Showing papers on "Metric (mathematics) published in 1990"
TL;DR: This paper characterize real-time systems by giving a classification of such quantitative temporal properties, and extends the usual models for temporal logic by including a distance function to measure time and analyzes what restrictions should be imposed on such a function.
Abstract: This paper is motivated by the need for a formal specification method for real-time systems. In these systemsquantitative temporal properties play a dominant role. We first characterize real-time systems by giving a classification of such quantitative temporal properties. Next, we extend the usual models for temporal logic by including a distance function to measure time and analyze what restrictions should be imposed on such a function. Then we introduce appropriate temporal operators to reason about such models by turning qualitative temporal operators into (quantitative) metric temporal operators and show how the usual quantitative temporal properties of real-time systems can be expressed in this metric temporal logic. After we illustrate the application of metric temporal logic to real-time systems by several examples, we end this paper with some conclusions.
1,230 citations
TL;DR: In this paper, the Ricci-flat Kahler metric is calculated in the vicinity of the nodes for the conifold, the resolution and the deformation, and it is shown that, owing to a topological obstruction, the manifold obtained as the result of independently resolving and deforming the nodes of a conifolds in general cannot be Kahler.
743 citations
01 Jan 1990
TL;DR: In this article, Gromov's theory of hyperbolic spaces and groups is introduced, and complete proofs of some basic theorems which are due to gromov are given, as well as some important developments on isoperimetric inequalities, automatic groups, and the metric structure on the boundary of a space.
Abstract: The book is an introduction of Gromov's theory of hyperbolic spaces and hyperbolic groups It contains complete proofs of some basic theorems which are due to Gromov, and emphasizes some important developments on isoperimetric inequalities, automatic groups, and the metric structure on the boundary of a hyperbolic space
431 citations
TL;DR: In this paper, it was shown that the topological properties of the symplectic diffeomorphism groups are related to the topology of the phase space geometry of the manifold.
Abstract: In this paper we show that symplectic maps have surprising topological properties. In particular, we construct an interesting metric for the symplectic diffeomorphism groups, which is related, but not obviously, to the topological properties of symplectic maps and phase space geometry. We also prove a certain number of generalised symplectic fixed point theorems and give an application to a Hamiltonian system.
412 citations
TL;DR: This work has developed a multi-level theory of spatial representation of the environment based upon the observation and re-acquisition of distinctive visual events, i.e., landmarks, that provides the theoretical foundations for a visual memory database that smoothly integrates available metric knowledge of relative or absolute angles and distances.
372 citations
TL;DR: The proposed approach derives models of problematic components, based on their measurable attributes and those of their development processes, which provide a basis for forecasting which components are likely to share the same high-risk properties.
Abstract: The identification of high-risk components early in the life cycle is addressed. A solution that casts this as a classification problem is examined. The proposed approach derives models of problematic components, based on their measurable attributes and those of their development processes. The models provide a basis for forecasting which components are likely to share the same high-risk properties, such as being error-prone or having a high development cost. Developers can use these classification techniques to localize the troublesome 20% of the system. The method for generating the models, called automatic generation of metric-based classification trees, uses metrics from previous releases or projects to identify components that are historically high-risk. >
293 citations
TL;DR: The parsimony principle is applied to the reconstruction of the evolution of homologous sequences where recombinations or horizontal transfer can occur, and a dynamic programming algorithm is presented that finds the most parsimonious history that fits a given set of sequences.
Abstract: The parsimony principle states that a history of a set of sequences that minimizes the amount of evolution is a good approximation to the real evolutionary history of the sequences. This principle is applied to the reconstruction of the evolution of homologous sequences where recombinations or horizontal transfer can occur. First it is demonstrated that the appropriate structure to represent the evolution of sequences with recombinations is a family of trees each describing the evolution of a segment of the sequence. Two trees for neighboring segments will differ by exactly the transfer of a subtree within the whole tree. This leads to a metric between trees based on the smallest number of such operations needed to convert one tree into the other. An algorithm is presented that calculates this metric. This metric is used to formulate a dynamic programming algorithm that finds the most parsimonious history that fits a given set of sequences. The algorithm is potentially very practical, since many groups of sequences defy analysis by methods that ignore recombinations. These methods give ambiguous or contradictory results because the sequence history cannot be described by one phylogeny, but only a family of phylogenies that each describe the history of a segment of the sequences. The generalization of the algorithm to reconstruct gene conversions and the possibility for heuristic versions of the algorithm for larger data sets are discussed.
288 citations
TL;DR: For a very large number of Calabi-Yau manifolds of many different numerical invariants and hence distinct homotopy types, the relevant moduli spaces can be assembled into a connected web.
282 citations
TL;DR: In this article, a parametric approach is proposed in order to introduce a well-defined metric on the class of autoregressive integrated moving-average (ARIMA) invertible models as the Euclidean distance between their auto-gressive expansions.
Abstract: . In a number of practical problems where clustering or choosing from a set of dynamic structures is needed, the introduction of a distance between the data is an early step in the application of multivariate statistical methods. In this paper a parametric approach is proposed in order to introduce a well-defined metric on the class of autoregressive integrated moving-average (ARIMA) invertible models as the Euclidean distance between their autoregressive expansions. Two case studies for clustering economic time series and for assessing the consistency of seasonal adjustment procedures are discussed. Finally, some related proposals are surveyed and some suggestions for further research are made.
269 citations
TL;DR: In this paper, a strong regularity theorem is proved, which shows that the usual constraint qualification conditions ensuring the regularity of the set-valued maps expressing feasibility in optimization problems, are in fact minimal assumptions.
Abstract: A strong regularity theorem is proved, which shows that the usual constraint qualification conditions ensuring the regularity of the set-valued maps expressing feasibility in optimization problems, are in fact minimal assumptions. These results are then used to derive calculus rules for second-order tangent sets, allowing us in turn to obtain a second-order (Lagrangian) necessary condition for optimality which completes the usual one of positive semidefiniteness on the Hessian of the Lagrangian function.
256 citations
TL;DR: Some Bianchi-type string cosmological models are presented in this article, where the physical implications of the models are briefly discussed and the physical properties of the Bianchi models are discussed.
Abstract: Some Bianchi-type string-cosmological models are presented here. The physical implications of the models are briefly discussed
TL;DR: The eigenvector method deals with two questions simultaneously, closeness and order, and they belong to the field topology of order as mentioned in this paper, and the metric idea of closeness is inadequate to judge what is a good approximation to data involving order relations.
22 Oct 1990
TL;DR: Deterministic competitive k-server algorithms are given for all k and all metric spaces and the competitive ratio can be proved is exponential in the number of servers, which settles the k- server conjecture.
Abstract: Deterministic competitive k-server algorithms are given for all k and all metric spaces. This settles the k-server conjecture of M.S. Manasse et al. (1988) up to the competitive ratio. The best previous result for general metric spaces was a three-server randomized competitive algorithm and a nonconstructive proof that a deterministic three-server competitive algorithm exists. The competitive ratio the present authors can prove is exponential in the number of servers. Thus, the question of the minimal competitive ratio for arbitrary metric spaces is still open. The methods set forth here also give competitive algorithms for a natural generalization of the k-server problem, called the k-taxicab problem. >
TL;DR: Computer simulation is used to evaluate the performance of a sequential decoder that uses this metric in conjunction with the stack algorithm, and results are achieved comparable to those obtained using the much more complicated optimal receiver.
Abstract: The application of sequential decoding to the detection of data transmitted over the additive white Gaussian noise channel by K asynchronous transmitters using direct-sequence spread-spectrum multiple access (DS/SSMA) is considered. A modification of R.M. Fano's (1963) sequential-decoding metric, allowing the messages from a given user to be safely decoded if its E/sub b//N/sub 0/ exceeds -1.6 dB, is presented. Computer simulation is used to evaluate the performance of a sequential decoder that uses this metric in conjunction with the stack algorithm. In many circumstances, the sequential decoder achieves results comparable to those obtained using the much more complicated optimal receiver. >
TL;DR: In this article, a complete classification for almost contact metric manifolds through the study of the covariant derivative of the fundamental 2-form on those manifolds was obtained, and the classification was extended to almost contact manifold.
Abstract: It is obtained a complete classification for almost contact metric manifolds through the study of the covariant derivative of the fundamental 2- form on those manifolds.
TL;DR: In this article, the authors proposed a quantitative measure for the flexibility of a design to withstand uncertainties in the continuous parameters and discrete states, denoted as the expected stochastic flexibility E(SF).
TL;DR: Both a new iterative grid-search technique and the iterative Fourier-transform algorithm are used to illuminate the relationships among the ambiguous images nearest a given object, error metric minima, and stagnation points of phase-retrieval algorithms.
Abstract: Both a new iterative grid-search technique and the iterative Fourier-transform algorithm are used to illuminate the relationships among the ambiguous images nearest a given object, error metric minima, and stagnation points of phase-retrieval algorithms. Analytic expressions for the subspace of ambiguous solutions to the phase-retrieval problem are derived for 2 × 2 and 3 × 2 objects. Monte Carlo digital experiments using a reduced-gradient search of these subspaces are used to estimate the probability that the worst-case nearest ambiguous image to a given object has a Fourier modulus error of less than a prescribed amount. Probability distributions for nearest ambiguities are estimated for different object-domain constraints.
TL;DR: In this paper, conformal and related changes of the product metric on the product of two almost contact metric manifolds are studied, and it is shown that if one factor is Sasakian, the other is not, but locally the second factor is of the type studied by Kenmotsu.
Abstract: This paper studies conformal and related changes of the product metric on the product of two almost contact metric manifolds. It is shown that if one factor is Sasakian, the other is not, but that locally the second factor is of the type studied by Kenmotsu. The results are more general and given in terms of trans-Sasakian, a-Sasakian and s-Kenmotsu structures.
TL;DR: A general adaptive model unifying existing models for pattern learning, unifying many existing models (including that of neural nets), is proposed, and suggests how various propositional object (class) descriptions might be generated based on the outputs of the learning processes.
TL;DR: This embedding allows us to obtain a general lower bound for the Rao distance, which is itself a distance, and is suggested to be employed for statistical purposes, taking into account the similitude of the above related metrics.
01 Jan 1990
TL;DR: In this paper, the nodal sets of eigenfunctions are discussed and the basic tools for proving unique continuation theorems are Carleman inequalities for second-order elliptic operators.
Abstract: Publisher Summary This chapter discusses the nodal sets of eigenfunctions. The basic tools for proving unique continuation theorems are Carleman inequalities. In his original paper, Aronszajn established such inequalities for second-order elliptic operators with C2,1 coefficients. Twice differentiable coefficients were needed for the use of geodesic polar coordinates. A substantial improvement was made in later joint work by Aronszajn, Krzywicki, and Szarski. They established strong unique continuation for second-order elliptic operators with C0,1 coefficients. In the Lipschitz case, one makes a preliminary conformal change in the metric associated to the second-order operator. This conformally changed metric has a coordinate representation with the necessary good properties of geodesic polar coordinates.
TL;DR: The notion of a single metric, called relative complexity, which assigns a single value to each program in a program set to order the programs by their complexity is developed, which may serve as a leading indicator as to the set of programs that will require large amounts of system resources during the development and maintenance phases.
TL;DR: Local metrics are described and are generalized to the multi-class case and Properties of various possible generalizations are compared, and the results of a simulation study are described.
TL;DR: In this paper, the authors studied the moduli space M of anti-self-dual connections on a principal bundle over an ALE hyperkahler 4-manifold.
Abstract: We study the (framed) moduli space M of anti-self-dual connections on a principal bundle over an ALE hyperkahler 4-manifold. It has the natural Riemannian metric g M and the hyperkahler structure (I M , J M , K M ) induced from those on the base manifold
TL;DR: In this paper, a geometrical approach to statistical thermodynamics is proposed, and it is shown that any r-parameter generalised Gibbs distribution leads to a Riemannian metric of parameter space.
Abstract: A geometrical approach to statistical thermodynamics is proposed. It is shown that any r-parameter generalised Gibbs distribution leads to a Riemannian metric of parameter space. The components of the metric tensor are represented by second moments of stochastic variables. The scalar curvature R, as a geometrical invariant, is a function of the second and third moments, so is strictly connected with fluctuations of the system. In the case of a real gas, R is positive and tends to infinity as the system approaches the critical point. In the case of an ideal gas, R=0. The obtained results, and the results of the authors previous work, suggests that for a wide class of models R tends to + infinity near the critical point. They treat R as a measure of the stability of the system. They propose some sort of statistical principle: only such models may be accepted for which R tends to infinity if the system is approaching the critical point. It is shown that, if this criterion is adopted for a class of models for which the scaling hypothesis holds, then they obtain the new inequalities for the critical indices. These inequalities are in good agreement with model calculations and experiment.
TL;DR: In this paper, the authors give necessary and sufficient conditions for extending a family of point-to-set maps to a point-set map which can be applied to abstract algorithms with global convergence.
03 Jul 1990
TL;DR: An inclusion relation of neighbourhoods in both topologies is proved, which is the basis of an efficient obstacle avoidance local method in the configuration space R/sup 2/*S/sup 1/ of a car-like robot system.
Abstract: Deals with the problem of motion planning for a car-like robot (i.e. nonholonomic mobile robot whose turning radius is lower bounded). The main contribution is the introduction of a new metric in the configuration space R/sup 2/*S/sup 1/ of such a system. This metric is defined from the length of the shortest paths in the absence of obstacles. The authors study the relations between the new induced topology and the classical one. This study leads to new theoretical issues about sub-Riemannian geometry and to practical results for motion planning. In particular they prove an inclusion relation of neighbourhoods in both topologies, which is the basis of an efficient obstacle avoidance local method. >
TL;DR: In this paper, it was shown that a magnetic monopole on hyperbolic space is determined, up to gauge equivalence, by its asymptotic boundary value, using the ADHM construction which specializes to a discrete Nahm equation.
Abstract: The authors show that a magnetic monopole on hyperbolic space is determined, up to gauge equivalence, by its asymptotic boundary value. Their basic tool is the ADHM construction which specializes to a discrete Nahm equation. They also construct a complete metric on the moduli spaces.