Finite Metrics Research Articles

A Note on the Uniqueness of Coherent Decompositions

In2the concept of a coherent decomposition of a finite metric is introduced and it is conjectured that every such metric can be decomposed into a coherent sum of prime metrics in a unique way. In this note we give a counterexample to this conjecture.

First- and second-derivative estimators for cyclic closed-queueing networks

We consider a cyclic closed-queueing network with arbitrary service time distributions and derive first- and second-derivative estimators of some finite horizon performance metrics with respect to a parameter of any one of the service distributions. Our approach is based on observing a single sample path of this system and evaluating first- and second-order effects on departure times as a result of the parameter perturbation. We then define an estimator as a conditional expectation over appropriate observable quantities, using smoothed perturbation analysis techniques. This process recovers the first-derivative estimator along the way and gives new insights into event order change phenomena which are of higher order. Despite the complexity of the analysis, the final algorithms we obtain are relatively simple. Further, we show that our estimators are unbiased and include some numerical examples. We also show the use of our estimators in obtaining approximations of the entire system response surface as a function of system parameters.

On the Generalized Roundness of Finite Metric Spaces

In this paper we show that the generalized roundness of a finite metric space can be bounded from below by a strictly positive constant that only depends upon the number of points in the space.

Harmonic Calculus on Limits of Networks and Its Application to Dendrites

The main purpose of this paper is to give a general framework to analysis on fractals including finitely ramified self-similar sets, random fractals, Canter sets, dendrites, and the recurrent case of infinitely ramified self-similar sets. We study a limit of a sequence of electrical networks satisfying certain compatibility, which is a generalization of the decimation invariance of random walks playing an important role in constructing diffusion processes on self-similar sets. As a limit, we propose notions of finite resistance forms and effective resistance metrics. Also it is shown that a finite resistance form induces an effective resistance metric and vice versa. A finite resistance form becomes a regular Dirichlet form if the domain is dense in L2-space. In such a case, the effective resistance metric is thought of as the intrinsic metric for the Dirichlet form. In the latter half of the paper we apply the general framework to dendrites, which are topological spaces containing no loops. A shortest path metric, where all arcs are geodesics, on a dendrite is shown to be an effective resistance metric and the corresponding finite resistance form turns out to be a local regular Dirichlet form. Furthermore, we establish a simple relation between the Hausdorff dimensions and the spectral dimensions of dendrites with shortest path metrics.

Split decomposition: a technique to analyze viral evolution.

A clustering technique allowing a restricted amount of overlapping and based on an abstract theory of coherent decompositions of finite metrics is used to analyze the evolution of foot-and-mouth disease viruses. The emerging picture is compatible with the existence of viral populations with a quasispecies structure and illustrates various forms of evolution of this virus family. In addition, it allows the correlation of these forms with geographic occurrence.

Applications of Deviation Inequalities on Finite Metric Sets

Mathematische NachrichtenVolume 153, Issue 1 p. 33-41 Article Applications of Deviation Inequalities on Finite Metric Sets Jesús Bastero, Jesús Bastero Departamento of Matematicas Facultad de Ciencias Universidad de Zaragoza 50009 Zaragoza SpainSearch for more papers by this authorJulio Bernués, Julio Bernués Departamento of Matematicas Facultad de Ciencias Universidad de Zaragoza 50009 Zaragoza Spain The two named authors are partially supported by Grant DGICYT PS 87-0059. The second named author is also supported by D.G.A. (Spain)Search for more papers by this author Jesús Bastero, Jesús Bastero Departamento of Matematicas Facultad de Ciencias Universidad de Zaragoza 50009 Zaragoza SpainSearch for more papers by this authorJulio Bernués, Julio Bernués Departamento of Matematicas Facultad de Ciencias Universidad de Zaragoza 50009 Zaragoza Spain The two named authors are partially supported by Grant DGICYT PS 87-0059. The second named author is also supported by D.G.A. (Spain)Search for more papers by this author First published: 1991 https://doi.org/10.1002/mana.19911530104Citations: 2 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume153, Issue11991Pages 33-41 RelatedInformation

Gravitational calorons

Finite temperature solutions to euclidean gravity (i.e. with ++++ signature) are constructed on the analogy of the “caloron” solutions of the Yang-Mills field. In contrast to the known finite temperature metrics, the imaginary time coordinate (τ) is not a cyclic coordinate here. The metric components are periodic functions of τ. The zero-temperature limit of these solutions gives non-trivial metrics including in particular gravitational instantons corresponding to multicenter metrics of Taub-NUT type. Finite temperature solutions with non self-dual curvature are also found.

Imbedding a Finite Metric set in an N-Dimensional Minkowski Space

Imbedding a Finite Metric set in an N-Dimensional Minkowski Space