The Bootstrap

I Eelsenstein. Confidence limits on phylogenies An approach using the bootstrap. Evolution 39 783-791, 1985. 

Techniques to use for evaluations have been discussed by Cox and Tikvart (42), Hanna (43) and Weil et al. (44). Hanna (45) shows how resampling of evaluation data will allow use of the bootstrap and jackknife techniques so that error bounds can be placed about estimates. 

The start-up and bias supply eireuit provides the operating voltage for the eontrol IC and power switeh drive seetions. This eireuit is sometimes ealled the bootstrap start-up circuit. Sinee all of the power drawn and delivered by this eireuit is eonsidered a loss, it is important to keep its overall funetion as effi-eient as possible. 

Designing the bootstrap start-up eireuit (refer to Seetion 3.10)... 

The apparent terminal model reactivity ratios are then r => aK and c =rR, K It follows that rABVBf = rABrBA - const. The bootstrap effect does not require the terminal model and other models (penultimate, complex participation) in combination with the bootstrap effect have been explored.103,1 4215 Variants on the theory have also appeared where the local monomer concentration is a function of the monomer feed composition.11[Pg.431]

The effects of solvent on reactivity ratios and polymerization kinetics have been analyzed for many copolymerizations in terms of this theory.98 These include copolymerizations of S with MAH,"7 118 S with MAA,112 S with MMA,116 117 "9 121 S with HEMA,122 S with BA,123,124 S with AN,103415 125 S with MAN,112 S with AM,11" BA with MM A126,127 and tBA with HEMA.128 It must, however, be pointed out that while the experimental data for many systems are consistent with a bootstrap effect, it is usually not always necessary to invoke the bootstrap effect for data interpretation. Many authors have questioned the bootstrap effect and much effort has been put into finding evidence both for or against the theory.69 70 98 129 "0 If a bootstrap effect applies, then reactivity ratios cannot be determined by analysis of composition or sequence data in the normal manner discussed in Section 7.3.3. 

Studies on the reactions of small model radicals with monomers provide indirect support but do not prove the bootstrap effect.111 Krstina et ahL i showed that the reactivities of MMA and MAN model radicals towards MMA, S and VAc were independent of solvent. However, small but significant solvent effects on reactivity ratios are reported for MMA/VAc111 and MMA S 7 copolymerizations. For the model systems, where there is no polymer coil to solvate, there should be no bootstrap effect and reactivities are determined by the global monomer ratio [Ma0]/[Mb0].1j1... 

B. Efron and R. Tibshirani, An Introduction to the Bootstrap. Wiley, New York, 1993,... 

Porter PS, Rao ST, Ku J-Y, Poirot RL, Dakins M (1997) Small sample properties of nonparametric bootstrap t confidence intervals. J Air Waste Management Assoc 47 1197-1203 Powell R, Hergt J, Woodhead J (2002) Improving isochron calcttlatiorrs with robust statistics and the bootstrap. Chem Geol 185 191- 204... 

Efron B (1982) The jackknife, the bootstrap and other resampling techniques. Society for Industrial and Applied Mathematics, Philadelphia, PA... 

Efron B, Tibshirani R (1993) An introduction to the bootstrap. Chapman and Hall, London... 

In DC-DC converters, we can somewhat slow the turn-on of Fets if we insert a small resistor (10 to 20Q. typically) in series with the decoupling capacitor of their respective driver stages. For example, a small resistor can be placed in series with the bootstrap capacitor of the third-generation switcher family I used to cover. That helped with almost 10 to 20% of customers, but somehow this trick didn t find its way into the applications information section of their datasheet. If the Fets are external, we can try a small resistor in series with the Gate, but this affects both the turn-on and turnoff (with such low threshold voltages, a diode in parallel to the resistor will not do anything). 

So, if you can access the gates of the Fets, try putting in small resistors in series with them. If it is a switcher IC (with no access to the gates), try inserting a small resistor in series with the decoupling capacitor of the driver supply (usually a 0.1 pF capacitor attached to the Vdd pin and/or the bootstrap pin). Better still, pick an IC with less aggressive drive to start with. Because otherwise it will commit suicide sooner or later. 

It was in article [52] where the main reason responsible for the above-mentioned peculiarities was explicitly formulated and substantiated. Its authors related these peculiarities with partitioning of monomer molecules between the bulk of a reaction mixture and the domain of a growing polymer radical. This phenomenon induced by preferential sorption of one of the monomers in such a domain is known as the bootstrap effect. This term was introduced by Harwood [53], because when growing a polymer radical can control under certain conditions its own microenvironment. This original concept enabled him to interpret many interesting features peculiar to this phenomenon. Particularly, he managed to qualitatively explain the similarity of the sequence distribution in copolymerization products of the same composition prepared in different solvents under noticeable discrepancies in composition of monomer mixtures. 

Efron, B., Tibshirani, R. J. An Introduction to the Bootstrap. Chapman Hall, London, United Kingdom, 1993. 

The qualification concept was used by Wargo and Drennen to verify the homogeneity of solid mixtures. Qualitative analytical algorithms based on the Bootstrap Error-adjusted Single-sample Technique (BEST) proved sensitive to variations in sample homogeneity. Plugge and van der Vlies converted NIR spectra into polar coordinates and used them to calculate the Mahalanobis distance in order to identify nonhomogene-ous samples. 

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