Least bias

The most spectacular applications of ECLs are the possibiUty of direct overwrite (DOW) with laser modulation (79,80) and of magnetically iaduced superresolution (81,82). The stacks comprise at least a storage layer s and a bias layer b. For both appHcations, the storage layer s has the lower and the higher at room temperature when compared to the bias layer b. At room temperature, b is homogeneously magnetized (initialized) by an external permanent magnet is about 400 kA/m (5 kOe)). 

The schematic model is depicted in Fig. 8. As the bias voltage increases, the number of the molecular orbitals available for conduction also increases (Fig. 8) and it results in the step-wise increase in the current. It was also found that the conductance peak plotted vs. the bias voltage decreases and broadens with increasing temperature to ca. 1 K. This fact supports the idea that transport of carriers from one electrode to another can take place through one molecular orbital delocalising over whole length of the CNT, or at least the distance between two electrodes (140 nm). In other words, individual CNTs work as coherent quantum wires. 

An improvement of this method—the so-called biased sampling [55] (or inversely restrieted sampling)—suggests to look ahead at least one step in order to overcome the attrition. Consider a SAW of i steps on a -coordination number lattice. To add the / + 1st step one first checks which of the = q — neighboring sites are empty. If k qQ > k>0) sites are empty one takes one of these with equal probability 1 /A if A = 0 the walk is terminated and one starts from the beginning. This reduces the attrition dramatically. Now each A-step walk has a probability PAr( i ) = Ylf=i so that dense configurations are clearly more probable. To compensate for this bias, each chain does not count as 1 in the sample but with a weight... 

The answer is patently no —not because of any general sceptical-philosophical scruples about induction, but because of the particular fact that the impression of consistent predictive success for Mendeleev s scheme is a complete misrepresentation of history a classic example of an effect (Mendeleev s predictive success ) created by selection-bias. Mendeleev made any number of predictions on the basis of his scheme (or rather schemes—there are at least 65 versions of Mendeleev s table, published and unpublished). Many of these predictions (depending on how exactly they are individuated)—perhaps a majority—were unsuccessful. 

M-Acyliminium cyclizations of optically active mono- and di-oxygenated hydroxylactam derivatives have been used in the synthesis of a number of natural products. In case of a five-membered lactam the oxygen function adjacent to the iminium carbon directs attack of the internal nucleophile from the least hindered side, opposite to the substituent. In the examples given the size of the newly formed ring is determined by the electronic bias of the alkene substituent. 

A pH/Ion-meter with a resolution of only 0.1 mV is not sufficient because the ensuing quantization noise introduces an apparent deviation of at least 0.2%, and, more important in this particular case, these systematic effects lead to a bias that is strongly dependent on small shifts in 0. (See Fig. 4.24, left side.)... 

A very human kind of information storage breakdown referred to in the earlier anecdote is publication bias. This refers to the tendency of researchers to publish or otherwise make visible experimental results or conclusions that are considered a success or otherwise further the designs of the researcher but to discard results that are considered a failure (or at least to downplay... 

In practice, the choice of parameters to be refined in the structural models requires a delicate balance between the risk of overfitting and the imposition of unnecessary bias from a rigidly constrained model. When the amount of experimental data is limited, and the model too flexible, high correlations between parameters arise during the least-squares fit, as is often the case with monopole populations and atomic displacement parameters [6], or with exponents for the various radial deformation functions [7]. 

Note that the variance does not depend on the true value x, and the mean estimator x has the least variance. The finite sampling bias is the difference between the estimate x and the true value x, and represents the finite sampling systematic part of the generalized error... 

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