29713643
Structural conditions for cycle completable graphs
Abstract We first review the matrix completion problem that motivated cycle completable graphs. We then discuss prior and give new structural characterizations of these graphs, along with their relationship to chordal and series-parallel graphs.
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.
17884377
Converse to the Parter-Wiener theorem: The case of non-trees
Through a succession of results, it is known that if the graph of an Hermitian matrix A is a tree and if for some index j, @l@?@s(A)@?@s(A(j)), then there is an index i such that the multiplicity of @l in @s(A(i)) is one more than that in A. We exhibit a converse to this result by showing that it is generally true only for trees. In particular, it is shown that the minimum rank of a positive semidefinite matrix with a given graph G is =
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.
21779382
Computational Engineering and Science Program at the University of Utah
We describe a new graduate program at the Univesity of Utah that we consider a first step towards the modernization of the University's curriculum in what we call "Computational Engineering and Science" (CES). Our goal is to provide a mechanism by which a graduate student can obtain integrated expertise and skills in all areas that are required for the solution of a particular computational problem.
10157262
Topology-Preserving Smoothing of Vector Fields
Proposes a technique for topology-preserving smoothing of sampled vector fields. The vector field data is first converted into a scalar representation in which time surfaces implicitly exist as level sets. We then locally analyze the dynamic behavior of the level sets by placing geometric primitives in the scalar field and by subsequently distorting these primitives with respect to local variations in this field. From the distorted primitives, we calculate the curvature normal and we use the normal magnitude and its direction to separate distinct flow features. Geometrical and topological considerations are then combined to successively smooth dense flow fields, at the same time retaining their topological structure.
18085576
Semantic errors - diagnosis and repair
In compiler technology, semantic error handling has too often used ad hoc techniques and terse messages of fixed content. In contrast, we present general models of diagnosis and repair of semantic errors and illustrate their use in the York Ada Workbench Compiler. The diagnostic model focuses upon the problem of selecting suitable information from which the programmer can locate and correct an error; following a brief discussion of an approach in which <underline>filters</underline> are applied to reports, and we give a more extensive account of a new approach using an <underline>interactive diagnostic interpreter</underline>. The repair model is based upon the idea of <underline>plastic</underline> nodes which are introduced into the compiler's internal representation of a program to replace <underline>normal</underline> nodes which are missing or erroneous.
47143488
The Evaluation of User Interface Notations
Over the last decade a wide range of graphical, tabular and textual notations have been proposed to support the design of human-computer interfaces. These notations are intended to strip away the clutter of implementation details that frequently obscure interaction properties. Unfortunately, relatively little work has been done to evaluate the usability of these notations for ‘real-world’ interfaces. We have, therefore, conducted an empirical evaluation of the User Action Notation (UAN), State Transition Networks (STN) and temporal logic ‘in the wild’. By this we mean that our subjects were drawn from realistic samples of users and designers. We also presented our subjects with realistic descriptions of two user interfaces. This avoids a weakness of previous investigations that have used ‘toy examples’. The results of our investigation show a strong preference amongst our subjects for the use of natural language descriptions. More surprisingly, our results also suggest a link between the frequency of comprehension errors and positive attitude statements towards particular notations. In other words, our subjects made most errors with the notations that they liked the best. This suggests that while graphical notations, such as state transition networks, have a strong intuitive appeal they may also create significant problems for real-world development tasks.