To asses the role of interleukin 7 (IL-7) in the thymic reconstitution of CD4 T cells observed in... more To asses the role of interleukin 7 (IL-7) in the thymic reconstitution of CD4 T cells observed in children after successful antiretroviral therapy, a longitudinal study in five vertically HIV-1-infected children was carried out. Thymic function, IL-7 plasma levels, viral load, and T-lymphocytes subsets were determined every 2 or 3 months for about 90 months. In all the children, the drop in CD4+ T cells below 5–10% was associated with a marked increase in IL-7 plasma levels. The drastic decrease in viral load after treatment, led in all the cases to a recover of CD4 to levels higher than 30%, which was associated to an increase in thymic production of T cells and followed by a decrease in IL-7 to the normal levels. We conclude that the drop in CD4 in HIV children would induce an increase of IL-7 as part of a homeostatic mechanism. IL-7 would induce the thymus to produce new T cells to recover the normal levels of CD4 when the viral load was low and so the thymic function was not inhibited. The increase in the thymic production of new T cells recovers the CD4 population, and leads to a normalization of IL-7 levels.
We present a simple and unified technique to establish convergence of various minimization method... more We present a simple and unified technique to establish convergence of various minimization methods. These contain the (conceptual) proximal point method, as well as implementable forms such as bundle algorithms, including the classical subgradient relaxation algorithm with divergent series.
Given a real valued function f, defined on a locally convex topological space X, locally Lipschit... more Given a real valued function f, defined on a locally convex topological space X, locally Lipschitzian, and Gateaux-differentiable on a dense subset D in X, we have studied under what hypotheses Charke's generalized gradient can be written as $$\partial f(x) = \overline {co} {\text{ }}\{ w^* \mathop {\lim }\limits_{y \to x} \nabla f(y)/ y \in D\} {\text{ }},$$ It is shown that this formula is valid in particular when f is regular or semismooth. By using this characterization, some properties known to hold true in finite dimension are generalized and other new properties are established. In particular, a characterization of semismooth functions is given in terms of the continuity of the directional derivative. Finally, characterizations for the directional derivative and generalized gradient of marginal functions are obtained. In particular, Mifflin's result stating that lower-C1 functions are semismooth is generalized.
This work deals with the spectral analysis of set-valued operators from a Banach space X into its... more This work deals with the spectral analysis of set-valued operators from a Banach space X into its dual space X *. The main goal of the paper is to study semicontinuity properties of the spectrum operator.
To asses the role of interleukin 7 (IL-7) in the thymic reconstitution of CD4 T cells observed in... more To asses the role of interleukin 7 (IL-7) in the thymic reconstitution of CD4 T cells observed in children after successful antiretroviral therapy, a longitudinal study in five vertically HIV-1-infected children was carried out. Thymic function, IL-7 plasma levels, viral load, and T-lymphocytes subsets were determined every 2 or 3 months for about 90 months. In all the children, the drop in CD4+ T cells below 5–10% was associated with a marked increase in IL-7 plasma levels. The drastic decrease in viral load after treatment, led in all the cases to a recover of CD4 to levels higher than 30%, which was associated to an increase in thymic production of T cells and followed by a decrease in IL-7 to the normal levels. We conclude that the drop in CD4 in HIV children would induce an increase of IL-7 as part of a homeostatic mechanism. IL-7 would induce the thymus to produce new T cells to recover the normal levels of CD4 when the viral load was low and so the thymic function was not inhibited. The increase in the thymic production of new T cells recovers the CD4 population, and leads to a normalization of IL-7 levels.
We present a simple and unified technique to establish convergence of various minimization method... more We present a simple and unified technique to establish convergence of various minimization methods. These contain the (conceptual) proximal point method, as well as implementable forms such as bundle algorithms, including the classical subgradient relaxation algorithm with divergent series.
Given a real valued function f, defined on a locally convex topological space X, locally Lipschit... more Given a real valued function f, defined on a locally convex topological space X, locally Lipschitzian, and Gateaux-differentiable on a dense subset D in X, we have studied under what hypotheses Charke's generalized gradient can be written as $$\partial f(x) = \overline {co} {\text{ }}\{ w^* \mathop {\lim }\limits_{y \to x} \nabla f(y)/ y \in D\} {\text{ }},$$ It is shown that this formula is valid in particular when f is regular or semismooth. By using this characterization, some properties known to hold true in finite dimension are generalized and other new properties are established. In particular, a characterization of semismooth functions is given in terms of the continuity of the directional derivative. Finally, characterizations for the directional derivative and generalized gradient of marginal functions are obtained. In particular, Mifflin's result stating that lower-C1 functions are semismooth is generalized.
This work deals with the spectral analysis of set-valued operators from a Banach space X into its... more This work deals with the spectral analysis of set-valued operators from a Banach space X into its dual space X *. The main goal of the paper is to study semicontinuity properties of the spectrum operator.
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