Continuity of Multimarginal Optimal Transport with Repulsive Cost

open3siWe provide sharp conditions for the finiteness and the continuity of multimarginal optimal transport with repulsive cost, expressed in terms of a suitable concentration property of the measure. To achieve this result, we analyze the Kantorovich potentials of the optimal plans, and we estimate the distance of any optimal plan from the regions where the cost is infinite.openColombo M.; Di Marino S; Stra F.Colombo, M.; Di Marino, S; Stra, F

Linear Lipschitz and C-1 extension operators through random projection

We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C-1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C-l extension theorem by Whitney [8] to Banach spaces. (C) 2020 Elsevier Inc. All rights reserved

Linear Lipschitz and C1 extension operators through random projection

We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C1 extension theorem by Whitney [8] to Banach spaces

Postural stabilization and balance assessment in Charcot–Marie–Tooth 1A subjects

AbstractThe aim of the present study was to assess postural stabilization skill in adult subjects affected by Charcot–Marie–Tooth disease (CMT) type 1A. For this purpose ground reaction force (GRF) was measured by means of a piezoelectric force platform during the sit-to-stand (STS) movement, until a steady state erect posture was achieved. Specific indexes to quantify Centre of Mass acceleration, both during postural stabilization and during quiet standing, were computed using a mathematical model. Forty-seven CMT1A subjects were recruited for the study, and the control group was formed by forty-one age- and sex-matched healthy subjects.The results show that CMT1A subjects are less stable than controls during the quiet stance. Greater difficulty (high values of Yinf, the final instability rate) to maintain erect posture appears to be mainly associated with plantar-flexor muscle weakness, rather than to damage of the proprioceptive system. The worst performances shown by CMT1A subjects in the stabilization phase (high values of I, the global index of postural stabilization performance) seem to be associated with reduced muscle strength and the loss of large sensory nerve fibres.Distal muscle weakness appears to affect both postural stabilization and quiet erect posture. The presented protocol and the analysis of postural stabilization parameters provide useful information on CMT1A balance disorders