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.

Structural information content of networks: Graph entropy based on local vertex functionals

In this paper we define the structural information content of graphs as their corresponding graph entropy. This definition is based on local vertex functionals obtained by calculating-spheres via the algorithm of Dijkstra. We prove that the graph entropy and, hence, the local vertex functionals can be computed with polynomial time complexity enabling the application of our measure for large graphs. In this paper we present numerical results for the graph entropy of chemical graphs and discuss resulting properties. (C) 2007 Elsevier Ltd. All rights reserved.

Discrete Conditional Phase-type models utilising classification trees: Application to modelling health service capacities

Discrete Conditional Phase-type (DC-Ph) models consist of a process component (survival distribution) preceded by a set of related conditional discrete variables. This paper introduces a DC-Ph model where the conditional component is a classification tree. The approach is utilised for modelling health service capacities by better predicting service times, as captured by Coxian Phase-type distributions, interfaced with results from a classification tree algorithm. To illustrate the approach, a case-study within the healthcare delivery domain is given, namely that of maternity services. The classification analysis is shown to give good predictors for complications during childbirth. Based on the classification tree predictions, the duration of childbirth on the labour ward is then modelled as either a two or three-phase Coxian distribution. The resulting DC-Ph model is used to calculate the number of patients and associated bed occupancies, patient turnover, and to model the consequences of changes to risk status.

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

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.

Comparing large graphs efficiently by margins of feature vectors

Measuring the structural similarity of graphs is a challenging and outstanding problem. Most of the classical approaches of the so-called exact graph matching methods are based on graph or subgraph isomorphic relations of the underlying graphs. In contrast to these methods in this paper we introduce a novel approach to measure the structural similarity of directed and undirected graphs that is mainly based on margins of feature vectors representing graphs. We introduce novel graph similarity and dissimilarity measures, provide some properties and analyze their algorithmic complexity. We find that the computational complexity of our measures is polynomial in the graph size and, hence, significantly better than classical methods from, e.g. exact graph matching which are NP-complete. Numerically, we provide some examples of our measure and compare the results with the well-known graph edit distance. (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.