Showing papers on "Metric (mathematics) published in 1988"

Aspects of underspecification theory

Abstract: An evaluation metric in Universal Grammar provides a means of selecting between possible grammars for a particular language. The evaluation metric as conceived in Chomsky & Halle (1968; henceforth SPE) prefers the grammar in which only the idiosyncratic properties are lexically listed and predictable properties are derived. The essence of underspecification theory is to supply such predictable distinctive features or feature specifications by rule. Viewed in this way, the general idea of underspecification has always been a part of any theory of phonology that includes such an evaluation metric.

Sensitivity analysis of nonlinear programs and differentiability properties of metric projections

Abstract: This paper is concerned with a study of differentiability properties of the optimal value function and an associated optimal solution of a parametrized nonlinear program. Second order analysis is presented essentially under the Mangasarian-Fromovitz constraint qualification when the corresponding vector of Lagrange multipliers is not necessarily unique. It is shown that under certain regularity conditions the optimal value function possesses second order directional derivatives and the optimal solution mapping is directionally differentiable. The results obtained are applied to an investigation of metric projections in finite-dimensional spaces.

Nonlinear Psychophysical Dynamics

Abstract: Contents: General Qualitative Dynamics of Some Nonlinear Systems. Choice of a Recursive Core Equation. A Recursive Loop System Using . A Subjective Weber Function and Output Uncertainty. A Generic Dynamic Mapping of Environment onto . Further Variants on Mapping of Inputs. Cascading of the Loop. Elementary Identification of Variants and Parameters. Matching Data Patterns and Theory Patterns. Metric or Nonmetric Scaling: Properties of Outputs. Analogues of SDT and Isocriterion Plots. Range and Transposition Effects. Mixing and Attenuation. R sum .

Four applications of conformal equivalence to geometry and dynamics

Abstract: Conformal equivalence theorem from complex analysis says that every Riemannian metric on a compact surface with negative Euler characteristics can be obtained by multiplying a metric of constant negative curvature by a scalar function. This fact is used to produce information about the topological and metric entropies of the geodesic flow associated with a Riemannian metric, geodesic length spectrum, geodesic and harmonic measures of infinity and Cheeger asymptotic isoperimetric constant. The method is rather uniform and is based on a comparison of extremals for variational problems for conformally equivalent metrics.

Delay test generation. I. Concepts and coverage metrics

Abstract: An approach to test for delay faults is presented. A variable size delay fault model is used to represent these failures. The nominal gate delays with the manufacturing tolerances are an integral part of the model and are used in the propagation of simplified waveforms through the logic network. The faulty waveforms are functions of the variable-size delay fault. For each fault and test pattern, a threshold is computed such that this fault is detected if its size exceeds epsilon . This threshold is used (along with the minimum slack at the fault site) to determine a metric called quality. The quality of detection for a fault measures how close the test came to exposing the ideally smallest-size fault at that point. This metric (together with the traditional fault coverage) gives a complete measure of the goodness of the test. >

Systolic architectures for vector quantization

Abstract: A family of architectural techniques are proposed which offer efficient computation of weighted Euclidean distance measures for nearest-neighbor codebook searching. The general approach uses a single metric comparator chip in conjunction with a linear array of inner product processor chips. Very high vector-quantization (VQ) throughout can be achieved for many speech and image-processing applications. Several alternative configurations allow reasonable tradeoffs between speed and VLSI chip area required. >

On the invariant mass conjecture in general relativity

Abstract: An asymptotic symmetries theorem is proved under certain hypotheses on the behaviour of the metric at spatial infinity. This implies that the Einstein-von Freud-ADM mass can be invariantly assigned to an asymptotically flat four dimensional end of an asymptotically empty solution of Einstein equations if the metric is a no-radiation metric or if the end is defined in terms of a collection of boost-type domains.

Hyper-Kähler metrics and a generalization of the Bogomolny equations

Abstract: We generalize the Bogomolny equations to field equations on ℝ3 ⊘ ℝn and describe a twistor correspondence. We consider a general hyper-Kahler metric in dimension 4n with an action of the torusTn compatible with the hyper-Kahler structure. We prove that such a metric can be described in terms of theTn-solution of the field equations coming from the twistor space of the metric.

Nonlinear Lagrangians and the significance of the metric

Abstract: Recent investigations of nonlinear general relativistic gravitational Lagrangians have focused on the fact that these theories can be recast in standard Einstein form if the metric is redefined. It has been claimed that this result shows that these other theories are equivalent to the standard Einstein theory with additional fields. However, in this letter it is pointed out that the coupling to matter defines what the physically measured metric will be, so that the freedom of identification of an arbitrarily defined 2-tensor field as the metric is not justified. Simply, geodesics provide an operational definition of the metric.

Sigma model solitons and their moduli space metrics

Abstract: We discuss the supersymmetric σ model and its soliton solutions in 2+1 dimensions. We classify supersymmetric maps and derive Bogomolny bounds. We also give the modified superalgebra and describe the metric on the parameter space of solitons.

On optimal realizations of finite metric spaces by graphs

Abstract: Graph realizations of finite metric spaces have widespread applications, for example, in biology, economics, and information theory. The main results of this paper are:1.Finding optimal realizations of integral metrics (which means all distances are integral) is NP-complete.2.There exist metric spaces with a continuum of optimal realizations. Furthermore, two conditions necessary for a weighted graph to be an optimal realization are given and an extremal problem arising in connection with the realization problem is investigated.

Method and apparatus for path planning

Abstract: A method and apparatus for path planning are presented. Path planning involves propagating cost waves in a configuration space representation of a task space. A space variant metric and budding are used for cost wave propagation. The disclosed method and apparatus are readily adaptable to robots with n degrees of freedom.

Thermodynamic geometry and the metrics of Weinhold and Gilmore.

Abstract: The thermodynamic geometries of Gibbs, Weinhold, and Gilmore are compared and the benefits of each are pointed out along with the structures which must be abandoned in order to reap the benefits. While the measurement of distances is not required (or even meaningful) in a traditional Gibbsian picture, Weinhold's metric can be used to measure distances in the equation-of-state surface. Using Weinhold's metric for more than a single state of equilibrium necessitates abandoning a Gibbsian picture of convex surfaces of thermodynamic states. Gilmore's metric, on the other hand, is compatible with standard Gibbsian thermodynamics. This metric measures distance in the potential surface of statistical mechanics rather than the equation-of-state surface of equilibrium thermodynamics.

Evaluation of dimensions and entropies of chaotic systems

Abstract: Accurate evaluations of fractal dimensions are limited by intrinsic properties of strange attractors (lacunarity, nonuniformity) and by statistical effects (finite number of data points). The application of the fixed-mass (nearest-neighbor distance) method is studied in view of these limitations, showing that the method is also well suited for the measurement of large dimensions. The tuning of the algorithm and the problems inherent in the analysis of experimental systems (small number of data points, noise, and drifts) are analyzed with reference to several computer experiments. The evaluation of the metric entropies of experimental signals by means of the same algorithm is discussed.

Where the sign of the metric makes a difference.

Abstract: The groups Pin(n,m) and Pin(m,n) are not isomorphic, and the obstruction classes to their respective bundles are different. It follows that for nonorientable superstring theories the contributions to a Polyakov path integral from surfaces with positive metric are different from the contributions from those with negative metrics.

Algebraic data type and process specifications based on projection spaces

Abstract: The algebraic approach to the semantics of (nonterminating) processes based on the metric completion of process algebras is extended in two directions. Instead of adopting the predefined metric, it is proposed to define the metric internally, using a suitable family of projections as part of the specification and deal with projection spaces rather than metric spaces. It is also proposed to define the data type along with the processes, to allow nonconstant actions and internally defined communication functions. Combined data type and process specifications find a suitable basis for their algebraic semantics in projection algebras.

Improved metrics in image processing applied to the Hilditch skeleton

Abstract: An algorithm is presented in which binary object pixels are addressed and processed in order of increasing distance from the background. The distances are defined as path lengths. The metric can be chosen to obtain arbitrarily good approximations of the Euclidean metric. The algorithm incorporates an efficient propagation method in which extensive use is made of directional information. It is applied to the Hilditch skeleton and proves to be as fast as the best of the other Hilditch skeletonization algorithms available in software. >

Distribution of the symmetric difference metric on phylogenetic trees

Abstract: The symmetric difference metric has been useful in comparing phylogenetic trees derived from DNA sequence data. The main result shown here is that the frequency of pairs of binary trees a given distance apart is described by a limiting Poisson distribution, with $e^{ -1 / 8} \approx 88$ percent of all pairs maximally distant. Asymptotic bounds on the distribution are derived, and the asymptotic mean and variance of the normalized metric on the class of all phylogenetic trees is also calculated. The results rely on simple combinatorial constructions and analytic properties of appropriate generating functions.

On common fixed points of compatible mappings in metric and Banach spaces

Abstract: We prove a number of results concerning the existence of common fixed points of a family of maps satisfying certain contractive conditions in metric and Banach spaces. Results dealing with the stucture of the set of common fixed points of such maps are also given. Our work is an improvement upon the previously known results.

Shift invariant manifolds and nonlinear analytic function theory

Abstract: The ultimate goal of our campaign is to generalize a substantial collection of results in classical complex variables to highly nonlinear situations. In [BH1] and subsequent works (c. f. [BGR],[H]) it was shown how an extension of the classical Beurling-Lax-Halmos theorem to Hilbert spasces with a signed bilinear form (indefinite metric) could be regarded as the key to many theorems in complex analysis. Thus our approach to the nonlinear case is to first extend our indefinite metric Beurling-Lax-Halmos theory to nonlinear situations that is the subject of this article.

Evolution on sequence space and tensor products of representation spaces

Abstract: A connection between evolutionary mutation-selection dynamics on sequence space and linear representations of the hyper-octahedral group (interpreted as the isometry group of the space of {0, 1-sequences relative to the Hamming distance metric) and other such wreath product groups is established and studied.