New perspectives on forbidden symmetries, quasicrystals, and Penrose tilings

Quasicrystals are solids with quasiperiodic atomic structures and symmetries forbidden to ordinary periodic crystals—e.g., 5-fold symmetry axes. A powerful model for understanding their structure and properties has been the two-dimensional Penrose tiling. Recently discovered properties of Penrose tilings suggest a simple picture of the structure of quasicrystals and shed new light on why they form. The results show that quasicrystals can be constructed from a single repeating cluster of atoms and that the rigid matching rules of Penrose tilings can be replaced by more physically plausible cluster energetics. The new concepts make the conditions for forming quasicrystals appear to be closely related to the conditions for forming periodic crystals.

An endogenous rate of time preference, the Penrose effect, and dynamic optimality of environmental quality.

In the present paper, the endogenous theory of time preference is extended to analyze those processes of capital accumulation and changes in environmental quality that are dynamically optimum with respect to the intertemporal preference ordering of the representative individual of the society in question. The analysis is carried out within the conceptual framework of the dynamic analysis of environmental quality, as has been developed by a number of economists for specific cases of the fisheries and forestry commons. The duality principles on intertemporal preference ordering and capital accumulation are extended to the situation where processes of capital accumulation are subject to the Penrose effect, which exhibit the marginal decrease in the effect of investment in private and social overhead capital upon the rate at which capital is accumulated. The dynamically optimum time-path of economic activities is characterized by the proportionality of two systems of imputed, or efficient, prices, one associated with the given intertemporal ordering and another associated with processes of accumulation of private and social overhead capital. It is particularly shown that the dynamically optimality of the processes of capital accumulation involving both private and social overhead capital is characterized by the conditions that are identical with those involving private capital, with the role of social overhead capital only indirectly exhibited.

Comparison of potency of inhaled beclomethasone and budesonide in New Zealand: retrospective study of computerised general practice records

Objective To determine whether inhaled budesonide and beclomethasone are equipotent in the treatment of asthma in primary care.

Five-fold symmetry in crystalline quasicrystal lattices

To demonstrate that crystallographic methods can be applied to index and interpret diffraction patterns from well-ordered quasicrystals that display non-crystallographic 5-fold symmetry, we have characterized the properties of a series of periodic two-dimensional lattices built from pentagons, called Fibonacci pentilings, which resemble aperiodic Penrose tilings. The computed diffraction patterns from periodic pentilings with moderate size unit cells show decagonal symmetry and are virtually indistinguishable from that of the infinite aperiodic pentiling. We identify the vertices and centers of the pentagons forming the pentiling with the positions of transition metal atoms projected on the plane perpendicular to the decagonal axis of quasicrystals whose structure is related to crystalline η phase alloys. The characteristic length scale of the pentiling lattices, evident from the Patterson (autocorrelation) function, is ∼τ2 times the pentagon edge length, where τ is the golden ratio. Within this distance there are a finite number of local atomic motifs whose structure can be crystallographically refined against the experimentally measured diffraction data.

Interleukin 4 suppresses c-kit ligand-induced expression of cytosolic phospholipase A2 and prostaglandin endoperoxide synthase 2 and their roles in separate pathways of eicosanoid synthesis in mouse bone marrow-derived mast cells.

Mouse bone marrow-derived mast cells (BMMCs) developed with interleukin 3 (IL-3) can be stimulated by c-kit ligand (KL) and accessory cytokines over a period of hours for direct delayed prostaglandin (PG) generation or over a period of days to prime for augmented IgE-dependent PG and leukotriene (LT) production, as previously reported. We now report that IL-4 is counterregulatory for each of these distinct KL-dependent responses. BMMCs cultured for 4 days with KL + IL-3 or with KL + IL-10 produced 5- to 7-fold more PGD2 and approximately 2-fold more LTC4 in response to IgE-dependent activation than BMMCs maintained in IL-3 alone. IL-4 inhibited the priming for increased IgE-dependent PGD2 and LTC4 production to the level obtained by activation of BMMCs maintained in IL-3 alone with an IC50 of approximately 0.2 ng/ml. IL-4 inhibited the KL-induced increase in expression of cytosolic phospholipase A2 (cPLA2) but had no effect on the incremental expression of PG endoperoxide synthase 1 (PGHS-1) and hematopoietic PGD2 synthase or on the continued baseline expression of 5-lipoxygenase, 5-lipoxygenase activating protein, and LTC4 synthase. BMMCs stimulated by KL + IL-10 for 10 h exhibited a delayed phase of PGD2 generation, which was dependent on de novo induction of PGHS-2. IL-4 inhibited the induction of PGHS-2 expression and the accompanying cytokine-initiated delayed PGD2 generation with an IC50 of approximately 6 ng/ml. IL-4 had no effect on the expression of PGHS-2 and the production of PGD2 elicited by addition of IL-1 beta to the combination of KL + IL-10. IL-4 had no effect on the immediate phase of eicosanoid synthesis elicited by KL alone or by IgE and antigen in BMMCs maintained in IL-3. Thus, the counterregulatory action of IL-4 on eicosanoid generation is highly selective for the induced incremental expression of cPLA2 and the de novo expression of PGHS-2, thereby attenuating time-dependent cytokine-regulated responses to stimulation via Fc epsilon receptor I and stimulation via c-kit, respectively.