Restricted and Unrestricted Coverings of Complete Bipartite Graphs with Hexagons

A minimal covering of a graph G with isomorphic copies of graph H is a set {H1, H2, H3, ... , Hn} where Hi is isomorphic to H, the vertex set of Hi is a subset of G, the edge set of G is a subset of the union of Hi\u27s, and the cardinality of the union of Hi\u27s minus G is minimum. Some studies have been made of covering the complete graph in which case an added condition of the edge set of Hi is the subset of the edge set of G for all i which implies no additional restrictions. However, if G is not the complete graph, then this condition may have implications. We will give necessary and sufficient conditions for minimal coverings of complete bipartite graph with 6-cycles, which we call minimal unrestricted coverings. We also give necessary and sufficient conditions for minimal coverings of the complete bipartite graph with 6-cycles with the added condition the edge set of Hi is a subset of G for all i, and call these minimal restricted coverings

Quantification of corticosteroid-induced skin vasoconstriction: visual ranking, chromameter measurement or digital image analysis

Topical corticosteroid formulations have been evaluated by visual grading protocols for many years. Toward a more objective methodology, several instrumental methods have been evaluated for applicability in quantifying the vasoconstriction side-effect that follows corticosteroid application to the skin. Although the chromameter has been adopted by regulatory bodies throughout the world as the current standard for topical bioequivalence determinations, there is considerable criticism of this instrument from several quarters. A preliminary comparison reported here indicates that digital image analysis provides statistically significant results that are similar to those obtained by visual assessment techniques, and shows considerably greater precision than that obtained by the chromameter. Continued evaluation of objective assessment techniques, such as digital imaging, and continued modernisation of regulatory bioequivalence requirements will assist in protecting patients and optimising clinical results

Bioequivalence testing of topical dermatological formulations, the gap between science and legislation

Bioavailability concerns for topical dermatological products are complex and it is especially difficult to determine the bioequivalence of similar topical formulations. Since only small amounts of drug dispersed in an appropriate vehicle are applied to the skin, the amount of drug that actually reaches the systemic circulation is often too small to be easily quantified. Additionally, it can be argued that the relevance of any serum/plasma concentration-time curve of a topical agent is questionable, since the curve reflects the amount of drug after the active moiety has left the site of action. For some topical drugs e.g., topical corticosteroids, it is possible to perform a pharmacodynamic bioassay to obtain acceptable bioequivalence data. In this case, the intensity of the side effect of blanching (vasoconstriction) in the skin caused by topical corticosteroids can be measured. The response is directly proportional to the clinical efficacy, and the skin blanching assay has proved to be a reliable procedure for the determination of topical corticosteroid bioavailability. Recently, we had sight of the results of a topical bioequivalence study, which was conducted for the registration of a new generic corticosteroid cream formulation. In this trial the new formulation was compared to two equivalent product from the local market and bioequivalence was demonstrated by the investigators for all three products. These results were examined with interest as the respective reference products have been used repeatedly as standard formulations in our laboratory. However, one of these reference formulations has consistently shown superior bioavailability in our trials, but was not demonstrated to be superior in the study results examined. In the present publication an overview of topical bioequivalence testing in general is given and the difficulties occurring in practice, for topical corticosteroid formulations in particular, are demonstrated

Analysis of chromameter results obtained from corticosteroid-induced skin blanching assay: comparison of visual and chromameter data

In a Guidance document, the American FDA recommends the use of a Minolta chromameter rather than the human eye for the quantitative assessment of the pharmacodynamic blanching response produced by topical application of corticosteroids. The purpose of this study was to compare the appropriateness of the human eye and two models of chromameter for the estimation of skin blanching, in terms of the quality of the data generated by each method. The corticosteroid-induced skin blanching from four different betamethasone 17-valerate cream formulations was compared in a typical human skin blanching trial. The optimized assay methodology routinely practised in our laboratories was utilized. The blanching responses were assessed visually by three trained, independent observers and recorded by two chromameters (Minolta model CR-200 and model CR-300). The topical availability of the four creams was determined using visual scoring and chromameter measurements. All data were manipulated in such a manner as to produce a blanching response versus time profile from which AUBC analysis could be performed. Good correlation was observed between the visual assessments made by three independent observers. In contrast, moderate correlation was determined between visual, CR-200 and CR-300 measurements. Surprisingly, no direct linear relationship between the AUBCs produced by the two chromameters was observed indicating that the quality of the data obtained from the two instruments may not be equal. This investigation also indicated that the use of the chromameter is not completely objective. Visual scoring and chromameter measurement produce data sets that differ in quality. Each procedure needs to be validated and investigators have to be trained for both visual assessment and the operation of the chromameter, particularly with regard to the manipulation of the measuring head of the instrument

The space shuttle launch vehicle aerodynamic verification challenges

The Space Shuttle aerodynamics and performance communities were challenged to verify the Space Shuttle vehicle (SSV) aerodynamics and system performance by flight measurements. Historically, launch vehicle flight test programs which faced these same challenges were unmanned instrumented flights of simple aerodynamically shaped vehicles. However, the manned SSV flight test program made these challenges more complex because of the unique aerodynamic configuration powered by the first man-rated solid rocket boosters (SRB). The analyses of flight data did not verify the aerodynamics or performance preflight predictions of the first flight of the Space Transportation System (STS-1). However, these analyses have defined the SSV aerodynamics and verified system performance. The aerodynamics community also was challenged to understand the discrepancy between the wind tunnel and flight defined aerodynamics. The preflight analysis challenges, the aerodynamic extraction challenges, and the postflight analyses challenges which led to the SSV system performance verification and which will lead to the verification of the operational ascent aerodynamics data base are presented

Chromametry: measuring precision of diurnal and local variation of human forearm skin colour

Chromameters are compact portable instruments used for the assessment of surface colour based on the tristimulus analysis of a reflected xenon light pulse, and have been used for the quantification of erythema in the study of irritant dermatitis, and corticosteroid-induced skin blanching in the vasoconstriction assay. The variability and the reproducibility of chromameter results were investigated since it is known that the location and application force of the measuring head on the skin and the orthostatic maneuver of the arms influence the colour measurement. Furthermore the diurnal variation and the homogeneity of forearm skin colour were investigated

Individualising drug dispensaries in a university hospital

BACKGROUND: In hospitals and other healthcare institutions drugs are routinely stored in designated satellite areas on the wards. Often ad hoc decisions are made by clinicians and nurses regarding drug type and quantity to be stored. As a result the number of different drugs and drug packages in storage tends to increase, which may lead to inefficient drug handling and become a potential risk factor in the medication control process. Based on an extended analysis of drug inventories on three different wards it was hypothesized that a ward-individualised formulary (WIF) can halve the number of different drugs and drug packages in a drug dispensary and hence reduce bound capital, money lost through expired drugs, and facilitate safer drug handling. The interdisciplinary intervention described here took place on three 40-bed wards in a 700-bed university hospital housing patients in general internal medicine, haematology, nephrology and oncology. METHODS: A WIF was defined by including all drugs from the hospital formulary ordered at least three times in the past six months. A pharmacist, a nurse and a clinician reviewed the inclusion list of drugs and clinicians were strongly encouraged to prescribe drugs primarily from the WIF. Drugs excluded from the WIF were removed from the drug dispensaries and the number of included drug packages stored in the remote dispensaries was reduced according to their order history. Drug inventory on the wards was monitored from February 2004 to April 2006. RESULTS: The initial drug dispensary inventories on wards A, B and C consisted of 2031, 1667 and 1536 packages with 943, 897 and 831 different drugs valued at h 83 931, h 44 590 and h 57 285. respectively. After adjusting the drug dispensaries according to the WIF drug dispensary inventories on wards A, B and C consisted of 808 (-60%), 600 (-64%) and 485 (-68%) packages with 415 (-56%), 334 (-63%) and 376 (-55%) different drugs valued euro 28 012 (-67%), euro 10 381 (-77%) an euro 17 898 (-69%). The overall reductions the number of packages, the different drugs and the drug value were comparable (<50%) and remained low during the entire observation time (A: 18 months, B: 13 months, C: 8 months). CONCLUSION: Rearranging dispensaries by individualizing the drug inventory according to the needs of the ward by introducing a WIF is a valuable means to significantly (<50%) reduce [1] the number of drug packages, [2] the number of different drugs stored and [3] the capital bound drugs. The positive effects of the WIF are supported by the interdisciplinary interaction of the different professional groups involved in the medication process. The leaner drug dispensaries offer optimal basic conditions for introducing new IT-based systems to further increase the safety of the medication process

Comparison of visual CR-200 and CR-300 chromameter data obtained from the corticosteroid-induced skin-blanching assay

In a recent Guidance document the American FDA recommended the use of a chromameterrather thanthe human eye for the assessment of the pharmacodynamic blanching response produced after topical application of corticosteroids. The purpose of this study was to investigate the appropriateness of the human eye and two types of chromameter for the estimation of skin blanching