Optimal Recombination in Genetic Algorithms

This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We consider efficient reductions of the ORPs, allowing to establish polynomial solvability or NP-hardness of the ORPs, as well as direct proofs of hardness results

Reflection Groups and Differential Forms

We study differential forms invariant under a finite reflection group over a field of arbitrary characteristic. In particular, we prove an analogue of Saito's freeness criterion for invariant differential 1-forms. We also discuss how twisted wedging endows the invariant forms with the structure of a free exterior algebra in certain cases. Some of the results are extended to the case of relative invariants with respect to a linear character.Comment: 16 page

Developmental and Anatomical Patterns Of IL-2 Gene Expression in Vivo in The Murine Thymus

Interleukin-2 (IL-2) is a potent growth factor that mature T lymphocytes synthesize and use as a proliferation signal. Much controversy has arisen concerning whether it is used to drive the extensive proliferation of immature pre-T cells in the thymus. Immature thymocytes acquire the competence to express IL-2 at an early stage, but it has remained uncertain whether they are activated to exercise this competence in vivo. Therefore, we have used in situ hybridization and immunohistochemistry on serial sections obtained from fetal and adult thymuses of normal C57BL/6 mice and of mice bearing the scid defect to determine where, when, and whether IL-2 is expressed in vivo. Our results show a striking spatial and temporal pattern of IL-2 expression in the normal fetal thymus. We detected a burst of IL-2 mRNA accumulation at day 14.5 of gestation, which rapidly decreased by day 15. At day 15, we observed maximal IL-2 protein production that subsequently decreased by day 16 of gestation. Both in situ hybridization and immunohistochemical staining revealed an unexpectedly strict localization of IL-2 expressing cells to patches around the periphery of the fetal thymus, creating a previously unrecognized compartment of high IL-2 protein content. IL-2 production in the day-15 fetal thymus appeared to be unaffected by the scid mutation, indicating that this response is likely to be T-cell receptor (TcR)-independent. Several features distinguish the IL-2 induction pattern in the adult thymus from that in the fetal thymus. In the normal adult thymus, IL-2-expressing cells are extremely rare (found at a frequency of 10^(-7)), but they are reproducibly detectable as isolated cells in the outer cortex and subcapsular region of the thymus. Unlike the fetal thymic IL-2 producers, the IL-2 producers in the adult thymus are completely eliminated in mice homozygous for the scid mutation. This suggests that the IL-2-expressing cells in the normal adult thymus are of a more mature phenotype than the immature, TcR-negative cells that accumulate in the scid adult thymus. Thus, our work demonstrates that two developmentally distinct types of cell interactions induce IL-2 expression in vivo: one, a broadly localized interaction in day 14-15 fetal thymus that is unaffected by the scid mutation; the other, a rare event that occurs asynchronously from late fetal through adult life, but which is completely eliminated by the scid defect. These results imply that significant differences exist between the physiological processing of thymocytes in the fetal and postnatal thymic microenvironments

Spontaneous Expression of Interleukin-2 In Vivo in Specific Tissues of Young Mice

In situ hybridization and immunohistochemistry were used to determine the spectrum of tissues in which interleukin-2 (IL-2) mRNA and protein are found in healthy, normal young mice. In neonatal animals, IL-2 is expressed specifically by distinct, isolated cells at three major sites: the thymus, skin, and gut. Based on morphology and distribution, the IL-2-expressing cells resemble CD3ε + T cells that are also present in all these locations. Within the thymus of postweanling animals, both TcRαβ and TcRγδ lineage cells secrete "haloes" of the cytokine that diffuse over many cell diameters. Within the skin, isolated cells expressing IL-2 are seen at birth in the mesenchyme, and large numbers of IL-2-expressing cells are localized around hair follicles in the epidermis in 3-week-old animals. At this age, a substantial subset of CD3ε + cells is similarly localized in the skin. Significantly, by 5 weeks of age and later when the CD3ε + cells are evenly distributed throughout the epidermis, IL-2 RNA and protein expression are no longer detectable. Finally, within the intestine, IL-2 protein is first detected in association with a few discrete, isolated cells at day 16 of gestation and the number of IL-2 reactive cells increases in frequency through El9 and remains abundant in adult life. In postnatal animals, the frequency of IL- 2-positive cells in villi exceeds by greater than fivefold that found in mesenteric lymph node or Peyer's patches. Overall, these temporal and spatial patterns of expression provide insight into the regulation of IL-2 in vivo and suggest a role for IL-2 expression distinct from immunological responses to antigen