Search results for "Carn"

2020

Abstract This paper is related to the problem of finding a good notion of rectifiability in sub-Riemannian geometry. In particular, we study which kind of results can be expected for smooth hypersurfaces in Carnot groups. Our main contribution will be a consequence of the following result: there exists a C ∞ -hypersurface S without characteristic points that has uncountably many pairwise non-isomorphic tangent groups on every positive-measure subset. The example is found in a Carnot group of topological dimension 8, it has Hausdorff dimension 12 and so we use on it the Hausdorff measure H 12 . As a consequence, we show that any Lipschitz map defined on a subset of a Carnot group of Hausdorf…

Universal differentiability sets and maximal directional derivatives in Carnot groups

2019

We show that every Carnot group G of step 2 admits a Hausdorff dimension one `universal differentiability set' N such that every real-valued Lipschitz map on G is Pansu differentiable at some point of N. This relies on the fact that existence of a maximal directional derivative of f at a point x implies Pansu differentiability at the same point x. We show that such an implication holds in Carnot groups of step 2 but fails in the Engel group which has step 3.

A metric characterization of Carnot groups

2013

We give a short axiomatic introduction to Carnot groups and their subRiemannian and subFinsler geometry. We explain how such spaces can be metrically described as exactly those proper geodesic spaces that admit dilations and are isometrically homogeneous.

Remarks about the Besicovitch Covering Property in Carnot groups of step 3 and higher

2016

International audience

Nowhere differentiable intrinsic Lipschitz graphs

2021

We construct intrinsic Lipschitz graphs in Carnot groups with the property that, at every point, there exist infinitely many different blow-up limits, none of which is a homogeneous subgroup. This provides counterexamples to a Rademacher theorem for intrinsic Lipschitz graphs.

A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries

2017

AbstractCarnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks.We consider them as special cases of graded groups and as homogeneous metric spaces.We discuss the regularity of isometries in the general case of Carnot-Carathéodory spaces and of nilpotent metric Lie groups.

Regional differences of substrate oxidation capacity in rat hearts: effects of extra load and endurance training.

1990

Male rats, aged 17 weeks at the end of experiments, were divided into four groups. Two groups lived in normal cage conditions with or without extra load (20% of the body weight) and two groups were trained by running with or without extra load for 8 weeks. Oxidation rates of succinate, glutamate + malate, palmitoylcarnitine, and pyruvate, and the activities of lactate dehydrogenase, citrate synthase, isocitrate dehydrogenase and cytochrome oxidase were measured in homogenates of the right ventricle and in those of the subendocardial and subepicardial layers of the left ventricle. Oxidation rates of succinate and palmitoylcarnitine tended to be higher in the subendocardium than in the subepi…

Goethe's dream

2009

The German philosopher Immanuel Kant (1724–1804) defined living organisms as objects with an intrinsic purpose, which are self‐organized in such a way that every part is a function of the whole and the whole is a function of every part, and in which “nothing is for nothing”. Kant already anticipated the tension between agency and structure, and between forward and backward causation. He also perceived living beings as entities that, being extremely complex, are not amenable to descriptions based on laws that are similar to the fundamental laws of physics: “There will never be a Newton of a grass blade,” he wrote. Less metaphorically, Kant believed that science would not be able to understan…

Nitrate/oxygen co-sensing by an NreA/NreB sensor complex ofStaphylococcus carnosus

2013

In Staphylococci maximal induction of nitrate reductase (narGHJI genes) requires anaerobic conditions, the presence of nitrate, and the NreABC regulatory system. Aerobic regulation is effected by the NreB/NreC two-component system. The role of the nitrate receptor NreA in nitrate induction and its relation to aerobic regulation was analysed in Staphylococcus carnosus. Nitrate induction of a narG-lip reporter gene required presence of NreB/NreC. When nreA was deleted, nitrate was no longer required for maximal induction, suggesting that NreA is a nitrate regulated inhibitor of NreB/NreC. In vitro, NreA and mutant NreA(Y95A) decreased NreB phosphorylation in part or completely, which was due …

Mboat7 down-regulation by hyper-insulinemia induces fat accumulation in hepatocytes.

2020

Background: Naturally occurring variation in Membrane-bound O-acyltransferase domain-containing 7 (MBOAT7), encoding for an enzyme involved in phosphatidylinositol acyl-chain remodelling, has been associated with fatty liver and hepatic disorders. Here, we examined the relationship between hepatic Mboat7 down-regulation and fat accumulation. Methods: Hepatic MBOAT7 expression was surveyed in 119 obese individuals and in experimental models. MBOAT7 was acutely silenced by antisense oligonucleotides in C57Bl/6 mice, and by CRISPR/Cas9 in HepG2 hepatocytes. Findings: In obese individuals, hepatic MBOAT7 mRNA decreased from normal liver to steatohepatitis, independently of diabetes, inflammatio…