Invariant accuracy

In our papers we have used the Invariant Accuracy of Prediction lAP) criterion, which exactly coincides with the AUC, and it is calculated as ... 

Computationally, it is more convenient to calculate the estimate of prediction accuracy on ES as an Invariant Accuracy IA), which equals 2AUC P) — 1 and can be calculated as a result of comparison of estimates P(C+) for positive and P(C ) for negative examples through all pairs (each positive example and each negative example) in a form ... 

Recent mathematical work suggests that—especially for nonlinear phenomena—certain geometric properties can be as important as accuracy and (linear) stability. It has long been known that the flows of Hamiltonian systems posess invariants and symmetries which describe the behavior of groups of nearby trajectories. Consider, for example, a two-dimensional Hamiltonian system such as the planar pendulum H = — cos(g)) or the... 

Now, in principle, the angle of contact between a liquid and a solid surface can have a value anywhere between 0° and 180°, the actual value depending on the particular system. In practice 6 is very difficult to determine with accuracy even for a macroscopic system such as a liquid droplet resting on a plate, and for a liquid present in a pore having dimensions in the mesopore range is virtually impossible of direct measurement. In applications of the Kelvin equation, therefore, it is almost invariably assumed, mainly on grounds of simplicity, that 0 = 0 (cos 6 = 1). In view of the arbitrary nature of this assumption it is not surprising that the subject has attracted attention from theoreticians. 

Electronic instrumentation is available for the measurement of D.C. and A.C. voltage, current and power as well as impedance. Such instruments usually have higher sensitivities, operating frequencies and input impedance than is normally found in the electromechanical instrumentation described above. However, they may need to incorporate amplifiers and they invariably need power to operate the final display. Hence, an independent power source is needed. Both mains and battery units are available. The accuracy of measurement is very dependent on the amplifier, and bandwidth and adequate gain are important qualities. 

Cutting fluids provide benefits such as extended tool life, dimensional accuracy and good surface finish, all of which contribute to high rates of production. Almost invariably, the coolant that adheres to workpieces is relied on to protect ferrous components against corrosion while they are waiting further machining or assembly operations. 

In connexion with the scientific data the two terminologies accuracy and precision are invariably practised synonymously, but there exists a clear distinction between them as discussed below ... 

Almost all contemporary ab initio molecular electronic structure calculations employ basis sets of Gaussian-type functions in a pragmatic approach in which no error bounds are determined but the accuracy of a calculation is assessed by comparison with quantities derived from experiment[l] [2]. In this quasi-empirical[3] approach each basis set is calibrated [4] for the treatment of a particular range of atoms, for a particular range of properties, and for a particular range of methods. Molecular basis sets are almost invariably constructed from atomic basis sets. In 1960, Nesbet[5] pointed out that molecular basis sets containing only basis sets necessary to reach to atomic Hartree-Fock limit, the isotropic basis set, cannot possibly account for polarization in molecular interactions. Two approaches to the problem of constructing molecular basis sets can be identified ... 

But what precision is required The answer to this question is two-fold. One scale of precision is set by the previous experimental tests of CPT invariance the new tests must simply have better accuracy in order to be interesting. The so far best (albeit indirect) experimental test has been obtained from the comparison of the masses of neutral kaons K° and K°, which are known to be equal with the accuracy of 1 part in 1018 (i.e. (mKo — mxo)/mKo < 10 18) [22]. 

Previous investigations (Brady, 1949 Grayson, 1952 Bonner, 1952) in the Purdue laboratories were concerned with the influence of alkyl groups on the rate of ionization of phenyldimethylcarbinyl chloride. These studies indicated that first-order rate constants could be determined with high accuracy for the solvolysis reaction. Moreover, the entropies of activation were invariant in this series of halides. These considerations led to further study of other substituted phenyldimethylcarbinyl chlorides in an attempt to gain a further understanding of the influence of substituent groups on relative reactivity and as a possible model reaction for the assessment of parameters for electron-deficient reactions. 

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