Formal concept analysis

The analysis of empirical datasets may lead to empirical partial orders, which do not necessarily fulfill the axioms of lattices. The school around Wille (Wille 1987 and Ganter Wille 1996) has shown how it is possible nevertheless to construct a lattice. The resulting lattices and the analysis based on them is called "Formal concept analysis". As lattices fulfill more axioms than posets generally, one gets a richer theory of them. Especially it is possible to generate a set of implications. See chapter by Kerber, p. 355 for introductory examples. 

For example, the first of these implications might be considered as the hypothesis zinc comes with cadmium . The second implication relates the pollution of the herb layer by cadmium and sulfur with traffic. Thus, formal concept analysis helps in formulating valuable working hypotheses. 

Ganter B, Wille R (1999) Formal Concept Analysis - Mathematical Foundations. Springer Verlag, Berlin... 

Bartel HG and Briiggemann R (1998) Application of formal concept analysis to structure-activity relationships. Fresenius J Anal Chem 361 23-28... 

Berichte des IGB, Heft 6, Sonderheft I, 1998, IGB, Berlin, pp 111-117 Bartel HG (2000) Formal Concept Analysis and Chemometrics Chemical Composition of Ancient Egyptian Bronze artifacts. Match Commun Math Comput Chem 42 25-38... 

Lounkine E, Auer J, Bajorath J (2008) Formal concept analysis for the identification of molecular fiagment combinations specific for active and highly potent compounds. J Med Chem 51 5342-5348... 

He, N., Riimmer, P., Kroening, D. Test-case generation for embedded Simulink via formal concept analysis. In DAG, pp. 224-229 (2011)... 

Although the concept of patient variability had been articulated by the middle of the twentieth century, the concept that a difference between two groups could be due to chance was slow to be accepted. The first clinical trial to use a formal statistical analysis reportedly occurred in 1962. The study involved a comparison of antibody production after yellow fever vaccination by two different methods. Several years later (1966) a critique of statistical methods used in medical journal manuscripts suggested a lack of proper study design and data analysis. In this critique, the authors canonized the criterion of P < 0.05 for a difference between two groups to be considered not due to chance. 

The first way of applying the concepts of inherent safety is work through the guidewords during each formal hazards analysis (HAZIDs and HAZOPs). Maher et al. (2011) discuss the use of HAZIDs to promote inherently safer designs. 

The modal constitution of things and humans requires a model of modalities , an analysis and a synthesis of the modalities of human actions in a material and social context shaped by a web of connections and arrangements. These modalities refer to the classical modal terms (necessity/obligation, possibility/permissibility, impossibility/impermissibility, contingency/Uberty). But they are not just some formal concepts, they are also meant to reflect some informal experiences of human beings who produce some situated judgments as lived and expressed in modal terms. Moreover, this view is not a static picture, but refers to a dynamic pnxress in which the scope of possibilities of the users can vary depending upon the variation of the elements and their relations that make a world. 

This course of the curves of the thermal transition between the isotropic and anisotropic phases not only derives from the specific features of polymers in comparison to low-molecular-weight substances, but also from the fact that the firee volume in the system increases with an increase in the temperature, and this results in an increase in the probability of independent arrangement of the macromolecules in solution. However, this also simultaneously means broadening of the concentration regions of the isotropic-anisotropic phase transition. The inflection of the phase equilibrium curves discussed in the studies cited above thus not only follows from the formal topological analysis but also from the thermodynamic concepts of the structure of liquids. 

In this paper, we propose and investigate formal concepts that aim to overcome this bias. They support the construction of FMEA tables solely based on the system model and the failure modes, i.e., without requiring the set of effects as input. More concretely, given a system specification in the Architecture Analysis and Design Language (AADL), we show how to derive relations that characterize the effects of failures based on the state transition system of that specification. We also demonstrate the benefits and limitations of these concepts on a satellite case study. 

When applying this concept to the Avrami formulation the phantom nuclei have to be taken into account. They will now be located in both the untransformable as well as the transformed regions. The analysis proceeds as previously with either Eq. (9.26) or (9.27). Neither the fraction transformed nor untransformable appear explicity in either of these equations. Hence, in order to introduce the influence of the untransformable fraction on the extent of the transformation a decrease in N(r) with the level of crystallinity, or time, needs to be postulated. Several efforts have been made to resolve the problem in this manner.(63-66) However, they all involve postulating an arbitrary retardation in either the nucleation rate, the hneal growth rate, or in both. There is no physical or molecular basis for the functions that have been proposed. The normalization procedure that led to Eq. (9.42) was an effort to account for the fractions of untransformable material in the kinetics. The formalism of nucleation and growth has also been applied to the development of the stable crystalline state from a metastable one, rather than from the pure melt.(66a) Formally, the analysis is qualitatively similar to the two-stage series process that was discussed previously.(54,55)... 

Section II introduces the formal framework for the definition anc description of process trends at all levels of detail qualitative, order-of magnitude, and analytic. A detour through the basic concepts of scale-spact filtering is necessary in order to see the connection between the concept o process trends and the classical material on signal analysis. Within th( framework of scale-space filtering we can then elucidate the notions o episode, scale, local filtering, structure of scale, distinguishec features, and others. 

The spin-Hamiltonian formalism is a crutch in the sense that it is a parameterized theory, but it provides a common theoretical frame for the various experimental techniques with a minimum number of adjustable parameters that describe the essential physics of the system under investigation. Even more important is the fact that the same parameters can be derived relatively easily from quantum chemical calculations. Therefore, theoreticians appreciate the concept as a convenient place to rest in the analysis of experimental data by theoretical means [123, 124]. 

The actual calculation consists of minimizing the intramolecular potential energy, or steric energy, as a function of the nuclear coordinates. The potential-energy expressions derive from the force-field concept that features in vibrational spectroscopic analysis according to the G-F-matrix formalism [111]. The G-matrix contains as elements atomic masses suitably reduced to match the internal displacement coordinates (matrix D) in defining the vibrational kinetic energy T of a molecule ... 

The first section explains the concepts of EIA and RA and the existing approaches to their integration. This is followed by an analysis of the current situation with ecological input into EIA and discussion on how the formal EcoRA framework provides for site-specific ecosystem risk assessment. The subsequent section reviews the CLL approach and its applicability for assessing ecological effects in EIA. Finally, a model for assessment of ecosystem risks within EIA using the CLL approach is proposed. 

Classification is both a basic concept and a collection of techniques which are necessary prerequisites for further analysis of data when the members of a set of data are (or can be) each described by several variables. At least some degree of classification (which is broadly defined as the dividing of the members of a group into smaller groups in accordance with a set of decision rules) is necessary prior to any data collection. Whether formally or informally, an investigator has to decide... 

An essential concept in multivariate data analysis is the mathematical combination of several variables into a new variable that has a certain desired property (Figure 2.14). In chemometrics such a new variable is often called a latent variable, other names are component or factor. A latent variable can be defined as a formal combination (a mathematical function or a more general algorithm) of the variables a latent variable summarizes the variables in an appropriate way to obtain acertain property. The value of a latent variable is called score. Most often linear latent variables are used given by... 

This localization scheme permits tire assignment of hybridization both to the atomic lone pairs and to each atom s contributions to its bond orbitals. Hybridization is a widely employed and generally useful chemical concept even though it has no formal basis in the absence of high-syrnmetry constraints. Witli NBO analysis, tire percent s and p character (and d, f, etc.) is immediately evident from tire coefficients of tire AO basis functions from which the NAO or NBO is formed. In addition, population analysis can be carried out using the NBOs to derive partial atomic charges (NPA, see Section 9.1.3.2). 

The overall concept of all of the following tools is that of risk analysis or risk assessment. Risk analysis helps to decide whether an aspect is GMP-critical or not. The risk analysis can be performed in a formal or more informal way. Following are two popular and import types of risk analysis. Another method, the fault tree analysis (FTA), has recently been used in the area of computer validation. This method is not described here, as it is a complex form of risk analysis. 

To circumvent the above problems with mass action schemes, it is necessary to use a more general thermodynamic formalism based on parameters known as interaction coefficients, also called Donnan coefficients in some contexts (Record et al, 1998). This approach is completely general it requires no assumptions about the types of interactions the ions may make with the RNA or the kinds of environments the ions may occupy. Although interaction parameters are a fundamental concept in thermodynamics and have been widely applied to biophysical problems, the literature on this topic can be difficult to access for anyone not already familiar with the formalism, and the application of interaction coefficients to the mixed monovalent-divalent cation solutions commonly used for RNA studies has received only limited attention (Grilley et al, 2006 Misra and Draper, 1999). For these reasons, the following theory section sets out the main concepts of the preferential interaction formalism in some detail, and outlines derivations of formulas relevant to monovalent ion-RNA interactions. Section 3 presents example analyses of experimental data, and extends the preferential interaction formalism to solutions of mixed salts (i.e., KC1 and MgCl2). The section includes discussions of potential sources of error and practical considerations in data analysis for experiments with both mono- and divalent ions. 

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