Showing papers on "Network theory published in 1970"

Multiparameter sensitivity problems in network theory

Abstract: The paper presents a survey of the literature as it pertains to the problem of multiparameter sensitivity in network theory. In particular, a critical appraisal is made of several multiparameter sensitivity functions, and the problems involved in their computation are considered. Several procedures for their evaluation are described, with attention focused on the auxilliary network approach of Leeds and Ugron and the adjoint network approach of Director and Rohrer. Another approach considered is the so-called direct approach, in which an algorith, is used to obtain directly the partial derivaties of the network function.

The English Auxiliaries: A Relational Network Description.

Abstract: This is the second of two papers comparing relational network theory with transformational theory. In Reich 1970b we defined some basic nodes and compared relational network theory with a subset of transformational theory which is commonly acknowledged to be linguistically inadequate. In this paper we shall review the types of problems which context-free phrase-structure grammars cannot adequately handle. We shall then show that each of these problems occurs in that portion of English grammar which is concerned with the English auxiliaries; thus a good test of any proposed grammatical theory is whether or not it can be used to describe a grammar of the auxiliaries in an acceptable way. Finally, we shall describe in detail a relational network grammar of the auxiliaries and attempt to demonstrate that relational network theory passes this test.

On applications of graph/network theory to problems in communication systems

Abstract: Graph/network theory results are applicable to problems in communications. As a representative example, the node coloring problem in graph theory is applicable to the channel assignment problem in cellular mobile communication systems. The node coloring problem is NP-complete, meaning that optimally solving it is very difficult. Therefore, we use heuristic algorithms for the channel assignment problem. In this case, the graph theory results show the legitimacy of using heuristic techniques. On the other hand, we can directly apply graph theory to communication problems. For example, on contents delivery services in the Internet, we place mirror servers that provide the same contents on the network. Location problems on flow networks are applicable to mirror server allocation problems. In a simple case, we can efficiently solve the problem. In this paper, we concentrate on multi-hop wireless networks and consider the relationship between their problems and the results of graph/network theory.

A quantitative measure of the passivity and activity of networks

Abstract: It is shown that a rational basis exists for stating that one network is more passive or more active than another. In fact, a quantitative measure of passivity is developed that assigns to each network a single number that can be calculated in a relatively simple way. This measure is shown to have many of those properties that one would expect on physical grounds. It also allows one to study many fundamental design problems in a rational manner. For example, one now has a basis for designing the maximally lossy loading network that could support oscillations with a given active network.

Foundations of computer- aided circuit design by singular imbedding

Abstract: Although computer-aided circuit analysis has advanced quite rapidly in the last few years, there is considerable room for applications of network theory to the computer-aided design of electronic networks. In this paper the scope of network theory is generalized to include multiterminal networks in which the voltages and currents are related by inequality as well as equality relations. Two classes of new singular elements useful in electronic network design are introduced. The first class generalizes the allowed v-i pairs of a nullator and its multiterminal counterparts. The second constrains the allowed pairs of the norator and its multiterminal counterparts. The new singular elements are used to constrain network variables and to represent bounded adjustable elements. In this way the role of the objectives and element constraints are handled in a unified scheme. By imbedding these elements in a network, the synthesis problem is transformed into a problem of analysis of a circuit containing singular elements. Although the method is applicable to a wide variety of circuits, only the dc linear case is treated here. By keeping a linear formulation throughout, the analysis can be done with linear programming techniques with the corresponding theoretical and computational advantages. On-line programs for interactive time-share use have been written, and their flow charts are given in the paper. They provide a very efficient on-line design system that avoids the iterative analysis optimization approach. The gains achieved in computation time are of several orders of magnitude, and the solutions are guaranteed to be found.