Skip to main content

Distances in Earth Science and Astronomy

  • 1550 Accesses

Abstract

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.

Keywords

  • 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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-662-44342-2_25
  • Chapter length: 40 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-3-662-44342-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   149.00
Price excludes VAT (USA)

References

  1. Abels H. The Gallery Distance of Flags, Order, Vol. 8, pp. 77–92, 1991.

    MathSciNet  MATH  Google Scholar 

  2. 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. 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. Akerlof G.A. Social Distance and Social Decisions, Econometrica, Vol. 65–5, pp. 1005–1027, 1997.

    MathSciNet  Google Scholar 

  5. Amari S. Differential–geometrical Methods in Statistics, Lecture Notes in Statistics, Springer–Verlag, 1985.

    MATH  Google Scholar 

  6. Ambartzumian R. A Note on Pseudo–metrics on the Plane, Z. Wahrsch. Verw. Gebiete, Vol. 37, pp. 145–155, 1976.

    MathSciNet  MATH  Google Scholar 

  7. Arnold R. and Wellerding A. On the Sobolev Distance of Convex Bodies, Aeq. Math., Vol. 44, pp. 72–83, 1992.

    MathSciNet  MATH  Google Scholar 

  8. 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.

    MathSciNet  MATH  Google Scholar 

  9. 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.

    MathSciNet  MATH  Google Scholar 

  10. Barabási A.L. The Physics of the Web, Physics World, July 2001.

    Google Scholar 

  11. 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. Barbilian D. Einordnung von Lobayschewskys Massenbestimmung in either Gewissen Allgemeinen Metrik der Jordansche Bereiche, Casopis Mathematiky a Fysiky, Vol. 64, pp. 182–183, 1935.

    MATH  Google Scholar 

  13. Barceló C., Liberati S. and Visser M. Analogue Gravity, Living Rev. Rel. Vol. 8, 2005; arXiv: gr–qc/0505065, 2005.

    Google Scholar 

  14. 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.

    MathSciNet  MATH  Google Scholar 

  15. Basseville M. Distances measures for signal processing and pattern recognition, Signal Processing, Vol. 18, pp. 349–369, 1989.

    MathSciNet  Google Scholar 

  16. Basseville M. Distances measures for statistical data processing – An annotated bibliography, Signal Processing, Vol. 93, pp. 621–633, 2013.

    Google Scholar 

  17. Batagelj V. Norms and Distances over Finite Groups, J. of Combinatorics, Information and System Sci., Vol. 20, pp. 243–252, 1995.

    Google Scholar 

  18. Beer G. On Metric Boundedness Structures, Set–Valued Analysis, Vol. 7, pp. 195–208, 1999.

    MathSciNet  MATH  Google Scholar 

  19. 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. 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. 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.

    MathSciNet  Google Scholar 

  22. Bloch I. On fuzzy distances and their use in image processing under unprecision, Pattern Recognition, Vol. 32, pp. 1873–1895, 1999.

    Google Scholar 

  23. 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.

    MathSciNet  MATH  Google Scholar 

  24. Blumenthal L.M. Theory and Applications of Distance Geometry, Chelsea Publ., New York, 1970.

    MATH  Google Scholar 

  25. Borgefors G. Distance Transformations in Digital Images, Comp. Vision, Graphic and Image Processing, Vol. 34, pp. 344–371, 1986.

    Google Scholar 

  26. 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’Brien C. Minimization via the Subway metric, Honor Thesis, Dept. of Math., Ithaca College, New York, 2003.

    Google Scholar 

  28. 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. Brualdi R.A., Graves J.S. and Lawrence K.M. Codes with a Poset Metric, Discrete Math., Vol. 147, pp. 57–72, 1995.

    MathSciNet  MATH  Google Scholar 

  30. Bryant V. Metric Spaces: Iteration and Application, Cambridge Univ. Press, 1985.

    MATH  Google Scholar 

  31. Buckley F. and Harary F. Distance in Graphs, Redwood City, CA: Addison–Wesley, 1990.

    MATH  Google Scholar 

  32. 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. 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. Busemann H. and Kelly P.J. Projective Geometry and Projective Metrics, Academic Press, New York, 1953.

    MATH  Google Scholar 

  35. Busemann H. The Geometry of Geodesics, Academic Press, New York, 1955.

    MATH  Google Scholar 

  36. Busemann H. and Phadke B.B. Spaces with Distinguished Geodesics, Marcel Dekker, New York, 1987.

    MATH  Google Scholar 

  37. 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. Calude C.S., Salomaa K. and Yu S. Metric Lexical Analysis, Springer–Verlag, 2001.

    Google Scholar 

  39. Cameron P.J. and Tarzi S. Limits of cubes, Topology and its Appl., Vol. 155, pp. 1454–1461, 2008.

    MathSciNet  MATH  Google Scholar 

  40. 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. 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. 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. Chentsov N.N. Statistical Decision Rules and Optimal Inferences, Nauka, Moscow, 1972.

    Google Scholar 

  44. Chepoi V. and Fichet B. A Note on Circular Decomposable Metrics, Geom. Dedicata, Vol. 69, pp. 237–240, 1998.

    MathSciNet  MATH  Google Scholar 

  45. 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. 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. 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. Copson E.T. Metric Spaces, Cambridge Univ. Press, 1968.

    MATH  Google Scholar 

  49. Corazza P. Introduction to metric–preserving functions, Amer. Math. Monthly, Vo. 104, pp. 309–323, 1999.

    Google Scholar 

  50. Cormode G. Sequence Distance Embedding, PhD Thesis, Univ. of Warwick, 2003.

    Google Scholar 

  51. 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. 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. 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.

    MathSciNet  MATH  Google Scholar 

  54. Das P.P. and Chatterji B.N. Knight’s Distance in Digital Geometry, Pattern Recognition Letters, Vol. 7, pp. 215–226, 1988.

    MATH  Google Scholar 

  55. Das P.P. Lattice of Octagonal Distances in Digital Geometry, Pattern Recognition Letters, Vol. 11, pp. 663–667, 1990.

    MATH  Google Scholar 

  56. Das P.P. and Mukherjee J. Metricity of Super–knight’s Distance in Digital Geometry, Pattern Recognition Letters, Vol. 11, pp. 601–604, 1990.

    MATH  Google Scholar 

  57. 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. Day W.H.E. The Complexity of Computing Metric Distances between Partitions, Math. Social Sci., Vol. 1, pp. 269–287, 1981.

    MATH  Google Scholar 

  59. Deza M.M. and Dutour M. Voronoi Polytopes for Polyhedral Norms on Lattices, arXiv:1401.0040 [math.MG], 2013.

    Google Scholar 

  60. 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. 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. Deza M.M. and Laurent M. Geometry of Cuts and Metrics, Springer, 1997.

    Google Scholar 

  63. Deza M.M., Petitjean M. and Matkov K. (eds) Mathematics of Distances and Applications, ITHEA, Sofia, 2012.

    Google Scholar 

  64. Ding L. and Gao S. Graev metric groups and Polishable subgroups, Advances in Mathematics, Vol. 213, pp. 887–901, 2007.

    MathSciNet  MATH  Google Scholar 

  65. Ehrenfeucht A. and Haussler D. A New Distance Metric on Strings Computable in Linear Time, Discrete Appl. Math., Vol. 20, pp. 191–203, 1988.

    MathSciNet  MATH  Google Scholar 

  66. Encyclopedia of Math., Hazewinkel M. (ed.), Kluwer Academic Publ., 1998. Online edition: http://eom.springer.de/default.htm

  67. Ernvall S. On the Modular Distance, IEEE Trans. Inf. Theory, Vol. 31–4, pp. 521–522, 1985.

    MathSciNet  Google Scholar 

  68. 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. Farrán J.N. and Munuera C. Goppa–like Bounds for the Generalized Feng–Rao Distances, Discrete Appl. Math., Vol. 128, pp. 145–156, 2003.

    MathSciNet  MATH  Google Scholar 

  70. Fazekas A. Lattice of Distances Based on 3D–neighborhood Sequences, Acta Math. Academiae Paedagogicae Nyiregyháziensis, Vol. 15, pp. 55–60, 1999.

    MathSciNet  MATH  Google Scholar 

  71. 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. 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. Ferguson N. Empire: The Rise and Demise of the British World Order and Lessons for Global Power, Basic Books, 2003.

    Google Scholar 

  74. Foertsch T. and Schroeder V. Hyperbolicity, CAT( − 1)–spaces and the Ptolemy Inequality, Math. Ann., Vol. 350, pp. 339–356, 2011.

    MathSciNet  MATH  Google Scholar 

  75. Frankild A. and Sather–Wagstaff S. The set of semidualizing complexes is a nontrivial metric space, J. Algebra, Vol. 308, pp. 124–143, 2007.

    MathSciNet  MATH  Google Scholar 

  76. Frieden B.R. Physics from Fisher information, Cambridge Univ. Press, 1998.

    Google Scholar 

  77. Gabidulin E.M. and Simonis J. Metrics Generated by Families of Subspaces, IEEE Transactions on Information Theory, Vol. 44–3, pp. 1136–1141, 1998.

    MathSciNet  Google Scholar 

  78. Giles J.R. Introduction to the Analysis of Metric Spaces, Australian Math. Soc. Lecture Series, Cambridge Univ. Press, 1987.

    Google Scholar 

  79. 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. 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.

    MathSciNet  MATH  Google Scholar 

  81. Goppa V.D. Rational Representation of Codes and (L,g)–codes, Probl. Peredachi Inform., Vol. 7–3, pp. 41–49, 1971.

    MathSciNet  Google Scholar 

  82. Gotoh O. An Improved Algorithm for Matching Biological Sequences, J. of Molecular Biology, Vol. 162, pp. 705–708, 1982.

    Google Scholar 

  83. 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. 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. 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. Hall E.T. The Hidden Dimension, Anchor Books, New York, 1969.

    Google Scholar 

  87. 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. 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. 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. Hemmerling A. Effective Metric Spaces and Representations of the Reals, Theoretical Comp. Sci., Vol. 284–2, pp. 347–372, 2002.

    MathSciNet  Google Scholar 

  91. 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. Hofstede G. Culture’s Consequences: International Differences in Work–related Values, Sage Publ., California, 1980.

    Google Scholar 

  93. Huber K. Codes over Gaussian Integers, IEEE Trans. Inf. Theory, Vol. 40–1, pp. 207–216, 1994.

    Google Scholar 

  94. Huber K. Codes over Eisenstein–Jacobi Integers, Contemporary Math., Vol. 168, pp. 165–179, 1994.

    Google Scholar 

  95. 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. 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. Isbell J. Six Theorems about Metric Spaces, Comment. Math. Helv., Vol. 39, pp. 65–74, 1964.

    MathSciNet  MATH  Google Scholar 

  98. 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.

    MATH  Google Scholar 

  99. 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. 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. Klein R. Voronoi Diagrams in the Moscow Metric, Graphtheoretic Concepts in Comp. Sci., Vol. 6, pp. 434–441, 1988.

    Google Scholar 

  102. Klein R. Concrete and Abstract Voronoi Diagrams, Lecture Notes in Comp. Sci., Springer–Verlag, 1989.

    MATH  Google Scholar 

  103. Klein D.J. and Randic M. Resistance distance, J. of Math. Chemistry, Vol. 12, pp. 81–95, 1993.

    MathSciNet  Google Scholar 

  104. 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. 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. 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. 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.

    MathSciNet  MATH  Google Scholar 

  108. 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. Luczak E. and Rosenfeld A. Distance on a Hexagonal Grid, IEEE Trans. on Comp., Vol. 25–5, pp. 532–533, 1976.

    Google Scholar 

  110. Mak King–Tim and Morton A.J. Distances between Traveling Salesman Tours, Discrete Appl. Math., Vol. 58, pp. 281–291, 1995.

    Google Scholar 

  111. Martin K. A foundation for computation, Ph.D. Thesis, Tulane University, Department of Math., 2000.

    Google Scholar 

  112. 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.

    MathSciNet  MATH  Google Scholar 

  113. Mascioni V. Equilateral Triangles in Finite Metric Spaces, The Electronic J. Combinatorics, Vol. 11, 2004, R18.

    Google Scholar 

  114. S.G. Matthews, Partial metric topology, Research Report 212, Dept. of Comp. Science, University of Warwick, 1992.

    Google Scholar 

  115. McCanna J.E. Multiply–sure Distances in Graphs, Congressus Numerantium, Vol. 97, pp. 71–81, 1997.

    MathSciNet  Google Scholar 

  116. Melter R.A. A Survey of Digital Metrics, Contemporary Math., Vol. 119, 1991.

    Google Scholar 

  117. Monjardet B. On the Comparison of the Spearman and Kendall Metrics between Linear Orders, Discrete Math., Vol. 192, pp. 281–292, 1998.

    MathSciNet  MATH  Google Scholar 

  118. 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. Mucherino A., Lavor C., Liberti L. and Maculan N. (eds.) Distance Geometry, Springer, 2013.

    Google Scholar 

  120. Murakami H. Some Metrics on Classical Knots, Math. Ann., Vol. 270, pp. 35–45, 1985.

    MathSciNet  MATH  Google Scholar 

  121. 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. 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. Okabe A., Boots B. and Sugihara K. Spatial Tessellation: Concepts and Applications of Voronoi Diagrams, Wiley, 1992.

    Google Scholar 

  124. 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. 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. 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. Ophir A. and Pinchasi R. Nearly equal distances in metric spaces, Discrete Appl. Math., Vol. 174, pp. 122–127, 2014.

    MathSciNet  MATH  Google Scholar 

  128. 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. 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. 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. Petz D. Monotone Metrics on Matrix Spaces, Linear Algebra Appl., Vol. 244, 1996.

    Google Scholar 

  132. PlanetMath.org, http://planetmath.org/encyclopedia/

  133. Rachev S.T. Probability Metrics and the Stability of Stochastic Models, Wiley, New York, 1991.

    MATH  Google Scholar 

  134. 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.

    MathSciNet  MATH  Google Scholar 

  135. Resnikoff H.I. On the geometry of color perception, AMS Lectures on Math. in the Life Sciences, Vol. 7, pp. 217–232, 1974.

    MathSciNet  Google Scholar 

  136. 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. 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. Rosenfeld A. and Pfaltz J. Distance Functions on Digital Pictures, Pattern Recognition, Vol. 1, pp. 33–61, 1968.

    MathSciNet  Google Scholar 

  139. 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. Rummel R.J. Understanding Conflict and War, Sage Publ., California, 1976.

    Google Scholar 

  141. Schweizer B. and Sklar A. Probabilistic Metric Spaces, North–Holland, 1983.

    Google Scholar 

  142. Selkow S.M. The Tree–to–tree Editing Problem, Inform. Process. Lett., Vol. 6–6, pp. 184–186, 1977.

    MathSciNet  Google Scholar 

  143. 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.

    MathSciNet  MATH  Google Scholar 

  144. Tai K.–C. The Tree–to–tree Correction Problem, J. of the Association for Comp. Machinery, Vol. 26, pp. 422–433, 1979.

    MathSciNet  MATH  Google Scholar 

  145. 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. Tymoczko D. The Geometry of Musical Chords, Science, Vol. 313, Nr. 5783, pp. 72–74, 2006.

    Google Scholar 

  147. 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. Vardi Y. Metrics Useful in Network Tomography Studies, Signal Processing Letters, Vol. 11–3, pp. 353–355, 2004.

    Google Scholar 

  149. 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. Watts D.J. Small Worlds: The Dynamics of Networks between Order and Randomness, Princeton Univ. Press, 1999.

    Google Scholar 

  151. Weinberg S. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York, 1972.

    Google Scholar 

  152. Weisstein E.W. CRC Concise Encyclopedia of Math., CRC Press, 1999.

    Google Scholar 

  153. Weiss I. Metric 1–spaces, arXiv:1201.3980[math.MG], 2012.

    Google Scholar 

  154. 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. Wikipedia, the Free Encyclopedia, http://en.wikipedia.org

  156. Wilson D.R. and Martinez T.R. Improved Heterogeneous Distance Functions, J. of Artificial Intelligence Research, Vol. 6, p. 134, 1997.

    MathSciNet  Google Scholar 

  157. 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. Yianilos P.N. Normalized Forms for Two Common Metrics, NEC Research Institute, Report 91–082–9027–1, 1991.

    Google Scholar 

  159. Young N. Some Function–Theoretic Issues in Feedback Stabilisation, Holomorphic Spaces, MSRI Publication, Vol. 33, 1998.

    Google Scholar 

  160. 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. Zelinka B. On a Certain Distance between Isomorphism Classes of Graphs, Casopus. Pest. Mat., Vol. 100, pp. 371–373, 1975.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Deza, M.M., Deza, E. (2014). Distances in Earth Science and Astronomy. In: Encyclopedia of Distances. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44342-2_25

Download citation