Distances in Earth Science and Astronomy



In Geography, spatial scales are shorthand terms for distances, sizes and areas. For example, micro, meso, macro, mega may refer to local (0.001–1), regional (1–100), continental (100–10,000), global ( > 10,000) km, respectively.


Solar Wind Plume Height Virgo Cluster Volcanic Explosivity Index Space Syntax 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [Abel91]
    Abels H. The Gallery Distance of Flags, Order, Vol. 8, pp. 77–92, 1991.MathSciNetzbMATHGoogle Scholar
  2. [AAH00]
    Aichholzer O., Aurenhammer F. and Hurtado F. Edge Operations on Non–crossing Spanning Trees, Proc. 16–th European Workshop on Computational Geometry CG’2000, pp. 121–125, 2000.Google Scholar
  3. [AACLMP98]
    Aichholzer O., Aurenhammer F., Chen D.Z., Lee D.T., Mukhopadhyay A. and Papadopoulou E. Voronoi Diagrams for Direction–sensitive Distances, Proc. 13th Symposium on Computational Geometry, ACM Press, New York, 1997.Google Scholar
  4. [Aker97]
    Akerlof G.A. Social Distance and Social Decisions, Econometrica, Vol. 65–5, pp. 1005–1027, 1997.MathSciNetGoogle Scholar
  5. [Amar85]
    Amari S. Differential–geometrical Methods in Statistics, Lecture Notes in Statistics, Springer–Verlag, 1985.zbMATHGoogle Scholar
  6. [Amba76]
    Ambartzumian R. A Note on Pseudo–metrics on the Plane, Z. Wahrsch. Verw. Gebiete, Vol. 37, pp. 145–155, 1976.MathSciNetzbMATHGoogle Scholar
  7. [ArWe92]
    Arnold R. and Wellerding A. On the Sobolev Distance of Convex Bodies, Aeq. Math., Vol. 44, pp. 72–83, 1992.MathSciNetzbMATHGoogle Scholar
  8. [Badd92]
    Baddeley A.J. Errors in Binary Images and an L p Version of the Hausdorff Metric, Nieuw Archief voor Wiskunde, Vol. 10, pp. 157–183, 1992.MathSciNetzbMATHGoogle Scholar
  9. [BaFa07]
    Baier R. and Farkhi E. Regularity and Integration of Set–Valued Maps Represented by Generalized Steiner Points Set–Valued Analysis, Vol. 15, pp. 185–207, 2007.MathSciNetzbMATHGoogle Scholar
  10. [Bara01]
    Barabási A.L. The Physics of the Web, Physics World, July 2001.Google Scholar
  11. [Barb12]
    Barbaresco F. Information Geometry of Covariance Matrix: Cartan–Siegel Homogenous Bounded Domains, Mostow–Berger Fibration and Fréchet Median, in Matrix Information Geometry, Bhatia R. and Nielsen F. (eds.) Springer, 2012.Google Scholar
  12. [Barb35]
    Barbilian D. Einordnung von Lobayschewskys Massenbestimmung in either Gewissen Allgemeinen Metrik der Jordansche Bereiche, Casopis Mathematiky a Fysiky, Vol. 64, pp. 182–183, 1935.zbMATHGoogle Scholar
  13. [BLV05]
    Barceló C., Liberati S. and Visser M. Analogue Gravity, Living Rev. Rel. Vol. 8, 2005; arXiv: gr–qc/0505065, 2005.Google Scholar
  14. [BLMN05]
    Bartal Y., Linial N., Mendel M. and Naor A. Some Low Distortion Metric Ramsey Problems, Discrete and Computational Geometry, Vol. 33, pp. 27–41, 2005.MathSciNetzbMATHGoogle Scholar
  15. [Bass89]
    Basseville M. Distances measures for signal processing and pattern recognition, Signal Processing, Vol. 18, pp. 349–369, 1989.MathSciNetGoogle Scholar
  16. [Bass13]
    Basseville M. Distances measures for statistical data processing – An annotated bibliography, Signal Processing, Vol. 93, pp. 621–633, 2013.Google Scholar
  17. [Bata95]
    Batagelj V. Norms and Distances over Finite Groups, J. of Combinatorics, Information and System Sci., Vol. 20, pp. 243–252, 1995.Google Scholar
  18. [Beer99]
    Beer G. On Metric Boundedness Structures, Set–Valued Analysis, Vol. 7, pp. 195–208, 1999.MathSciNetzbMATHGoogle Scholar
  19. [BGLVZ98]
    Bennet C.H., Gács P., Li M., Vitánai P.M.B. and Zurek W. Information Distance, IEEE Transactions on Information Theory, Vol. 44–4, pp. 1407–1423, 1998.Google Scholar
  20. [BGT93]
    Berrou C., Glavieux A. and Thitimajshima P. Near Shannon Limit Error–correcting Coding and Decoding: Turbo–codes, Proc. of IEEE Int. Conf. on Communication, pp. 1064–1070, 1993.Google Scholar
  21. [BFK99]
    Blanchard F., Formenti E. and Kurka P. Cellular Automata in the Cantor, Besicovitch and Weyl Topological Spaces, Complex Systems, Vol. 11, pp. 107–123, 1999.MathSciNetGoogle Scholar
  22. [Bloc99]
    Bloch I. On fuzzy distances and their use in image processing under unprecision, Pattern Recognition, Vol. 32, pp. 1873–1895, 1999.Google Scholar
  23. [BCFS97]
    Block H.W., Chhetry D., Fang Z. and Sampson A.R. Metrics on Permutations Useful for Positive Dependence, J. of Statistical Planning and Inference, Vol. 62, pp. 219–234, 1997.MathSciNetzbMATHGoogle Scholar
  24. [Blum70]
    Blumenthal L.M. Theory and Applications of Distance Geometry, Chelsea Publ., New York, 1970.zbMATHGoogle Scholar
  25. [Borg86]
    Borgefors G. Distance Transformations in Digital Images, Comp. Vision, Graphic and Image Processing, Vol. 34, pp. 344–371, 1986.Google Scholar
  26. [BrLi04]
    Bramble D.M. and Lieberman D.E. Endurance Running and the Evolution of Homo, Nature, Vol. 432, pp. 345–352, 2004.Google Scholar
  27. [O’Bri03]
    O’Brien C. Minimization via the Subway metric, Honor Thesis, Dept. of Math., Ithaca College, New York, 2003.Google Scholar
  28. [BKMR00]
    Broder A.Z., Kumar S. R., Maaghoul F., Raghavan P., Rajagopalan S., Stata R., Tomkins A. and Wiener G. Graph Structure in the Web: Experiments and Models, Proc. 9–th WWW Conf., Amsterdam, 2000.Google Scholar
  29. [BGL95]
    Brualdi R.A., Graves J.S. and Lawrence K.M. Codes with a Poset Metric, Discrete Math., Vol. 147, pp. 57–72, 1995.MathSciNetzbMATHGoogle Scholar
  30. [Brya85]
    Bryant V. Metric Spaces: Iteration and Application, Cambridge Univ. Press, 1985.zbMATHGoogle Scholar
  31. [BuHa90]
    Buckley F. and Harary F. Distance in Graphs, Redwood City, CA: Addison–Wesley, 1990.zbMATHGoogle Scholar
  32. [Bull12]
    Bullough E. “Psychical Distance” as a Factor in Art and as an Aesthetic Principle, British J. of Psychology, Vol. 5, pp. 87–117, 1912.Google Scholar
  33. [BBI01]
    Burago D., Burago Y. and Ivanov S. A Course in Metric Geometry, Amer. Math. Soc., Graduate Studies in Math., Vol. 33, 2001.Google Scholar
  34. [BuKe53]
    Busemann H. and Kelly P.J. Projective Geometry and Projective Metrics, Academic Press, New York, 1953.zbMATHGoogle Scholar
  35. [Buse55]
    Busemann H. The Geometry of Geodesics, Academic Press, New York, 1955.zbMATHGoogle Scholar
  36. [BuPh87]
    Busemann H. and Phadke B.B. Spaces with Distinguished Geodesics, Marcel Dekker, New York, 1987.zbMATHGoogle Scholar
  37. [Cair01]
    Cairncross F. The Death of Distance 2.0: How the Communication Revolution will Change our Lives, Harvard Business School Press, second edition, 2001.Google Scholar
  38. [CSY01]
    Calude C.S., Salomaa K. and Yu S. Metric Lexical Analysis, Springer–Verlag, 2001.Google Scholar
  39. [CaTa08]
    Cameron P.J. and Tarzi S. Limits of cubes, Topology and its Appl., Vol. 155, pp. 1454–1461, 2008.MathSciNetzbMATHGoogle Scholar
  40. [CHKSS07]
    Carmi S., Havlin S., Kirkpatrick S., Shavitt Y. and Shir E. A model of internet topology using k–shell decomposition, Proc. Nat. Acad. Sci., Vol. 104, pp. 11150–11154, 2007.Google Scholar
  41. [Cha08]
    Cha S.–H. Taxonomy of nominal type histogram distance measures, Proc. American Conf. on Appl, Math., World Scientific and Engineering Academy and Society (WREAS) Stevens Point, Wisconsin, US, pp. 325–330, 2008.Google Scholar
  42. [ChLu85]
    Cheng Y.C. and Lu S.Y. Waveform Correlation by Tree Matching, IEEE Trans. Pattern Anal. Machine Intell., Vol. 7, pp. 299–305, 1985.Google Scholar
  43. [Chen72]
    Chentsov N.N. Statistical Decision Rules and Optimal Inferences, Nauka, Moscow, 1972.Google Scholar
  44. [ChFi98]
    Chepoi V. and Fichet B. A Note on Circular Decomposable Metrics, Geom. Dedicata, Vol. 69, pp. 237–240, 1998.MathSciNetzbMATHGoogle Scholar
  45. [ChSe00]
    Choi S.W. and Seidel H.–P. Hyperbolic Hausdorff Distance for Medial Axis Transform, Research Report MPI–I–2000–4–003 of Max–Planck–Institute für Informatik, 2000.Google Scholar
  46. [CLMNWZ05]
    Coifman R.R., Lafon S., A.B., Maggioni M., Nadler B., Warner F., Zucker S.W. Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps, Proc. of the National Academy of Sciences, Vol. 102, No. 21, pp. 7426–7431, 2005.Google Scholar
  47. [COR05]
    Collado M.D., Ortuno–Ortin I. and Romeu A. Vertical Transmission of Consumption Behavior and the Distribution of Surnames, mimeo, Universidad de Alicante, 2005.Google Scholar
  48. [Cops68]
    Copson E.T. Metric Spaces, Cambridge Univ. Press, 1968.zbMATHGoogle Scholar
  49. [Cora99]
    Corazza P. Introduction to metric–preserving functions, Amer. Math. Monthly, Vo. 104, pp. 309–323, 1999.Google Scholar
  50. [Corm03]
    Cormode G. Sequence Distance Embedding, PhD Thesis, Univ. of Warwick, 2003.Google Scholar
  51. [CPQ96]
    Critchlow D.E., Pearl D.K. and Qian C. The Triples Distance for Rooted Bifurcating Phylogenetic Trees, Syst. Biology, Vol. 45, pp. 323–334, 1996.Google Scholar
  52. [CCL01]
    Croft W. B., Cronon–Townsend S. and Lavrenko V. Relevance Feedback and Personalization: A Language Modeling Perspective, in DELOS–NSF Workshop on Personalization and Recommender Systems in Digital Libraries, pp. 49–54, 2001.Google Scholar
  53. [CKK03]
    Cuijpers R.H., Kappers A.M.L and Koenderink J.J. The metrics of visual and haptic space based on parallelity judgements, J. Math. Psychology, Vol. 47, pp. 278–291, 2003.MathSciNetzbMATHGoogle Scholar
  54. [DaCh88]
    Das P.P. and Chatterji B.N. Knight’s Distance in Digital Geometry, Pattern Recognition Letters, Vol. 7, pp. 215–226, 1988.zbMATHGoogle Scholar
  55. [Das90]
    Das P.P. Lattice of Octagonal Distances in Digital Geometry, Pattern Recognition Letters, Vol. 11, pp. 663–667, 1990.zbMATHGoogle Scholar
  56. [DaMu90]
    Das P.P. and Mukherjee J. Metricity of Super–knight’s Distance in Digital Geometry, Pattern Recognition Letters, Vol. 11, pp. 601–604, 1990.zbMATHGoogle Scholar
  57. [Dau05]
    Dauphas N. The U/Th Production Ratio and the Age of the Milky Way from Meteorites and Galactic Halo Stars, Nature, Vol. 435, pp. 1203–1205, 2005.Google Scholar
  58. [Day81]
    Day W.H.E. The Complexity of Computing Metric Distances between Partitions, Math. Social Sci., Vol. 1, pp. 269–287, 1981.zbMATHGoogle Scholar
  59. [DeDu13]
    Deza M.M. and Dutour M. Voronoi Polytopes for Polyhedral Norms on Lattices, arXiv:1401.0040 [math.MG], 2013.Google Scholar
  60. [DeDu03]
    Deza M.M. and Dutour M. Cones of Metrics, Hemi–metrics and Super–metrics, Ann. of European Academy of Sci., pp. 141–162, 2003.Google Scholar
  61. [DeHu98]
    Deza M. and Huang T. Metrics on Permutations, a Survey, J. of Combinatorics, Information and System Sci., Vol. 23, Nrs. 1–4, pp. 173–185, 1998.Google Scholar
  62. [DeLa97]
    Deza M.M. and Laurent M. Geometry of Cuts and Metrics, Springer, 1997.Google Scholar
  63. [DPM12]
    Deza M.M., Petitjean M. and Matkov K. (eds) Mathematics of Distances and Applications, ITHEA, Sofia, 2012.Google Scholar
  64. [DiGa07]
    Ding L. and Gao S. Graev metric groups and Polishable subgroups, Advances in Mathematics, Vol. 213, pp. 887–901, 2007.MathSciNetzbMATHGoogle Scholar
  65. [EhHa88]
    Ehrenfeucht A. and Haussler D. A New Distance Metric on Strings Computable in Linear Time, Discrete Appl. Math., Vol. 20, pp. 191–203, 1988.MathSciNetzbMATHGoogle Scholar
  66. [EM98]
    Encyclopedia of Math., Hazewinkel M. (ed.), Kluwer Academic Publ., 1998. Online edition:
  67. [Ernv85]
    Ernvall S. On the Modular Distance, IEEE Trans. Inf. Theory, Vol. 31–4, pp. 521–522, 1985.MathSciNetGoogle Scholar
  68. [EMM85]
    Estabrook G.F., McMorris F.R. and Meacham C.A. Comparison of Undirected Phylogenetic Trees Based on Subtrees of Four Evolutionary Units, Syst. Zool, Vol. 34, pp. 193–200, 1985.Google Scholar
  69. [FaMu03]
    Farrán J.N. and Munuera C. Goppa–like Bounds for the Generalized Feng–Rao Distances, Discrete Appl. Math., Vol. 128, pp. 145–156, 2003.MathSciNetzbMATHGoogle Scholar
  70. [Faze99]
    Fazekas A. Lattice of Distances Based on 3D–neighborhood Sequences, Acta Math. Academiae Paedagogicae Nyiregyháziensis, Vol. 15, pp. 55–60, 1999.MathSciNetzbMATHGoogle Scholar
  71. [FeWa08]
    Feng J. and Wang T.M. Characterization of protein primary sequences based on partial ordering, J. Theor. Biology, Vol. 254, pp. 752–755, 2008.Google Scholar
  72. [Fell97]
    Fellous J–M. Gender Discrimination and Prediction on the Basis of Facial Metric Information, Vision Research, Vol. 37, pp. 1961–1973, 1997.Google Scholar
  73. [Ferg03]
    Ferguson N. Empire: The Rise and Demise of the British World Order and Lessons for Global Power, Basic Books, 2003.Google Scholar
  74. [FoSc06]
    Foertsch T. and Schroeder V. Hyperbolicity, CAT( − 1)–spaces and the Ptolemy Inequality, Math. Ann., Vol. 350, pp. 339–356, 2011.MathSciNetzbMATHGoogle Scholar
  75. [FrSa07]
    Frankild A. and Sather–Wagstaff S. The set of semidualizing complexes is a nontrivial metric space, J. Algebra, Vol. 308, pp. 124–143, 2007.MathSciNetzbMATHGoogle Scholar
  76. [Frie98]
    Frieden B.R. Physics from Fisher information, Cambridge Univ. Press, 1998.Google Scholar
  77. [GaSi98]
    Gabidulin E.M. and Simonis J. Metrics Generated by Families of Subspaces, IEEE Transactions on Information Theory, Vol. 44–3, pp. 1136–1141, 1998.MathSciNetGoogle Scholar
  78. [Gile87]
    Giles J.R. Introduction to the Analysis of Metric Spaces, Australian Math. Soc. Lecture Series, Cambridge Univ. Press, 1987.Google Scholar
  79. [GoMc80]
    Godsil C.D. and McKay B.D. The Dimension of a Graph, Quart. J. Math. Oxford Series (2), Vol. 31, pp. 423–427, 1980.Google Scholar
  80. [GOJKK02]
    Goh K.I., Oh E.S., Jeong H., Kahng B. and Kim D. Classification of Scale Free Networks, Proc. Nat. Acad. Sci. US, Vol. 99, pp. 12583–12588, 2002.MathSciNetzbMATHGoogle Scholar
  81. [Gopp71]
    Goppa V.D. Rational Representation of Codes and (L,g)–codes, Probl. Peredachi Inform., Vol. 7–3, pp. 41–49, 1971.MathSciNetGoogle Scholar
  82. [Goto82]
    Gotoh O. An Improved Algorithm for Matching Biological Sequences, J. of Molecular Biology, Vol. 162, pp. 705–708, 1982.Google Scholar
  83. [GKC04]
    Grabowski R., Khosa P. and Choset H. Development and Deployment of a Line of Sight Virtual Sensor for Heterogeneous Teams, Proc. IEEE Int. Conf. on Robotics and Automation, New Orleans, 2004.Google Scholar
  84. [Grub93]
    Gruber P.M. The space of Convex Bodies in Handbook of Convex Geometry, Gruber P.M. and Wills J.M. (eds.), Elsevier Sci. Publ., 1993.Google Scholar
  85. [HSEFN95]
    Hafner J., Sawhney H.S., Equitz W., Flickner M. and Niblack W. Efficient Color Histogram Indexing for Quadratic Form Distance Functions, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 17–7, pp. 729–736, 1995.Google Scholar
  86. [Hall69]
    Hall E.T. The Hidden Dimension, Anchor Books, New York, 1969.Google Scholar
  87. [Hami66]
    Hamilton W.R. Elements of Quaternions, second edition 1899–1901 enlarged by C.J. Joly, reprinted by Chelsea Publ., New York, 1969.Google Scholar
  88. [HRJM13]
    Harispe S., Ranwez S., Janaqi S. and Montmain J. Semantic Measures for the Comparison of Units of Language, Concepts or Instances from Text and Knowledge Base Analysis, arXiv:1310.1285[cs.CL], 2013.Google Scholar
  89. [HeMa02]
    Head K. and Mayer T. Illusory Border Effects: Distance mismeasurement inflates estimates of home bias in trade, CEPII Working Paper No 2002–01, 2002.Google Scholar
  90. [Hemm02]
    Hemmerling A. Effective Metric Spaces and Representations of the Reals, Theoretical Comp. Sci., Vol. 284–2, pp. 347–372, 2002.MathSciNetGoogle Scholar
  91. [High89]
    Higham N.J. Matrix Nearness Problems and Applications, in Applications of Matrix Theory, Gover M.J.C. and Barnett S. (eds.), pp. 1–27. Oxford University Press, 1989.Google Scholar
  92. [Hofs80]
    Hofstede G. Culture’s Consequences: International Differences in Work–related Values, Sage Publ., California, 1980.Google Scholar
  93. [Hube94a]
    Huber K. Codes over Gaussian Integers, IEEE Trans. Inf. Theory, Vol. 40–1, pp. 207–216, 1994.Google Scholar
  94. [Hube94b]
    Huber K. Codes over Eisenstein–Jacobi Integers, Contemporary Math., Vol. 168, pp. 165–179, 1994.Google Scholar
  95. [HFPMC02]
    Huffaker B., Fomenkov M., Plummer D.J., Moore D. and Claffy K., Distance Metrics in the Internet, Proc. IEEE Int. Telecomm. Symp. (ITS–2002), 2002.Google Scholar
  96. [InVe00]
    Indyk P. and Venkatasubramanian S. Approximate Congruence in Nearly Linear Time, Proc. 11th ACM–SIAM symposium on Discrete Algorithms, pp. 354–260, San Francisco, 2000.Google Scholar
  97. [Isbe64]
    Isbell J. Six Theorems about Metric Spaces, Comment. Math. Helv., Vol. 39, pp. 65–74, 1964.MathSciNetzbMATHGoogle Scholar
  98. [IKP90]
    Isham C.J., Kubyshin Y. and Penteln P. Quantum Norm Theory and the Quantization of Metric Topology, Class. Quantum Gravity, Vol. 7, pp. 1053–1074, 1990.zbMATHGoogle Scholar
  99. [IvSt95]
    Ivanova R. and Stanilov G. A Skew–symmetric Curvature Operator in Riemannian Geometry, in Symposia Gaussiana, Conf. A, Behara M., Fritsch R. and Lintz R. (eds.), pp. 391–395, 1995.Google Scholar
  100. [JWZ94]
    Jiang T., Wang L. and Zhang K. Alignment of Trees – an Alternative to Tree Edit, in Combinatorial Pattern Matching, Lecture Notes in Comp. Science, Vol. 807, Crochemore M. and Gusfield D. (eds.), Springer–Verlag, 1994.Google Scholar
  101. [Klei88]
    Klein R. Voronoi Diagrams in the Moscow Metric, Graphtheoretic Concepts in Comp. Sci., Vol. 6, pp. 434–441, 1988.Google Scholar
  102. [Klei89]
    Klein R. Concrete and Abstract Voronoi Diagrams, Lecture Notes in Comp. Sci., Springer–Verlag, 1989.zbMATHGoogle Scholar
  103. [KlRa93]
    Klein D.J. and Randic M. Resistance distance, J. of Math. Chemistry, Vol. 12, pp. 81–95, 1993.MathSciNetGoogle Scholar
  104. [Koel00]
    Koella J.C. The Spatial Spread of Altruism Versus the Evolutionary Response of Egoists, Proc. Royal Soc. London, Series B, Vol. 267, pp. 1979–1985, 2000.Google Scholar
  105. [KoSi88]
    Kogut B. and Singh H. The Effect of National Culture on the Choice of Entry Mode, J. of Int. Business Studies, Vol. 19–3, pp. 411–432, 1988.Google Scholar
  106. [KKN02]
    Kosheleva O., Kreinovich V. and Nguyen H.T. On the Optimal Choice of Quality Metric in Image Compression, Fifth IEEE Southwest Symposium on Image Analysis and Interpretation, 7–9 April 2002, Santa Fe, IEEE Comp. Soc. Digital Library, Electronic edition, pp. 116–120, 2002.Google Scholar
  107. [LaLi81]
    Larson R.C. and Li V.O.K. Finding Minimum Rectilinear Distance Paths in the Presence of Barriers, Networks, Vol. 11, pp. 285–304, 1981.MathSciNetzbMATHGoogle Scholar
  108. [LCLMV04]
    Li M., Chen X., Li X., Ma B. and Vitányi P. The Similarity Metric, IEEE Trans. Inf. Theory, Vol. 50–12, pp. 3250–3264, 2004.Google Scholar
  109. [LuRo76]
    Luczak E. and Rosenfeld A. Distance on a Hexagonal Grid, IEEE Trans. on Comp., Vol. 25–5, pp. 532–533, 1976.Google Scholar
  110. [MaMo95]
    Mak King–Tim and Morton A.J. Distances between Traveling Salesman Tours, Discrete Appl. Math., Vol. 58, pp. 281–291, 1995.Google Scholar
  111. [Mart00]
    Martin K. A foundation for computation, Ph.D. Thesis, Tulane University, Department of Math., 2000.Google Scholar
  112. [MaSt99]
    Martin W.J. and Stinson D.R. Association Schemes for Ordered Orthogonal Arrays and (T, M, S)–nets, Can. J. Math., Vol. 51, pp. 326–346, 1999.MathSciNetzbMATHGoogle Scholar
  113. [Masc04]
    Mascioni V. Equilateral Triangles in Finite Metric Spaces, The Electronic J. Combinatorics, Vol. 11, 2004, R18.Google Scholar
  114. [Matt92]
    S.G. Matthews, Partial metric topology, Research Report 212, Dept. of Comp. Science, University of Warwick, 1992.Google Scholar
  115. [McCa97]
    McCanna J.E. Multiply–sure Distances in Graphs, Congressus Numerantium, Vol. 97, pp. 71–81, 1997.MathSciNetGoogle Scholar
  116. [Melt91]
    Melter R.A. A Survey of Digital Metrics, Contemporary Math., Vol. 119, 1991.Google Scholar
  117. [Monj98]
    Monjardet B. On the Comparison of the Spearman and Kendall Metrics between Linear Orders, Discrete Math., Vol. 192, pp. 281–292, 1998.MathSciNetzbMATHGoogle Scholar
  118. [Morg76]
    Morgan J.H. Pastoral ecstasy and the authentic self: Theological meanings in symbolic distance, Pastoral Psychology, Vol. 25–2, pp. 128–137, 1976.Google Scholar
  119. [MLLM13]
    Mucherino A., Lavor C., Liberti L. and Maculan N. (eds.) Distance Geometry, Springer, 2013.Google Scholar
  120. [Mura85]
    Murakami H. Some Metrics on Classical Knots, Math. Ann., Vol. 270, pp. 35–45, 1985.MathSciNetzbMATHGoogle Scholar
  121. [NeWu70]
    Needleman S.B. and Wunsh S.D. A general Method Applicable to the Search of the Similarities in the Amino Acids Sequences of Two Proteins, J. of Molecular Biology, Vol. 48, pp. 443–453, 1970.Google Scholar
  122. [NiSu03]
    Nishida T. and Sugihara K. FEM–like Fast Marching Method for the Computation of the Boat–Sail Distance and the Associated Voronoi Diagram, Technical Reports, METR 2003–45, Dept. Math. Informatics, The University of Tokyo, 2003.Google Scholar
  123. [OBS92]
    Okabe A., Boots B. and Sugihara K. Spatial Tessellation: Concepts and Applications of Voronoi Diagrams, Wiley, 1992.Google Scholar
  124. [OkBi08]
    Okada D. and M. Bingham P.M. Human uniqueness–self–interest and social cooperation, J. Theor. Biology, Vol. 253–2, pp. 261–270, 2008.Google Scholar
  125. [OSLM04]
    Oliva D., Samengo I., Leutgeb S. and Mizumori S. A Subjective Distance between Stimuli: Quantifying the Metric Structure of Representations, Neural Computation, Vol. 17–4, pp. 969–990, 2005.Google Scholar
  126. [OnGi96]
    Ong C.J. and Gilbert E.G. Growth distances: new measures for object separation and penetration, IEEE Transactions in Robotics and Automation, Vol. 12–6, pp. 888–903, 1996.Google Scholar
  127. [Ophi14]
    Ophir A. and Pinchasi R. Nearly equal distances in metric spaces, Discrete Appl. Math., Vol. 174, pp. 122–127, 2014.MathSciNetzbMATHGoogle Scholar
  128. [Orli32]
    Orlicz W. Über eine Gewisse Klasse von Raumen vom Typus B , Bull. Int. Acad. Pol. Series A, Vol. 8–9, pp. 207–220, 1932.Google Scholar
  129. [OASM03]
    Ozer H., Avcibas I., Sankur B. and Memon N.D. Steganalysis of Audio Based on Audio Quality Metrics, Security and Watermarking of Multimedia Contents V (Proc. of SPIEIS and T), Vol. 5020, pp. 55–66, 2003.Google Scholar
  130. [Page65]
    Page E.S. On Monte–Carlo Methods in Congestion Problem. 1. Searching for an Optimum in Discrete Situations, J. Oper. Res., Vol. 13–2, pp. 291–299, 1965.Google Scholar
  131. [Petz96]
    Petz D. Monotone Metrics on Matrix Spaces, Linear Algebra Appl., Vol. 244, 1996.Google Scholar
  132. [PM]
  133. [Rach91]
    Rachev S.T. Probability Metrics and the Stability of Stochastic Models, Wiley, New York, 1991.zbMATHGoogle Scholar
  134. [ReRo01]
    Requardt M. and Roy S. Quantum Spacetime as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces, Class. Quantum Gravity, Vol. 18, pp. 3039–3057, 2001.MathSciNetzbMATHGoogle Scholar
  135. [Resn74]
    Resnikoff H.I. On the geometry of color perception, AMS Lectures on Math. in the Life Sciences, Vol. 7, pp. 217–232, 1974.MathSciNetGoogle Scholar
  136. [RiYi98]
    Ristad E. and Yianilos P. Learning String Edit Distance, IEEE Transactions on Pattern Recognition and Machine Intelligence, Vol. 20–5, pp. 522–532, 1998.Google Scholar
  137. [RRHD10]
    Rocher T., Robine M., Hanna P. and Desainte–Catherine M. A Survey of Chord Distances With Comparison for Chord Analysis, Proc. Int. Comp. Music Conf., pp. 187–190, New York, 2010.Google Scholar
  138. [RoPf68]
    Rosenfeld A. and Pfaltz J. Distance Functions on Digital Pictures, Pattern Recognition, Vol. 1, pp. 33–61, 1968.MathSciNetGoogle Scholar
  139. [RTG00]
    Rubner Y., Tomasi C. and Guibas L.J. The Earth Mover’s Distance as a Metric for Image Retrieval, Int. J. of Comp. Vision, Vol. 40–2, pp. 99–121, 2000.Google Scholar
  140. [Rumm76]
    Rummel R.J. Understanding Conflict and War, Sage Publ., California, 1976.Google Scholar
  141. [ScSk83]
    Schweizer B. and Sklar A. Probabilistic Metric Spaces, North–Holland, 1983.Google Scholar
  142. [Selk77]
    Selkow S.M. The Tree–to–tree Editing Problem, Inform. Process. Lett., Vol. 6–6, pp. 184–186, 1977.MathSciNetGoogle Scholar
  143. [ShKa79]
    Sharma B.D. and Kaushik M.L. Limits intensity random and burst error codes with class weight considerations, Elektron. Inform.–verarb. Kybernetik, Vol. 15, pp. 315–321, 1979.MathSciNetzbMATHGoogle Scholar
  144. [Tai79]
    Tai K.–C. The Tree–to–tree Correction Problem, J. of the Association for Comp. Machinery, Vol. 26, pp. 422–433, 1979.MathSciNetzbMATHGoogle Scholar
  145. [Tail04]
    Tailor B. Introduction: How Far, How Near: Distance and Proximity in the Historical Imagination, History Workshop J., Vol. 57, pp. 117–122, 2004.Google Scholar
  146. [Tymo06]
    Tymoczko D. The Geometry of Musical Chords, Science, Vol. 313, Nr. 5783, pp. 72–74, 2006.Google Scholar
  147. [ToSa73]
    Tomimatsu A. and Sato H. New Exact Solution for the Gravitational Field of a Spinning Mass, Phys. Rev. Letters, Vol. 29, pp. 1344–1345, 1972.Google Scholar
  148. [Vard04]
    Vardi Y. Metrics Useful in Network Tomography Studies, Signal Processing Letters, Vol. 11–3, pp. 353–355, 2004.Google Scholar
  149. [VeHa01]
    Veltkamp R.C. and Hagendoorn M. State–of–the–Art in Shape Matching, in Principles of Visual Information Retrieval, Lew M. (ed.), pp. 87–119, Springer–Verlag, 2001.Google Scholar
  150. [Watt99]
    Watts D.J. Small Worlds: The Dynamics of Networks between Order and Randomness, Princeton Univ. Press, 1999.Google Scholar
  151. [Wein72]
    Weinberg S. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York, 1972.Google Scholar
  152. [Weis99]
    Weisstein E.W. CRC Concise Encyclopedia of Math., CRC Press, 1999.Google Scholar
  153. [Weis12]
    Weiss I. Metric 1–spaces, arXiv:1201.3980[math.MG], 2012.Google Scholar
  154. [Well86]
    Wellens R.A. Use of a Psychological Model to Assess Differences in Telecommunication Media, in Teleconferencing and Electronic Communication, Parker L.A. and Olgren O.H. (eds.), pp. 347–361, Univ. of Wisconsin Extension, 1986.Google Scholar
  155. [WFE]
    Wikipedia, the Free Encyclopedia,
  156. [WiMa97]
    Wilson D.R. and Martinez T.R. Improved Heterogeneous Distance Functions, J. of Artificial Intelligence Research, Vol. 6, p. 134, 1997.MathSciNetGoogle Scholar
  157. [WoPi99]
    Wolf S. and Pinson M.H. Spatial–Temporal Distortion Metrics for In–Service Quality Monitoring of Any Digital Video System, Proc. of SPIE Int. Symp. on Voice, Video, and Data Commun., September 1999.Google Scholar
  158. [Yian91]
    Yianilos P.N. Normalized Forms for Two Common Metrics, NEC Research Institute, Report 91–082–9027–1, 1991.Google Scholar
  159. [Youn98]
    Young N. Some Function–Theoretic Issues in Feedback Stabilisation, Holomorphic Spaces, MSRI Publication, Vol. 33, 1998.Google Scholar
  160. [YOI03]
    Yutaka M., Ohsawa Y. and Ishizuka M. Average–Clicks: A New Measure of Distance on the World Wide Web, J. Intelligent Information Systems, Vol. 20–1, pp. 51–62, 2003.Google Scholar
  161. [Zeli75]
    Zelinka B. On a Certain Distance between Isomorphism Classes of Graphs, Casopus. Pest. Mat., Vol. 100, pp. 371–373, 1975.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Ecole Normale SupérieureParisFrance
  2. 2.Moscow State Pedagogical UniversityMoscowRussia

Personalised recommendations