Set Of Primitive Functions Research Articles

A new genetic programming framework based on reaction systems

This paper presents a new genetic programming framework called Evolutionary Reaction Systems. It is based on a recently defined computational formalism, inspired by chemical reactions, called Reaction Systems, and it has several properties that distinguish it from other existing genetic programming frameworks, making it interesting and worthy of investigation. For instance, it allows us to express complex constructs in a simple and intuitive way, and it lightens the final user from the task of defining the set of primitive functions used to build up the evolved programs. Given that Evolutionary Reaction Systems is new and it has small similarities with other existing genetic programming frameworks, a first phase of this work is dedicated to a study of some important parameters and their influence on the algorithm’s performance. Successively, we use the best parameter setting found to compare Evolutionary Reaction Systems with other well established machine learning methods, including standard tree-based genetic programming. The presented results show that Evolutionary Reaction Systems are competitive with, and in some cases even better than, the other studied methods on a wide set of benchmarks.

Making control systems visible

In this paper we discuss how to support interface design of automatic control systems in a systematic way, that is, how to identify the information that should be displayed in a cognitive relevant way and how to visualize this information content in the interface efficiently. First, a means-ends hierarchical structure is adopted to build the functional model of a control system. Then, a set of functional primitives is proposed, and their behavioural explanations are given. These primitives are used to describe the functions in a functional model of a control system. Based on the functional model, the necessary information to be visualized in the interface can then be identified. Third, a library of graphical presentations for the set of functional primitives is set up. To overcome the problem of display complexity and improve operators’ cognitive workload, the concept of “functional macro” is adopted. Furthermore, several principles are proposed to explain how to map a functional model to interface displays. Finally, how to use this approach to support interface design of automatic control systems is explained in detail by using the electrical and hydraulic controller (EHC) of a nuclear power plant (NPP) as an example. A simple experiment showed that the display design of EHC in this study could be more helpful to identify the modes of EHC than a SSSI design. Reusability of the set of functional primitives and their graphical presentations make this approach possible to support designing displays of various control systems.

Display Design of Process Systems Based on Functional Modelling

The prevalent way to present information in industrial computer displays is by using piping and instrumentation diagrams. Such interfaces have sometimes resulted in difficulties for operators because they are not sufficient to fulfil their needs. A systematic way that supports interface design therefore has to be considered. In the new design framework, two questions must be answered. Firstly, a modelling method is required to describe a process system. Such a modelling method can define the information content that must be displayed in interfaces. Secondly, how to communicate this information to operators efficiently must be considered. This will provide a basis for determining the visual forms that the information should take. This study discusses interface design of human–machine systems from these two points of view. Based on other scholars’ work, a comprehensive set of functional primitives is summarised as a basis to build a functional model of process systems. A library of geometrical presentations for these primitives is then developed. To support effective interface design, the concept of ‘functional macro’ is introduced and a way to map functional model to interface display is illustrated by applying several principles. To make our ideas clear, a central heating system is taken as an example and its functional model is constructed. Based on the functional model, the information to be displayed is determined. Several functional macros are then found in the model and their corresponding displays are constructed. Finally, by using the library of geometrical presentations for functional primitives and functional macros, the display hierarchy of the central heating system is developed. Reusability of functional primitives makes it possible to use the methodology to support interface design of different process systems.

Computational imagery

After many years of neglect, the topic of mental imagery has recently emerged as an active area of research and debate in the cognitive science community. This article proposes a concept of computational imagery, which has potential applications to problems whose solutions by humans involve the use of mental imagery. Computational imagery can be defined as the ability to represent, retrieve, and reason about spatial and visual information not explicitly stored in long-term memory. The article proposes a knowledge representation scheme for computational imagery that incorporates three representations: a long-term memory, descriptive representation and two working-memory representations, corresponding to the distinct visual and spatial components of mental imagery. The three representations, and a set of primitive functions, are specified using a formal theory of arrays and implemented in the array-based language Nial. Although results of studies in mental imagery provide initial motivation for the representations and functionality of the scheme, our ultimate concerns are expressive power, inferential adequacy, and efficiency.

Computational Imagery

After many years of neglect, the topic of mental imagery has recently emerged as an active area of research and debate in the cognitive science community. This article proposes a concept of computational imagery, which has potential applications to problems whose solutions by humans involve the use of mental imagery. Computational imagery can be defined as the ability to represent, retrieve, and reason about spatial and visual information not explicitly stored in long‐term memory.The article proposes a knowledge representation scheme for computational imagery that incorporates three representations: a long‐term memory, descriptive representation and two working‐memory representations, corresponding to the distinct visual and spatial components of mental imagery. The three representations, and a set of primitive functions, are specified using a formal theory of arrays and implemented in the array‐based language Nial. Although results of studies in mental imagery provide initial motivation for the representations and functionality of the scheme, our ultimate concerns are expressive power, inferential adequacy, and efficiency.

Integral-Transform-Generated Basis Sets

Two alternative versions of a procedure for generating new basis sets via the integral-transform (IT) method are outlined. The first version (fixed shape function, set of primitive functions) is tested on 3-electron (Z=2, 3, 4, 5) and 4-electron (Z=3, 4, 5, 6) atomic systems (ground state) and the 21P excited state of He. The set of primitive functions are either hydrogenic or Slater orbitals and the shape function is the square pulse that generates the Hulthèn transforms. In these calculations, a conjecture about the dependence of the parameters of higher principal quantum number (n) IT orbitals on the parameters of lower n IT orbitals is also tested and substantiated. The second version (single primitive function, set of shape functions) is tested on the 21P state of He. The primitive function is a 1s Gaussian function, the set of shape functions is related to the set of generalized Laguerre polynomials Lnv-1(x). The first member of this set gives kv(qr), the reduced modified Bessel function of the second kind, already used in ground state atomic and molecular calculations. The results are analyzed critically.

The M-valued calculus of non-contradiction

The 2-valued calculus of non-contradiction of Dexter has been extended to 3-valued logic. The methods used were, however, too complicated to be capable of generalisation to m-valued logics. The object of the present paper is to give an alternative method of generalising Dexter's work to m-valued logics with one designated truth-value. The rule of procedure is generalised in the same way as before, but the deductive completeness of the system is proved by applying results of Rosser and Turquette. The system has an infinite set of primitive functions, written n(P1, P2, …, Pr) (r = 1,2, …). With the notation of Post, n(P1, P2, …, Pr) has the same truth-value as ~(P1 & P2 & … & Pr). Thus n(P) is Post's primitive ~P, and we can define & byWe use n2(P1, P2, …, Pr) as an abbreviation for n(n(P1, P2, …, Pr)); similarly for higher powers of n. But if we set up the 1-1 correspondence of truth-values i ↔ m−i+1, then & corresponds to ∨ and ~m−1 corresponds to ~. Hence the functional completeness of our system follows from a theorem of Post.We define the functions N(P), N(P, Q) byThus the truth-value of N(P) is undesignated if and only if the truth-value of P is designated, and the truth-value of N(P, Q) is undesignated if and only if the truth-values of P and Q are both designated.