Metrics definition

Each factor is broken down into measurable criteria (sub-factors). A criterion is directly measurable via at least one specific metric. Definitions of 7 of the 26 existing criteria in QUIM are presented below. These definitions all assume a particular context of use or stated conditions for an application feature. Minimal Action. Capability of the application to help users achieve their tasks in a minimum number of steps Minimal Memory Load. Whether a user is required to keep minimal amount of information in mind in order to achieve a specified task [6] Operability. Amount of effort necessary to operate and control an application Privacy. Whether users personal information is appropriately protected Security. Capability of the application to protect information and data so that unauthorized persons or systems cannot read or modify them and authorized persons or systems are not denied access [16] Load... 

For the Berry phase, we shall quote a definition given in [164] ""The phase that can be acquired by a state moving adiabatically (slowly) around a closed path in the parameter space of the system. There is a further, somewhat more general phase, that appears in any cyclic motion, not necessarily slow in the Hilbert space, which is the Aharonov-Anandan phase [10]. Other developments and applications are abundant. An interim summai was published in 1990 [78]. A further, more up-to-date summary, especially on progress in experimental developments, is much needed. (In Section IV we list some publications that report on the experimental determinations of the Berry phase.) Regarding theoretical advances, we note (in a somewhat subjective and selective mode) some clarifications regarding parallel transport, e.g., [165], This paper discusses the projective Hilbert space and its metric (the Fubini-Study metric). The projective Hilbert space arises from the Hilbert space of the electronic manifold by the removal of the overall phase and is therefore a central geometrical concept in any treatment of the component phases, such as this chapter. 

We must now mention, that traditionally it is the custom, especially in chemo-metrics, for outliers to have a different definition, and even a different interpretation. Suppose that we have a fc-dimensional characteristic vector, i.e., k different molecular descriptors are used. If we imagine a fe-dimensional hyperspace, then the dataset objects will find different places. Some of them will tend to group together, while others will be allocated to more remote regions. One can by convention define a margin beyond which there starts the realm of strong outliers. "Moderate outliers stay near this margin. 

The matrix gp, represents the components of a covariant second-order tensor called the metric tensor , because it defines distance measurement with respect to coordinates To illustrate the application of this definition in the... 

Metrologia International Committee of Weights and Measures (CIPM) Pavilion de Breteuil Parc de St. Cloud, Prance Includes articles on scientific metrology worldwide, improvements in measuring techniques and standards, definitions of units, and the activities of various bodies created by the International Metric Convention. 

A U.S. definition foi 3" is accepted wodd wide. For conversion to metric,... 

PROPERTY SYMBOL BRITISH UNITS METRIC UNITS DEFINITIONS ... 

The English system of units is complicated compared to the metric system. In the English system, the units of mass are pounds-mass (Ibm) and the units of weight are pounds-force (Ibf). By definition, a weight (i.e., force) of one Ibf equals the force produced by one Ibm under the acceleration of gravity. Therefore, the constant, g, which has the same numerical value as g (32.17) and units of Ibm-ft/lbf-sec, is used in the definition of weight ... 

SI (Systeme International) The International System of units a collection of definitions of units and symbols and their deployment. It is an extension and rational ization of the metric system. See also Appendix IB. side chain A hydrocarbon substituent on a hydrocarbon chain. 

Prototypical application examples. To provide a more concrete notion of the type of systems where our approaches are expected to be particularly helpful and useful, we conclude this section with a sample of prototypical examples of what the performance metric, y, in the problem statement (2) may represent, together with a definition of the corresponding systems ... 

Both situations with categorical and continuous, real-valued performance metrics will be considered and analyzed. Since Taguchi loss functions provide quality cost models that allow the different objectives to be expressed on a commensurate basis, for continuous performance variables only minor modifications in the problem definition of the approach presented in Section V are needed. On the other hand, if categorical variables are chosen to characterize the system s multiple performance metrics, important modifications and additional components have to be incorporated into the basic learning methodology described in Section IV. 

Since these loss functions express quality costs on a common and commensurate basis, extending the learning methodology of Section V to a situation with P objectives is straightforward. All one has to do is replace the original definition of the y performance metric [Eq. (23)] by the following more general version ... 

Given a space G, let g (x) be the closest model in G to the real function, fix). As it is shown in Appendbc 1, if /e G and the L°° error measure [Eq. (4)] is used, the real function is also the best function in G, g = f, independently of the statistics of the noise and as long as the noise is symmetrically bounded. In contrast, for the measure [Eq. (3)], the real function is not the best model in G if the noise is not zero-mean. This is a very important observation considering the fact that in many applications (e.g., process control), the data are corrupted by non-zero-mean (load) disturbances, in which cases, the error measure will fail to retrieve the real function even with infinite data. On the other hand, as it is also explained in Appendix 1, if f G (which is the most probable case), closeness of the real and best functions, fix) and g (x), respectively, is guaranteed only in the metric that is used in the definition of lig). That is, if lig) is given by Eq. (3), g ix) can be close to fix) only in the L -sense and similarly for the L definition of lig). As is clear,... 

Equations (56) and (57) give six constrains and define the BF-system uniquely. The internal coordinates qk(k = 1,2, , 21) are introduced so that the functions satisfy these equations at any qk- In the present calculations, 6 Cartesian coordinates (xi9,X29,xi8,Xn,X2i,X3i) from the triangle Og — H9 — Oi and 15 Cartesian coordinates of 5 atoms C2,C4,Ce,H3,Hy are taken. These 21 coordinates are denoted as qk- Their explicit numeration is immaterial. Equations (56) and (57) enable us to express the rest of the Cartesian coordinates (x39,X28,X38,r5) in terms of qk. With this definition, x, ( i, ,..., 21) are just linear functions of qk, which is convenient for constructing the metric tensor. Note also that the symmetry of the potential is easily established in terms of these internal coordinates. This naturally reduces the numerical effort to one-half. Constmction of the Hamiltonian for zero total angular momentum J = 0) is now straightforward. First, let us consider the metric. 

In order to solve Laplace s equation we have to find also expressions for the metric coefficients. By definition, the elementary displacements along coordinate lines are... 

Generally, two vectors that are orthogonal in S will be oblique in 5 , unless the vectors are parallel to the coordinate axes. This is illustrated in Fig. 32.4. Furthermore, if X and y are orthogonal vectors in S, then the vectors W x and W" y are orthogonal in 5 ,. This follows from the definition of orthogonality in the metric W (eq. 32.12) ... 

Hence, for any irreversible enzyme inactivator, we can quantify the effectiveness of inactivation using the second-order rate constant kanJKi. This constant thus becomes the key metric that the medicinal chemist can use in exploring the SAR of enzyme inactivation by a series of compounds. In terms of individual rate constants, the definitions of both nact and A) depend on the details of the mechanisms of inactivation, as will be described below. 

The author anticipates that many readers will find the results reported here to be commonplace. If so, then why do we so often report the individual peak capacities of the two dimensions and their product as the 2D peak capacity One answer—the conservative one—is that the latter is indeed the maximum number of peaks that can be separated, in agreement with the definition. A more realistic answer is that it is easy to do and appears more impressive than it really is—especially to those who fund our work. In fact, as a practical metric it is often nonsense. Because orthogonality is so difficult to achieve, especially in 2DLC, the peak capacity is a measure of only instrumental potential, not of separation potential, and consideration of... 

Fig. 7. Size scale associated with soil mineral particles, organic components, pores and aggregations of mineral and organic components (Baldock 2002). The definitions of pore size have used those developed by IUPAC (micropores < 2 nm, mesopores 2-50 nm and macropores > 50 nm). Alternatively, the pore sizes corresponding to the lower ( /m = - 1500 kPa) and upper ( /m = - 100 kPa) limits of water availability to plants may be used to define the boundaries between the different classes of pore size. /m is soil water metric potential.

Clustering techniques are mostly based on the concept of similarity expressed through the definition of a metric (distances calculus rule) in... 

The idea of a vector space is usefully extended to an infinite number of dimensions for continuous functions. Given a function /(e.g.,/ = sinx) and a definition domain (e.g., 0 to In), the coordinates of / = sin x will be the infinite number of values of the function over the definition domain. This definition is consistent with that of Euclidian spaces if a metric is defined. In about the same way as the squared norm of the n-vector x(xux2,. .., x ) is... 

The definition of these metrics appears somewhat arbitrary and is hard to understand in the framework of statistical reasoning. In particular, the meaning of maximum and minimum terms in the definition of the Chinchilli and the rho metrics cannot be easily verified. The fact that an arbitrarily defined index performs better for an arbitrarily selected set of experimental data cannot be accepted as a general proof of validation. 

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