Metric Regularity of the Sum of Multifunctions and Applications

In this work, we use the theory of error bounds to study metric regularity of the sum of two multifunctions, as well as some important properties of variational systems. We use an approach based on the metric regularity of epigraphical multifunctions. Our results subsume some recent results by Durea and Strugariu.Comment: Submitted to JOTA 37 page

Directional metric pseudo subregularity of set-valued mappings: a general model

This paper investigates a new general pseudo subregularity model which unifies some important nonlinear (sub)regularity models studied recently in the literature. Some slope and abstract coderivative characterizations are established. © 2019, Springer Nature B.V

Variational analysis of paraconvex multifunctions

Our aim in this article is to study the class of so-called ρ- paraconvex multifunctions from a Banach space X into the subsets of another Banach space Y. These multifunctions are defined in relation with a modulus function ρ: X→ [0 , + ∞) satisfying some suitable conditions. This class of multifunctions generalizes the class of γ- paraconvex multifunctions with γ> 1 introduced and studied by Rolewicz, in the eighties and subsequently studied by A. Jourani and some others authors. We establish some regular properties of graphical tangent and normal cones to paraconvex multifunctions between Banach spaces as well as a sum rule for coderivatives for such class of multifunctions. The use of subdifferential properties of the lower semicontinuous envelope function of the distance function associated to a multifunction established in the present paper plays a key role in this study. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature

Directional Hölder Metric Regularity

This paper sheds new light on regularity of multifunctions through various characterizations of directional Hölder /Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations , we show that directional Hölder /Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directional Hölder /Lipschitz metric regularity to investigate the stability and the sensitivity analysis of parameterized optimization problems are also discussed

Directional Holder metric regularity

This paper sheds new light on regularity of multifunctions through various characterizations of directional Holder/Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Holder/Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directional Holder/Lipschitz metric regularity to investigate the stability and the sensitivity analysis of parameterized optimization problems are also discussed

Osteosynthesis metal plate system for bone fixation using bicortical screws: numerical–experimental characterization

This study reports the numerical and experimental characterization of a standard immobilization system currently being used to treat simple oblique bone fractures of femoral diaphyses. The procedure focuses on the assessment of the mechanical behavior of a bone stabilized with a dynamic compression plate (DCP) in a neutralization function, associated to a lag screw, fastened with surgical screws. The non-linear behavior of cortical bone tissue was revealed through four-point bending tests, from which damage initiation and propagation occurred. Since screw loosening was visible during the loading process, damage parameters were measured experimentally in independent pull-out tests. A realistic numerical model of the DCP-femur setup was constructed, combining the evaluated damage parameters and contact pairs. A mixed-mode (I+II) trapezoidal damage law was employed to mimic the mechanical behavior of both the screw–bone interface and bone fractures. The numerical model replicated the global behavior observed experimentally, which was visible by the initial stiffness and the ability to preview the first loading peak, and bone crack satisfactorily.This research was funded by the Portuguese Foundation for Science and Technology (FCT), grant numbers SFRH/BD/143736/2019, UIDB/CVT/00772/2020, LA/P/0059/2020, UIDB/04033/2020, PTDC/EME-SIS/28225/2017, UID/EEA/04436/2019 and Laboratório Associado de Energia, Transportes e Aeronáutica (LAETA), grant number UID/EMS/50022/2020

Hes1 Is Required for Appropriate Morphogenesis and Differentiation during Mouse Thyroid Gland Development

Notch signalling plays an important role in endocrine development, through its target gene Hes1. Hes1, a bHLH transcriptional repressor, influences progenitor cell proliferation and differentiation. Recently, Hes1 was shown to be expressed in the thyroid and regulate expression of the sodium iodide symporter (Nis). To investigate the role of Hes1 for thyroid development, we studied thyroid morphology and function in mice lacking Hes1. During normal mouse thyroid development, Hes1 was detected from E9.5 onwards in the median anlage, and at E11.5 in the ultimobranchial bodies. Hes1−/− mouse embryos had a significantly lower number of Nkx2-1-positive progenitor cells (p<0.05) at E9.5 and at E11.5. Moreover, Hes1−/− mouse embryos showed a significantly smaller total thyroid surface area (−40 to −60%) compared to wild type mice at all study time points (E9.5−E16.5). In both Hes1−/− and wild type mouse embryos, most Nkx2-1-positive thyroid cells expressed the cell cycle inhibitor p57 at E9.5 in correlation with low proliferation index. In Hes1−/− mouse embryos, fusion of the median anlage with the ultimobranchial bodies was delayed by 3 days (E16.5 vs. E13.5 in wild type mice). After fusion of thyroid anlages, hypoplastic Hes1−/− thyroids revealed a significantly decreased labelling area for T4 (−78%) and calcitonin (−65%) normalized to Nkx2-1 positive cells. Decreased T4-synthesis might be due to reduced Nis labelling area (−69%). These findings suggest a dual role of Hes1 during thyroid development: first, control of the number of both thyrocyte and C-cell progenitors, via a p57-independent mechanism; second, adequate differentiation and endocrine function of thyrocytes and C-cells

Pemphigus autoimmunity: Hypotheses and realities

The goal of contemporary research in pemphigus vulgaris and pemphigus foliaceus is to achieve and maintain clinical remission without corticosteroids. Recent advances of knowledge on pemphigus autoimmunity scrutinize old dogmas, resolve controversies, and open novel perspectives for treatment. Elucidation of intimate mechanisms of keratinocyte detachment and death in pemphigus has challenged the monopathogenic explanation of disease immunopathology. Over 50 organ-specific and non-organ-specific antigens can be targeted by pemphigus autoimmunity, including desmosomal cadherins and other adhesion molecules, PERP cholinergic and other cell membrane (CM) receptors, and mitochondrial proteins. The initial insult is sustained by the autoantibodies to the cell membrane receptor antigens triggering the intracellular signaling by Src, epidermal growth factor receptor kinase, protein kinases A and C, phospholipase C, mTOR, p38 MAPK, JNK, other tyrosine kinases, and calmodulin that cause basal cell shrinkage and ripping desmosomes off the CM. Autoantibodies synergize with effectors of apoptotic and oncotic pathways, serine proteases, and inflammatory cytokines to overcome the natural resistance and activate the cell death program in keratinocytes. The process of keratinocyte shrinkage/detachment and death via apoptosis/oncosis has been termed apoptolysis to emphasize that it is triggered by the same signal effectors and mediated by the same cell death enzymes. The natural course of pemphigus has improved due to a substantial progress in developing of the steroid-sparing therapies combining the immunosuppressive and direct anti-acantholytic effects. Further elucidation of the molecular mechanisms mediating immune dysregulation and apoptolysis in pemphigus should improve our understanding of disease pathogenesis and facilitate development of steroid-free treatment of patients