Tutte polynomial of pseudofractal scale-free web

The Tutte polynomial of a graph is a 2-variable polynomial which is quite important in both combinatorics and statistical physics. It contains various numerical invariants and polynomial invariants, such as the number of spanning trees, the number of spanning forests, the number of acyclic orientations, the reliability polynomial, chromatic polynomial and flow polynomial. In this paper, we study and gain recursive formulas for the Tutte polynomial of pseudofractal scale-free web (PSW) which implies logarithmic complexity algorithm is obtained to calculate the Tutte polynomial of PSW although it is NP-hard for general graph. We also obtain the rigorous solution for the the number of spanning trees of PSW by solving the recurrence relations derived from Tutte polynomial, which give an alternative approach for explicitly determining the number of spanning trees of PSW. Further more, we analysis the all-terminal reliability of PSW and compare the results with that of Sierpinski gasket which has the same number of nodes and edges with PSW. In contrast with the well-known conclusion that scale-free networks are more robust against removal of nodes than homogeneous networks (e.g., exponential networks and regular networks). Our results show that Sierpinski gasket (which is a regular network) are more robust against random edge failures than PSW (which is a scale-free network). Whether it is true for any regular networks and scale-free networks, is still a unresolved problem.Comment: 19pages,7figures. arXiv admin note: text overlap with arXiv:1006.533

Genotype-specific responses in Atlantic salmon (Salmo salar) subject to dietary fish oil replacement by vegetable oil: a liver transcriptomic analysis

<p>Abstract</p> <p>Background</p> <p>Expansion of aquaculture is seriously limited by reductions in fish oil (FO) supply for aquafeeds. Terrestrial alternatives such as vegetable oils (VO) have been investigated and recently a strategy combining genetic selection with changes in diet formulations has been proposed to meet growing demands for aquaculture products. This study investigates the influence of genotype on transcriptomic responses to sustainable feeds in Atlantic salmon.</p> <p>Results</p> <p>A microarray analysis was performed to investigate the liver transcriptome of two family groups selected according to their estimated breeding values (EBVs) for flesh lipid content, 'Lean' or 'Fat', fed diets containing either FO or a VO blend. Diet principally affected metabolism genes, mainly of lipid and carbohydrate, followed by immune response genes. Genotype had a much lower impact on metabolism-related genes and affected mostly signalling pathways. Replacement of dietary FO by VO caused an up-regulation of long-chain polyunsaturated fatty acid biosynthesis, but there was a clear genotype effect as fatty acyl elongase (elovl2) was only up-regulated and desaturases (Δ5 fad and Δ6 fad) showed a higher magnitude of response in Lean fish, which was reflected in liver fatty acid composition. Fatty acid synthase (FAS) was also up-regulated by VO and the effect was independent of genotype. Genetic background of the fish clearly affected regulation of lipid metabolism, as PPARα and PPARβ were down-regulated by the VO diet only in Lean fish, while in Fat salmon SREBP-1 expression was up-regulated by VO. In addition, all three genes had a lower expression in the Lean family group than in the Fat, when fed VO. Differences in muscle adiposity between family groups may have been caused by higher levels of hepatic fatty acid and glycerophospholipid synthesis in the Fat fish, as indicated by the expression of FAS, 1-acyl-sn-glycerol-3-phosphate acyltransferase and lipid phosphate phosphohydrolase 2.</p> <p>Conclusions</p> <p>This study has identified metabolic pathways and key regulators that may respond differently to alternative plant-based feeds depending on genotype. Further studies are required but data suggest that it will be possible to identify families better adapted to alternative diet formulations that might be appropriate for future genetic selection programmes.</p

Motif co-regulation and co-operativity are common mechanisms in transcriptional, post-transcriptional and post-translational regulation

A substantial portion of the regulatory interactions in the higher eukaryotic cell are mediated by simple sequence motifs in the regulatory segments of genes and (pre-)mRNAs, and in the intrinsically disordered regions of proteins. Although these regulatory modules are physicochemically distinct, they share an evolutionary plasticity that has facilitated a rapid growth of their use and resulted in their ubiquity in complex organisms. The ease of motif acquisition simplifies access to basal housekeeping functions, facilitates the co-regulation of multiple biomolecules allowing them to respond in a coordinated manner to changes in the cell state, and supports the integration of multiple signals for combinatorial decision-making. Consequently, motifs are indispensable for temporal, spatial, conditional and basal regulation at the transcriptional, post-transcriptional and post-translational level. In this review, we highlight that many of the key regulatory pathways of the cell are recruited by motifs and that the ease of motif acquisition has resulted in large networks of co-regulated biomolecules. We discuss how co-operativity allows simple static motifs to perform the conditional regulation that underlies decision-making in higher eukaryotic biological systems. We observe that each gene and its products have a unique set of DNA, RNA or protein motifs that encode a regulatory program to define the logical circuitry that guides the life cycle of these biomolecules, from transcription to degradation. Finally, we contrast the regulatory properties of protein motifs and the regulatory elements of DNA and (pre-)mRNAs, advocating that co-regulation, co-operativity, and motif-driven regulatory programs are common mechanisms that emerge from the use of simple, evolutionarily plastic regulatory modules

Changing perspectives on the internationalization of R&D and innovation by multinational enterprises: a review of the literature

Internationalization of R&D and innovation by Multinational Enterprises (MNEs) has undergone a gradual and comprehensive change in perspective over the past 50 years. From sporadic works in the late 1950s and in the 1960s, it became a systematically analysed topic in the 1970s, starting with pioneering reports and “foundation texts”. Our review unfolds the theoretical and empirical evolution of the literature from dyadic interpretations of centralization versus decentralization of R&D by MNEs to more comprehensive frameworks, wherein established MNEs from Advanced Economies still play a pivotal role, but new players and places also emerge in the global generation and diffusion of knowledge. Hence views of R&D internationalization increasingly rely on concepts, ideas and methods from IB and other related disciplines such as industrial organization, international economics and economic geography. Two main findings are highlighted. First, scholarly research pays an increasing attention to the network-like characteristics of international R&D activities. Second, different streams of literature have emphasized the role of location- specific factors in R&D internationalization. The increasing emphasis on these aspects has created new research opportunities in some key areas, including inter alia: cross-border knowledge sourcing strategies, changes in the geography of R&D and innovation, and the international fragmentation of production and R&D activities