Extended formulations for combinatorial polytopes

Magdeburg, Univ., Fak. für Mathematik, Diss., 2012

Polyhedral and combinatorial aspects in optimization

Magdeburg, Univ., Fak. für Mathematik, Habil.-Schr., 2012

Journal of Natural Philosophy, Chemistry & the Arts.

v. 2 (1799)

Journal of Natural Philosophy, Chemistry & the Arts.

v. 5 (1802)

Journal of Natural Philosophy, Chemistry & the Arts.

v. 28 (1811)

Journal of Natural Philosophy, Chemistry & the Arts.

v. 9 (1804)

Journal of Natural Philosophy, Chemistry & the Arts.

v. 3 (1800)

Journal of Natural Philosophy, Chemistry & the Arts.

v. 15 (1806)

Journal of Natural Philosophy, Chemistry & the Arts.

v. 4 (1801)

Sizes of linear descriptions in combinatorial optimization

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Univ., Dissertation, 2015

Seasonal variation of the effect of high-carbohydrate and high-protein diets on the intermediate metabolism of Parastacus brasiliensis (Crustacea, Decapoda, Parastacidae) maintained in the laboratory

The goal of this study was to evaluate the effect of a high-carbohydrate diet (HC) and a high-protein diet (HP) on the metabolism of the crayfish Parastacus brasiliensis (Von Martens, 1869), collected in different seasons and maintained in the laboratory for 15 days. Crayfish were collected monthly from January 2002 to January 2004 at São Francisco de Paula, Southern Brazil, in Guarapirá stream. In the laboratory, the animals were kept submerged in aquariums under controlled conditions. They were fed ad libitum, for 15 days with either a HC or HP diet. At the end of this period, haemolymph samples were collected, as were hepatopancreas, gills, and abdominal muscle that were removed for determination of glycogen, free glucose, lipids, and triglycerides. The haemolymph samples were used for determination of glucose, proteins, lipids, and triglycerides. Statistical analysis (ANOVA) revealed significant seasonal differences in biochemical composition in crayfish maintained on HC or HP diets. Independent of the diets offered to the animals and the controlled conditions for 15 days, the indications of seasonality were unchanged. The observed changes seemed to be related to the reproductive period. Moreover, the HC diet increased all energy reserves in adult parastacids, which may aid in reproduction.

Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

Results of An International Study of Quantitative BCR/ABL Assays Using Defined RNA Samples

Molecular monitoring of BCR/ABL transcripts by real time quantitative reverse transcription PCR (qRT-PCR) is an essential technique for clinical management of patients with BCR/ABL-positive CML and ALL. Though quantitative BCR/ABL assays are performed in hundreds of laboratories worldwide, results among these laboratories cannot be reliably compared due to heterogeneity in test methods, data analysis, reporting, and lack of quantitative standards. Recent efforts towards standardization have been limited in scope. Aliquots of RNA were sent to clinical test centers worldwide in order to evaluate methods and reporting for e1a2, b2a2, and b3a2 transcript levels using their own qRT-PCR assays. Total RNA was isolated from tissue culture cells that expressed each of the different BCR/ABL transcripts. Serial log dilutions were prepared, ranging from 100 to 10-5, in RNA isolated from HL60 cells. Laboratories performed 5 independent qRT-PCR reactions for each sample type at each dilution. In addition, 15 qRT-PCR reactions of the 10-3 b3a2 RNA dilution were run to assess reproducibility within and between laboratories. Participants were asked to run the samples following their standard protocols and to report cycle threshold (Ct), quantitative values for BCR/ABL and housekeeping genes, and ratios of BCR/ABL to housekeeping genes for each sample RNA. Thirty-seven (n=37) participants have submitted qRT-PCR results for analysis (36, 37, and 34 labs generated data for b2a2, b3a2, and e1a2, respectively). The limit of detection for this study was defined as the lowest dilution that a Ct value could be detected for all 5 replicates. For b2a2, 15, 16, 4, and 1 lab(s) showed a limit of detection at the 10-5, 10-4, 10-3, and 10-2 dilutions, respectively. For b3a2, 20, 13, and 4 labs showed a limit of detection at the 10-5, 10-4, and 10-3 dilutions, respectively. For e1a2, 10, 21, 2, and 1 lab(s) showed a limit of detection at the 10-5, 10-4, 10-3, and 10-2 dilutions, respectively. Log %BCR/ABL ratio values provided a method for comparing results between the different laboratories for each BCR/ABL dilution series. Linear regression analysis revealed concordance among the majority of participant data over the 10-1 to 10-4 dilutions. The overall slope values showed comparable results among the majority of b2a2 (mean=0.939; median=0.9627; range (0.399 - 1.1872)), b3a2 (mean=0.925; median=0.922; range (0.625 - 1.140)), and e1a2 (mean=0.897; median=0.909; range (0.5174 - 1.138)) laboratory results (Fig. 1-3)). Thirty-four (n=34) out of the 37 laboratories reported Ct values for all 15 replicates and only those with a complete data set were included in the inter-lab calculations. Eleven laboratories either did not report their copy number data or used other reporting units such as nanograms or cell numbers; therefore, only 26 laboratories were included in the overall analysis of copy numbers. The median copy number was 348.4, with a range from 15.6 to 547,000 copies (approximately a 4.5 log difference); the median intra-lab %CV was 19.2% with a range from 4.2% to 82.6%. While our international performance evaluation using serially diluted RNA samples has reinforced the fact that heterogeneity exists among clinical laboratories, it has also demonstrated that performance within a laboratory is overall very consistent. Accordingly, the availability of defined BCR/ABL RNAs may facilitate the validation of all phases of quantitative BCR/ABL analysis and may be extremely useful as a tool for monitoring assay performance. Ongoing analyses of these materials, along with the development of additional control materials, may solidify consensus around their application in routine laboratory testing and possible integration in worldwide efforts to standardize quantitative BCR/ABL testing.