Relevant bibliographies by topics / Discrete metric

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Discrete metric'

Author: Grafiati
Published: 4 June 2021
Last updated: 14 February 2022

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Journal articles on the topic "Discrete metric"

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Zeng, Wei, Ren Guo, Feng Luo, and Xianfeng Gu. "Discrete heat kernel determines discrete Riemannian metric." Graphical Models 74, no. 4 (July 2012): 121–29. http://dx.doi.org/10.1016/j.gmod.2012.03.009.

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Agarwal, Ravi P., Mohamed Jleli, and Bessem Samet. "Some Integral Inequalities Involving Metrics." Entropy 23, no. 7 (July 8, 2021): 871. http://dx.doi.org/10.3390/e23070871.

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In this work, we establish some integral inequalities involving metrics. Moreover, some applications to partial metric spaces are given. Our results are extension of previous obtained metric inequalities in the discrete case.
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Plewik, Szymon, and Marta Walczyńska. "On metric $\sigma$-discrete spaces." Banach Center Publications 108 (2016): 239–53. http://dx.doi.org/10.4064/bc108-0-18.

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MOORS, WARREN B. "FRAGMENTABILITY BY THE DISCRETE METRIC." Bulletin of the Australian Mathematical Society 91, no. 2 (January 5, 2015): 303–10. http://dx.doi.org/10.1017/s0004972714000926.

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AbstractIn a recent paper, topological spaces $(X,{\it\tau})$ that are fragmented by a metric that generates the discrete topology were investigated. In the present paper we shall continue this investigation. In particular, we will show, among other things, that such spaces are ${\it\sigma}$-scattered, that is, a countable union of scattered spaces, and characterise the continuous images of separable metrisable spaces by their fragmentability properties.
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Burdyuk, V. Ya, and I. V. Burdyuk. "Discrete and continuous metric spaces." Cybernetics and Systems Analysis 28, no. 6 (November 1992): 950–52. http://dx.doi.org/10.1007/bf01291301.

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HUANG, WEN, JIAN LI, JEAN-PAUL THOUVENOT, LEIYE XU, and XIANGDONG YE. "Bounded complexity, mean equicontinuity and discrete spectrum." Ergodic Theory and Dynamical Systems 41, no. 2 (October 7, 2019): 494–533. http://dx.doi.org/10.1017/etds.2019.66.

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We study dynamical systems that have bounded complexity with respect to three kinds metrics: the Bowen metric $d_{n}$, the max-mean metric $\hat{d}_{n}$ and the mean metric $\bar{d}_{n}$, both in topological dynamics and ergodic theory. It is shown that a topological dynamical system $(X,T)$ has bounded complexity with respect to $d_{n}$ (respectively $\hat{d}_{n}$) if and only if it is equicontinuous (respectively equicontinuous in the mean). However, we construct minimal systems that have bounded complexity with respect to $\bar{d}_{n}$ but that are not equicontinuous in the mean. It turns out that an invariant measure $\unicode[STIX]{x1D707}$ on $(X,T)$ has bounded complexity with respect to $d_{n}$ if and only if $(X,T)$ is $\unicode[STIX]{x1D707}$-equicontinuous. Meanwhile, it is shown that $\unicode[STIX]{x1D707}$ has bounded complexity with respect to $\hat{d}_{n}$ if and only if $\unicode[STIX]{x1D707}$ has bounded complexity with respect to $\bar{d}_{n}$, if and only if $(X,T)$ is $\unicode[STIX]{x1D707}$-mean equicontinuous and if and only if it has discrete spectrum.
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Khatsymovsky, V. M. "On the discrete Christoffel symbols." International Journal of Modern Physics A 34, no. 30 (October 30, 2019): 1950186. http://dx.doi.org/10.1142/s0217751x19501860.

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The piecewise flat space–time is equipped with a set of edge lengths and vertex coordinates. This defines a piecewise affine coordinate system and a piecewise affine metric in it, the discrete analogue of the unique torsion-free metric-compatible affine connection or of the Levi-Civita connection (or of the standard expression of the Christoffel symbols in terms of metric) mentioned in the literature, and, substituting this into the affine connection form of the Regge action of our previous work, we get a second-order form of the action. This can be expanded over metric variations from simplex to simplex. For a particular periodic simplicial structure and coordinates of the vertices, the leading order over metric variations is found to coincide with a certain finite difference form of the Hilbert–Einstein action.
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Aslanyan, Levon H. "Metric decompositions and the discrete isoperimetry." IFAC Proceedings Volumes 33, no. 20 (July 2000): 457–62. http://dx.doi.org/10.1016/s1474-6670(17)38092-8.

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Barcelo, Hélène, Valerio Capraro, and Jacob A. White. "Discrete homology theory for metric spaces." Bulletin of the London Mathematical Society 46, no. 5 (June 17, 2014): 889–905. http://dx.doi.org/10.1112/blms/bdu043.

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Fabel, Paul. "Metric spaces with discrete topological fundamental group." Topology and its Applications 154, no. 3 (February 2007): 635–38. http://dx.doi.org/10.1016/j.topol.2006.08.004.

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Dissertations / Theses on the topic "Discrete metric"

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Putwain, Rosemary Johanna. "Partial translation algebras for certain discrete metric spaces." Thesis, University of Southampton, 2010. https://eprints.soton.ac.uk/170227/.

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The notion of a partial translation algebra was introduced by Brodzki, Niblo and Wright in [11] to provide an analogue of the reduced group C*-algebra for metric spaces. Such an algebra is constructed from a partial translation structure, a structure which any bounded geometry uniformly discrete metric space admits; we prove that these structures restrict to subspaces and are preserved by uniform bijections, leading to a new proof of an existing theorem. We examine a number of examples of partial translation structures and the algebras they give rise to in detail, in particular studying cases where two different algebras may be associated with the same metric space. We introduce the notion of a map between partial translation structures and use this to describe when a map of metric spaces gives rise to a homomorphism of related partial translation algebras. Using this homomorphism, we construct a C*-algebra extension for subspaces of groups, which we employ to compute K-theory for the algebra arising from a particular subspace of the integers. We also examine a way to form a groupoid from a partial translation structure, and prove that in the case of a discrete group the associated C*-algebra is the same as the reduced group C*-algebra. In addition to this we present several subsidiary results relating to partial translations and cotranslations and the operators these give rise to.
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Lopez, Marcos D. "Discrete Approximations of Metric Measure Spaces with Controlled Geometry." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439305529.

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Maier, Daniela [Verfasser], and Guido [Akademischer Betreuer] Schneider. "Nonlinear phenomena on metric and discrete necklace graphs / Daniela Maier ; Betreuer: Guido Schneider." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2019. http://d-nb.info/1195529481/34.

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Tsuchiya, Luciana Yoshie 1977. "Um estudo de reticulados q-ários com a métrica da soma." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306600.

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Orientador: Sueli Irene Rodrigues Costa
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica.
Made available in DSpace on 2018-08-20T13:21:10Z (GMT). No. of bitstreams: 1 Tsuchiya_LucianaYoshie_M.pdf: 11296327 bytes, checksum: 3b12c518b500ac555263de03beead341 (MD5) Previous issue date: 2012
Resumo: Reticulados no 'R^n' são conjuntos discretos de pontos gerados como combinações inteiras de vetores linearmente independentes. A estrutura e as propriedades de reticulados vêm sendo exploradas em diversas áreas, dentre elas a Teoria da Informação. Neste trabalho fizemos um estudo de reticulados q-ários na métrica da soma, os quais estão relacionados aos códigos q-ários. Iniciamos com o estudo de reticulados gerais abordando questões como, densidade de empacotamento, determinação da região de Voronoi, equivalência de reticulados e processos de decodificação, fazendo um paralelo destas questões na métrica euclidiana e na métrica da soma. Em seguida, no Capitulo 2, tratamos brevemente os conceitos de códigos corretores de erros, onde os códigos q-ários estão inseridos e códigos lineares definidos sobre corpos finitos. No estudo dos códigos q-ários consideramos a distancia de Lee que e uma alternativa a usual métrica de Hamming. Por fim, no Capitulo 3, abordamos os reticulados q-ários que são obtidos a partir de códigos q-ários pelo processo conhecido como Construção A. Estudamos uma forma de se decodificar um reticulado q-ário via a Construção A, usando a decodificação do código e vice-versa e discutimos um algoritmo de decodificação (Lee Sphere Decoding) para reticulados q-ários que possuem matriz geradora de formato especial
Abstract: Lattices in 'R^n' are discrete sets of points generated as integer combinations of linearly independent vectors. The structure and properties of lattices have been explored in several areas, including Information Theory. In this work, we study q-ary lattices which are obtained from q-ary codes in the sum metric. We begin the study of general lattices, approaching topics as packing density, Voronoi regions, lattice equivalence and decoding processes, considering both the Euclidean and sum metric. In Chapter 2, we introduce some error correcting codes concepts focusing on q-ary codes and the more general class of linear codes defined over finite fields. In the study of q-ary codes, we consider the Lee distance, as an extension and alternative to the usual Hamming metric. Finally, in Chapter 3, we approach the q-ary latt ices, which are obtained from q-ary codes via the so called Construction A. We study a q-ary lattice decoding process, relate it to the associate code decoding and discuss a decoding algorithm for lattices which have special generator matrices
Mestrado
Matematica
Mestre em Matemática
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Champion, Daniel James. "Mobius Structures, Einstein Metrics, and Discrete Conformal Variations on Piecewise Flat Two and Three Dimensional Manifolds." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/145313.

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Spherical, Euclidean, and hyperbolic simplices can be characterized by the dihedral angles on their codimension-two faces. These characterizations analyze the Gram matrix, a matrix with entries given by cosines of dihedral angles. Hyperideal hyperbolic simplices are non-compact generalizations of hyperbolic simplices wherein the vertices lie outside hyperbolic space. We extend recent characterization results to include fully general hyperideal simplices. Our analysis utilizes the Gram matrix, however we use inversive distances instead of dihedral angles to accommodate fully general hyperideal simplices.For two-dimensional triangulations, an angle structure is an assignment of three face angles to each triangle. An angle structure permits a globally consistent scaling provided the faces can be simultaneously scaled so that any two contiguous faces assign the same length to their common edge. We show that a class of symmetric Euclidean angle structures permits globally consistent scalings. We develop a notion of virtual scaling to accommodate spherical and hyperbolic triangles of differing curvatures and show that a class of symmetric spherical and hyperbolic angle structures permit globally consistent virtual scalings.The double tetrahedron is a triangulation of the three-sphere obtained by gluing two congruent tetrahedra along their boundaries. The pentachoron is a triangulation of the three-sphere obtained from the boundary of the 4-simplex. As piecewise flat manifolds, the geometries of the double tetrahedron and pentachoron are determined by edge lengths that gives rise to a notion of a metric. We study notions of Einstein metrics on the double tetrahedron and pentachoron. Our analysis utilizes Regge's Einstein-Hilbert functional, a piecewise flat analogue of the Einstein-Hilbert (or total scalar curvature) functional on Riemannian manifolds.A notion of conformal structure on a two dimensional piecewise flat manifold is given by a set of edge constants wherein edge lengths are calculated from the edge constants and vertex based parameters. A conformal variation is a smooth one parameter family of the vertex parameters. The analysis of conformal variations often involves the study of degenerating triangles, where a face angle approaches zero. We show for a conformal variation that remains weighted Delaunay, if the conformal parameters are bounded then no triangle degenerations can occur.
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Lesser, Alice. "Optimal and Hereditarily Optimal Realizations of Metric Spaces." Doctoral thesis, Uppsala University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8297.

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This PhD thesis, consisting of an introduction, four papers, and some supplementary results, studies the problem of finding an optimal realization of a given finite metric space: a weighted graph which preserves the metric's distances and has minimal total edge weight. This problem is known to be NP-hard, and solutions are not necessarily unique.

It has been conjectured that extremally weighted optimal realizations may be found as subgraphs of the hereditarily optimal realization Γd, a graph which in general has a higher total edge weight than the optimal realization but has the advantages of being unique, and possible to construct explicitly via the tight span of the metric.

In Paper I, we prove that the graph Γd is equivalent to the 1-skeleton of the tight span precisely when the metric considered is totally split-decomposable. For the subset of totally split-decomposable metrics known as consistent metrics this implies that Γd is isomorphic to the easily constructed Buneman graph.

In Paper II, we show that for any metric on at most five points, any optimal realization can be found as a subgraph of Γd.

In Paper III we provide a series of counterexamples; metrics for which there exist extremally weighted optimal realizations which are not subgraphs of Γd. However, for these examples there also exists at least one optimal realization which is a subgraph.

Finally, Paper IV examines a weakened conjecture suggested by the above counterexamples: can we always find some optimal realization as a subgraph in Γd? Defining extremal optimal realizations as those having the maximum possible number of shortest paths, we prove that any embedding of the vertices of an extremal optimal realization into Γd is injective. Moreover, we prove that this weakened conjecture holds for the subset of consistent metrics which have a 2-dimensional tight span

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Winden, Matthew Wayne. "INTEGRATING STATED PREFERENCE CHOICE ANALYSIS AND MULTI-METRIC INDICATORS IN ENVIRONMENTAL VALUATION." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1343325594.

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Simmer, Jan [Verfasser], Olaf [Akademischer Betreuer] Post, and Olaf [Gutachter] Post. "Approximation of energy forms on finitely ramified fractals by discrete graphs and related metric measure spaces / Jan Simmer ; Gutachter: Olaf Post ; Betreuer: Olaf Post." Trier : Universität Trier, 2021. http://d-nb.info/1230135057/34.

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Dinh, Ngoc Thach. "Observateur par intervalles et observateur positif." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112335/document.

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Cette thèse est construite autour de deux types d'estimation de l'état d'un système, traités séparément. Le premier problème abordé concerne la construction d'observateurs positifs basés sur la métrique de Hilbert. Le second traite de la synthèse d'observateurs par intervalles pour différentes familles de systèmes dynamiques et la construction de lois de commande robustes qui stabilisent ces systèmes.Un système positif est un système dont les variables d'état sont toujours positives ou nulles lorsque celles-ci ont des conditions initiales qui le sont. Les systèmes positifs apparaissent souvent de façon naturelle dans des applications pratiques où les variables d'état représentent des quantités qui n'ont pas de signification si elles ont des valeurs négatives. Dans ce contexte, il parait naturel de rechercher des observateurs fournissant des estimées elles aussi positives ou nulles. Dans un premier temps, notre contribution réside dans la mise au point d'une nouvelle méthode de construction d'observateurs positifs sur l'orthant positif. L'analyse de convergence est basée sur la métrique de Hilbert. L'avantage concurrentiel de notre méthode est que la vitesse de convergence peut être contrôlée.Notre étude concernant la synthèse d'observateurs par intervalles est basée sur la théorie des systèmes dynamiques positifs. Les observateurs par intervalles constituent un type d'observateurs très particuliers. Ce sont des outils développés depuis moins de 15 ans seulement : ils trouvent leur origine dans les travaux de Gouzé et al. en 2000 et se développent très rapidement dans de nombreuses directions. Un observateur par intervalles consiste en un système dynamique auxiliaire fournissant un intervalle dans lequel se trouve l'état, en considérant que l'on connait des bornes pour la condition initiale et pour les quantités incertaines. Les observateurs par intervalles donnent la possibilité de considérer le cas où des perturbations importantes sont présentes et fournissent certaines informations à tout instant
This thesis presents new results in the field of state estimation based on the theory of positive systems. It is composed of two separate parts. The first one studies the problem of positive observer design for positive systems. The second one which deals with robust state estimation through the design of interval observers, is at the core of our work.We begin our thesis by proposing the design of a nonlinear positive observer for discrete-time positive time-varying linear systems based on the use of generalized polar coordinates in the positive orthant. For positive systems, a natural requirement is that the observers should provide state estimates that are also non-negative so they can be given a physical meaning at all times. The idea underlying the method is that first, the direction of the true state is correctly estimated in the projective space thanks to the Hilbert metric and then very mild assumptions on the output map allow to reconstruct the norm of the state. The convergence rate can be controlled.Later, the thesis is continued by studying the so-called interval observers for different families of dynamic systems in continuous-time, in discrete-time and also in a context "continuous-discrete" (i.e. a class of continuous-time systems with discrete-time measurements). Interval observers are dynamic extensions giving estimates of the solution of a system in the presence of various type of disturbances through two outputs giving an upper and a lower bound for the solution. Thanks to interval observers, one can construct control laws which stabilize the considered systems
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Siramdasu, Yaswanth. "Discrete Tire Model Application for Vehicle Dynamics Performance Enhancement." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/74394.

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Tires are the most influential component of the vehicle as they constitute the only contact between the vehicle and the road and have to generate and transmit forces necessary for the driver to control the vehicle. The demand for the tire models are increasing due to the need to study the variations of force generation mechanisms due to various variables such as load, pressure, speed, and road surface irregularities. Another need from the vehicle manufactures is the study of potential incompatibilities associated with safety systems such as Anti-lock Braking System (ABS) and Electronic Stability Control (ESC) and tires. For vehicle dynamic simulations pertaining to the design of safety systems such as ABS, ESC and ride controllers, an accurate and computationally efficient tire model is required. As these control algorithms become more advanced, they require accurate and extended validity in the range of frequencies required to cover dynamic response due to short wavelength road disturbances, braking and steering torque variations. Major thrust has been provided by the tire industry to develop simulation models that accurately predict the dynamic response of tires without the use of computationally intensive tools such as FEA. The objectives of this research are • To develop, implement and validate a rigid ring tire model and a simulation tool to assist both tire designers and the automotive industry in analyzing the effects of tire belt vibrations, road disturbances, and high frequency brake and steering torque variations on the handling, braking, and ride performances of the vehicle. • To further enhance the tire model by considering dynamic stiffness changes and temperature dependent friction properties. • To develop, and implement novel control algorithms for braking, stability, and ride performance improvements of the vehicle
Ph. D.
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Books on the topic "Discrete metric"

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Discrete iterations: A metric study. Berlin: Springer-Verlag, 1986.

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Kirk, William A. Handbook of Metric Fixed Point Theory. Dordrecht: Springer Netherlands, 2001.

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Discrete Mathematics with Applications, Metric Edition. Blue Kingfisher, 2019.

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Discrete Iterations: A Metric Study (Springer Series in Computational Mathematics). Springer, 1986.

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Dribus, Benjamin F. Discrete Causal Theory: Emergent Spacetime and the Causal Metric Hypothesis. Springer, 2018.

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Dribus, Benjamin F. Discrete Causal Theory: Emergent Spacetime and the Causal Metric Hypothesis. Springer, 2017.

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Walsh, Bruce, and Michael Lynch. Short-term Changes in the Mean: 2. Truncation and Threshold Selection. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198830870.003.0014.

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The selection intensity, the mean change in a trait within a generation expressed in phenotypic standard deviations, provides an important metric for comparing the strength of selection over designs. Further, under truncation selection (only individuals above some threshold leave offspring), the selection intensity is a function of the fraction saved, and hence the breeder's equation is often expressed in terms of the selection intensity. An important special case of truncation selection is a threshold trait, wherein an individual only expresses a particular phenotype when its underlying liability value exceeds some threshold. This chapter examines selection on such traits, and generalizes this binary-trait setting (with binomial residuals) to other classes of discrete traits, wherein some underling linear model (generating the threshold) is this transformed via a generalized linear mixed model into an observed trait value.
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Golan, Amos. Info-Metrics and Statistical Inference. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199349524.003.0012.

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This chapter is the first of a two-chapter sequence looking into the relationship between info-metrics and the more familiar statistical methods of inference, with an emphasis on information-theoretic methods. In this chapter I concentrate on discrete models. The relationship between info-metrics and information-theoretic statistical methods is established via duality theory, which provides a way for specifying all inferential methods as constrained optimization models. Since the objective here is to compare different approaches and philosophies, the analysis and examples are kept simple. A main result is that, for discrete problems, the maximum-likelihood approach is a special case of the info-metrics framework. To show this, I reconstruct the likelihood model as a constrained optimization problem. The relevant diagnostics and statistics are developed and discussed. I conclude the chapter with a detailed summary of the benefits of info-metrics for inference of discrete problems. Two detailed case studies are provided.
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Stark, David, ed. The Performance Complex. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198861669.001.0001.

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What’s valuable? Market competition provides one kind of answer. Competitions offer another. On one side, competition is an ongoing and seemingly endless process of pricings; on the other, competitions are discrete and bounded in time and location, with entry rules, judges, scores, and prizes. This book examines what happens when ever more activities in domains of everyday life are evaluated and experienced in terms of performance metrics. Unlike organized competitions, such systems are ceaseless and without formal entry. Instead of producing resolutions, their scorings create addictions. To understand these developments, this book explores discrete contests (architectural competitions, international music competitions, and world press photo competitions); shows how the continuous updating of rankings is both a device for navigating the social world and an engine of anxiety; and examines the production of such anxiety in settings ranging from the pedagogy of performance in business schools to struggling musicians coping with new performance metrics in online platforms. In the performance society, networks of observation—in which all are performing and keeping score—are entangled with a system of emotionally charged preoccupations with one’s positioning within the rankings. From the bedroom to the boardroom, pharmaceutical companies and management consultants promise enhanced performance. This assemblage of metrics, networks, and their attendant emotional pathologies is herein regarded as the performance complex.
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Golan, Amos. Prior Information. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199349524.003.0008.

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In this chapter I introduce and quantify prior information and show how to incorporate it into the info-metrics framework. The priors developed arise from fundamental properties of the system, from logical reasoning, or from empirical observations. I start the chapter with the derivation of priors for discrete distributions, which can be handled via the grouping property, and a detailed derivation of surprisal analysis. Constructing priors for continuous distributions is more challenging. That problem is tackled via the method of transformation groups, which is related to the mathematical concept of group theory. That method works for both discrete and continuous functions. The last approaches I discuss are based on empirical information. The close relationship between priors, treatment effects, and score functions is discussed and demonstrated in the last section. Visual illustrations of the theory and numerous theoretical and applied examples are provided.
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Book chapters on the topic "Discrete metric"

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Dribus, Benjamin F. "The Causal Metric Hypothesis." In Discrete Causal Theory, 65–135. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50083-6_2.

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Kapovich, Michael. "Ultralimits of Metric Spaces." In Hyperbolic Manifolds and Discrete Groups, 219–25. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4913-5_9.

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Rebatel, Fabien, and Édouard Thiel. "Metric Bases for Polyhedral Gauges." In Discrete Geometry for Computer Imagery, 116–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-19867-0_10.

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Goncharenko, Vasily, and Alexander Tuzikov. "Watershed Segmentation with Chamfer Metric." In Discrete Geometry for Computer Imagery, 518–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11907350_44.

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Deza, Antoine, Komei Fukuda, Dmitrii Pasechnik, and Masanori Sato. "On the Skeleton of the Metric Polytope." In Discrete and Computational Geometry, 125–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-47738-1_10.

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Saucan, Emil. "Metric Curvatures Revisited: A Brief Overview." In Modern Approaches to Discrete Curvature, 63–114. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58002-9_2.

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Hotz, Ingrid, and Hans Hagen. "Isometric Embedding for a Discrete Metric." In Geometric Modeling for Scientific Visualization, 19–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-07443-5_2.

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Deza, Antoine, Komei Fukuda, Tomohiko Mizutani, and Cong Vo. "On the Face Lattice of the Metric Polytope." In Discrete and Computational Geometry, 118–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-44400-8_12.

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Eklund, Patrik, and Fredrik Georgsson. "Unraveling the Thrill of Metric Image Spaces." In Discrete Geometry for Computer Imagery, 275–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-49126-0_21.

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Rebatel, Fabien, and Édouard Thiel. "On Dimension Partitions in Discrete Metric Spaces." In Discrete Geometry for Computer Imagery, 11–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-37067-0_2.

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Conference papers on the topic "Discrete metric"

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Maridas, Roswita Amalanathan, and B. Vijayalakshmi. "Discrete metric graphs." In PROCEEDINGS OF INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS RESEARCH (ICAMR - 2019). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0016907.

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Andrews, Matthew, Mohammad Taghi Hajiaghayi, Howard Karloff, and Ankur Moitra. "Capacitated Metric Labeling." In Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2011. http://dx.doi.org/10.1137/1.9781611973082.76.

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Sidiropoulos, Anastasios, Dingkang Wang, and Yusu Wang. "Metric embeddings with outliers." In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2017. http://dx.doi.org/10.1137/1.9781611974782.43.

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Indyk, Piotr, and Tal Wagner. "Near-Optimal (Euclidean) Metric Compression." In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2017. http://dx.doi.org/10.1137/1.9781611974782.45.

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Gomes, Viviane M., Joao R. B. Paiva, Geovanne P. Furriel, Bruno C. M. Aniceto, Lais F. A. Silva, Wesley P. Calixto, Elder G. Domingues, Gelson CRUZ JUNIOR, and Bernardo A. RODRIGUES. "COMPLEXITY METRIC APPLIED TO DISCRETE EVENTS SYSTEMS." In 6th International Conference on Nonlinear Science and Complexity. São José dos Campos, Brazil: INPE Instituto Nacional de Pesquisas Espaciais, 2016. http://dx.doi.org/10.20906/cps/nsc2016-0077.

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Lolakapuri, Phani Raj, Umang Bhaskar, Ramasuri Narayanam, Gyana R. Parija, and Pankaj S. Dayama. "Computational Aspects of Equilibria in Discrete Preference Games." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/67.

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Abstract:
We study the complexity of equilibrium computation in discrete preference games. These games were introduced by Chierichetti, Kleinberg, and Oren (EC '13, JCSS '18) to model decision-making by agents in a social network that choose a strategy from a finite, discrete set, balancing between their intrinsic preferences for the strategies and their desire to choose a strategy that is `similar' to their neighbours. There are thus two components: a social network with the agents as vertices, and a metric space of strategies. These games are potential games, and hence pure Nash equilibria exist. Since their introduction, a number of papers have studied various aspects of this model, including the social cost at equilibria, and arrival at a consensus. We show that in general, equilibrium computation in discrete preference games is PLS-complete, even in the simple case where each agent has a constant number of neighbours. If the edges in the social network are weighted, then the problem is PLS-complete even if each agent has a constant number of neighbours, the metric space has constant size, and every pair of strategies is at distance 1 or 2. Further, if the social network is directed, modelling asymmetric influence, an equilibrium may not even exist. On the positive side, we show that if the metric space is a tree metric, or is the product of path metrics, then the equilibrium can be computed in polynomial time.
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Kleinberg, Robert, and Aleksandrs Slivkins. "Sharp Dichotomies for Regret Minimization in Metric Spaces." In Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2010. http://dx.doi.org/10.1137/1.9781611973075.68.

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Huang, Zhiyi, and Aaron Roth. "Exploiting Metric Structure for Efficient Private Query Release." In Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2013. http://dx.doi.org/10.1137/1.9781611973402.39.

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Ekelschot, Dirk, Marco Ceze, Scott M. Murman, and Anirban Garai. "Parallel high-order anisotropic meshing using discrete metric tensors." In AIAA Scitech 2019 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2019. http://dx.doi.org/10.2514/6.2019-1993.

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Taira, K., J. Frankel, and M. Keyhani. "Metric analysis for the modified discrete least-squares method." In 40th AIAA Aerospace Sciences Meeting & Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2002. http://dx.doi.org/10.2514/6.2002-658.

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