Order preserving and order reversing operators on the class of convex functions in Banach spaces

A remarkable result by S. Artstein-Avidan and V. Milman states that, up to pre-composition with affine operators, addition of affine functionals, and multiplication by positive scalars, the only fully order preserving mapping acting on the class of lower semicontinuous proper convex functions defined on $\mathbb{R}^n$ is the identity operator, and the only fully order reversing one acting on the same set is the Fenchel conjugation. Here fully order preserving (reversing) mappings are understood to be those which preserve (reverse) the pointwise order among convex functions, are invertible, and such that their inverses also preserve (reverse) such order. In this paper we establish a suitable extension of these results to order preserving and order reversing operators acting on the class of lower semicontinous proper convex functions defined on arbitrary infinite dimensional Banach spaces.Comment: 19 pages; Journal of Functional Analysis, accepted for publication; a better presentation of certain parts; minor corrections and modifications; references and thanks were adde

Preconditioned conjugate gradient method for generalized least squares problems

AbstractA variant of the preconditioned conjugate gradient method to solve generalized least squares problems is presented. If the problem is min (Ax − b)TW−1(Ax − b) with A ∈ Rm×n and W ∈ Rm×m symmetric and positive definite, the method needs only a preconditioner A1 ∈ Rn×n, but not the inverse of matrix W or of any of its submatrices. Freund's comparison result for regular least squares problems is extended to generalized least squares problems. An error bound is also given

Epigenetic marks in an adaptive water stress-responsive gene in tomato roots under normal and drought conditions

Tolerance to water deficits was evolutionarily relevant to the conquest of land by primitive plants. In this context, epigenetic events may have played important roles in the establishment of drought stress responses. We decided to inspect epigenetic marks in the plant organ that is crucial in the sensing of drought stress: the root. Using tomato as a crop model plant, we detected the methylated epialleles of Asr2, a protein-coding gene widespread in the plant kingdom and thought to alleviate restricted water availability. We found 3 contexts (CG, CNG, and CNN) of methylated cytosines in the regulatory region of Solanum lycopersicum Asr2 but only one context (CG) in the gene body. To test the hypothesis of a link between epigenetics marks and the adaptation of plants to drought, we explored the cytosine methylation status of Asr2 in the root resulting from water-deficit stress conditions. We found that a brief exposure to simulated drought conditions caused the removal of methyl marks in the regulatory region at 77 of the 142 CNN sites. In addition, the study of histone modifications around this model gene in the roots revealed that the distal regulatory region was rich in H3K27me3 but that its abundance did not change as a consequence of stress. Additionally, under normal conditions, both the regulatory and coding regions contained the typically repressive H3K9me2 mark, which was lost after 30 min of water deprivation. As analogously conjectured for the paralogous gene Asr1, rapidly acquired new Asr2 epialleles in somatic cells due to desiccation might be stable enough and heritable through the germ line across generations, thereby efficiently contributing to constitutive, adaptive gene expression during the evolution of desiccation-tolerant populations or species.Fil: González, Rodrigo Matías. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Fisiología, Biología Molecular y Neurociencias. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Fisiología, Biología Molecular y Neurociencias; ArgentinaFil: Ricardi, Martiniano María. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Fisiología, Biología Molecular y Neurociencias. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Fisiología, Biología Molecular y Neurociencias; ArgentinaFil: Iusem, Norberto Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Fisiología, Biología Molecular y Neurociencias. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Fisiología, Biología Molecular y Neurociencias; Argentin

Motzkin predecomposable sets

We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family