A new generally applicable method to solve differential equations, based on neural networks, is proposed. Straightforward to implement, finite differences and coordinate transformations are not used. The neural network provides a flexible and compact base for representing the solution, found through the global minimization of an error functional. As a proof of principle, a two-dimensional ideal magnetohydrodynamic plasma equilibrium is solved. Since no particular topology is assumed, the technique is especially promising for the three-dimensional plasma equilibrium problem.

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The humoral hypercalcemia factor parathyroid hormone-related protein is a paracrine-signaling molecule that regulates the development of several organ systems, including the skin. In pathologic circumstances such as hypercalcemia and in development, parathyroid hormone-related protein signaling appears to be mediated by the type I parathyroid hormone/parathyroid hormone-related protein receptor. In order to clarify the role of the ligand and receptor pair in cutaneous biology, gene expression was monitored in a series of murine skin samples ranging from embryonic day 14 to 2 y with in situ hybridization and RNase protection. In all samples, high levels of parathyroid hormone-related protein transcripts were exclusively expressed in the developing and adult hair follicle but were not observed in the interfollicular epidermis. In the adult, parathyroid hormone-related protein mRNA expression was dynamically regulated as a function of the murine hair cycle in a way similar to other signaling molecules that regulate the anagen to catagen transition. PTH receptor transcripts were abundantly expressed in the developing dermis. In the adult skin, PTH receptor mRNA was markedly reduced, but again demonstrated hair-cycle-dependent expression. The dorsal skin of the keratin 14-parathyroid hormone-related protein mouse was used to evaluate the impact of overexpression of the peptide on the murine hair cycle. All types of hair were 30-40% shorter in adult keratin 14-parathyroid hormone-related protein mice as compared with wild-type littermates. This appeared to result from a premature entry into the catagen phase of the hair cycle. Finally, the relationship between parathyroid hormone-related protein signaling and other growth factors that regulate the hair cycle was examined by cross-breeding experiments employing keratin 14-parathyroid hormone-related protein mice and fibroblast growth factor-5-knockout mice. It appears that parathyroid hormone-related protein and fibroblast growth factor-5 regulate the anagen to catagen transition by independent pathways.

PSES is a chimeric enhancer containing enhancer elements from prostate-specific antigen (PSA) and prostate-specific membrane antigen (PSMA) genes that are prevalently expressed in androgen-independent prostate cancers. PSES shows strong activity equivalent to cytomegalovirus (CMV) promoter, specifically in PSA/PSMA-positive prostate cancer cells, the major cell types in prostate cancer in the absence of androgen. We developed a recombinant adenovirus (AdE4P-SESE1a) by placing adenoviral E1a and E4 genes under the control of the bidirectional enhancer PSES and enhanced green fluorescent protein gene for the purpose of intratumoral virus tracking under the control of CMV promoter. Because of PSES being very weak in nonprostatic cells, including HEK293 and HER911 that are frequently used to produce recombinant adenovirus, AdE4PSESE1a can only be produced in the HER911E4 cell line which expresses both E1 and E4 genes. AdE4PSESE1a showed similar viral replication and tumor cell killing activities to wild-type adenovirus in PSA/PSMApositive prostate cancer cells. The viral replication and tumor cell killing activities were dramatically attenuated in PSA/ PSMA-negative cells. To test whether AdE4PSESE1a could be used to target prostate tumors in vivo, CWR22rv s.c. tumors were induced in nude mice and treated with AdE4PSESE1a via intratumoral and tail vein injection. Compared to tumors treated with control virus, the growth of CWR22rv tumors was dramatically inhibited by AdE4PSESE1a via tail vein injection or intratumoral injection. These data show that adenoviral replication can be tightly controlled in a novel fashion by controlling adenoviral E1a and E4 genes simultaneously with a single enhancer. (Cancer Res 2005; 65(5): 1941-51)