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We investigate the notion of aWasserstein median as an alternative to the Wasserstein barycenter, which has become popular but may be sensitive to outliers. In terms of robustness to corrupted data, we indeed show that Wasserstein medians have a breakdown point of approximately 1/2. We give explicit constructions of Wasserstein medians in dimension one which enable us to obtain Lp estimates (which do not hold in higher dimensions). We also address dual and multimarginal reformulations. In convex subsets of Rd, we connect Wasserstein medians to a minimal (multi)flow problem à la Beckmann and a system of PDEs of Monge--Kantorovich-type, for which we propose a p-Laplacian approximation. Our analysis eventually leads to a new numerical method to compute Wasserstein medians, which is based on a Douglas--Rachford scheme applied to the minimal flow formulation of the problem. [ABSTRACT FROM AUTHOR]

Background: In recent years, physical exercise has been investigated for its potential as a therapeutic tool in patients with end-stage renal disease (ESRD) undergoing hemodialysis maintenance treatment (HD). It has been shown that regular practice of moderate-intensity exercise can improve certain aspects of immune function and exert anti-inflammatory effects, having been associated with low levels of pro-inflammatory cytokines and high levels of anti-inflammatory cytokines., Purpose: The aim of this review is to examine the studies carried out in this population that analyzed the effect of intradialytic exercise on the inflammatory state and evaluate which exercise modality is most effective., Methods: The search was carried out in the MEDLINE, CINAHL Web of Science and Cochrane Central Register of Controlled Trials databases from inception to June 2022. The PEDro scale was used to assess methodological quality, and the Cochrane Risk of Bias Tool and MINORS were used to evaluate the risk of bias. The quality of evidence was assessed with GRADE scale. The outcome measures were systemic inflammation biomarkers., Results: Mixed results were found in terms of improving inflammation biomarkers, such as CRP, IL-6 or TNFα, after exercise. Aerobic exercise seems to improve systemic inflammation when performed at medium intensity while resistance training produced better outcomes when performed at high intensity. However, some studies reported no differences after exercise and these results should be taken with caution., Conclusions: The low quality of the evidence suggests that aerobic and resistance exercise during HD treatment improves systemic inflammation biomarkers in patients with ESRD. In any case, interventions that increase physical activity in patients with ESRD are of vital importance as sedentary behaviors are associated with mortality. More studies are needed to affirm solid conclusions and to make intervention parameters, such as modality, dose, intensity or duration, sufficiently clear.

Background: Viral vectors are invaluable tools to transfer genes and/or regulatory sequences into differentiated cells such as pancreatic cells. To date, several kinds of viral vectors have been used to transduce different pancreatic cell types, including insulin-producing β cells. However, few studies have used vectors derived from « simple » retroviruses, such as avian α- or mouse γ-retroviruses, despite their high experimental convenience. Moreover, such vectors were never designed to specifically target transgene expression into β cells., Results: We here describe two novel α- or SIN (Self-Inactivating) γ-retrovectors containing the RIP (Rat Insulin Promoter) as internal promoter. These two retrovectors are easily produced in standard BSL2 conditions, rapidly concentrated if needed, and harbor a large multiple cloning site. For the SIN γ-retrovector, either the VSV-G (pantropic) or the retroviral ecotropic (rodent specific) envelope was used. For the α-retrovector, we used the A type envelope, as its receptor, termed TVA, is only naturally present in avian cells and can efficiently be provided to mammalian β cells through either exogenous expression upon cDNA transfer or gesicle-mediated delivery of the protein. As expected, the transgenes cloned into the two RIP-containing retrovectors displayed a strong preferential expression in β over non-β cells compared to transgenes cloned in their non-RIP (CMV- or LTR-) regulated counterparts. We further show that RIP activity of both retrovectors mirrored fluctuations affecting endogenous INSULIN gene expression in human β cells. Finally, both α- and SIN γ-retrovectors were extremely poorly mobilized by the BXV1 xenotropic retrovirus, a common invader of human cells grown in immunodeficient mice, and, most notably, of human β cell lines., Conclusion: Our novel α- and SIN γ-retrovectors are safe and convenient tools to stably and specifically express transgene(s) in mammalian β cells. Moreover, they both reproduce some regulatory patterns affecting INSULIN gene expression. Thus, they provide a helpful tool to both study the genetic control of β cell function and monitor changes in their differentiation status.

The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of N player games. Analysis of Nash equilibria is however a complex issue when the number of players is large. In this article, we emphasize the role of optimal transport theory in (i) the passage from Nash to Cournot-Nash equilibria as the number of players tends to infinity and (ii) the analysis of Cournot-Nash equilibria., (© 2014 The Author(s) Published by the Royal Society. All rights reserved.)