Robustness in scale-free networks: Comparing directed and undirected networks

In this paper, scale-free networks and their functional robustness with respect to structural perturbations of the network are studied. Two types of perturbations are distinguished: random perturbations and attacks. The robustness of directed and undirected scale-free networks is studied numerically for two different measures and the obtained results are compared. For random perturbations, the results indicate that the strength of the perturbation plays a crucial role. In general, directed scale-free networks are more robust than undirected scale-free networks.

A similarity measure for graphs with low computational complexity

We present and analyze an algorithm to measure the structural similarity of generalized trees, a new graph class which includes rooted trees. For this, we represent structural properties of graphs as strings and define the similarity of two Graphs as optimal alignments of the corresponding property stings. We prove that the obtained graph similarity measures are so called Backward similarity measures. From this we find that the time complexity of our algorithm is polynomial and, hence, significantly better than the time complexity of classical graph similarity methods based on isomorphic relations. (c) 2006 Elsevier Inc. All rights reserved.

Information theoretic measures of UHG graphs with low computational complexity

We introduce a novel graph class we call universal hierarchical graphs (UHG) whose topology can be found numerously in problems representing, e.g., temporal, spacial or general process structures of systems. For this graph class we show, that we can naturally assign two probability distributions, for nodes and for edges, which lead us directly to the definition of the entropy and joint entropy and, hence, mutual information establishing an information theory for this graph class. Furthermore, we provide some results under which conditions these constraint probability distributions maximize the corresponding entropy. Also, we demonstrate that these entropic measures can be computed efficiently which is a prerequisite for every large scale practical application and show some numerical examples. (c) 2007 Elsevier Inc. All rights reserved.

Progressive loss of epidermal growth factor receptor in a subpopulation of breast cancers: implications in target-directed therapeutics

Understanding the molecular etiology and heterogeneity of disease has a direct effect on cancer therapeutics. To identify novel molecular changes associated with breast cancer progression, we conducted phosphoproteomics of the MCF10AT model comprising isogenic, ErbB2- and ErbB3-positive, xenograft-derived cell lines that mimic different stages of breast cancer. Using in vitro animal model and clinical breast samples, our study revealed a marked reduction of epidermal growth factor receptor (EGFR) expression with breast cancer progression. Such diminution of EGFR expression was associated with increased resistance to Gefitinib/Iressa in vitro. Fluorescence in situ hybridization showed that loss of EGFR gene copy number was one of the key mechanisms behind the low/null expression of EGFR in clinical breast tumors. Statistical analysis on the immunohistochemistry data of EGFR expression from 93 matched normal and breast tumor samples showed that (a) diminished EGFR expression could. be detected as early as in the preneoplastic lesion (ductal carcinoma in situ) and this culminated in invasive carcinomas; (b) EGFR expression levels could distinguish between normal tissue versus carcinoma in situ and invasive carcinoma with high statistical significance (P

Detecting Anomalies in Graphs with Numeric Labels

This paper presents Yagada, an algorithm to search labelled graphs for anomalies using both structural data and numeric attributes. Yagada is explained using several security-related examples and validated with experiments on a physical Access Control database. Quantitative analysis shows that in the upper range of anomaly thresholds, Yagada detects twice as many anomalies as the best-performing numeric discretization algorithm. Qualitative evaluation shows that the detected anomalies are meaningful, representing a com- bination of structural irregularities and numerical outliers.

Imitating micelles as a way to control coordination self-assembly: cage-polymer switching directed rationally by solvent polarity or pH

Disguising a metal complex as a micelle by using amphiphilic phosphine ligands enables it to switch between a coordination polymer and a discrete cage in response to solvent polarity or pH; this medium-dependent behaviour of the complex is rational because it parallels that of true micelles.

A comparative analysis of multidimensional features of objects resembling sets of graphs

In the present paper, we introduce a notion of a style representing abstract, complex objects having characteristics that can be represented as structured objects. Furthermore, we provide some mathematical properties of such styles. As a main result, we present a novel approach to perform a meaningful comparative analysis of such styles by defining and using graph-theoretic measures. We compare two styles by comparing the underlying feature sets representing sets of graph structurally. To determine the structural similarity between the underlying graphs, we use graph similarity measures that are computationally efficient. More precisely, in order to compare styles, we map each feature set to a so-called median graph and compare the resulting median graphs. As an application, we perform an experimental study to compare special styles representing sets of undirected graphs and present numerical results thereof. (C) 2007 Elsevier Inc. All rights reserved.

Topological mappings between graphs, trees and generalized trees

We present novel topological mappings between graphs, trees and generalized trees that means between structured objects with different properties. The two major contributions of this paper are, first, to clarify the relation between graphs, trees and generalized trees, a graph class recently introduced. Second, these transformations provide a unique opportunity to transform structured objects into a representation that might be beneficial for a processing, e.g., by machine learning techniques for graph classification. (c) 2006 Elsevier Inc. All rights reserved.

Synthesis of a tri(organoplatinum) complex via the double directed lithiation of a mono(organoplatinum) precursor

The new diarylplatinum complex Cis-[Pt(PEt(3))(2){C6H3(CH(2)NMe(2))(2)-3,5}(2)] 1, containing four free amine coordination sites, undergoes directed lithiation with Bu(t)Li and subsequent transmetallation with [PtCl2(SEt(2))(2)] to give a triplatinum species 3 which reductively eliminates the diplatinum complex[ClPt{2,6-(Me(2)NCH(2))(2)C6H2-C6H2(CH(2)NMe(2))(2)-2,6}PtCl] 4.

Enantioselective formal total synthesis of the Dendrobatidae frog toxin, (+)-pumiliotoxin B, via O-directed alkyne free radical hydrostannation

Herein we describe our application of the O-directed free radical hydrostannation of disubstituted alkyl-acetylenes (with Ph3SnH and Et3B) to the (+)-pumiliotoxin B total synthesis problem. Specifically, we report on the use of this method in the synthesis of the Overman alkyne 8, and thereby demonstrate the great utility of this process in a complex natural product total synthesis setting for the very first time. We also report here on a new, stereocontrolled, and highly practical enantioselective pathway to Overman's pyrrolidine epoxide partner 9 for 8, which overcomes the previous requirement for use of preparative HPLC to separate the 1:1 mixture of diastereomeric epoxides that was obtained in the original synthesis of 9.