centric VDF Graph Transformations for Practical FPGA Implementation

Realising memory intensive applications such as image and video processing on FPGA requires creation of complex, multi-level memory hierarchies to achieve real-time performance; however commerical High Level Synthesis tools are unable to automatically derive such structures and hence are unable to meet the demanding bandwidth and capacity constraints of these applications. Current approaches to solving this problem can only derive either single-level memory structures or very deep, highly inefficient hierarchies, leading in either case to one or more of high implementation cost and low performance. This paper presents an enhancement to an existing MC-HLS synthesis approach which solves this problem; it exploits and eliminates data duplication at multiple levels levels of the generated hierarchy, leading to a reduction in the number of levels and ultimately higher performance, lower cost implementations. When applied to synthesis of C-based Motion Estimation, Matrix Multiplication and Sobel Edge Detection applications, this enables reductions in Block RAM and Look Up Table (LUT) cost of up to 25%, whilst simultaneously increasing throughput.

Efficient edge domination in regular graphs

An induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p ≥ 3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-complete. © 2008 Elsevier B.V. All rights reserved.

Edge-choosability of Planar Graphs

According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s Theorem ∆(G) ≤χ' (G)≤∆(G) + 1. We prove that if G is a planar graph without 7-cycles with ∆(G)≠5,6 , or without adjacent 4-cycles with ∆(G)≠5, or with no 3-cycles adjacent to 5-cycles, then G is edge-(∆ + 1)-choosable.

Backbone Colouring of Graphs

Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by at least q. The minimum number k for which there is a backbone k-colouring of (G,H) is the backbone chromatic number, BBCq(G,H). It has been proved that backbone k-colouring of (G,T) is at most 4 if G is a connected C4-free planar graph or non-bipartite C5-free planar graph or Cj-free, j∈{6,7,8} planar graph without adjacent triangles. In this thesis we improve the results mentioned above and prove that 2-backbone k-colouring of any connected planar graphs without adjacent triangles is at most 4 by using a discharging method. In the second part of this thesis we further improve these results by proving that for any graph G with χ(G) ≥ 4, BBC(G,T) = χ(G). In fact, we prove the stronger result that a backbone tree T in G exists, such that ∀ uv ∈ T, |f(u)-f(v)|=2 or |f(u)-f(v)| ≥ k-2, k = χ(G). For the case that G is a planar graph, according to Four Colour Theorem, χ(G) = 4; so, BBC(G,T) = 4.

Strongly distance-balanced graphs and graph products

A graph G is strongly distance-balanced if for every edge uv of G and every i 0 the number of vertices x with d.x; u/ D d.x; v/ 1 D i equals the number of vertices y with d.y; v/ D d.y; u/ 1 D i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distance-balanced. It is also proved that connected components of the direct product of two bipartite graphs are strongly distancebalanced if and only if both factors are strongly distance-balanced. Additionally, a new characterization of distance-balanced graphs and an algorithm of time complexity O.mn/ for their recognition, wheremis the number of edges and n the number of vertices of the graph in question, are given

Designing Novel Antitrypanosomal Agents from a Mixed Graph-Theoretical Substructural Approach

Chagas disease is nowadays the most serious parasitic health problem. This disease is caused by Trypanosoma cruzi. The great number of deaths and the insufficient effectiveness of drugs against this parasite have alarmed the scientific community worldwide. In an attempt to overcome this problem, a model for the design and prediction of new antitrypanosomal agents was obtained. This used a mixed approach, containing simple descriptors based on fragments and topological substructural molecular design descriptors. A data set was made up of 188 compounds, 99 of them characterized an antitrypanosomal activity and 88 compounds that belong to other pharmaceutical categories. The model showed sensitivity, specificity and accuracy values above 85%. Quantitative fragmental contributions were also calculated. Then, and to confirm the quality of the model, 15 structures of molecules tested as antitrypanosomal compounds (that we did not include in this study) were predicted, taking into account the information on the abovementioned calculated fragmental contributions. The model showed an accuracy of 100% which means that the ""in silico"" methodology developed by our team is promising for the rational design of new antitrypanosomal drugs. (C) 2009 Wiley Periodicals, Inc. J Comput Chem 31: 882-894. 2010

Design of novel antituberculosis compounds using graph-theoretical and substructural approaches

The increasing resistance of Mycobacterium tuberculosis to the existing drugs has alarmed the worldwide scientific community. In an attempt to overcome this problem, two models for the design and prediction of new antituberculosis agents were obtained. The first used a mixed approach, containing descriptors based on fragments and the topological substructural molecular design approach (TOPS-MODE) descriptors. The other model used a combination of two-dimensional (2D) and three-dimensional (3D) descriptors. A data set of 167 compounds with great structural variability, 72 of them antituberculosis agents and 95 compounds belonging to other pharmaceutical categories, was analyzed. The first model showed sensitivity, specificity, and accuracy values above 80% and the second one showed values higher than 75% for these statistical indices. Subsequently, 12 structures of imidazoles not included in this study were designed, taking into account the two models. In both cases accuracy was 100%, showing that the methodology in silico developed by us is promising for the rational design of antituberculosis drugs.

Graph matching : fast candidate elimination using machine learning techniques

Graph matching is an important class of methods in pattern recognition. Typically, a graph representing an unknown pattern is matched with a database of models. If the database of model graphs is large, an additional factor in induced into the overall complexity of the matching process. Various techniques for reducing the influence of this additional factor have been described in the literature. In this paper we propose to extract simple features from a graph and use them to eliminate candidate graphs from the database. The most powerful set of features and a decision tree useful for candidate elimination are found by means of the C4.5 algorithm, which was originally proposed for inductive learning of classication rules. Experimental results are reported demonstrating that effcient candidate elimination can be achieved by the proposed procedure.

Preserving utility in social network graph anonymization

To protect from privacy disclosure, the social network graph is modified in order to hide the information that potentially be used to disclose person's identity. However, when the social network graph is changed, it is a great challenge to balance between the privacy gained and the loss of data utility. In this paper, we address this problem. We propose a new graph topological-based metric to improve utility preservation in social network graph anonymization. We compare the proposed approach with the amount-of-edge-change metric that popularly used in most of previous works. Experimental evaluation shows that our approach generates anonymized social network with improved utility preservation.

Edge Colourings of Graphs Avoiding Monochromatic Matchings of a Given Size

Let k and l be positive integers. With a graph G, we associate the quantity c(k,l)(G), the number of k-colourings of the edge set of G with no monochromatic matching of size l. Consider the function c(k,l) : N --> N given by c(k,l)(n) = max {c(k,l)(G): vertical bar V(G)vertical bar = n}, the maximum of c(k,l)(G) over all graphs G on n vertices. In this paper, we determine c(k,l)(n) and the corresponding extremal graphs for all large n and all fixed values of k and l.

A graph theoretic approach to testing associations between disparate sources of functional genomic data

The last few years have seen the advent of high-throughput technologies to analyze various properties of the transcriptome and proteome of several organisms. The congruency of these different data sources, or lack thereof, can shed light on the mechanisms that govern cellular function. A central challenge for bioinformatics research is to develop a unified framework for combining the multiple sources of functional genomics information and testing associations between them, thus obtaining a robust and integrated view of the underlying biology. We present a graph theoretic approach to test the significance of the association between multiple disparate sources of functional genomics data by proposing two statistical tests, namely edge permutation and node label permutation tests. We demonstrate the use of the proposed tests by finding significant association between a Gene Ontology-derived "predictome" and data obtained from mRNA expression and phenotypic experiments for Saccharomyces cerevisiae. Moreover, we employ the graph theoretic framework to recast a surprising discrepancy presented in Giaever et al. (2002) between gene expression and knockout phenotype, using expression data from a different set of experiments.