The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry

The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Euclidean distances. These yield solutions that are invariant under inversion, i.e., the same whether elastic stiffness or compliance are considered. The Frobenius distance function, which corresponds to common notions of Euclidean length, is not invariant although it is simple to apply using projection operators. A complete description of the Euclidean projection method is presented. The three metrics are considered at a level of detail far greater than heretofore, as we develop the general framework to best fit a given set of moduli onto higher elastic symmetries. The procedures for finding the closest elasticity tensor are illustrated by application to a set of 21 moduli with no underlying symmetry.Comment: 48 pages, 1 figur

The Hardness of Code Equivalence over Fq\mathbf{F}_q and its Application to Code-based Cryptography

International audienceThe code equivalence problem is to decide whether two linear codes over F_q are equivalent, that is identical up to a linear isometry of the Hamming space. In this paper, we review the hardness of code equivalence over F_q due to some recent negative results and argue on the possible implications in code-based cryptography. In particular, we present an improved version of the three-pass identification scheme of Girault and discuss on a connection between code equivalence and the hidden subgroup problem

Serotonin and Dopamine Protect from Hypothermia/Rewarming Damage through the CBS/ H2S Pathway

Biogenic amines have been demonstrated to protect cells from apoptotic cell death. Herein we show for the first time that serotonin and dopamine increase H2S production by the endogenous enzyme cystathionine-β-synthase (CBS) and protect cells against hypothermia/rewarming induced reactive oxygen species (ROS) formation and apoptosis. Treatment with both compounds doubled CBS expression through mammalian target of rapamycin (mTOR) and increased H2S production in cultured rat smooth muscle cells. In addition, serotonin and dopamine treatment significantly reduced ROS formation. The beneficial effect of both compounds was minimized by inhibition of their re-uptake and by pharmacological inhibition of CBS or its down-regulation by siRNA. Exogenous administration of H2S and activation of CBS by Prydoxal 5′-phosphate also protected cells from hypothermic damage. Finally, serotonin and dopamine pretreatment of rat lung, kidney, liver and heart prior to 24 h of hypothermia at 3°C followed by 30 min of rewarming at 37°C upregulated the expression of CBS, strongly reduced caspase activity and maintained the physiological pH compared to untreated tissues. Thus, dopamine and serotonin protect cells against hypothermia/rewarming induced damage by increasing H2S production mediated through CBS. Our data identify a novel molecular link between biogenic amines and the H2S pathway, which may profoundly affect our understanding of the biological effects of monoamine neurotransmitters

Four-dimensional compact projective planes of orbit type (1,1)

We consider 4-dimensional flexible projective planes with the following properties: The collineation group is a 6-dimensional solvable Lie group which fixes some flag ∞ ∈ W. Furthermore, the collineation group has a 1-dimensional orbit both on W and on the pencil of lines through {∞}. We show that there are three different families of planes with these properties.Betten, Dieter; Polster, Burkar