Abstract domains

Working on experimental data at Edgewood drew me relentlessly into a deepening vortex of mathematics and other abstract domains, such as electronic circuits. I would often visit the Biostatistics Office and talk to John Atkinson about his LGP-30 computer, and how I could learn to use it. It was a monstrous device, one end taking in long ribbons of paper punched with holes that told it what to do and the other end typing answers without fingers on another role of paper, like the tapes that activate a player piano. 

There are many chemometric methods to build initial estimates some are particularly suitable when the data consists of the evolutionary profiles of a process, such as evolving factor analysis (see Figure 11.4b in Section 11.3) [27, 28, 51], whereas some others mathematically select the purest rows or the purest columns of the data matrix as initial profiles. Of the latter approach, key-set factor analysis (KSFA) [52] works in the FA abstract domain, and other procedures, such as the simple-to-use interactive self-modeling analysis (SIMPLISMA) [53] and the orthogonal projection approach (OPA) [54], work with the real variables in the data set to select rows of purest variables or columns of purest spectra, that are most dissimilar to each other. In these latter two methods, the profiles are selected sequentially so that any new profile included in the estimate is the most uncorrelated to all of the previously selected ones. 

Astr6e uses various abstract domains to compute program invariants providing detailed information about the values of variables and the relations between them in every possible execution context [6]. All computed invariants can be inspected by the users depending on the option setting they can be observed either at each statement or in the beginning of each function, and they can be context-insensitive or context-sensitive. In the latter case the computed abstract values are shown separately for each execution context. 

Min6, A. Weakly Relational Numerical Abstract Domains. PhD thesis, Ecole Polytechnique, Palaiseau, France (December 2004),... 

In Sec. B4.3 we introduced the concept of functionality and the concept of the functional domain. In particular, we discussed the existence of a transition from the functional domain into the physical domain that is, a transition from an abstract domain in which there are only requirements on services (essentially activities) to a domain in which these requirements are reflected onto an architecture, i.e. a set of interacting physical elements. 

Report accessibility Public domain source documents available - also abstracts... 

We can go through the same argument while remaining completely in the domain of abstract Hilbert space. Thus, starting with Eq. (8-6) and using Eq. (8-7) we have... 

The purpose of defining these classes of constraints and variables is that this will enable us to conveniently express general notions of equivalence and dominance, without explicit reference to the flowshop domain, but at a more abstract level. 

The CrossFire Beilstein database is the world s largest compilation of chemical facts. This database indexes three primary data domains substances, reactions and literature. The substance domain stores structural information with aU associated facts and literature references, including chemical, physical and bioactivity data. The reaction domain details the preparation of substances, enabling scientists to investigate specific reaction pathways with reaction search queries. The literature domain includes citations, titles and abstracts, which are hyperhnked to the substance and reaction domain entries. It contains over 320 million experimental data, over 10 million reactions and data indexed from over 175 journals. 

The aim of factor analysis is to calculate a rotation matrix R which rotates the abstract factors (V) (principal components) into interpretable factors. The various algorithms for factor analysis differ in the criterion to calculate the rotation matrix R. Two classes of rotation methods can be distinguished (i) rotation procedures based on general criteria which are not specific for the domain of the data and (ii) rotation procedures which use specific properties of the factors (e.g. non-negativity). 

In analytical chemistry, calibration represents a set of operations that connects quantities in the sample domain with quantities in the signal domain (see Sect. 2.3, Fig. 2.12). In Table 6.1 the real analytical quantities and properties behind the abstract input and output quantities are listed. 

Abstract. We present a method to construct pairs of isospectral quantum graphs which are not isometric. These graphs are the analogues of the family of isospectral domains in R2 which were first introduced by Gordon, Webb and Wolpert (C. Gordon et.al., 1992), recently enlarged by P. Buser el. al. (P. Buser et.al., 1994), and discussed further by Okada et. al. (Y. Okada et.al., 2001). 

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