The Baker–Campbell–Hausdorff (BCH) series and the Zassenhaus product are of fundamental importance for the theory of Lie groups and their applications in physics and physical chemistry. Standard ...methods for the explicit construction of the BCH and Zassenhaus terms yield polynomial representations, which must be translated into the usually required commutator representation. We prove that a new translation proposed recently yields a correct representation of the BCH and Zassenhaus terms. This representation entails fewer terms than the well-known Dynkin–Specht–Wever representation, which is of relevance for practical applications. Furthermore, various methods for the computation of the BCH and Zassenhaus terms are compared, and a new efficient approach for the calculation of the Zassenhaus terms is proposed.
Mathematica implementations for the most efficient algorithms are provided together with comparisons of efficiency.
Polarization mode dispersion (PMD), especially in "old" fibers, is considered harmful for installation and upgrading of trunk lines. An optical PMD equalizer should have several or many differential ...group delay (DGD) sections with polarization transformers in between which can endlessly transform any input polarization into a principal state of the following DGD section. The sections must practically have fixed DGDs unless there is only one section. The small-signal baseband transfer function for PMD, higher order PMD, and the necessary number of sections as well as their control by the output signals of an electrical filter bank in the receiver are also discussed in this context. Several PMD equalizers have been realized and successfully tested in transmission systems with bit rates of 10, 20, and 40 Gb/s. The systems operated stably with well-opened eye diagrams for DGDs ranging between 0 and 1.7 bit durations. Best performance is obtained from a distributed PMD equalizer with one piece of polarization-maintaining fiber twisted by 64 stepper motors. The principle can also be realized in LiNbO/sub 3/.
“Proof-of-principle” that cell replacement therapy works for neurodegeneration has been reported, but only using donor cells collected from fetal brain tissue obtained from surgical terminations of ...pregnancy. Surgical terminations of pregnancy represent an increasingly limited supply of donor cells due to the tendency towards performing medical termination in much of Europe. This imposes a severe constraint on further experimental and clinical cell transplantation research. Therefore, we explore here the feasibility of using medical termination tissue as a donor source. Products of conception were retrieved from surgical terminations over the last 7 years and from medical terminations over the last 2.5 years. The number of collections that yielded fetal tissue, viable brain tissue, and identifiable brain regions (ganglionic eminence, ventral mesencephalon, and neocortex) were recorded. We studied cell viability, cell physiological properties, and differentiation potential both in vitro and following transplantation into the central nervous system of rodent models of neurodegenerative disease. Within equivalent periods, we were able to collect substantially greater numbers of fetal remains from medical than from surgical terminations of pregnancy, and the medical terminations yielded a much higher proportion of identifiable and dissectible brain tissue. Furthermore, we demonstrate that harvested cells retain the capacity to differentiate into neurons with characteristics appropriate to the region from which they are dissected. We show that, contrary to widespread assumption, medical termination of pregnancy-derived fetal brain cells represent a feasible and more readily available source of human fetal tissue for experimental cell transplantation with the potential for use in future clinical trials in human neurodegenerative disease.
The collection of adverse event data is an important component of clinical trials, but it is not clear whether solicited or unsolicited collection methods are better at distinguishing drug effects ...from the effects of placebo. The objective of this analysis is to compare the reporting rates and the ability to detect drug-placebo differences with spontaneous versus solicited adverse event collection methods.
Adverse events were collected by spontaneous (unsolicited) reporting and by structured questionnaires in three randomised, double-blind clinical trials. For both spontaneous and solicited adverse event collection methods, a drug/placebo (D/P) reporting ratio was computed by dividing the reporting rate for the experimental drug by the reporting rate for placebo for each adverse event. An index (Sp-So index) was calculated by dividing the spontaneous D/P ratio by the solicited D/P ratio. A number >1.0 indicates that the spontaneous adverse event collection method is more effective in distinguishing the drug from placebo and a number <1.0 suggests that the solicited adverse event collection method is more effective in distinguishing the drug from placebo.
Reporting rates were greater when events were solicited than when the spontaneous reporting approach was used. The Sp-So index was >1.0 for 22 of the 29 (75.9%) events examined, suggesting that spontaneous collection of adverse events is more effective in distinguishing drug effect from placebo than the solicited approach. However, more statistically significant differences between drug and placebo were detected by the solicited method (nine events) than the spontaneous method (five events). This is due, in part, to the fact that differences in the percentages of adverse events between drug and placebo (rather than ratios of event rates) were more often greater when the solicited approach was used.
As expected, adverse events collected by solicitation leads to higher reporting rates. However, it is not clear that solicitation of events leads to greater ability to detect drug-placebo differences. By using a ratio to assess drug-placebo differences, spontaneous reporting provided larger drug-placebo differences more often than solicitation.
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