Ground state phase diagram of the repulsive fermionic t−t′t-t^{\prime} Hubbard model on the square lattice from weak-coupling

We obtain a complete and exact in the weak-coupling limit ($U \rightarrow 0$) ground state phase diagram of the repulsive fermionic Hubbard model on the square lattice for filling factors $0 < n < 2$ and next-nearest-neighbour hopping amplitudes $0 \le t^{\prime} \le 0.5$. Phases are distinguished by the symmetry and the number of nodes of the superfluid order parameter. The phase diagram is richer than may be expected and typically features states with a high --- higher than that of the fundamental mode of the corresponding irreducible representation --- number of nodes. The effective coupling strength in the Cooper channel $\lambda$, which determines the critical temperature $T_c$ of the superfluid transition, is calculated in the whole parameter space and regions with high values of $\lambda$ are identified. It is shown that besides the expected increase of $\lambda$ near the Van Hove singularity line, joining the ferromagnetic and antiferromagnetic points, another region with high values of $\lambda$ can be found at quarter filling and $t^{\prime}=0.5$ due to the presence of a line of nesting at $t^{\prime} \ge 0.5$. The results can serve as benchmarks for controlled non-perturbative methods and guide the ongoing search for high-$T_c$ superconductivity in the Hubbard model.Comment: 11 Pages, 9 Figure

The control of decidual prolactin production during human pregnancy

Decidual prolactin (PRL) is identical to pituitary PRL according to its chemical, biological, and immunological properties. The factors involved in the regulation of PRL production from pituitary and decidua, however, are different. Although much is known about the factors that modulate the pituitary production of PRL, very little is known about the control of decidual PRL synthesis and release. The studies in this thesis were undertaken to investigate the control of decidual PRL production during human pregnancy.When this study was carried out, the exact cellular origin of decidual PRL remained unclear. Using the in situ hybridization with a human pituitary PRL cDNA probe, validated by Northern blot analysis, together with immunocytochemistry to co- localize PRL mRNA and its protein product, decidual cells in the utero- placental unit were identified conclusively, for the first time, as the only source of PRL synthesis.As the decidual cells are one of the main targets of progesterone and estradiol action within the uterus, studies were carried out to examine the effect of these steroids on decidual PRL production. Firstly, the relationship between decidualization and PRL production at different stages of human pregnancy was examined using in situ hybridization and Northern blot to assess PRL mRNA level, immunocytochemistry to examine the PRL content inside the decidual cells and redioimmunoassay to measure PRL output in amniotic fluid. The results clearly show that PRL gene expression in human decidua paralleled the degree of decidualization which was resulted from the action of sex steroids. Further studies were performed to reveal how important the effect of progesterone on decidual PRL production was during early pregnancy by blocking the action of progesterone with the antiprogesterone (RU486) in vivo. Withdrawal of progesterone action in vivo only resulted in suppression of decidual PRL production associated with morphological de- decidualization in decidua parietalis free of trophoblast, while no such effect occurred in decidua capsularis which had trophoblast attached. The results indicated that decidual PRL production was not only dependent on progesterone, but also potentially on factors derived from the trophoblast. Finally, the effects of both oestrogen and progesterone, either alone or in combination on PRL 111 production by human term decidual cells, were investigated. This study clearly demonstrated that oestrogen and progesterone acted synergistically to maintain decidualization and consequent production of PRL by decidual cells which was further confirmed by studies of the immunolocalization of oestradiol and progesterone receptor. Progesterone induced and maintained PRL production via its receptor mechanism resulting in decidualization. Oestrogen modulated progesterone function at the progesterone receptor level, thus beeing indirectly involved in modulating PRL production.Because the blastocyst- induced decidualization probably augments that initiated by sex steroids in human pregnancy, the potential PRL releasing activity associated with placenta was explored by adding placenta- conditioned medium and hCG, one of the major placenta proteins, to the cultured decidua. The results supported the concept that a local regulatory mechanism for decidual PRL production might exist which was related to placenta, but not hCG. The adenyl cyclase system (abcAMP) failed to effect, while TPA, testing the DAG pathway, inhibited decidual PRL production by term decidual cells.Unlike pituitary PRL, dopamine had no effect on decidual PRL production. In situ hybridization appeared to indicate the presence of dopamine D2 receptors on decidual cells but Northern analysis and PCR of decidual mRNA with primers to both rat and human dopamine D2 receptors failed to confirm the presence of dopamine D2 receptors. Decidual cells transfected with the dopamine D2 construct aslo failed to response to dopamine (bromocriptin) suggesting the second messenger system associated with signal transduction of dopamine D2 receptor may not be functional.These results support the concept that decidual cells are the only source of PRL in the utero- placental unit. The major control of release is the rate synthesis of PRL and this is related to the degree and maintenance of decidualization, induced and maintained by a synergistic action of oestradiol and progesterone. Dopamine is not a controller of decidual PRL production

Data Visualization in Online Educational Research

This chapter presents a general and practical guideline that is intended to introduce the traditional visualization methods (word clouds), and the advanced visualization methods including interactive visualization (heatmap matrix) and dynamic visualization (dashboard), which can be applied in quantitative, qualitative, and mixed-methods research. This chapter also presents the potentials of each visualization method for assisting researchers in choosing the most appropriate one in the web-based research study. Graduate students, educational researchers, and practitioners can contribute to take strengths from each visual analytical method to enhance the reach of significant research findings into the public sphere. By leveraging the novel visualization techniques used in the web-based research study, while staying true to the analytical methods of research design, graduate students, educational researchers, and practitioners will gain a broader understanding of big data and analytics for data use and representation in the field of education