A fit between theory and method is essential in theory – guided empirical research. Achieving such a fit in process tracing is less straightforward than it may seem at first glance. There are two different types of processes that one can theorise and, consequently, two varieties of process tracing. The two varieties are introduced by empirical examples and distinguished with respect to four characteristics. Failure to determine the form of process tracing at hand may lead to invalid causal inferences.

Robinson’s unification algorithm can be identified as the underlying machinery of both C. Meredith’s rule D (condensed detachment) in propositional logic and of the construction of principal types in lambda calculus and combinatory logic. In combinatory logic, it also plays a crucial role in the construction of Meyer, Bunder & Powers’ Fool’s model. This paper now considers pattern matching, the unidirectional variant of unification, as a basis for logical inference, typing, and a very simple and natural model for untyped combinatory logic. An analysis of the new typing scheme will enable us to characterize a large class of terms of combinatory logic which do not change their principal type when being weakly reduced. We also consider the question whether the major or the minor premisse should be used as the fixed pattern.

Clay mineral quantification by XRD is difficult when mixed-layer clay minerals and discrete clay types are both present. New procedures for peak decomposition and pattern simulation offer increased opportunities to obtain mineral abundance estimates. This proposed methodological sequence, for quantitative representation (QR) of complex clay samples, involves: (1) determination of layer type, mixed-layer proportion and order (R); (2) simulation of XRD patterns using MULCALC, an adaptation of NEWMOD; and (3) interpretation of the clay assemblage by fitting the whole pattern with CLAY++, a statistical program. The product is a QR of individual phases or a summation of layer types. The absence of quantitative reference standards means results cannot be checked for accuracy, but the statistical fit is highly reproducible and less prone to operator error. The QRs may be obtained with simulated or actual reference mineral patterns in the database. Results for freshwater marsh samples illustrate the approach.

A Relative Positions-Constrained pattern Matching (RPCM) method for underwater gravity-aided inertial navigation is presented in this paper. In this method the gravity patterns are constructed based on the relative positions of points in a trajectory, which are calculated by Inertial Navigation System (INS) indications. In these patterns the accumulated errors of INS indicated positions are cancelled and removed. Thus the new constructed gravity patterns are more accurate and reliable while the process of matching can be constrained, and the probability of mismatching also can be reduced. Two gravity anomaly maps in the South China Sea were chosen to construct a simulation test. Simulation results show that with this RPCM method, the shape of the trajectory in gravity-aided navigation is not as restricted as that in traditional Terrain Contour Matching (TERCOM) algorithms. Moreover, the performance included matching success rates and position accuracies are highly improved in the RPCM method, especially for the trajectories that are not in straight lines. Thus the proposed method is effective and suitable for practical navigation.

Multiwords are words in which a single symbol can be replaced by a nonempty set of symbols. They extend the notion of partial words. A word w is certain in a multiword M if it occurs in every word that can be obtained by selecting one single symbol among the symbols provided in each position of M. Motivated by a problem on incomplete databases, we investigate a variant of the pattern matching problem which is to decide whether a word w is certain in a multiword M. We study the language CERTAIN(w) of multiwords in which w is certain. We show that this regular language is aperiodic for three large families of words. We also show its aperiodicity in the case of partial words over an alphabet with at least three symbols.

We generalize a theorem due to Keilson on the approximate exponentiality of waiting times for rare events in regenerative processes. We use the result to investigate the limit distribution for a family of first entrance times in a sequence of Ehrenfest urn models. As a second application, we consider approximate pattern matching, a problem arising in molecular biology and other areas.

Abstraction and generalization of layout design cases generate new knowledge that is more widely applicable to use than specific design cases. The abstraction and generalization of design cases into hierarchical levels of abstractions provide the designer with the flexibility to apply any level of abstract and generalized knowledge for a new layout design problem. Existing case-based layout learning (CBLL) systems abstract and generalize cases into single levels of abstractions, but not into a hierarchy. In this paper, we propose a new approach, termed customized viewpoint—spatial (CV–S), which supports the generalization and abstraction of spatial layouts into hierarchies along with a supporting system, SPIDA (SPatial Intelligent Design Assistant).

Given a finite collection of strings of letters from a fixed alphabet, it is of interest, in the contexts of data compression and DNA sequencing, to find the length of the shortest string which contains each of the given strings as a consecutive substring. In order to analyze the average behavior of the optimal superstring length, substrings of specified lengths are considered with the letters selected independently at random. An asymptotic expression is obtained for the savings from compression, i.e. the difference between the uncompressed (concatenated) length and the optimal superstring length.