On local linearization of control systems

We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that local topological linearization implies local smooth linearization, at generic points. At arbitrary points, it implies local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at "strongly" singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology

Variational and Geometric Structures of Discrete Dirac Mechanics

In this paper, we develop the theoretical foundations of discrete Dirac mechanics, that is, discrete mechanics of degenerate Lagrangian/Hamiltonian systems with constraints. We first construct discrete analogues of Tulczyjew's triple and induced Dirac structures by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides a means of deriving discrete Lagrange-Dirac and nonholonomic Hamiltonian systems. In particular, this yields nonholonomic Lagrangian and Hamiltonian integrators. We also introduce discrete Lagrange-d'Alembert-Pontryagin and Hamilton-d'Alembert variational principles, which provide an alternative derivation of the same set of integration algorithms. The paper provides a unified treatment of discrete Lagrangian and Hamiltonian mechanics in the more general setting of discrete Dirac mechanics, as well as a generalization of symplectic and Poisson integrators to the broader category of Dirac integrators.Comment: 26 pages; published online in Foundations of Computational Mathematics (2011

Keystone symposium: The role of microenvironment in tumor induction and progression, Banff, Canada, 5–10 February 2005

The first Keystone symposium on the role of microenvironment in tumor induction and progression attracted 274 delegates from 13 countries to Banff in the heart of the Canadian Rockies. The meeting was organized by Mina Bissell, Ronald DePinho and Luis Parada, and was held concurrently with the Keystone symposium on cancer and development, chaired by Matthew Scott and Roeland Nusse. The 30 oral presentations and over 130 posters provided an excellent forum for discussing emerging data in this rapidly advancing field

Modeling Time in Computing: A Taxonomy and a Comparative Survey

The increasing relevance of areas such as real-time and embedded systems, pervasive computing, hybrid systems control, and biological and social systems modeling is bringing a growing attention to the temporal aspects of computing, not only in the computer science domain, but also in more traditional fields of engineering. This article surveys various approaches to the formal modeling and analysis of the temporal features of computer-based systems, with a level of detail that is suitable also for non-specialists. In doing so, it provides a unifying framework, rather than just a comprehensive list of formalisms. The paper first lays out some key dimensions along which the various formalisms can be evaluated and compared. Then, a significant sample of formalisms for time modeling in computing are presented and discussed according to these dimensions. The adopted perspective is, to some extent, historical, going from "traditional" models and formalisms to more modern ones.Comment: More typos fixe

CD34 marks angiogenic tip cells in human vascular endothelial cell cultures

The functional shift of quiescent endothelial cells into tip cells that migrate and stalk cells that proliferate is a key event during sprouting angiogenesis. We previously showed that the sialomucin CD34 is expressed in a small subset of cultured endothelial cells and that these cells extend filopodia: a hallmark of tip cells in vivo. In the present study, we characterized endothelial cells expressing CD34 in endothelial monolayers in vitro. We found that CD34-positive human umbilical vein endothelial cells show low proliferation activity and increased mRNA expression of all known tip cell markers, as compared to CD34-negative cells. Genome-wide mRNA profiling analysis of CD34-positive endothelial cells demonstrated enrichment for biological functions related to angiogenesis and migration, whereas CD34-negative cells were enriched for functions related to proliferation. In addition, we found an increase or decrease of CD34-positive cells in vitro upon exposure to stimuli that enhance or limit the number of tip cells in vivo, respectively. Our findings suggest cells with virtually all known properties of tip cells are present in vascular endothelial cell cultures and that they can be isolated based on expression of CD34. This novel strategy may open alternative avenues for future studies of molecular processes and functions in tip cells in angiogenesis

Tumour vascularization: sprouting angiogenesis and beyond

Tumour angiogenesis is a fast growing domain in tumour biology. Many growth factors and mechanisms have been unravelled. For almost 30 years, the sprouting of new vessels out of existing ones was considered as an exclusive way of tumour vascularisation. However, over the last years several additional mechanisms have been identified. With the discovery of the contribution of intussusceptive angiogenesis, recruitment of endothelial progenitor cells, vessel co-option, vasculogenic mimicry and lymphangiogenesis to tumour growth, anti-tumour targeting strategies will be more complex than initially thought. This review highlights these processes and intervention as a potential application in cancer therapy. It is concluded that future anti-vascular therapies might be most beneficial when based on multimodal anti-angiogenic, anti-vasculogenic mimicry and anti-lymphangiogenic strategies

Chronic Cigarette Smoke Causes Oxidative Damage and Apoptosis to Retinal Pigmented Epithelial Cells in Mice

The purpose of this study was to determine whether mice exposed to chronic cigarette smoke develop features of early age-related macular degeneration (AMD). Two month old C57Bl6 mice were exposed to either filtered air or cigarette smoke in a smoking chamber for 5 h/day, 5 days/week for 6 months. Eyes were fixed in 2.5% glutaraldehyde/2% paraformaldehyde and examined for ultrastructural changes by transmission electron microscopy. The contralateral eye was fixed in 2% paraformaldehyde and examined for oxidative injury to the retinal pigmented epithelium (RPE) by 8-oxo-7,8-dihydro-2′-deoxyguanosine (8-OHdG) immunolabeling and apoptosis by TUNEL labeling. Mice exposed to cigarette smoke had immunolabeling for 8-OHdG in 85±3.7% of RPE cells counted compared to 9.5±3.9% in controls (p<0.00001). Bruch membrane was thicker in mice exposed to smoke (1086±332 nm) than those raised in air (543±132 nm; p = 0.0069). The two most pronounced ultrastructural changes (severity grading scale from 0–3) seen were a loss of basal infoldings (mean difference in grade = 1.98; p<0.0001), and an increase in intracellular vacuoles (mean difference in grade = 1.7; p<0.0001). Ultrastructural changes to Bruch membrane in cigarette-smoke exposed mice were smaller in magnitude but consistently demonstrated significantly higher grade injury in cigarette-exposed mice, including basal laminar deposits (mean difference in grade = 0.54; p<0.0001), increased outer collagenous layer deposits (mean difference in grade = 0.59; p = 0.002), and increased basal laminar deposit continuity (mean difference in grade = 0.4; p<0.0001). TUNEL assay showed a higher percentage of apoptotic RPE from mice exposed to cigarette smoke (average 8.0±1.1%) than room air (average 0±0%; p = 0.043). Mice exposed to chronic cigarette smoke develop evidence of oxidative damage with ultrastructural degeneration to the RPE and Bruch membrane, and RPE cell apoptosis. This model could be useful for studying the mechanism of smoke induced changes during early AMD

Retinoic Acid Mediates Regulation of Network Formation by COUP-TFII and VE-Cadherin Expression by TGFβ Receptor Kinase in Breast Cancer Cells

Tumor development, growth, and metastasis depend on the provision of an adequate vascular supply. This can be due to regulated angiogenesis, recruitment of circulating endothelial progenitors, and/or vascular transdifferentiation. Our previous studies showed that retinoic acid (RA) treatment converts a subset of breast cancer cells into cells with significant endothelial genotypic and phenotypic elements including marked induction of VE-cadherin, which was responsible for some but not all morphological changes. The present study demonstrates that of the endothelial-related genes induced by RA treatment, only a few were affected by knockdown of VE-cadherin, ruling it out as a regulator of the RA-induced endothelial genotypic switch. In contrast, knockdown of the RA-induced gene COUP-TFII prevented the formation of networks in Matrigel but had no effect on VE-cadherin induction or cell fusion. Two pan-kinase inhibitors markedly blocked RA-induced VE-cadherin expression and cell fusion. However, RA treatment resulted in a marked and broad reduction in tyrosine kinase activity. Several genes in the TGFβ signaling pathway were induced by RA, and specific inhibition of the TGFβ type I receptor blocked both RA-induced VE-cadherin expression and cell fusion. Together these data indicate a role for the TGFβ pathway and COUP-TFII in mediating the endothelial transdifferentiating properties of RA

Paramagnetic and fluorescent liposomes for target-specific imaging and therapy of tumor angiogenesis

Angiogenesis is essential for tumor growth and metastatic potential and for that reason considered an important target for tumor treatment. Noninvasive imaging technologies, capable of visualizing tumor angiogenesis and evaluating the efficacy of angiostatic therapies, are therefore becoming increasingly important. Among the various imaging modalities, magnetic resonance imaging (MRI) is characterized by a superb spatial resolution and anatomical soft-tissue contrast. Revolutionary advances in contrast agent chemistry have delivered versatile angiogenesis-specific molecular MRI contrast agents. In this paper, we review recent advances in the preclinical application of paramagnetic and fluorescent liposomes for noninvasive visualization of the molecular processes involved in tumor angiogenesis. This liposomal contrast agent platform can be prepared with a high payload of contrast generating material, thereby facilitating its detection, and is equipped with one or more types of targeting ligands for binding to specific molecules expressed at the angiogenic site. Multimodal liposomes endowed with contrast material for complementary imaging technologies, e.g., MRI and optical, can be exploited to gain important preclinical insights into the mechanisms of binding and accumulation at angiogenic vascular endothelium and to corroborate the in vivo findings. Interestingly, liposomes can be designed to contain angiostatic therapeutics, allowing for image-supervised drug delivery and subsequent monitoring of therapeutic efficacy