Redundant properties

Thullberg, M., Bartkova, J., Khan, S., Hansen, K, Ronnstrand, L., Lukas, J., et al. (2000). Distinct versus redundant properties among members of the INK4 family of cyclin-dependent kinase mhihitors,. FEBS Letters, 470, 161-166. 

Readers with experience in chemometrics will have noticed that, like principal components analysis (PCA), MDS is a dimensionality reduction method. For each molecule, a large number of attributes (similarity to each other molecule) is reduced to a much smaller number of coordinates in an abstract property space, which reproduce the original data within an established error. The pertinent difference is that PCA uses the matrix of correlations between a set of (redundant) properties, which are usually obtained from a table of those properties for an initial set of molecules. In contrast, MDS uses a matrix of similarities between each pair of molecules (or substituents). 

Given a table of redundant properties, one could calculate dissimilarities as Euclidean distances and use MDS instead of PCA. Whereas the results would be similar, this is usually wasteful, because the number of molecules is typically much greater than the number of properties. However, if the similarities are best calculated from a nonlinear function of the properties, such as Tanimoto coefficients computed from two bit strings, the results would not be similar and nonlinear MDS should be used. One then gets back a set of latent properties (dimensions) for which Euclidean distance approximates the desired similarities. Thus, a simple rule of thumb is For redundant properties as input use PCA, for metric similarities as input use classical MDS, for nonmetric similarities use numerically refined MDS. 

The most effective specification is that which accomplishes the desired result with the fewest requirements. Properties and performance should be emphasized rather than how the objectives ate to be achieved. Excessive demonstration of emdition on the part of the writer or failure to recognize the usually considerable processing expertise held by the vendor results in a lengthy and overly detailed document that generally is counterproductive. Redundancy may lead to technical inconsistency. A requirement that cannot be assessed by a prescribed test method or quantitative inspection technique never should be included in the specifications. Wherever possible, tests should be easy to perform and highly correctable with service performance. Tests that indicate service life are especially useful. Standard test references, eg, ASTM methods, ate the most desirable, and those that ate needed should be selected carefully and the numbers of such references should be minimized. To eliminate unnecessary review activity by the would-be complier, the description of a standard test should not be paraphrased or condensed unless the original test is referenced. 

From the definition of a partial molar quantity and some thermodynamic substitutions involving exact differentials, it is possible to derive the simple, yet powerful, Duhem data testing relation (2,3,18). Stated in words, the Duhem equation is a mole-fraction-weighted summation of the partial derivatives of a set of partial molar quantities, with respect to the composition of one of the components (2,3). For example, in an / -component system, there are n partial molar quantities, Af, representing any extensive molar property. At a specified temperature and pressure, only n — 1) of these properties are independent. Many experiments, however, measure quantities for every chemical in a multicomponent system. It is this redundance in reported data that makes thermodynamic consistency tests possible. 

Safety-critical projects can further exploit the precision available with Catalysis, using advanced facilities (see Section 3.5.2, Redundant Specifications Can Be Useful) to formally check important properties that the design should exhibit. 

In analytical redundancy schemes, the resulting difference generated from the consistency checking of different variables is called a residual signal. The residual should be by convention zero-valued when the system is normal and should diverge from zero when a fault occurs. This zero and non-zero property of the residual is used to determine whether or not a fault has occurred. Analytical redundancy makes use of a quantitative model of the monitored process and is therefore often referred to as the model-based approach to fault diagnosis. 

Removing redundancies reduced the number of compounds in this set to about 1.8 million. An additional set of criteria based upon properties associated with druglikeness were used to further reduce the set, which we called the Commercial Research Chemicals Directory (CRCD), to just above one miUion compounds. The... 

We have noted the importance of the similar property principle, which would imply that a set of compounds exhibiting some degree of structural redundancy,... 

Practically in every general chemistry textbook, one can find a table presenting the Standard (Reduction) Potentials in aqueous solution at 25 °C, sometimes in two parts, indicating the reaction condition acidic solution and basic solution. In most cases, there is another table titled Standard Chemical Thermodynamic Properties (or Selected Thermodynamic Values). The former table is referred to in a chapter devoted to Electrochemistry (or Oxidation - Reduction Reactions), while a reference to the latter one can be found in a chapter dealing with Chemical Thermodynamics (or Chemical Equilibria). It is seldom indicated that the two types of tables contain redundant information since the standard potential values of a cell reaction ( n) can be calculated from the standard molar free (Gibbs) energy change (AG" for the same reaction with a simple relationship... 

The accurate quantum mechanical first-principles description of all interactions within a transition-metal cluster represented as a collection of electrons and atomic nuclei is a prerequisite for understanding and predicting such properties. The standard semi-classical theory of the quantum mechanics of electrons and atomic nuclei interacting via electromagnetic waves, i.e., described by Maxwell electrodynamics, turns out to be the theory sufficient to describe all such interactions (21). In semi-classical theory, the motion of the elementary particles of chemistry, i.e., of electrons and nuclei, is described quantum mechanically, while their electromagnetic interactions are described by classical electric and magnetic fields, E and B, often represented in terms of the non-redundant four components of the 4-potential, namely the scalar potential and the vector potential A. 

Now, from our manipulations above we can easily see that F can be constructed from a skeleton matrix obtained using only a P2 list, since the Fock operator is totally symmetric. However, this far from ideal, since we would like to avoid the redundancies that arise unless we use the Pi list of two-electron integrals, or, here, supermatrix elements. We define first a matrix Y(IJKL) with the property that the IJ block is given by... 

Indicator Variables Indicator variables are binary variables having a value of either 0 or 1, indicating if a particular structural or substructural characteristic is present or is missing in the molecular graph. Indicator variables are used by some authors in QSPR equations presenting correlations between a property and descriptors, including indicator variables. However, indicator variables are redundant. Instead of using an indicator, a QSPR model can be split into two separate models, one for all those compounds for which the indicator variable is zero, and one for all those compounds for which the indicator variable is 1. 

Vendors consider this information proprietary and are hesitant to reveal catalyst preparation methods and properties that may jeopardize their marketing position. No attempt has been made in Table XXIII to identify advantages or redundancies in different manufacturers catalyst products. 

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