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

Polybrominated Diphenyl Ether (PBDE) Levels in an Expanded Market Basket Survey of U.S. Food and Estimated PBDE Dietary Intake by Age and Sex

OBJECTIVES: Our objectives in this study were to expand a previously reported U.S. market basket survey using a larger sample size and to estimate levels of PBDE intake from food for the U.S. general population by sex and age. METHODS: We measured concentrations of 13 polybrominated diphenyl ether (PBDE) congeners in food in 62 food samples. In addition, we estimated levels of PBDE intake from food for the U.S. general population by age (birth through ≥60 years of age) and sex. RESULTS: In food samples, concentrations of total PBDEs varied from 7.9 pg/g (parts per trillion) in milk to 3,726 pg/g in canned sardines. Fish were highest in PBDEs (mean, 1,120 pg/g; median, 616 pg/g; range, 11.14–3,726 pg/g). This was followed by meat (mean, 383 pg/g; median, 190 pg/g; range, 39–1,426 pg/g) and dairy products (mean, 116 pg/g; median, 32.2 pg/g; range, 7.9–683 pg/g). However, using estimates for food consumption (excluding nursing infants), meat accounted for the highest U.S. dietary PBDE intake, followed by dairy and fish, with almost equal contributions. Adult females had lower dietary intake of PBDEs than did adult males, based on body weight. We estimated PBDE intake from food to be 307 ng/kg/day for nursing infants and from 2 ng/kg/day at 2–5 years of age for both males and females to 0.9 ng/kg/day in adult females. CONCLUSION: Dietary exposure alone does not appear to account for the very high body burdens measured. The indoor environment (dust, air) may play an important role in PBDE body burdens in addition to food

Vascular time-activity variation in patients undergoing 123I-MIBG myocardial scintigraphy: implications for quantification of cardiac and mediastinal uptake

For the quantification of cardiac (123)I-metaiodobenzylguanidine (MIBG) uptake, the mediastinum is commonly used as a reference region reflecting nonspecific background activity. However, variations in the quantity of vascular structures in the mediastinum and the rate of renal clearance of (123)I-MIBG from the blood pool may contribute to increased interindividual variation in uptake. This study examined the relationship between changes in heart (H) and mediastinal (M) counts and the change in vascular (123)I-MIBG activity, including the effect of renal function. Fifty-one subjects with ischemic heart disease underwent early (15 min) and late (4 h) anterior planar images of the chest following injection of (123)I-MIBG. Vascular (123)I-MIBG activity was determined from venous blood samples obtained at 2 min, 15 min, 35 min, and 4 h post-injection. From the vascular clearance curve of each subject, the mean blood counts/min per ml at the time of each acquisition and the slope of the clearance curve were determined. Renal function was expressed as the estimated creatinine clearance (e-CC) and the estimated glomerular filtration rate (e-GFR). Relations between H and M region of interest (ROI) counts/pixel, vascular activity, and renal function were then examined using linear regression. Changes in ROI activity ratios between early and late planar images could not be explained by blood activity, the slope of the vascular clearance curves, or estimates of renal function. At most 3% of the variation in image counts could be explained by changes in vascular activity (p = 0.104). The e-CC and e-GFR could at best explain approximately 1.5% of the variation in the slopes of the vascular clearance curve (p = 0.194). The change in measured H and M counts between early and late planar (123)I-MIBG images is unrelated to intravascular levels of the radiopharmaceutical. This suggests that changes in M counts are primarily due to decrease in soft tissue activity and scatter from the adjacent lung

Self-Organization, Layered Structure, and Aggregation Enhance Persistence of a Synthetic Biofilm Consortium

Microbial consortia constitute a majority of the earth’s biomass, but little is known about how these cooperating communities persist despite competition among community members. Theory suggests that non-random spatial structures contribute to the persistence of mixed communities; when particular structures form, they may provide associated community members with a growth advantage over unassociated members. If true, this has implications for the rise and persistence of multi-cellular organisms. However, this theory is difficult to study because we rarely observe initial instances of non-random physical structure in natural populations. Using two engineered strains of Escherichia coli that constitute a synthetic symbiotic microbial consortium, we fortuitously observed such spatial self-organization. This consortium forms a biofilm and, after several days, adopts a defined layered structure that is associated with two unexpected, measurable growth advantages. First, the consortium cannot successfully colonize a new, downstream environment until it selforganizes in the initial environment; in other words, the structure enhances the ability of the consortium to survive environmental disruptions. Second, when the layered structure forms in downstream environments the consortium accumulates significantly more biomass than it did in the initial environment; in other words, the structure enhances the global productivity of the consortium. We also observed that the layered structure only assembles in downstream environments that are colonized by aggregates from a previous, structured community. These results demonstrate roles for self-organization and aggregation in persistence of multi-cellular communities, and also illustrate a role for the techniques of synthetic biology in elucidating fundamental biological principles

On Poincare and logarithmic Sobolev inequalities for a class of singular Gibbs measures

This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular pair interaction. The functional inequalities come from convexity. We prove and characterize optimality in the case of quadratic confinement via a factorization of the measure. This optimality phenomenon holds for all beta Hermite ensembles including the Gaussian unitary ensemble, a famous exactly solvable model of random matrix theory. We further explore exact solvability by reviewing the relation to Dyson-Ornstein-Uhlenbeck diffusion dynamics admitting the Hermite-Lassalle orthogonal polynomials as a complete set of eigenfunctions. We also discuss the consequence of the log-Sobolev inequality in terms of concentration of measure for Lipschitz functions such as maxima and linear statistics.Comment: Minor improvements. To appear in Geometric Aspects of Functional Analysis -- Israel Seminar (GAFA) 2017-2019", Lecture Notes in Mathematics 225

Tissue Microenvironments Define and Get Reinforced by Macrophage Phenotypes in Homeostasis or during Inflammation, Repair and Fibrosis

Current macrophage phenotype classifications are based on distinct in vitro culture conditions that do not adequately mirror complex tissue environments. In vivo monocyte progenitors populate all tissues for immune surveillance which supports the maintenance of homeostasis as well as regaining homeostasis after injury. Here we propose to classify macrophage phenotypes according to prototypical tissue environments, e.g. as they occur during homeostasis as well as during the different phases of (dermal) wound healing. In tissue necrosis and/or infection, damage- and/or pathogen-associated molecular patterns induce proinflammatory macrophages by Toll-like receptors or inflammasomes. Such classically activated macrophages contribute to further tissue inflammation and damage. Apoptotic cells and antiinflammatory cytokines dominate in postinflammatory tissues which induce macrophages to produce more antiinflammatory mediators. Similarly, tumor-associated macrophages also confer immunosuppression in tumor stroma. Insufficient parenchymal healing despite abundant growth factors pushes macrophages to gain a profibrotic phenotype and promote fibrocyte recruitment which both enforce tissue scarring. Ischemic scars are largely devoid of cytokines and growth factors so that fibrolytic macrophages that predominantly secrete proteases digest the excess extracellular matrix. Together, macrophages stabilize their surrounding tissue microenvironments by adapting different phenotypes as feed-forward mechanisms to maintain tissue homeostasis or regain it following injury. Furthermore, macrophage heterogeneity in healthy or injured tissues mirrors spatial and temporal differences in microenvironments during the various stages of tissue injury and repair. Copyright (C) 2012 S. Karger AG, Base

Hybridization in parasites: consequences for adaptive evolution, pathogenesis and public health in a changing world

[No abstract available

The influence of the accessory genome on bacterial pathogen evolution

Bacterial pathogens exhibit significant variation in their genomic content of virulence factors. This reflects the abundance of strategies pathogens evolved to infect host organisms by suppressing host immunity. Molecular arms-races have been a strong driving force for the evolution of pathogenicity, with pathogens often encoding overlapping or redundant functions, such as type III protein secretion effectors and hosts encoding ever more sophisticated immune systems. The pathogens’ frequent exposure to other microbes, either in their host or in the environment, provides opportunities for the acquisition or interchange of mobile genetic elements. These DNA elements accessorise the core genome and can play major roles in shaping genome structure and altering the complement of virulence factors. Here, we review the different mobile genetic elements focusing on the more recent discoveries and highlighting their role in shaping bacterial pathogen evolution

Human hippocampal neurogenesis drops sharply in children to undetectable levels in adults.

New neurons continue to be generated in the subgranular zone of the dentate gyrus of the adult mammalian hippocampus. This process has been linked to learning and memory, stress and exercise, and is thought to be altered in neurological disease. In humans, some studies have suggested that hundreds of new neurons are added to the adult dentate gyrus every day, whereas other studies find many fewer putative new neurons. Despite these discrepancies, it is generally believed that the adult human hippocampus continues to generate new neurons. Here we show that a defined population of progenitor cells does not coalesce in the subgranular zone during human fetal or postnatal development. We also find that the number of proliferating progenitors and young neurons in the dentate gyrus declines sharply during the first year of life and only a few isolated young neurons are observed by 7 and 13 years of age. In adult patients with epilepsy and healthy adults (18-77 years; n = 17 post-mortem samples from controls; n = 12 surgical resection samples from patients with epilepsy), young neurons were not detected in the dentate gyrus. In the monkey (Macaca mulatta) hippocampus, proliferation of neurons in the subgranular zone was found in early postnatal life, but this diminished during juvenile development as neurogenesis decreased. We conclude that recruitment of young neurons to the primate hippocampus decreases rapidly during the first years of life, and that neurogenesis in the dentate gyrus does not continue, or is extremely rare, in adult humans. The early decline in hippocampal neurogenesis raises questions about how the function of the dentate gyrus differs between humans and other species in which adult hippocampal neurogenesis is preserved