Theory Reformulation Research Articles

Beam theory reformulation to implement various boundary conditions for generalized differential quadrature method

Generalized differential quadrature (GDQ) method is often used for static and dynamic analysis of structures due to its simplicity and low computational cost. The difficulty arises in the implementation of boundary conditions for higher-order differential equations. A few approaches exist to overcome this issue, but all are more complicated than the original GDQ, increasing the computational cost or having other limitations. In this paper, a novel approach is proposed where the order of the governing differential equations of Euler-Bernoulli and Reddy-Bickford beams is reduced from four to two by introducing a new dependent function. The generality and accuracy of the new approach are demonstrated through its application to the buckling and vibration analysis of different kind of composites, specifically beams made of functionally graded material (FGM), and porous material, considering various combinations of boundary conditions. High accuracy is achieved in comparison to literature.

A new approach for three-phase loads compensation based on the instantaneous reactive power theory

The original instantaneous reactive power theory or p–q theory has been systematically used in the control of active power filters (APFs). When the APF is connected in parallel to a non-linear and unbalanced load, the p–q theory application has allowed a compensation strategy named constant power to be obtained. This means that, after the APF connection, the instantaneous power supplied by the source is constant and it has the same value as the average power consumed by the load. Nevertheless, the use of other compensation strategies is possible: unity power factor or sinusoidal and balanced supply currents, among others. This paper shows that any compensation strategy may be developed into the p–q theory frame. Besides, the paper presents a p–q theory reformulation without using mapping matrices, which makes easier the obtention of the compensation currents. Finally, an exhaustive analysis of practical cases has been carried out at simulation and experimental level through a laboratory prototype which has allowed the proposed approach to be verified.

Mapping matrices against vectorial frame in the instantaneous reactive power compensation

The original instantaneous reactive power or p-q theory has been used in a systematic way in the control of active power filters (APFs). When the APF is switched in parallel to a nonlinear and unbalanced load, the application of p-q theory allows a constant power compensation strategy. This means that after the APF connection, the supply instantaneous power is constant and presents the same value as the load average power. The use of other compensation strategies such as unity power factor, sinusoidal or balanced supply currents, among others, is also possible, as the development of another compensation strategy is possible within the p-q theory frame. A p-q theory reformulation without using mapping matrices is presented, which makes obtaining compensation currents easier. Finally, an exhaustive analysis of practical cases has been carried out at simulation and experimental levels through a laboratory prototype that has allowed verification of the proposed approach.

Feature Selection vs Theory Reformulation: A Study of Genetic Refinement of Knowledge-based Neural Networks

Expert classification systems have proven themselves effective decision makers for many types of problems. However, the accuracy of such systems is often highly dependent upon the accuracy of a human expert's domain theory. When human experts learn or create a set of rules, they are subject to a number of hindrances. Most significantly experts are, to a greater or lesser extent, restricted by the tradition of scholarship which has preceded them and by an inability to examine large amounts of data in a rigorous fashion without the effects of boredom or frustration. As a result, human theories are often erroneous or incomplete. To escape this dependency, machine learning systems have been developed to automatically refine and correct an expert's domain theory. When theory revision systems are applied to expert theories, they often concentrate on the reformulation of the knowledge provided rather than on the reformulation or selection of input features. The general assumption seems to be that the expert has already selected the set of features that will be most useful for the given task. That set may, however, be suboptimal. This paper studies theory refinement and the relative benefits of applying feature selection versus more extensive theory reformulation.

Large N universality of the two-dimensional Yang-Mills string

We exhibit the gauge-group independence (“universality”) of all normalized non-intersecting Wilson loop expectation values in the large N limit of two-dimensional Yang-Mills theory. This universality is most easily understood via the string theory reformulation of these gauge theories. By constructing an isomorphism between the string maps contributing to normalized Wilson loop expectation values in the different theories, we prove the large N universality of these observables on any surface. The string calculation of the Wilson loop expectation value on the sphere also leads to an indication of the large N phase transition separating strong- and weak-coupling phases.

Explanation-based interpretation of open-textured concepts in logical models of legislation

In this paper we discuss a view of the Machine Learning technique called Explanation-Based Learning (EBL) or Explanation-Based Generalization (EBG) as a process for the interpretation of vague concepts in logic-based models of law. The open-textured nature of legal terms is a well-known open problem in the building of knowledge-based legal systems. EBG is a technique which creates generalizations of given examples on the basis of background domain knowledge. We relate these two topics by considering EBG's domain knowledge as corresponding to statute law rules, and EBG's training example as corresponding to a precedent case. By making the interpretation of vague predicates as guided by precedent cases, we use EBG as an effective process capable of creating a link between predicates appearing as open-textured concepts in law rules, and predicates appearing as ordinary language wording for stating the facts of a case. Standard EBG algorithms do not change the deductive closure of the domain theory. In the legal context, this is only adequate when concepts vaguely defined in some law rules can be reformulated in terms of other concepts more precisely defined in other rules. We call `theory reformulation' the process adopted in this situation of `complete knowledge'. In many cases, however, statutory law leaves some concepts completely undefined. We then propose extensions to the EBG standard that deal with this situation of `incomplete knowledge', and call `theory revision' the extended process. In order to fill in `knowledge gaps' we consider precedent cases supplemented by additional heuristic information. The extensions proposed treat heuristics represented by abstraction hierarchies with constraints and exceptions. In the paper we also precisely characterize the distinction between theory reformulation and theory revision by stating formal definitions and results, in the context of the Logic Programming theory. We offer this proposal as a possible contribution to cross fertilization between machine learning and legal reasoning methods.

The analysis of the transference: A matter of emphasis or of theory reformulation?

Evaluation de la theorie de l'analyse du transfert chez Merton Gill. Examen de deux monographies sur la technique, qui mettent l'accent sur la nature interactive et interpersonnelle du transfert, cas cliniques a l'appui

The Practitioner as Theoretician

Abstract This paper briefly reviews the role that theory plays in organizing and guiding social work practice. Its major focus is on the specification and legitimation of important functions that social work practice assumes in the testing and developing of theory. The theory development functions are identified as theory reformulation, the redirecting of theory and the generation of new theory. Recognition is given to the selective utilization of theory derived from social science contexts but a greater emphasis is placed on developing theory directly from social work practice contexts.