Some Computational Aspects of the Branch and Bound Method for Integer Programs

66 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1982.Different heuristics for the branch and bound method are tested on capital budgeting type integer programming problems. The standard up and down penalties are compared with Tomlin's improved penalties. The use of the 'priority order' derived from the objective coefficients is also examined. A new heuristic--"the nearer integer rule"--is introduced that reduces the time taken to find the optimal solution.The "pseudo-costs" of Benichou et. al. are examined and it is shown that there is no good basis for their use. The "BP Criterion" is compared to the "best-bound" rule for node selection and found to be inferior. A 'correction' for the depth of a node is suggested to improve the best-bound rule.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Box plots for cytokine positive T cell frequencies on stimulation with CSP peptides pre-vaccination, 1 month after the last vaccination and 12 months after the last vaccination, shown by cytokine and by vaccination group.

<p>Box plots show medians and inter-quartile ranges, the whiskers show 5^th to 95^th centiles, and outliers are shown by circles. Vaccination group is indicated by “RTS” for RTS,S/AS01_E and “Ctl” for rabies control. T cell phenotype is indicated by + and − for the cytokines shown far left. Significance is indicated by a horizontal line at p<0.0003 (using a Bonferroni correction for multiple comparisons).</p

Relationships of antibody levels and avidities with age.

<p>Antibody levels and avidity indices for each antigen are plotted against age. Linear regression lines are shown, as are the associated R squared and P values.</p

Characteristics of the study subjects.

*<p>Previous episodes only refer those clinical malaria episodes that occurred before May 2009, the sampling date.</p

A representative example of the identification and quantitation of RTS,S/AS01_E induced CSP-peptide reactive CD4+ T cells producing various cytokines.

<p>A) CD4+/CD8+ T cells were gated off the side scatter (SCC) Vs CD3 gate, after gating on lymphocytes on the SSC vs forward scatter (FSC) density plot. B) Determination of the percentages of IL2+, TNF+ and IFNγ CD4+ T cells following <i>in vitro</i> stimulations with nothing (Media control), CSP and SEB. C) An example of a typical gating tree showing the identification and quantitation of CD4+ T cells producing various combinations of IL2, TNF and IFNγ, following stimulation with nothing (media control), CSP or SEB, is shown. The resultant data was expressed as percentages of cytokine positive CD4+ T cells.</p

Kaplan Meier plot showing fraction of the RTS,S/AS01_E vaccinees experiencing an episode of clinical malaria, divided according to antibody and TNF+ only CD4+ cell anti-CSP responses.

<p>The 4 groups are as follows; 1) anti-CSP antibody titers below 40 EU/ml, TNF+ only CD4+ cells on CSP stimulation below median; 2) anti-CSP antibody titers above 40 EU/ml, TNF+ only CD4+ cells on CSP-peptide stimulation below median; 2) anti-CS antibody titers below 40 EU/ml, TNF+ CD4+ cells on CSP-peptide stimulation above median; 2) anti-CSP antibody titers above 40 EU/ml, TNF+ only CD4+ cells on CSP-peptide stimulation above median. The anti-CSP antibody titers are applied as a time-varying covariate.</p

Multivariable analysis of association between EI, age and cross sectional parasitaemia with antibody levels and avidities.

<p>Data was analysed by multivariable linear regression.</p

Antibody levels but not avidities were elevated in the presence of asymptomatic parasitaemia.

<p>Antibody levels (top panel) and avidities (lower panel) for children with (open symbols) and without (filled symbols) asymptomatic <i>P. falciparum</i> parasitaemia as determined by use of blood-films at sampling. Horizontal bars are medians. Statistical significance of differences was determined by Wilcoxon rank-sum test.</p

Multivariable logistic regression analysis for the effect avidity on clinical malaria.

<p>Multivariable logistic regression analysis for the effect avidity on clinical malaria.</p

Geometric means and 95% confidence intervals for cellular responses to CSP by vaccination group and t-test on log-transformed values for significance of difference.

<p>Pre-vac = prior to vaccination, Vac+1 = 1 month after final vaccination, Vac+12 = 12 months after final vaccination.</p