Convergence and Stability of the Inverse Scattering Series for Diffuse Waves

We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence, stability and approximation error of the serie

A priori convergence estimates for a rough Poisson-Dirichlet problem with natural vertical boundary conditions

Stents are medical devices designed to modify blood flow in aneurysm sacs, in order to prevent their rupture. Some of them can be considered as a locally periodic rough boundary. In order to approximate blood flow in arteries and vessels of the cardio-vascular system containing stents, we use multi-scale techniques to construct boundary layers and wall laws. Simplifying the flow we turn to consider a 2-dimensional Poisson problem that conserves essential features related to the rough boundary. Then, we investigate convergence of boundary layer approximations and the corresponding wall laws in the case of Neumann type boundary conditions at the inlet and outlet parts of the domain. The difficulty comes from the fact that correctors, for the boundary layers near the rough surface, may introduce error terms on the other portions of the boundary. In order to correct these spurious oscillations, we introduce a vertical boundary layer. Trough a careful study of its behavior, we prove rigorously decay estimates. We then construct complete boundary layers that respect the macroscopic boundary conditions. We also derive error estimates in terms of the roughness size epsilon either for the full boundary layer approximation and for the corresponding averaged wall law.Comment: Dedicated to Professor Giovanni Paolo Galdi 60' Birthda

Convergence Rates in L^2 for Elliptic Homogenization Problems

We study rates of convergence of solutions in L^2 and H^{1/2} for a family of elliptic systems {L_\epsilon} with rapidly oscillating oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of {L_\epsilon}. Most of our results, which rely on the recently established uniform estimates for the L^2 Dirichlet and Neumann problems in \cite{12,13}, are new even for smooth domains.Comment: 25 page

Entrepreneurial growth and ownership under market socialism in China: a longitudinal case study of small business growth

How firms grow is still a mystery and a definitive explanation remains elusive. This is especially the case for emerging economies, where the development of research into business growth has been notably slow whilst emerging business ventures are developing at hyper speed. Since most empirical studies have focused on the quantitative differences in growth across firms, this paper adopts a longitudinal case study approach to explore the qualitative differences in terms of how various types of firm achieve their growth outcomes in the organisational development process over a prolonged period of time. Through a theoretical lens which focuses on growth process approaches, this study not only demonstrates that entrepreneurial processes take different forms and dimensions in different contexts, but it also provides insights into the interactions of various organisational factors underpinning the strategies and changes that lead to contrasting growth outcomes. Case study findings assert that the ownership factor is a key contingent factor that shapes management structure and resources which, in turn, affect particular entrepreneurial outcomes. Furthermore, a combination of leadership style and the approach to knowledge management also play critical roles in the learning process which, tends to determine the strategy choice of either high or low value added product strategy. The findings of this research are that small firms with a low value product strategy can improve their survival chances and growth through the vertical broadening of a product portfolio in synchrony with increasing production and technology advancement. The case study companies show a tendency to reinforce their industry position by adopting contrasting choices for growth. The paper addresses the challenges and managerial implications for Western company managers in different growth contexts

Pleiotropic Roles of a Ribosomal Protein in Dictyostelium discoideum

The cell cycle phase at starvation influences post-starvation differentiation and morphogenesis in Dictyostelium discoideum. We found that when expressed in Saccharomyces cerevisiae, a D. discoideum cDNA that encodes the ribosomal protein S4 (DdS4) rescues mutations in the cell cycle genes cdc24, cdc42 and bem1. The products of these genes affect morphogenesis in yeast via a coordinated moulding of the cytoskeleton during bud site selection. D. discoideum cells that over- or under-expressed DdS4 did not show detectable changes in protein synthesis but displayed similar developmental aberrations whose intensity was graded with the extent of over- or under-expression. This suggested that DdS4 might influence morphogenesis via a stoichiometric effect – specifically, by taking part in a multimeric complex similar to the one involving Cdc24p, Cdc42p and Bem1p in yeast. In support of the hypothesis, the S. cerevisiae proteins Cdc24p, Cdc42p and Bem1p as well as their D. discoideum cognates could be co-precipitated with antibodies to DdS4. Computational analysis and mutational studies explained these findings: a C-terminal domain of DdS4 is the functional equivalent of an SH3 domain in the yeast scaffold protein Bem1p that is central to constructing the bud site selection complex. Thus in addition to being part of the ribosome, DdS4 has a second function, also as part of a multi-protein complex. We speculate that the existence of the second role can act as a safeguard against perturbations to ribosome function caused by spontaneous variations in DdS4 levels

Cancer Genomics Identifies Regulatory Gene Networks Associated with the Transition from Dysplasia to Advanced Lung Adenocarcinomas Induced by c-Raf-1

Background: Lung cancer is a leading cause of cancer morbidity. To improve an understanding of molecular causes of disease a transgenic mouse model was investigated where targeted expression of the serine threonine kinase c-Raf to respiratory epithelium induced initialy dysplasia and subsequently adenocarcinomas. This enables dissection of genetic events associated with precancerous and cancerous lesions. Methodology/Principal Findings: By laser microdissection cancer cell populations were harvested and subjected to whole genome expression analyses. Overall 473 and 541 genes were significantly regulated, when cancer versus transgenic and non-transgenic cells were compared, giving rise to three distinct and one common regulatory gene network. At advanced stages of tumor growth predominately repression of gene expression was observed, but genes previously shown to be upregulated in dysplasia were also up-regulated in solid tumors. Regulation of developmental programs as well as epithelial mesenchymal and mesenchymal endothelial transition was a hall mark of adenocarcinomas. Additionaly, genes coding for cell adhesion, i.e. the integrins and the tight and gap junction proteins were repressed, whereas ligands for receptor tyrosine kinase such as epi- and amphiregulin were up-regulated. Notably, Vegfr- 2 and its ligand Vegfd, as well as Notch and Wnt signalling cascades were regulated as were glycosylases that influence cellular recognition. Other regulated signalling molecules included guanine exchange factors that play a role in an activation of the MAP kinases while several tumor suppressors i.e. Mcc, Hey1, Fat3, Armcx1 and Reck were significantly repressed. Finally, probable molecular switches forcing dysplastic cells into malignantly transformed cells could be identified. Conclusions/Significance: This study provides insight into molecular pertubations allowing dysplasia to progress further to adenocarcinoma induced by exaggerted c-Raf kinase activity