31563337
The trees for which maximum multiplicity implies the simplicity of other eigenvalues
Among those real symmetric matrices whose graph is a given tree T, the maximum multiplicity is known to be the path cover number of T. An explicit characterization is given for those trees for which whenever the maximum multiplicity is attained, all other multiplicities are 1.
40520811
A note on cospectral graphs
Abstract The notion of a (1, x ) adjacency matrix is introduced, together with methods for dealing with it. It is shown that in many instances this adjacency matrix is superior to the usual (0, 1) adjacency matrix, and will distinguish cospectral pairs, when the latter will not. In those cases in which the (1, x ) adjacency matrix fares no better than the (0, 1) adjacency matrix, a good deal can be said about the matrices by which the cospectral pairs are similar.
14968728
Using Temporal Logic to Support the Specification and Prototyping of Interactive Control Systems
Abstract Accidents at Flixborough, Seveso, Bhopal, Three Mile Island, Windscale and Chernobyl have led to increasing concern over the safety and reliability of control systems. Human factors specialists have responded to this concern and have proposed a number of techniques which support the operator of such applications. Unfortunately, this work has not been accompanied by the provision of adequate tools which might enable a designer to carry it beyond the “laboratory bench” and on to the “shop floor”. The following paper exploits formal, mathematically based specification techniques to provide such a tool. Previous weaknesses of abstract specifications are identified and resolved. In particular, they have failed to capture the temporal properties which human factors specialists identify as crucial to the success or failure of interactive control systems. They also provide the non-formalist with an extremely poor impression of what it would be to like to interact with potential implementations. Temporal logic avoids these deficiencies. It can make explicit the sequential information which may be implicit within a design. Executable subsets of this formalization support prototyping and this provides a means of assessing the qualitative “look and feel” of potential implementations. A variety of presentation strategies, including structural decomposition and dialogue cycles, have been specified and incorporated directly into prototypes using temporal logic. Prelog, a tool for the Presentation and REndering of LOGic specifications, has been developed and its implementation is described.
15050037
Journeys in non-classical computation I: A grand challenge for computing research
1. The challengeA gateway event [35] is a change to a system that leads to the possibility of huge increases inkinds and levels of complexity. It opens up a whole new kind of phase space to the system’sdynamics.Gatewayeventsduringevolutionoflifeonearthincludetheappearanceofeukaryotes(organisms with a cell nucleus), an oxygen atmosphere, multi-cellular organisms and grass.Gatewayeventsduringthedevelopmentofmathematicsincludeeachinventionofanewclassofnumbers (negative, irrational, imaginary, ...), and dropping Euclid’s parallel postulate.A gateway event produces a profound and fundamental change to the system: Oncethrough the gateway, life is never the same again. We are currently poised on the threshold ofa signiﬁcant gateway event in computation: That of breaking free from many of our current“classical computational” assumptions. Our Grand Challenge for computer science isto journey through the gateway event obtained by breaking our current classicalcomputational assumptions, and thereby develop a mature science of Non-ClassicalComputation2. Journeys versus goals
35998651
Artificial Immune System Programming for Symbolic Regression
Artificial Immune Systems are computational algorithms which take their inspiration from the way in which natural immune systems learn to respond to attacks on an organism. This paper discusses how such a system can be used as an alternative to genetic algorithms as a way of exploring program-space in a system similar to genetic programming. Some experimental results are given for a symbolic regression problem. The paper ends with a discussion of future directions for the use of artificial immune systems in program induction.
39389167
Software Support for Incident Reporting Systems in Safety-Critical Applications
Incident reporting systems are playing an increasingly important role in the development and maintenance of safety-critical applications. The perceived success of the FAA's Aviation Safety Reporting System (ASRS) and the FDA's MedWatch has led to the establishment of similar national and international schemes. These enable individuals and groups to report their safety concerns in a confidential or anonymous manner. Unfortunately, many of these systems are becoming victims of their own success. The ASRS and MedWatch have both now received over 500,000 submissions. In the past, these systems have relied upon conventional database technology to support the indexing and retrieval of individual reports. However, there are several reasons why this technology is inadequate for many large-scale reporting schemes. In particular, the problems of query formation often result in poor precision and recall. This, in turn, has profound implications for safety-critical applications. Users may fail to identify similar incidents within national or international collections. This paper, therefore, shows how several alternative software architectures support incident report systems in safety-critical applications.
30236643
Towards a Prehistory of Evolutionary and Adaptive Computation in Music
A number of systems have been created which apply genetic algorithms, cellular automata, artificial life, agents, and other evolutionary and adaptive computation ideas in the creation of music. The aim of this paper is to examine the context in which such systems arose by looking for features of experimental music which prefigure the ideas used in such systems. A number of ideas are explored: the use of randomness in music, the view of compositions as parameterized systems, the idea of emergent structure in music and the idea of musicians performing the role of reactive agents.