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Introduction and Summary

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Quantitative Sociodynamics
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Abstract

The field of quantitative sociodynamics is still a rather young and very thrilling interdisciplinary research area which deals with the mathematical modelling of the temporal evolution of social systems.

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References

  1. Uhlenbeck GE (1973) The validity and the limitations of the Boltzmann-equation. In: Cohen EGD, Thirring W (eds) The Boltzmann equation. Springer, Wien

    Google Scholar 

  2. Helbing D (1993) Boltzmann-like and Boltzmann-Fokker-Planck equations as a foundation of behavioral models. Physica A 196:546–573

    Article  MathSciNet  MATH  Google Scholar 

  3. Hofbauer J, Sigmund K (1984) Evolutionstheorie und dynamische Systeme. Paul Parey, Berlin

    MATH  Google Scholar 

  4. Axelrod R, Dion D (1988) The further evolution of cooperation. Science 242:1385–1390

    Article  Google Scholar 

  5. Osgood CE, Tannenbaum PH (1955) The principle of congruity in the prediction of attitude change. Psychol Rev 62:42–55

    Article  Google Scholar 

  6. Stratonovich RL (1963, 1967) Topics in the theory of random noise, vols 1, 2. Gordon and Breach, New York

    Google Scholar 

  7. Haken H (1983) Advanced synergetics. Springer, Berlin

    MATH  Google Scholar 

  8. Helbing D (1992) A mathematical model for attitude formation by pair interactions. Behav Sci 37:190–214

    Article  Google Scholar 

  9. Langevin P (1908) On the theory of Brownian motion. Comptes Rendues Acad Sci Paris 146:530–533

    MATH  Google Scholar 

  10. Walls DF (1976) Non-equilibrium phase transitions in sociology. Collective Phenomena 2:125–130

    MathSciNet  Google Scholar 

  11. Pauli H (1928) In: Debye P (ed) Probleme der Modernen Physik. Hirzel, Leipzig

    Google Scholar 

  12. Weidlich W (1991) Physics and social science—the approach of synergetics. Phys Rep 204:1–163

    Article  MathSciNet  Google Scholar 

  13. Weidlich W, Haag G (1983) Concepts and models of a quantitative sociology. The dynamics of interacting populations. Springer, Berlin

    Book  MATH  Google Scholar 

  14. Helbing D (1992) A mathematical model for behavioral changes by pair interactions. In: Haag G, Mueller U, Troitzsch KG (eds) Economic evolution and demographic change. Formal models in social sciences. Springer, Berlin, pp 330–348

    Chapter  Google Scholar 

  15. von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton, NJ

    MATH  Google Scholar 

  16. Schweitzer F, Bartels J, Pohlmann L (1991) Simulation of opinion structures in social systems. In: Ebeling W, Peschel M, Weidlich W (eds) Models of selforganization in complex systems (MOSES). Akademie, Berlin

    Google Scholar 

  17. Lewin K (1951) Field theory in social science. Harper & Brothers, New York, NY

    Google Scholar 

  18. Coleman JS (1964) Introduction to mathematical sociology. The Free Press of Glencoe, New York, NY

    Google Scholar 

  19. Malchow H (1988) Spatial patterning of interacting and dispersing populations. Mem Fac Sci Kyoto Univ (Ser Biol) 13:83–100

    Google Scholar 

  20. Festinger L (1957) A theory of cognitive dissonance. Row & Peterson, Evanston, IL

    Google Scholar 

  21. Bartholomew DJ (1967) Stochastic models for social processes. Wiley, London

    Google Scholar 

  22. Domencich TA, McFadden D (1975) Urban travel demand. A behavioral analysis. North-Holland, Amsterdam, pp 61–69

    Google Scholar 

  23. Lewenstein M, Nowak A, Latané B (1992) Statistical mechanics of social impact. Phys Rev A 45(2):763–776

    Article  MathSciNet  Google Scholar 

  24. Haag G (1989) Dynamic decision theory: applications to urban and regional topics. Kluwer Academic, Dordrecht

    Book  Google Scholar 

  25. Feger H (1978) Konflikterleben und Konfliktverhalten. Huber, Bern

    Google Scholar 

  26. Weidlich W, Haag G (eds) (1988) Interregional migration. Springer, Berlin

    Google Scholar 

  27. Binney JJ, Dowrick NJ, Fisher AJ, Newman MEJ (1992) The theory of critical phenomena, Chap. 6: Mean-field theory. Clarendon Press, Oxford

    Google Scholar 

  28. Rapoport A (1983) Mathematical models in the social and behavioral sciences. Wiley, New York, NY

    MATH  Google Scholar 

  29. Helbing D (1993) Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory. Physica A 193:241–258

    Article  MathSciNet  Google Scholar 

  30. Reiner R, Weidlich W (1993) Der Beitrag der Synergetik zum Naturverständnis. In: Bien G, Gil Th, Wilke J (eds) Natur im Umbruch. Frommann-Holzboog, Stuttgart

    Google Scholar 

  31. Griffiths HB, Oldknow A (1993) Mathematics of models. Ellis Horwood, New York, NY

    Google Scholar 

  32. Haken H (1983) Advanced synergetics. Springer, Berlin

    MATH  Google Scholar 

  33. Haken H (1983) Synergetics, 3rd edn. Springer, Berlin

    Book  Google Scholar 

  34. Haken H (1988) Information and self-organization: a macroscopic approach to complex systems. Springer, Berlin

    MATH  Google Scholar 

  35. Hamblin RL, Jacobsen RB, Miller JLL (1973) A mathematical theory of social change. Wiley, New York, NY

    Google Scholar 

  36. Hauk M (1994) Evolutorische Ökonomik und private Transaktionsmedien. Lang, Frankfurt/Main

    Google Scholar 

  37. Haus JW, Kehr KW (1987) Diffusion in regular and disordered lattices. Phys Rep 150(5, 6): 263–406

    Article  Google Scholar 

  38. Heider F (1946) Attitudes and cognitive organization. J Psychol 21:107–112

    Article  Google Scholar 

  39. Heider F (1958) The psychology of interpersonal relations. Wiley, New York, NY

    Book  Google Scholar 

  40. Helbing D (1990) Physikalische Modellierung des dynamischen Verhaltens von Fußgängern. Master’s thesis, Georg-August University Göttingen

    Google Scholar 

  41. Helbing D (1991) A mathematical model for the behavior of pedestrians. Behav Sci 36: 298–310

    Article  Google Scholar 

  42. Helbing D (1992) A fluid-dynamic model for the movement of pedestrians. Complex Systems 6:391–415

    MathSciNet  MATH  Google Scholar 

  43. Helbing D (1992) Interrelations between stochastic equations for systems with pair interactions. Physica A 181:29–52

    Article  MathSciNet  Google Scholar 

  44. Helbing D (1992) A mathematical model for behavioral changes by pair interactions. In: Haag G, Mueller U, Troitzsch KG (eds) Economic evolution and demographic change. Formal models in social sciences. Springer, Berlin, pp 330–348

    Chapter  Google Scholar 

  45. Helbing D (1992) Models for pedestrian behavior. In: Natural structures. Principles, strategies, and models in architecture and nature. Sonderforschungsbereich 230, tuttgart, Part II

    Google Scholar 

  46. Helbing D (1993) Boltzmann-like and Boltzmann-Fokker-Planck equations as a foundation of behavioral models. Physica A 196:546–573

    Article  MathSciNet  MATH  Google Scholar 

  47. Helbing D (1993) Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory. Physica A 193:241–258

    Article  MathSciNet  Google Scholar 

  48. Helbing D (1994) A mathematical model for behavioral changes by pair interactions and its relation to game theory. Angewandte Sozialforschung 18(3):117–132

    Google Scholar 

  49. Hilborn RC (1994) Chaos and nonlinear dynamics. Oxford University Press, New York, NY

    MATH  Google Scholar 

  50. Hofbauer J, Schuster P, Sigmund K (1979) A note on evolutionarily stable strategies and game dynamics. J Theor Biol 81:609–612

    Article  MathSciNet  Google Scholar 

  51. Hofbauer J, Sigmund K (1988) The theory of evolution and dynamical systems. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  52. Horsthemke W, Lefever R (1984) Noise-induced transitions. Springer, Berlin

    MATH  Google Scholar 

  53. Huberman BA, Hogg T (1988) The behavior of computational ecologies. In: Huberman BA (ed) The ecology of computation. Elsevier, Amsterdam

    Google Scholar 

  54. Ising E (1925) Beitrag zur Theorie des Ferromagnetismus Zeitschrift der Physik. 31:253ff

    Google Scholar 

  55. van Kampen NG (1981) Stochastic processes in physics and chemistry. North-Holland, Amsterdam

    MATH  Google Scholar 

  56. Kennedy AM (1983) The adoption and diffusion of new industrial products: a literature review. Eur J Mark 17(3):31–88

    Article  Google Scholar 

  57. Kruskal JB, Wish M (1978) Multidimensional scaling. Sage, Beverly Hills, CA

    Google Scholar 

  58. Luce RD (1959) Individual choice behavior, Chap. 2.A: Fechner’s problem. Wiley, New York, NY

    Google Scholar 

  59. Luce RD, Raiffa H (1957) Games and decisions. Wiley, New York, NY

    MATH  Google Scholar 

  60. Luhmann N (1991) Soziale Systeme, 4th edn. Suhrkamp, Frankfurt/Main

    Google Scholar 

  61. Ma S-K (1976) Modern theory of critical phenomena. Benjamin, Reading, MA

    Google Scholar 

  62. Mahajan V, Peterson RA (1985) Models for innovation diffusion. Sage, London

    MATH  Google Scholar 

  63. Malchow H (1988) Spatial patterning of interacting and dispersing populations. Mem Fac Sci Kyoto Univ (Ser Biol) 13:83–100

    Google Scholar 

  64. Matheson I, Walls DF, Gardiner CW (1975) Stochastic models of first-order nonequilibrium phase transitions in chemical reactions. J Stat Phys 12(1):21–34

    Article  Google Scholar 

  65. McCauley JL (1993) Chaos dynamics and fractals. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  66. Montroll EW (1965) Model making in biological and behavioral sciences. In: Eringen AC (ed) Recent advances in engineering science, vol. I. Gordon and Breach, New York, NY

    Google Scholar 

  67. Montroll EW (1978) On some mathematical models of social phenomena. In: Lakshmikantham V (ed) Nonlinear equations in abstract spaces. Academic Press, New York, NY

    Google Scholar 

  68. Montroll EW, Badger WW (1974) Introduction to quantitative aspects of social phenomena. Gordon and Breach, New York, NY

    Google Scholar 

  69. Montroll EW, Shlesinger MF (1984) On the wonderful world of random walks. In: Lebowitz JL, Montroll EW (eds) Nonequilibrium phenomena II: from stochastics to hydrodynamics. North-Holland, Amsterdam

    Google Scholar 

  70. Montroll EW, West BJ (1979) On an enriched collection of stochastic processes. In: Montroll EW, Lebowitz JL (eds) Fluctuation phenomena. North-Holland, Amsterdam

    Google Scholar 

  71. Mosekilde E, Larsen E, Sterman JD (1991) Coping with complexity: deterministic chaos in human decisionmaking behavior. In: Casti JL, Karlqvist A (eds) Beyond belief: randomness, prediction and explanation in science. CRC Press, Boca Raton, FL, pp 199–229

    Google Scholar 

  72. Mosekilde E, Thomsen JS, Larsen ER, Sterman J (1992) Nonlinear interactions in the economy. In: Haag G, Mueller U, Troitzsch KG (eds) Economic evolution and demographic change. Formal models in social sciences. Springer, Berlin

    Google Scholar 

  73. von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton, NJ

    MATH  Google Scholar 

  74. Nicolis G, Malek-Mansour M, van Nypelseer A, Kitahara K (1976) The onset of instabilities in nonequilibrium systems. J Stat Phys 14(5):417–432

    Article  Google Scholar 

  75. Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems. From dissipative structures to order through fluctuations. Wiley, New York, NY

    MATH  Google Scholar 

  76. Oeding D (1963) Verkehrsbelastung und Dimensionierung von Gehwegen und anderen Anlagen des Fußgängerverkehrs, vol 22, Straßenbau und Straßenverkehrstechnik, Bonn. p 8, Fig. 10.

    Google Scholar 

  77. Older SJ (1968) Movement of pedestrians on footways in shopping streets. Traffic Eng Control 10:160–163

    Google Scholar 

  78. Olinick M (1978) An introduction to mathematical models in the social and life sciences. Addison-Wesley, Reading, MA, pp 59–65

    Google Scholar 

  79. Oppenheim I, Schuler KE, Weiss GH (eds) (1977) Stochastic processes in chemical physics: the master equation. MIT Press, Cambridge, MA

    Google Scholar 

  80. Ortúzar JdeD, Willumsen LG (1990) Modelling transport, Chap. 7: Discrete-choice models. Wiley, Chichester

    Google Scholar 

  81. Osgood CE, Tannenbaum PH (1955) The principle of congruity in the prediction of attitude change. Psychol Rev 62:42–55

    Article  Google Scholar 

  82. Parsons T (1967) Sociological theory and modern society. Free Press, New York, NY

    Google Scholar 

  83. Pauli H (1928) In: Debye P (ed) Probleme der Modernen Physik. Hirzel, Leipzig

    Google Scholar 

  84. Pearl R (1924) Studies in human biology. Williams & Wilkins, Baltimore, MD

    Google Scholar 

  85. Planck M (1917) In: Ãœber einen Satz der statistischen Dynamik und seine Erweiterung in der Quantentheorie, Sitzungsber Preuss Akad Wiss, pp 324ff

    Google Scholar 

  86. Prigogine I (1976) Order through fluctuation: self-organization and social system. In: Jantsch E, Waddington CH (eds) Evolution and consciousness. Human systems in transition. Addison-Wesley, Reading, MA

    Google Scholar 

  87. Prigogine I, Herman R (1971) Kinetic theory of vehicular traffic. Elsevier, New York, NY

    MATH  Google Scholar 

  88. Rapoport A (1983) Mathematical models in the social and behavioral sciences. Wiley, New York, NY

    MATH  Google Scholar 

  89. Rapoport A (1986) General system theory. Essential concepts and applications. Abacus Press, Tunbridge Wells, Kent

    Google Scholar 

  90. Rapoport A, Chammah MA (1965) Prisoner’s dilemma. A study in conflict and cooperation. University of Michigan Press, Ann Arbor, MI

    Google Scholar 

  91. Ravenstein E (1876) The birthplaces of the people and the laws of migration. Geogr Mag III:173–177

    Google Scholar 

  92. Reiner R, Munz M (1990) Ranking regression analysis of spatiotemporal variables. Environ Plan A 22:507–526

    Article  Google Scholar 

  93. Reiner R, Weidlich W (1993) Der Beitrag der Synergetik zum Naturverständnis. In: Bien G, Gil Th, Wilke J (eds) Natur im Umbruch. Frommann-Holzboog, Stuttgart

    Google Scholar 

  94. Schaffer WM, Olsen LF, Truty GL, Fulmer SL, Graser DJ (1988) Periodic and chaotic dynamics in childhood infections. In: Markus M, Müller StC, Nicolis G (eds) From chemical to biological organization. Springer, Berlin

    Google Scholar 

  95. Schüßler R (1989) Exit threats and cooperation under anonymity. J Conflict Resolut 33(4):728–749

    Article  Google Scholar 

  96. Schüßler R (1990) Threshold effects and the decline of cooperation. J Conflict Resolut 34(3):476–494

    Article  Google Scholar 

  97. Schuster HG (1988) Deterministic chaos, 2nd edn. VCH, Weinheim

    Google Scholar 

  98. Schuster P, Sigmund K, Hofbauer J, Wolff R (1981) Selfregulation of behavior in animal societies. Biol Cybern 40:1–25

    Article  MathSciNet  MATH  Google Scholar 

  99. Schweitzer F, Bartels J, Pohlmann L (1991) Simulation of opinion structures in social systems. In: Ebeling W, Peschel M, Weidlich W (eds) Models of selforganization in complex systems (MOSES). Akademie, Berlin

    Google Scholar 

  100. Stanley HE (1971) Introduction to phase transitions and critical phenomena. Oxford University Press, New York

    Google Scholar 

  101. Stratonovich RL (1963, 1967) Topics in the theory of random noise, vols 1, 2. Gordon and Breach, New York

    Google Scholar 

  102. Szép J, Forgó F (1985) Introduction to the theory of games. Akadémiai Kiadó, Budapest

    Book  MATH  Google Scholar 

  103. Taylor P, Jonker L (1978) Evolutionarily stable strategies and game dynamics. Math Biosci 40:145–156

    Article  MathSciNet  MATH  Google Scholar 

  104. Thom R (1975) Structural stability and morphogenesis. Benjamin, Reading, MA

    MATH  Google Scholar 

  105. Tuma NB, Hannan MT (1984) Social dynamics. Models and methods. Academic Press, Orlando, FL

    Google Scholar 

  106. Uhlenbeck GE (1973) The validity and the limitations of the Boltzmann-equation. In: Cohen EGD, Thirring W (eds) The Boltzmann equation. Springer, Wien

    Google Scholar 

  107. Valentin L (1981) Subatomic physics: nuclei and particles. North-Holland, Amsterdam, pp 127–130, 342–349

    Google Scholar 

  108. Verhulst PF (1845) Nuov Mem Acad Roy Bruxelles 18:1ff

    Google Scholar 

  109. Vorob’ev NN (1977) Game theory. Lectures for economists and system scientists. Springer, New York, NY

    Google Scholar 

  110. Walls DF (1976) Non-equilibrium phase transitions in sociology. Collective Phenomena 2:125–130

    MathSciNet  Google Scholar 

  111. Weidlich W (1971) The statistical description of polarization phenomena in society. Br J Math Stat Psychol 24:51

    Article  Google Scholar 

  112. Weidlich W (1972) The use of statistical models in sociology. Collective Phenomena 1:51–59

    Google Scholar 

  113. Weidlich W (1987) Quantitative social science. Physica Scripta 35:380–387

    Article  MathSciNet  MATH  Google Scholar 

  114. Weidlich W (1991) Physics and social science—the approach of synergetics. Phys Rep 204:1–163

    Article  MathSciNet  Google Scholar 

  115. Weidlich W (1994) Synergetic modelling concepts for sociodynamics with application to collective political opinion formation. J Math Sociol 18:267–291

    Article  MATH  Google Scholar 

  116. Weidlich W, Braun M (1992) The master equation approach to nonlinear economics. J Evol Econ 2:233–265

    Article  Google Scholar 

  117. Weidlich W, Haag G (1983) Concepts and models of a quantitative sociology. The dynamics of interacting populations. Springer, Berlin

    Book  MATH  Google Scholar 

  118. Weidlich W, Haag G (eds) (1988) Interregional migration. Springer, Berlin

    Google Scholar 

  119. Williams HCWL (1977) On the formation of travel demand models and economic evaluation measures of user benefit. Environ Plan A 9(3):285–344

    Article  Google Scholar 

  120. Williams WSC (1991) Nuclear and particle physics. Clarendon Press, Oxford, pp 56–61

    Google Scholar 

  121. Wunderlin A, Haken H (1984) Some applications of basic ideas and models of synergetics to sociology. In: Frehland E (ed) Synergetics—from microscopic to macroscopic order. Springer, Berlin

    Google Scholar 

  122. Young FW, Hamer RM (1987) Multidimensional scaling: history, theory, and applications. Lawrence Erlbaum Associates, Hillsdale, NJ

    Google Scholar 

  123. Zeeman EC (ed) (1977) Catastrophe theory. Addison-Wesley, London

    MATH  Google Scholar 

  124. Zeeman EC (1980) Population dynamics from game theory. In: Nitecki A, Robinson C (eds) Global theory of dynamical systems, Springer, Berlin

    Google Scholar 

  125. Ziman JM (1972) Principles of the theory of solids. Cambridge University Press, London

    Book  Google Scholar 

  126. Zipf GK (1946) The P1P2/D hypothesis on the intercity movement of persons. Am Sociol Rev 11:677–686

    Article  Google Scholar 

  127. Varian HR (1992) Microeconomic analysis, 3rd edn. Norton, New York, NY

    Google Scholar 

  128. Coleman J (1973) The mathematics of collective action. Heinemann Educational Books, London

    Google Scholar 

  129. Coleman JS (1990) Foundations of social theory. Belknap (Harvard University), Cambridge, MA

    Google Scholar 

  130. Daly AJ, Zachary S (1978) Improved multiple choice models. In: Hensher DA, Dalvi MQ (eds) Determinants of travel choice. Saxon House, Westmead

    Google Scholar 

  131. Buckley W (1967) Sociology and modern systems theory. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  132. Coleman JS (1964) Introduction to mathematical sociology. The Free Press of Glencoe, New York, NY

    Google Scholar 

  133. Diekmann A (1992) The log-logistic distribution as a model for social diffusion processes. J Sci Ind Res 51:285–290

    Google Scholar 

  134. Diekmann A, Mitter P (eds) (1984) Stochastic modelling of social processes. Academic Press, Orlando, FL

    Google Scholar 

  135. Domencich TA, McFadden D (1975) Urban travel demand. A behavioral analysis. North-Holland, Amsterdam, pp 61–69

    Google Scholar 

  136. Ebeling W (1991) Dynamics of competition and valuation in non-physical systems. In: Sydow A (ed) Handbook on computational systems analysis. Elsevier, Amsterdam

    Google Scholar 

  137. Ebeling W (1991) Stochastic models of competition processes in non-physical systems. Syst Anal Model Simul 8:3

    MATH  Google Scholar 

  138. Ebeling W, Jiménez-Montaño MA, Bruckner E, Scharnhorst A (1992) A stochastic model of technological evolution. In: Haag G, Mueller U, Troitzsch KG (eds) Economic evolution and demographic change. Formal models in social sciences. Springer, Berlin

    Google Scholar 

  139. Eigen M (1971) The selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58:465

    Article  Google Scholar 

  140. Eigen M, Schuster P (1979) The hypercycle. Springer, Berlin

    Book  Google Scholar 

  141. Fisher RA (1930) The genetical theory of natural selection. Oxford University Press, Oxford

    MATH  Google Scholar 

  142. Fokker AD (1914) Die mittlere Energie rotierender elektrischer Dipole im Strahlungsfeld. Annalen der Physik 348:810–820

    Article  Google Scholar 

  143. Gardiner CW (1985) Handbook of stochastic methods, 2nd edn. Springer, Berlin

    Google Scholar 

  144. Gardiner CW, McNeil KJ, Walls DF, Matheson IS (1976) Correlations in stochastic theories of chemical reactions. J Stat Phys 14(4):307–331

    Article  Google Scholar 

  145. Glance N, Hogg T, Huberman BA (1991) Computational ecosystems in a changing environment. Int J Mod Phys C 2(3):735–753

    Article  Google Scholar 

  146. Glance NS, Huberman BA (1992) Dynamics with expectations. Phys Lett A 165:432–440

    Article  Google Scholar 

  147. Goel NS, Maitra SC, Montroll EW (1971) On the Volterra and other nonlinear models of interacting populations. Rev Mod Phys 43(2):231–276

    Article  MathSciNet  Google Scholar 

  148. Goel NS, Richter-Dyn N (1974) Stochastic models in biology. Academic Press, New York, NY

    Google Scholar 

  149. Granovetter M, Soong R (1983) Threshold models of diffusion and collective behavior. J Math Sociol 9:165–179

    Article  MATH  Google Scholar 

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Helbing, D. (2010). Introduction and Summary. In: Quantitative Sociodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11546-2_1

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